Research ArticleAgent-Based Spatiotemporal Simulation of BiomolecularSystems within the Open Source MASON Framework

Gael Peacuterez-Rodriacuteguez1 Martiacuten Peacuterez-Peacuterez1 Daniel Glez-Pentildea1

Florentino Fdez-Riverola1 Nuno F Azevedo2 and Anaacutelia Lourenccedilo13

1 Escuela Superior de Ingenierıa Informatica (ESEI) Edificio Politecnico Universidad de Vigo Campus Universitario As Lagoas sn32004 Ourense Spain

2 LEPABE Department of Chemical Engineering Faculty of Engineering University of Porto Rua Dr Roberto Frias4200-465 Porto Portugal

3 Centre of Biological Engineering (CEB) University of Minho Campus de Gualtar 4710-057 Braga Portugal

Correspondence should be addressed to Analia Lourenco analiauvigoes

Received 19 August 2014 Accepted 30 October 2014

Academic Editor Juan F De Paz

Copyright copy 2015 Gael Perez-Rodrıguez et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Agent-based modelling is being used to represent biological systems with increasing frequency and success This paper presentsthe implementation of a new tool for biomolecular reaction modelling in the open source Multiagent Simulator of Neighborhoodsframework The rationale behind this new tool is the necessity to describe interactions at the molecular level to be able tograsp emergent and meaningful biological behaviour We are particularly interested in characterising and quantifying the variouseffects that facilitate biocatalysis Enzymes may display high specificity for their substrates and this information is crucial to theengineering and optimisation of bioprocesses Simulation results demonstrate thatmolecule distributions reaction rate parametersand structural parameters can be adjusted separately in the simulation allowing a comprehensive study of individual effects in thecontext of realistic cell environments While higher percentage of collisions with occurrence of reaction increases the affinity of theenzyme to the substrate a faster reaction (ie turnover number) leads to a smaller number of time steps Slower diffusion rates andmolecular crowding (physical hurdles) decrease the collision rate of reactants hence reducing the reaction rate as expected Alsothe random distribution of molecules affects the results significantly

1 Introduction

Microbial chemical factories have become an increasinglyimportant industrial platform with numerous applicationsin the food agriculture chemical and pharmaceutical indus-tries [1ndash5]

Recent advances in protein engineering metabolic engi-neering and synthetic biology have revolutionised our abilityto discover and design new biosynthetic pathways and engi-neer industrially viable strains [6ndash8] Metabolic engineeringoffers ways to enhance the yield and productivity of targetcompounds while combinatorial biosynthesis enables thecreation of novel derivatives [9ndash11]

The interplay of mathematical modelling and in sil-ico simulation with laboratory experiments is thus pivotalto elucidate the basic and presumably conserved designand engineering principles of the biological systems [12]Understanding the behaviour of a biological system whetherit is natural or engineered requires models that integratethe various interactions that occur at different spatial andtemporal scales However modelling the various scales andthe intra- and interscale interactions of a biological system isextremely complex and is considered an open and active areaof research [13ndash15]

Researchers are looking into novel approaches forabstraction for modelling bioprocesses that follow different

Hindawi Publishing CorporationBioMed Research InternationalVolume 2015 Article ID 769471 12 pageshttpdxdoiorg1011552015769471

2 BioMed Research International

biochemical and biophysical rules and for combining dif-ferent modules into larger models that still allow realisticsimulation with the computational power available today

This paper explores the potential application of agent-basedmodelling to such complexmodelling Notably the aimis to develop a computational infrastructure for multiscalebiomolecular modelling and simulation based on commonbiochemical and biophysical rules The novelty of the worklays on fully considering the spatial location of the moleculesand allowing for the description of intricatemicroscale struc-tures which enables the modelling of microbial behaviour inmore realistic and complex environments The prototype ofthe agent-based cellular simulator was developed in the opensource Multiagent Simulator of Neighborhoods (MASON)[16]The rationale behind the use ofMASON among existingagent-based frameworks lies in its general purpose and thusthe ability to support various levels of social complexityincluding different physics and agent logic Moreover thereis a project working on the development of a distributedversion of MASON which will certainly be required in orderto simulate complex metabolic models and in the futurewhole cell models

Test and validation experiments addressed the correctformulation of diffusion coefficient and reaction rate princi-ples Then a simple cellular system was formulated encom-passing most of the rules previously validated and account-ing for a realistic number of participants This experimentexposes the computational requirements imposed by a real-istic scenario and raises discussion about future lines ofresearch and development for agent-based biomodelling

The next sections of the paper describe the biologicaland computational rationale behind our simulator Section 2summarises the key points of agent-based modelling andearlier application of agent-based models to biological sys-tems Section 3 describes the biochemical and biophysicalrules that guided themodelling Section 4 presents the agent-based model and explains the structure and functionality ofthe different interacting agents involved in the system InSection 5 simulation results are compared to experimentalresults and noise is discussed Final conclusions resumecurrent achievements and draw main guidelines for futurework

2 Agent-Based Models andTheir Application in Biology

Agent-based modelling (ABM) is as a relatively newparadigm for engineering complex and distributed intelligentsystems [17] Typically this approach is considered suitablefor scenarios where there is a population of heterogeneousindividuals which display varied and adaptive behaviour

Generally agents can be defined as computer systems thatare situated in some environment and that are capable ofautonomous action in this environment based on mecha-nisms and representations somehow incorporated The earlywork of Wooldridge [18] described the general character-istics of an agent as follows autonomy that is agents canmake decisions about what to do without direct external

intervention of other systems reactivity that is agents aresituated in an environment can perceive it (at least to someextent) and are able to react to changes in it proactivenessthat is agents do not simply react to changes in the environ-ment but are also able to take the initiative social ability thatis agents can interact with other agents and participate insocial activities

In ABM the purpose is to ldquomonitorrdquo the behaviour ofthe agent from the perspective of the agent itself ratherthan the system as a whole [19] Each agent class hasmultiple manifestations in the form of a population of agentsthat interact in the shared environment Differing localconditions lead to different behavioural trajectories of theindividual agents and the heterogeneous behaviour of indi-vidual agents leads to the aggregated system dynamics Thisprocess enables the generation of a population of behaviouraloutputs from a single model producing system behaviouralspaces consistent with population-level biological observa-tion Moreover new information (eg finer degree of detail)can be added either through the introduction of new agentclasses or by the modification of existing agent rules withouthaving to reengineer the entire simulation

An agent-based model (ie the automaton) is thuscomposed of agents (autonomous entities) rules (logic ormathematical) a simulation environment (source of localinformation) and a set of initial and boundary conditionsAgents may be defined at multiple scales and the model canformalise the various behaviours through which individualsinteract with one another directly or indirectly throughthe shared environment This requires the preparation ofplausible and adequately detailed design plans for howcomponents at various system levels are thought to fit andfunction together In silico results should then be validatedagainst experimental outputs to reconcile different designplan hypotheses and render a realistic view of the system

Such individual-based modelling has the potential toreplicate cellular systems at its minimum components andthus help to understand the linkage from molecular levelevents to the emerging behaviour of the system [20ndash24] Inparticular the spatial nature of most agent-based modelsputs emphasis on behaviour driven by local interactionswhich matches closely with the mechanisms of stimu-lus and response observed in biology The Epitheliome arepresentation of the growth and repair characteristics ofepithelial cell populations is probably one of the earliestapplications [25] Other more recent applications relate tobiofilm formation [26] bacterial phenotypic switching [27]cancer development [28 29] bacterial virulence in surgicalsite infection [30] the development of restenosis in blood ves-sels [31] oxygenmetabolism in aerobic-anaerobic respiration[32] and the design of cellulase systems [33]

It is reasonable to say that ABM has become a popularbiomodelling approach and the new models are reachingout for increasingly more complex and higher resolutionproblems The key challenge is to be able to reproducedifferent scales realistically in terms of the number and typeof participants involved and the events taking place whilstbalancing the requirements of extendible model granularity

BioMed Research International 3

with computational tractability So far the use of generalpurpose graphical processing unit (GPGPU) technology andmulticore CPU processors are the favoured approaches toparallelise simulation algorithms [34 35]

3 A Novel Agent-Based SpatiotemporalBiomolecular Model

31 Modelling Environment and Overview A multiscaleagent-based model mimicking the biology of biochemicalreactions was developed using MASON version 16 [16] aJava based open source ABM framework that facilitatesmodel developmentThismodel includes agents representingcommon biochemical players such as metabolites cofactorsand enzymes The model also considers one physical barrierrepresenting the cell membrane and a number of geographi-cal hurdles accounting for themolecules known to exist in theintracellular space but not represented individually (to avoidunnecessary computational complexity)

The agent-based model is created on a continuous two-dimensional environment which corresponds to 5120583m2 Thedistance unit is given by the radius of the smallest moleculerepresented in themodel and corresponds to 0323times 10minus3 120583mThis value also establishes the upper limit for the velocity atwhich agents may move such that the smaller the radius ofthe molecule is the faster it will move and vice versa Thecorrespondence between simulation time steps and real timeis configurable and may be used to validate different results

The intracellular environment can be populated byenzymes some metabolites and cofactors (eg NAD+ andNADH) Once the simulation starts other types of agentssuch as other metabolites appear in the model in accordancewith the behavioural rules So the simulation only requiresdefining the particle radius and diffusion coefficient for eachspecies and the initial number of the molecules Agents arethen distributed randomly and may circulate freely

Every agent except obstacles is randomly initialisedwith a given orientation The behaviour of each agent isdetermined by the corresponding set of behavioural rulesand most notably its spatial location (Figure 1) In each timestep the model checks the current situation of the agents anddetermines which rule(s) should be executed and what inputvalues should be used

Given the circular shape of the agents the detection of acollision between agents is based on the Pythagorean Theo-rem for trianglesThat is collision is detected by knowing thatif the distance between the centres of the agents is less thantheir combined radius the agents are to collide

In the event of a collision the simulator identifies thetypes of the agents involved and looks for any behaviouralrules that may apply Either no rule applies and agents shouldbe reoriented or the matching rule should be executed andagents should be affected accordingly Agents are reorientedbased on the angle of collision and the correspondingdiffusion rate [36 37]

Most of the rules applicable in a scenario of collisioninvolve enzymes and metabolites that is the possible occur-rence of an enzymatic reaction (see Section 32)The reaction

Table 1 Agents behavioural rules and interacting agents

Agent Rules Interacts with

Enzyme (apoenzyme) Moving and binding Metabolite andcofactor

Metabolite Moving binding anddeath

Enzyme-cofactorcomplex

Cofactor Moving binding andreconverting

Enzyme and cellmembrane

Enzyme-cofactorcomplex(holoenzyme)

Moving reaction anddecoupling Metabolite

Obstacle Preventing movement All agents inmovement

probability is given by the probability of the collision andthe probability that a reaction occurs given that a collision isoccurringThe claim of the simulation is that it can reproducethe macroscopic enzymatic rate constants 119896

119898and 119896cat (mass

action kinetics) in homogeneous conditionsParticularly the number of agents representing metabo-

lites and enzymes needs to be compared with values reportedin the literature For this purpose at model construction weestablished a conversion mechanism between the numberof agents in the simulation and the number of moles cal-culated in laboratorial experiments In the literature valuesof molecules are typically represented as a concentration(eg mM) Molar concentrations can be modified to numberof molecules per volume unit by simply multiplying theconcentration by the Avogadro number Because this is a2D simulator a height also had to be indicated This wasassumed to be 0005 120583m an approximate typical height ofan enzyme The number of molecules in the simulator canthen be obtained multiplying the previous value by thearea of the simulation space and the estimated height Thediffusion rates and the sizes of the molecules can be generallyobtained directly from the literature or extrapolated usingsome already known correlations In our case diffusion wascalculated based on [38] which estimatesmolecular diffusionbased on the molecular mass of the species

Each type of agent can be tracked continuously in one runof simulation To facilitate the inspection and a dimensionalrepresentation distinct agent types are associated with differ-ent colours and sizes

32 Behavioural Rules of Agents in the Model The behav-ioural rules are twofold interaction of agents with theirenvironment and responses to the presence of other agents(Table 1) Specifically agents interact with the cell membrane(the physical boundary of the cell) and with the obstacles inthe intracellular space The cell is able to retrieve substratesfrom the extracellular space and release products to thisspace Other internally produced metabolites are to remainwithin cell boundaries

The obstacles aim to mimic the presence of other lowerlevel molecules in the intracellular space They are not rep-resented individually to preserve computational tractability(eg a bacterial cell contains approximately 2119864+10molecules

4 BioMed Research International

Start

Create the environment

Create agents and randomly distribute in environment

Set an initial random

movement for agents

For each agent

Calculate new

position

Verify agent within

environment boundaries

Reset position and

reinitiate movement

Verify if new position is

free

Set new position

Resolve collision

Finish loop

Finish simulation

NO

YES

YES

NO

Get neighbours

Finish step

While the agent is

alive or has orders

Figure 1 Decision process for the movement and rotation of an agent during the simulation

of water) but some form of representation was still requiredin order to model the diffusion rate and the orientation of themovement of the simulated molecules adequately

In certain cases the type of agent can be changed andconsequently the corresponding behavioural rules of the newtype would be applied to the agentThis transition is typicallybased on the spatial location of the agent its type and

the local environment One example of agent type reas-signment is the ldquorecyclingrdquo of NADH molecules to NAD+molecules whenever NADH agents collide with the cellmembrane

Regarding agent interaction enzymes interact with cofac-tors and metabolites Many enzymes require the assistance ofcofactors in biochemical transformations When an enzyme

BioMed Research International 5

agent and a cofactor agent collide the enzyme checkswhetherit requires the cofactor to operate If so a new agent represent-ing the enzyme-cofactor complex (holoenzyme) is created inreplacement of the two agents

The interaction between the enzymes (or enzyme-cofactor complexes) and metabolites represents catalysis andwas modelled according to Michaelis-Menten equation (seekinetic parameters section) In general metabolites andenzymes are supposed to react within a certain probabilitywhenever they collide and the enzymatic reaction may beconcluded in the same time step or after a number of timesteps

After the enzymatic reaction takes place that is theenzyme-cofactor complex collides with a substrate the com-plex is destroyed and the agents representing the enzymeand the cofactor are created again Likewise the agentsrepresenting the substrate disappear and new agents arecreated for the products of the reaction

33 Kinetic Parameters The critical part of developing ourmodel was related with incorporating kinetic informationon the cellular dynamics especially on different enzymaticreaction kinetics

Generally the kinetic scheme representing an enzymaticreaction under steady-state conditions is written as

E + S1198701

999448999471119870minus1

ES1198702

999448999471119870minus2

E + P (1)

where E represents the enzyme S is the substrate ES isthe enzyme-substrate complex and P is the product Theassociation rates 1198961 and 1198962 and the dissociation rates 119896 minus 1and 119896minus2 account for the substrate binding andproduct releaseforward and reverse processes respectively

Since the rate constants for the binding and unbindingreactions are either often unknown or difficult to determinemodelling has to rely on approximations also called aggre-gate rate laws such as theMichaelis-Menten kinetics [39 40]

119881 =119881max [S]119870119898+ [S]

(2)

or following the Lineweaver and Burk linear transformation

1

119881=119870119898

119881maxtimes1

[S]+1

119881max(3)

which represents the reaction rate at a substrate concentra-tion [S]119881max is themaximum rate that can be observed in thereaction considering the substrate is in excessTheMichaelisconstant119870

119898is a measure of the concentration of substrate at

which the rate of the reaction is one half its maximum 119881maxThat is 119870

119898is a relative measure of the affinity of the enzyme

for the substrate (how well it binds) Small 119870119898means tight

binding and large 119870119898means weak binding

The turnover number

119896cat =119881max[E]

(4)

where [E] equals total enzyme concentration represents thenumber of moles of product produced per number of molesof enzyme per unit time and is expressed in units of inversetime (119904minus1) That is the rate of the reaction when the enzymeis saturated with substrate

Having inmind the biologicalmeaning of the parameterswe hypothesised that the percentage of reactive collisionsbetween enzyme and metabolite and the number of simu-lation time steps could together be used to mimic the ratesexpressed by 119896

119898and 119896cat To corroborate this hypothesis

we conducted a series of experiments trying out differentpercentages of collision with reaction and number of timesteps and calculating the theoretical values of 119896

119898and 119896cat

The combination of simulation parameters was further vali-dated against experimental values retrieved from the enzymedatabase BRENDA [41]

4 Results and Discussion

To actually demonstrate that our design plan is functionallyplausible we recreated different scenarios of enzymatic activ-ity to show that the constructed model exhibits behavioursthat match those observed in the laboratory experiments

We present results obtained for the simulation of asimple scenario where an enzyme catalyses one substrate andreleases one productThese results are discussed theoreticallyin terms of enzyme affinity to substrate and catalytic effi-ciency and further tested against experimentally calculatedkinetic parameters

Then we show that the tool is able to model biochemicalpathways accounting for biochemical and biophysical lawsadequatelyWe describe the computational costs of represent-ingmore complex biomolecular scenariosWe discuss a num-ber of present commitments and simplifications necessary toensure computational tractability and point out ongoing linesof work

41 Approximation of Kinetic Parameters This process ofanalysis is somewhat similar to that performed in laboratoryexperimentsThat is we studied the behaviour of an identicalamount of enzyme in the presence of increasing concen-trations of substrate and measured the velocity of reactionby determining the rate of product formation Furthermorewe tested different (combinations of) simulation parametersnamely the percentage of collisions producing reaction andthe number of time steps taken by a reaction Based on theinterpretation of the Lineweaver-Burke plot which describesthe Michaelis-Menten laws for kinetic dynamics we calcu-lated the theoretical values of 119896

119898and 119896cat

Substrate concentrations ranged from 664119864 minus 02mMto 664119864 minus 01mM (200 molecules to 2000 moleculesapproximately) and there is a concentration of enzyme of498119864 minus 02mM (150 enzymes approximately) Simulationparameterisation mimicked ldquoextremerdquo scenarios (ie 100immediate reactive collisions very slow reactions and barelyany reactions occurring) as well as more common scenarios(ie midrange percentages of reactive collision and reactionduration) Moreover the experiment was replicated 3 times

6 BioMed Research International

(3 simulation runs for every concentration of substrate) andresults were averaged

The model assumes that a simulation tick correspondsto a configurable specific amount of time in the systemNotably our approach to real time-time step conversionfocused on framing realistic values of velocity of reactionand hence of 119896cat Regardless of the range of values of 119896cat tobe simulated we should be able to represent such enzymedynamics accurately by adjusting the equivalence in timesteps

Figure 2 shows the Lineweaver-Burke plots resultingfrom experiments considering the duration of the reactionconstant and equal to 1 time step representing 10 secondsSince the number of time steps that a reaction takes to beconcluded is considered somewhat equivalent to the velocityof the reaction the Lineweaver-Burke plots should convergeto a similar 119910-intersect Likewise different percentages ofreactive collision should describe different affinities of theenzyme for the substrate and this effect should be reflectedin the slope of the plots Most results were as expected therewas a convergence of the 119910-intersects and the higher thepercentage of reactive collision (ie lower values of 119896

119898) the

lower the value of the slopeFrom the Lineweaver-Burke plots and in particular

considering the linear regression model that approximatesthe equation

1

119881=119870119898

119881maxtimes1

[S]+1

119881max(5)

wewere able to estimate the values of 119896119898and 119896cat described by

the simulation parameters (Table 2) Again it was expectedthat higher percentages of reactive collision would relate tolower values of 119896

119898and vice versa whilst the value of 119896cat

should be less affected The presence of negative values for119896cat and 119896119898 for very low percentages of reactive collisionswas unexpected though This occurs because 119896cat for thosesituations is supposed to be very close to zero As this modelis stochastic small variations may lead the values of 119896cat tobecome negative hence affecting the values of 119896

119898as well

To further validate the approximation of the kineticparameters made by our model we tested them againstexperimentally validated data Six enzyme records fallingwithin the range of kinetic values calculated were randomlyselected from BRENDA database [41]

We selected the simulation scenarios producing themost similar approximation to the experimentally validatedkinetic parameters (Table 3) and compared the correspond-ing Lineweaver-Burke plots (Figure 3) As expected themoresimilar the approximations were to the real values the betterthe simulations performed In particular the number oftime steps stipulated for the duration of the reaction onlyaffects the value of 119896cat and thus can be used to validate thesimulation

42 A Two-Step Enzymatic Reaction After validating ourmodel for situations where only one enzymatic reactionoccurs we then studied the behaviour of our simulator whentwo enzymes are present in a two-stage process

Table 2 Approximation of kinetic parameters by different percent-ages of reactive collision and time steps

reactivecollision Time step 119896

119898(mM) 119896cat (s

minus1)

1 0 minus0850576595 minus00285144535 0 minus2996153951 minus687119864 minus 015 25 minus4656418568 minus977119864 minus 015 50 3439111157 808119864 minus 015 75 2918555171 625119864 minus 015 100 minus2179373575 minus392119864 + 0010 0 minus146001318 minus663194461615 0 1151508927 762333046425 0 087739 108119864 + 0025 5 136829 144119864 + 0025 25 245375 223119864 + 0025 50 120869 106119864 + 0025 75 070036 622119864 minus 0125 100 0531257304 452119864 minus 0134 1 318977 393119864 + 0050 0 071725 127119864 + 0075 0 365866 649119864 + 0075 5 306473 533119864 + 0075 25 113387 201119864 + 0075 50 060205 107119864 + 0075 75 037565 669119864 minus 0175 100 029693544 506119864 minus 0190 0 443222 817119864 + 0095 0 449601 844119864 + 0095 25 1277963717 239662133395 50 056747 111119864 + 0095 75 034196 688119864 minus 0195 100 0237537579 488119864 minus 01100 0 075547 160119864 + 00

Specifically we studied the catalytic activity of twoenzymes commonly present in aromatic aldehyde produc-tion the aryl-alcohol dehydrogenase (EC number 11190)and the benzaldehyde dehydrogenase (EC number 12128)

In particular the model encompasses the following twoequations

benzyl alcohol +NAD+ 997888rarr benzaldehyde +NADH +H+

benzaldehyde+NAD+ +H2O 997888rarr benzoate+NADH + 2H+

(6)

The model represented an area of approximately 1120583m2containing a concentration of 166mM (5119864+03molecules) ofeach type of enzyme 105 obstacles and initial concentrationsof 332119864 + 01mM and 332mM (1119864 + 05 molecules and1119864 + 04 molecules) for NAD+ and NADH respectivelyDuring simulation a concentration of 498119864 minus 01mM(1500 molecules) of benzyl alcohol that is the substrate of

BioMed Research International 7

050

100150200250300350400450500

1 3 5 7 9 11 13 15

1V

(itm

M)

1[S] (mM)

1007550253415

Linear (100)Linear (75)Linear (50)Linear (25)Linear (34)Linear (15)

y = 10596x + 24081

y = 11218x + 33688

y = 13112x + 43521

y = 19657x + 66475

y = 1629x + 5107

R2 = 09999

R2 = 1

R2 = 09999

R2 = 09999

R2 = 09993

R2 = 09993

y = 30326x + 26336

Figure 2 The Lineweaver-Burk plots obtained while simulating different percentages of reactive collision and a time step of 1 The markersrepresent the outputs of simulation and the lines represent the corresponding trend lines based on linear regression (equation also shown)

Table 3 An approximation between experimentally calculated kinetic parameters and the parameters simulated by our model

Enzyme identification Experimental kinetics Simulation parameters Approximated kinetics119896119898

119896cat reactive collision Time step 119896119898(mM) 119896cat (s

minus1)EC 1819mdashglutathione reductase activity 0404 039 25 100 0531257304 452119864 minus 01

EC 41111mdashaspartate 1-decarboxylase 0219 065 75 75 037565 669119864 minus 01

EC 1111mdashalcohol dehydrogenase 041 1 95 75 034196 688119864 minus 01

EC 111205mdashIMP dehydrogenase 17 19 25 25 245375 223119864 + 00

EC 341322mdashD-Ala-D-Ala dipeptidase 1 47 75 25 113387 201119864 + 00

EC 4111mdashpyruvate decarboxylase 18 12 25 5 136829 144119864 + 00

Table 4 The weight size and diffusion rate of the moleculesrepresented in the two-step enzymatic system

Species Molecularweight (gmol)

Particle radius(120583m)

Diffusion rate(120583m2s)

Benzyl alcohol 10814 0323 times 10minus3 4018 times 10minus14

NAD+ 66141 0657 times 10minus3 1975 times 10minus14

NADH 66343 0658 times 10minus3 1973 times 10minus14

Benzaldehyde 106121 0321 times 10minus3 4047 times 10minus14

Benzoate 12112 0338 times 10minus3 3843 times 10minus14

the first reaction was introduced gradually in the environ-ment specifically 10 at every 10 time steps

Agent size and velocity of movement were adjustedaccording to the molecular weight of the biological species(Table 4) Heaviermolecules have a larger radius and a slowerdiffusion rate Proportionally the agents representing benzylalcohol and benzaldehyde molecules should be two times

smaller and faster than the agents representing the moleculesof NAD+ and NADH

To facilitate visual inspection distinct agent types areassociated with different colours and proportional sizes Assuch it is possible to visually observe the evolving of thesimulation and at some extent observe how the agents aremoving and interacting with each other Specifically it ispossible to see how different agents traverse the environmentand how behavioural rules are triggered or take precedenceover each other

As illustrated in Figure 4 although the movement ofthe molecules of benzyl alcohol (green circles) is quite fastthese molecules are unable to interact with the correspond-ing enzyme (aryl-alcohol dehydrogenase named enzymeone and coloured yellow in the figure) unless the enzymehas already bound to a NAD+ molecule (ie creating theholoenzyme 1 coloured in black) Likewise interactions withthe second enzyme benzaldehyde dehydrogenase (magentacircles) are limited to the molecules of NAD+ (red circles)until the first reaction actually occurs and begins producingbenzaldehyde (blue circles) Furthermore it is possible to

8 BioMed Research International

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 20797x + 51479

R2 = 1

R2 = 09994

y = 23614x + 44449

1S (mMminus1)

TheoreticalSimulation

(a)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M) R2 = 1

R2 = 09991

y = 67643x + 30887

y = 11265x + 29988

1S (mMminus1)

TheoreticalSimulation

(b)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 82314x + 20077

y = 9982x + 29191

R2 = 1

R2 = 09984

TheoreticalSimulation

(c)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 17963x + 10567

y = 22109x + 90103

R2 = 1

R2 = 09982

1S (mMminus1)

TheoreticalSimulation

(d)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 42716x + 42716

y = 11353x + 10013

R2 = 1

R2 = 09999

TheoreticalSimulation

(e)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 30115x + 16731

y = 19058x + 13928

R2 = 1

R2 = 09991

1S (mMminus1)

TheoreticalSimulation

(f)

Figure 3The Lineweaver-Burk plots for experimentally calculated kinetic parameters (represented by a solid line) and simulation parameterssimulated by our model (represented by a dash dotted line) From top to bottom and from left to right the plots represent the activity of thefollowing enzymes glutathione reductase aspartate 1-decarboxylase alcohol dehydrogenase IMP dehydrogenase D-Ala-D-Ala dipeptidaseand pyruvate decarboxylase

observe the reconversion of the molecules of NADH (bluecircles) to molecules of NAD+ whenever the first hit thecell membrane (ie boundary of the environment) Likewiseit is possible to observe that obstacles are playing theirpart deflecting the movement of the other agents everyso often A detailed visual documentation of the two-stepenzymatic reaction simulation is available in supplementary

material (see Supplementary Material available online athttpdxdoiorg1011552014769471)

Numeric outputs detail these visual insights and presentdata about the movement of the different species thevelocity at which the reactions are taking place and thebehavioural system as a whole (Figure 5) The number ofagents representing the first substrate benzyl alcohol decays

BioMed Research International 9

NADHEnzyme one

Enzyme two

ObstaclesBenzaldehydeHaloenzyme 1

Haloenzyme 2

Benzyl alcoholBenzoateNAD+

Figure 4 Visual illustration of the evolving of the population of agents during the simulation steps

considerably in the first 2000 steps of simulation togetherwith the disappearance of agents representing NAD+ andthe creation of agents representing the aryl-alcohol dehy-drogenase haloenzyme This leads to the production of agrowing number of agents representing benzaldehyde and anincrease in the number of reactions occurring in the systemAs soon as benzaldehyde agents start to circulate in theenvironment and considering the continuous reconversionofNADHagents intoNAD+ agents the second reaction startsto occur This is reflected in a considerable decrease in thenumber of agents of benzaldehyde and a fairly proportionalincrease in the number of the agents representing benzoatethe product that will be ultimately excreted

43 System Performance This work describes the first phaseof development of the biomolecular simulator That is tosay that focus was set on identifying and implementing

themain biochemical and biophysical laws that would governthe model rather than implementing a realistic picture of themolecular landscape

As far as we know there has not been a previous attemptto simulate the effects of spatial localisation and temporalscales of individuals in the modelling of biomolecular sys-tems So before engaging into more complex scenarios itwas pivotal to take advantage of available experimental dataand ensure that the tool was able to account for basic cellulardynamics such as those governing enzymes adequately Nowthat we obtained a successful proof of concept we will workon system scalability in order to address more complexproblems

For this purpose we run preliminary performance tests tofind out the current scalability of our system Figure 6 sum-marises performance tests using an Intel I7 (2600) 34GHzprocessor with 6GB of RAM and runningWindows 8 64-bitThe tests accounted for three possible scenarios as follows

10 BioMed Research International

100

300

500

700

900

1100

0 5000 10000 15000

NumBenzyl alcohol

Num

ber o

f age

nts

Number of steps

(a)

89100

89300

89500

89700

89900

90100

0 5000 10000 15000

Num

ber o

f age

nts

Number of steps

89100911009310095100

0 16000

Detail

NumNAD+

(b)

Num

ber o

f age

nts

Number of steps

050

100150200250300350

0 5000 10000 15000

NumBenzal

(c)

9900

10100

10300

10500

10700

10900

0 5000 10000 15000

NumNADH

Num

ber o

f age

nts

Number of steps

(d)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 1

1732273237324732

0 10000

Detail

Num

ber o

f age

nts

Number of steps

(e)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 2

267836784678

0 15000

Detail

Num

ber o

f age

nts

Number of steps

(f)

80009000

100001100012000130001400015000

0 5000 10000 15000

NumReactions

40009000

14000

0 16000

Detail

Num

ber o

f age

nts

Number of steps

(g)

0

200

400

600

800

1000

0 5000 10000 15000

NumBenzoate

Num

ber o

f age

nts

Number of steps

(h)

Figure 5 The number of agents of different species interacting in the environment during 15000 simulation steps From top to bottom andfrom left to right the above plots represent the number of agents of benzyl alcohol NAD+ benzaldehyde NADH aryl-alcohol dehydrogenaseholoenzyme and benzaldehyde dehydrogenase holoenzyme At the bottom there is the number of occurring reactions and the number ofmolecules of benzoate excreted the extracellular medium

BioMed Research International 11

0

5000

10000

15000

20000

25000

30000

35000

0 50000 100000 150000 200000

Tim

e (m

s)

Number of agents

Only agentsAgents with movementAgents with movement and reactions

Figure 6 Performance of the tool in scenarios of increasingcomputational complexity

no action that is the agents are created but no diffusion orbehavioural rules are executed without reaction that is theagents are created and diffusion rules are activated but agentsdo not interact among themselves and with reaction thatis agents are created can move and can interact The threescenarios show a similar performance till the system reachesa population of 15119864 + 05 agents That is till this point thephysics governing agent movement and the introduction ofbehavioural rules do not affect simulation time significantlyCost resides on creating the system After that point thetime taken by the simulation of more elaborated scenariosthat is more agents in motion and more rules to manageis somewhat aggravated Over 25119864 + 05 agents the systembecomes computational unviable by a single machine

So in the near future we will investigate the use of dis-tributed and high-performance computing in the simulationofmore complex biomolecular systemsNamely we are inves-tigating the potential of the new distributed environmentof MASON the DMASON (httpwwwisislabitprojectsdmason) and the Biocellion framework [42]

5 Conclusions

ABM is increasingly popular in biology due to its naturalability to represent multiple scales of system decompositionintertwine complicated behaviours and deal with spatial-temporal constraints

The agent-based tool developed in this work aims tosupport biomolecular simulations and most notably provideinsights into catalytic efficiency in scenarios of industrialinterest Hence proof of concept was focused on the approx-imation of kinetic parameters The models correctly sim-ulated known enzymatic characteristics and yielded usefulpredictions that may guide future experimental design Italso provides a simulation variability that may reproduce theexperimental variation observed in lab experiments

Future development of the models presented here willinclude three-dimensional representation metabolic path-way simulation and accounting of extracellular substances

Moreover we plan to take into advantage the new DMA-SON platform to engage into distributed affordable sim-ulation and study more complex scenarios Other recenthigh-performance computing frameworks like Biocellionwill also be evaluated

After consolidation our tool will provide severalresources and services for the investigation of bacterial cellsin benefit of the research and industry communities

Conflict of Interests

The authors do not have any competing interests

Acknowledgments

The authors thank the Agrupamento INBIOMED fromDXPCTSUG-FEDER unha maneira de facer Europa(2012273) The research leading to these results has receivedfunding from the European Unionrsquos Seventh Frame-work Programme FP7REGPOT-2012-20131 under GrantAgreement no 316265 (BIOCAPS) and the [14VI05] Con-tract-Programme from theUniversity ofVigoThis documentreflects only the authorsrsquo views and the European Union isnot liable for any use that may be made of the informationcontained herein

References

[1] D Porro P Branduardi M Sauer and D Mattanovich ldquoOldobstacles and new horizons formicrobial chemical productionrdquoCurrent Opinion in Biotechnology C vol 30 pp 101ndash106 2014

[2] P Jeandet YVasserot T Chastang andECourot ldquoEngineeringmicrobial cells for the biosynthesis of natural compounds ofpharmaceutical significancerdquo BioMed Research Internationalvol 2013 Article ID 780145 13 pages 2013

[3] A Kondo J Ishii K Y Hara T Hasunuma and F Mat-suda ldquoDevelopment of microbial cell factories for bio-refinerythrough synthetic bioengineeringrdquo Journal of Biotechnologyvol 163 no 2 pp 204ndash216 2013

[4] J H Shin H U Kim D I Kim and S Y Lee ldquoProduction ofbulk chemicals via novel metabolic pathways in microorgan-ismsrdquo Biotechnology Advances vol 31 pp 925ndash935 2013

[5] C M Immethun A G Hoynes-OrsquoConnor A Balassy andT S Moon ldquoMicrobial production of isoprenoids enabled bysynthetic biologyrdquo Frontiers in Microbiology vol 4 article 752013

[6] Y Chen and J Nielsen ldquo Advances in metabolic pathway andstrain engineering paving the way for sustainable productionof chemical building blocksrdquo Current Opinion in Biotechnologyvol 24 pp 965ndash972 2013

[7] J W Lee D Na J M Park S Choi and S Y Lee ldquoSystemsmetabolic engineering of microorganisms for natural and non-natural chemicalsrdquo Nature Chemical Biology vol 8 pp 536ndash546 2012

[8] G Stephanopoulos ldquoSynthetic biology andmetabolic engineer-ingrdquo ACS Synthetic Biology vol 1 pp 514ndash525 2012

[9] T-M Lo W S Teo H Ling B Chen A Kang and MW Chang ldquoMicrobial engineering strategies to improve cellviability for biochemical productionrdquo Biotechnology Advancesvol 31 pp 903ndash914 2013

12 BioMed Research International

[10] K M Esvelt and H H Wang ldquoGenome-scale engineering forsystems and synthetic biologyrdquo Molecular Systems Biology vol9 p 641 2013

[11] M K Tiwari R R K Singh I Kim and J-K Lee ldquoCompu-tational approaches for rational design of proteins with novelfunctionalitiesrdquo Computational and Structural BiotechnologyJournal vol 2 Article ID e201209002 2012

[12] M Cvijovic J Almquist J Hagmar et al ldquoBridging the gaps insystems biologyrdquoMolecular Genetics and Genomics vol 289 no5 pp 727ndash734 2014

[13] N Tomar and R K De ldquoComparing methods for metabolicnetwork analysis and an application to metabolic engineeringrdquoGene vol 521 no 1 pp 1ndash14 2013

[14] A Chakrabarti L Miskovic K C Soh and V HatzimanikatisldquoTowards kinetic modeling of genome-scale metabolic net-works without sacrificing stoichiometric thermodynamic andphysiological constraintsrdquo Biotechnology Journal vol 8 no 9pp 1043ndash1057 2013

[15] A F Villaverde and J R Banga ldquoReverse engineering andidentification in systems biology strategies perspectives andchallengesrdquo Journal of the Royal Society Interface vol 11 no 91Article ID 20130505 2014

[16] S Luke C Cioffi-Revilla L Panait K Sullivan and G BalanldquoMASON a multiagent simulation environmentrdquo Simulationvol 81 no 7 pp 517ndash527 2005

[17] R Conte and M Paolucci ldquoOn agent-based modeling andcomputational social sciencerdquo Frontiers in Psychology vol 5article 668 2014

[18] M Wooldridge ldquoAgent-based software engineeringrdquo IEE Pro-ceedings Software vol 144 no 1 pp 26ndash37 1997

[19] E Bonabeau ldquoAgent-based modeling Methods and techniquesfor simulating human systemsrdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 99 no3 pp 7280ndash7287 2002

[20] N Cannata F Corradini E Merelli and L Tesei ldquoAgent-basedmodels of cellular systemsrdquo Methods in Molecular Biology vol930 pp 399ndash426 2013

[21] G An Q Mi J Dutta-Moscato and Y Vodovotz ldquoAgent-basedmodels in translational systems biologyrdquoWiley InterdisciplinaryReviews Systems Biology and Medicine vol 1 no 2 pp 159ndash1712009

[22] J O Dada and P Mendes ldquoMulti-scale modelling and simula-tion in systems biologyrdquo Integrative Biology vol 3 pp 86ndash962011

[23] H Kaul and Y Ventikos ldquoInvestigating biocomplexity throughthe agent-based paradigmrdquo Briefings in Bioinformatics vol 442013

[24] M Holcombe S Adra M Bicak et al ldquoModelling complexbiological systems using an agent-based approachrdquo IntegrativeBiology vol 4 no 1 pp 53ndash64 2012

[25] D CWalker J Southgate GHill et al ldquoThe epitheliome agent-based modelling of the social behaviour of cellsrdquo BioSystemsvol 76 no 1ndash3 pp 89ndash100 2004

[26] M B Biggs and J A Papin ldquoNovel multiscale modeling toolapplied to Pseudomonas aeruginosa biofilm formationrdquo PLoSONE vol 8 no 10 Article ID e78011 2013

[27] S M Stiegelmeyer andM C Giddings ldquoAgent-based modelingof competence phenotype switching in Bacillus subtilisrdquo Theo-retical Biology and Medical Modelling vol 10 article 23 2013

[28] G An and S Kulkarni ldquoAn agent-based modeling frameworklinking inflammation and cancer using evolutionary principles

Description of a generative hierarchy for the hallmarks of cancerand developing a bridge betweenmechanism and epidemiolog-ical datardquoMathematical Biosciences 2014

[29] J Wang L Zhang C Jing et al ldquoMulti-scale agent-basedmodeling on melanoma and its related angiogenesis analysisrdquoTheoretical Biology and Medical Modelling vol 10 article 412013

[30] V Gopalakrishnan M Kim and G An ldquoUsing an agent-basedmodel to examine the role of dynamic bacterial virulence poten-tial in the pathogenesis of surgical site infectionrdquo Advances inWound Care vol 2 no 9 pp 510ndash526 2013

[31] A E Curtin and L Zhou ldquoAn agent-based model of theresponse to angioplasty and bare-metal stent deployment in anatherosclerotic blood vesselrdquo PLoS ONE vol 9 no 4 Article IDe94411 2014

[32] K Bettenbrock H Bai M Ederer et al ldquoChapter Twomdashtowards a systems level understanding of the oxygen responseof Escherichia colirdquo in Advances in Microbial Physiology vol 6pp 65ndash114 2014

[33] A Apte R Senger and S S Fong ldquoDesigning novel cellulasesystems through agent-based modeling and global sensitivityanalysisrdquo Bioengineered vol 5 no 4 pp 243ndash253 2014

[34] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 30 no 21 pp3101ndash3108 2014

[35] S Kang S Kahan and B Momeni ldquoSimulating microbial com-munity patterning using Biocellionrdquo in Methods in MolecularBiology vol 1151 pp 233ndash253 2014

[36] I Millington Game Physics Engine Development How to Builda Robust Commercial-Grade Physics Engine for Your Game CRCPress Boca Raton Fla USA 2010

[37] G Palmer Physics for Game Programmers Apress 2005[38] T Kalwarczyk M Tabaka and R Holyst ldquoBiologisticsmdash

diffusion coefficients for complete proteome of Escherichiacolirdquo Bioinformatics vol 28 no 22 pp 2971ndash2978 2012

[39] K A Johnson and R S Goody ldquoThe original Michaelisconstant translation of the 1913 Michaelis-Menten paperrdquoBiochemistry vol 50 no 39 pp 8264ndash8269 2011

[40] A Cornish-Bowden ldquoThe origins of enzyme kineticsrdquo FEBSLetters vol 587 no 17 pp 2725ndash2730 2013

[41] M Scheer A Grote A Chang et al ldquoBRENDA the enzymeinformation system in 2011rdquo Nucleic Acids Research vol 39 no1 pp D670ndashD676 2011

[42] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 130 no 21 pp3101ndash3108 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

2 BioMed Research International

biochemical and biophysical rules and for combining dif-ferent modules into larger models that still allow realisticsimulation with the computational power available today

This paper explores the potential application of agent-basedmodelling to such complexmodelling Notably the aimis to develop a computational infrastructure for multiscalebiomolecular modelling and simulation based on commonbiochemical and biophysical rules The novelty of the worklays on fully considering the spatial location of the moleculesand allowing for the description of intricatemicroscale struc-tures which enables the modelling of microbial behaviour inmore realistic and complex environments The prototype ofthe agent-based cellular simulator was developed in the opensource Multiagent Simulator of Neighborhoods (MASON)[16]The rationale behind the use ofMASON among existingagent-based frameworks lies in its general purpose and thusthe ability to support various levels of social complexityincluding different physics and agent logic Moreover thereis a project working on the development of a distributedversion of MASON which will certainly be required in orderto simulate complex metabolic models and in the futurewhole cell models

Test and validation experiments addressed the correctformulation of diffusion coefficient and reaction rate princi-ples Then a simple cellular system was formulated encom-passing most of the rules previously validated and account-ing for a realistic number of participants This experimentexposes the computational requirements imposed by a real-istic scenario and raises discussion about future lines ofresearch and development for agent-based biomodelling

The next sections of the paper describe the biologicaland computational rationale behind our simulator Section 2summarises the key points of agent-based modelling andearlier application of agent-based models to biological sys-tems Section 3 describes the biochemical and biophysicalrules that guided themodelling Section 4 presents the agent-based model and explains the structure and functionality ofthe different interacting agents involved in the system InSection 5 simulation results are compared to experimentalresults and noise is discussed Final conclusions resumecurrent achievements and draw main guidelines for futurework

2 Agent-Based Models andTheir Application in Biology

Agent-based modelling (ABM) is as a relatively newparadigm for engineering complex and distributed intelligentsystems [17] Typically this approach is considered suitablefor scenarios where there is a population of heterogeneousindividuals which display varied and adaptive behaviour

Generally agents can be defined as computer systems thatare situated in some environment and that are capable ofautonomous action in this environment based on mecha-nisms and representations somehow incorporated The earlywork of Wooldridge [18] described the general character-istics of an agent as follows autonomy that is agents canmake decisions about what to do without direct external

intervention of other systems reactivity that is agents aresituated in an environment can perceive it (at least to someextent) and are able to react to changes in it proactivenessthat is agents do not simply react to changes in the environ-ment but are also able to take the initiative social ability thatis agents can interact with other agents and participate insocial activities

In ABM the purpose is to ldquomonitorrdquo the behaviour ofthe agent from the perspective of the agent itself ratherthan the system as a whole [19] Each agent class hasmultiple manifestations in the form of a population of agentsthat interact in the shared environment Differing localconditions lead to different behavioural trajectories of theindividual agents and the heterogeneous behaviour of indi-vidual agents leads to the aggregated system dynamics Thisprocess enables the generation of a population of behaviouraloutputs from a single model producing system behaviouralspaces consistent with population-level biological observa-tion Moreover new information (eg finer degree of detail)can be added either through the introduction of new agentclasses or by the modification of existing agent rules withouthaving to reengineer the entire simulation

An agent-based model (ie the automaton) is thuscomposed of agents (autonomous entities) rules (logic ormathematical) a simulation environment (source of localinformation) and a set of initial and boundary conditionsAgents may be defined at multiple scales and the model canformalise the various behaviours through which individualsinteract with one another directly or indirectly throughthe shared environment This requires the preparation ofplausible and adequately detailed design plans for howcomponents at various system levels are thought to fit andfunction together In silico results should then be validatedagainst experimental outputs to reconcile different designplan hypotheses and render a realistic view of the system

Such individual-based modelling has the potential toreplicate cellular systems at its minimum components andthus help to understand the linkage from molecular levelevents to the emerging behaviour of the system [20ndash24] Inparticular the spatial nature of most agent-based modelsputs emphasis on behaviour driven by local interactionswhich matches closely with the mechanisms of stimu-lus and response observed in biology The Epitheliome arepresentation of the growth and repair characteristics ofepithelial cell populations is probably one of the earliestapplications [25] Other more recent applications relate tobiofilm formation [26] bacterial phenotypic switching [27]cancer development [28 29] bacterial virulence in surgicalsite infection [30] the development of restenosis in blood ves-sels [31] oxygenmetabolism in aerobic-anaerobic respiration[32] and the design of cellulase systems [33]

It is reasonable to say that ABM has become a popularbiomodelling approach and the new models are reachingout for increasingly more complex and higher resolutionproblems The key challenge is to be able to reproducedifferent scales realistically in terms of the number and typeof participants involved and the events taking place whilstbalancing the requirements of extendible model granularity

BioMed Research International 3

with computational tractability So far the use of generalpurpose graphical processing unit (GPGPU) technology andmulticore CPU processors are the favoured approaches toparallelise simulation algorithms [34 35]

3 A Novel Agent-Based SpatiotemporalBiomolecular Model

31 Modelling Environment and Overview A multiscaleagent-based model mimicking the biology of biochemicalreactions was developed using MASON version 16 [16] aJava based open source ABM framework that facilitatesmodel developmentThismodel includes agents representingcommon biochemical players such as metabolites cofactorsand enzymes The model also considers one physical barrierrepresenting the cell membrane and a number of geographi-cal hurdles accounting for themolecules known to exist in theintracellular space but not represented individually (to avoidunnecessary computational complexity)

The agent-based model is created on a continuous two-dimensional environment which corresponds to 5120583m2 Thedistance unit is given by the radius of the smallest moleculerepresented in themodel and corresponds to 0323times 10minus3 120583mThis value also establishes the upper limit for the velocity atwhich agents may move such that the smaller the radius ofthe molecule is the faster it will move and vice versa Thecorrespondence between simulation time steps and real timeis configurable and may be used to validate different results

The intracellular environment can be populated byenzymes some metabolites and cofactors (eg NAD+ andNADH) Once the simulation starts other types of agentssuch as other metabolites appear in the model in accordancewith the behavioural rules So the simulation only requiresdefining the particle radius and diffusion coefficient for eachspecies and the initial number of the molecules Agents arethen distributed randomly and may circulate freely

Every agent except obstacles is randomly initialisedwith a given orientation The behaviour of each agent isdetermined by the corresponding set of behavioural rulesand most notably its spatial location (Figure 1) In each timestep the model checks the current situation of the agents anddetermines which rule(s) should be executed and what inputvalues should be used

Given the circular shape of the agents the detection of acollision between agents is based on the Pythagorean Theo-rem for trianglesThat is collision is detected by knowing thatif the distance between the centres of the agents is less thantheir combined radius the agents are to collide

In the event of a collision the simulator identifies thetypes of the agents involved and looks for any behaviouralrules that may apply Either no rule applies and agents shouldbe reoriented or the matching rule should be executed andagents should be affected accordingly Agents are reorientedbased on the angle of collision and the correspondingdiffusion rate [36 37]

Most of the rules applicable in a scenario of collisioninvolve enzymes and metabolites that is the possible occur-rence of an enzymatic reaction (see Section 32)The reaction

Table 1 Agents behavioural rules and interacting agents

Agent Rules Interacts with

Enzyme (apoenzyme) Moving and binding Metabolite andcofactor

Metabolite Moving binding anddeath

Enzyme-cofactorcomplex

Cofactor Moving binding andreconverting

Enzyme and cellmembrane

Enzyme-cofactorcomplex(holoenzyme)

Moving reaction anddecoupling Metabolite

Obstacle Preventing movement All agents inmovement

probability is given by the probability of the collision andthe probability that a reaction occurs given that a collision isoccurringThe claim of the simulation is that it can reproducethe macroscopic enzymatic rate constants 119896

119898and 119896cat (mass

action kinetics) in homogeneous conditionsParticularly the number of agents representing metabo-

lites and enzymes needs to be compared with values reportedin the literature For this purpose at model construction weestablished a conversion mechanism between the numberof agents in the simulation and the number of moles cal-culated in laboratorial experiments In the literature valuesof molecules are typically represented as a concentration(eg mM) Molar concentrations can be modified to numberof molecules per volume unit by simply multiplying theconcentration by the Avogadro number Because this is a2D simulator a height also had to be indicated This wasassumed to be 0005 120583m an approximate typical height ofan enzyme The number of molecules in the simulator canthen be obtained multiplying the previous value by thearea of the simulation space and the estimated height Thediffusion rates and the sizes of the molecules can be generallyobtained directly from the literature or extrapolated usingsome already known correlations In our case diffusion wascalculated based on [38] which estimatesmolecular diffusionbased on the molecular mass of the species

Each type of agent can be tracked continuously in one runof simulation To facilitate the inspection and a dimensionalrepresentation distinct agent types are associated with differ-ent colours and sizes

32 Behavioural Rules of Agents in the Model The behav-ioural rules are twofold interaction of agents with theirenvironment and responses to the presence of other agents(Table 1) Specifically agents interact with the cell membrane(the physical boundary of the cell) and with the obstacles inthe intracellular space The cell is able to retrieve substratesfrom the extracellular space and release products to thisspace Other internally produced metabolites are to remainwithin cell boundaries

The obstacles aim to mimic the presence of other lowerlevel molecules in the intracellular space They are not rep-resented individually to preserve computational tractability(eg a bacterial cell contains approximately 2119864+10molecules

4 BioMed Research International

Start

Create the environment

Create agents and randomly distribute in environment

Set an initial random

movement for agents

For each agent

Calculate new

position

Verify agent within

environment boundaries

Reset position and

reinitiate movement

Verify if new position is

free

Set new position

Resolve collision

Finish loop

Finish simulation

NO

YES

YES

NO

Get neighbours

Finish step

While the agent is

alive or has orders

Figure 1 Decision process for the movement and rotation of an agent during the simulation

of water) but some form of representation was still requiredin order to model the diffusion rate and the orientation of themovement of the simulated molecules adequately

In certain cases the type of agent can be changed andconsequently the corresponding behavioural rules of the newtype would be applied to the agentThis transition is typicallybased on the spatial location of the agent its type and

the local environment One example of agent type reas-signment is the ldquorecyclingrdquo of NADH molecules to NAD+molecules whenever NADH agents collide with the cellmembrane

Regarding agent interaction enzymes interact with cofac-tors and metabolites Many enzymes require the assistance ofcofactors in biochemical transformations When an enzyme

BioMed Research International 5

agent and a cofactor agent collide the enzyme checkswhetherit requires the cofactor to operate If so a new agent represent-ing the enzyme-cofactor complex (holoenzyme) is created inreplacement of the two agents

The interaction between the enzymes (or enzyme-cofactor complexes) and metabolites represents catalysis andwas modelled according to Michaelis-Menten equation (seekinetic parameters section) In general metabolites andenzymes are supposed to react within a certain probabilitywhenever they collide and the enzymatic reaction may beconcluded in the same time step or after a number of timesteps

After the enzymatic reaction takes place that is theenzyme-cofactor complex collides with a substrate the com-plex is destroyed and the agents representing the enzymeand the cofactor are created again Likewise the agentsrepresenting the substrate disappear and new agents arecreated for the products of the reaction

33 Kinetic Parameters The critical part of developing ourmodel was related with incorporating kinetic informationon the cellular dynamics especially on different enzymaticreaction kinetics

Generally the kinetic scheme representing an enzymaticreaction under steady-state conditions is written as

E + S1198701

999448999471119870minus1

ES1198702

999448999471119870minus2

E + P (1)

where E represents the enzyme S is the substrate ES isthe enzyme-substrate complex and P is the product Theassociation rates 1198961 and 1198962 and the dissociation rates 119896 minus 1and 119896minus2 account for the substrate binding andproduct releaseforward and reverse processes respectively

Since the rate constants for the binding and unbindingreactions are either often unknown or difficult to determinemodelling has to rely on approximations also called aggre-gate rate laws such as theMichaelis-Menten kinetics [39 40]

119881 =119881max [S]119870119898+ [S]

(2)

or following the Lineweaver and Burk linear transformation

1

119881=119870119898

119881maxtimes1

[S]+1

119881max(3)

which represents the reaction rate at a substrate concentra-tion [S]119881max is themaximum rate that can be observed in thereaction considering the substrate is in excessTheMichaelisconstant119870

119898is a measure of the concentration of substrate at

which the rate of the reaction is one half its maximum 119881maxThat is 119870

119898is a relative measure of the affinity of the enzyme

for the substrate (how well it binds) Small 119870119898means tight

binding and large 119870119898means weak binding

The turnover number

119896cat =119881max[E]

(4)

where [E] equals total enzyme concentration represents thenumber of moles of product produced per number of molesof enzyme per unit time and is expressed in units of inversetime (119904minus1) That is the rate of the reaction when the enzymeis saturated with substrate

Having inmind the biologicalmeaning of the parameterswe hypothesised that the percentage of reactive collisionsbetween enzyme and metabolite and the number of simu-lation time steps could together be used to mimic the ratesexpressed by 119896

119898and 119896cat To corroborate this hypothesis

we conducted a series of experiments trying out differentpercentages of collision with reaction and number of timesteps and calculating the theoretical values of 119896

119898and 119896cat

The combination of simulation parameters was further vali-dated against experimental values retrieved from the enzymedatabase BRENDA [41]

4 Results and Discussion

To actually demonstrate that our design plan is functionallyplausible we recreated different scenarios of enzymatic activ-ity to show that the constructed model exhibits behavioursthat match those observed in the laboratory experiments

We present results obtained for the simulation of asimple scenario where an enzyme catalyses one substrate andreleases one productThese results are discussed theoreticallyin terms of enzyme affinity to substrate and catalytic effi-ciency and further tested against experimentally calculatedkinetic parameters

Then we show that the tool is able to model biochemicalpathways accounting for biochemical and biophysical lawsadequatelyWe describe the computational costs of represent-ingmore complex biomolecular scenariosWe discuss a num-ber of present commitments and simplifications necessary toensure computational tractability and point out ongoing linesof work

41 Approximation of Kinetic Parameters This process ofanalysis is somewhat similar to that performed in laboratoryexperimentsThat is we studied the behaviour of an identicalamount of enzyme in the presence of increasing concen-trations of substrate and measured the velocity of reactionby determining the rate of product formation Furthermorewe tested different (combinations of) simulation parametersnamely the percentage of collisions producing reaction andthe number of time steps taken by a reaction Based on theinterpretation of the Lineweaver-Burke plot which describesthe Michaelis-Menten laws for kinetic dynamics we calcu-lated the theoretical values of 119896

119898and 119896cat

Substrate concentrations ranged from 664119864 minus 02mMto 664119864 minus 01mM (200 molecules to 2000 moleculesapproximately) and there is a concentration of enzyme of498119864 minus 02mM (150 enzymes approximately) Simulationparameterisation mimicked ldquoextremerdquo scenarios (ie 100immediate reactive collisions very slow reactions and barelyany reactions occurring) as well as more common scenarios(ie midrange percentages of reactive collision and reactionduration) Moreover the experiment was replicated 3 times

6 BioMed Research International

(3 simulation runs for every concentration of substrate) andresults were averaged

The model assumes that a simulation tick correspondsto a configurable specific amount of time in the systemNotably our approach to real time-time step conversionfocused on framing realistic values of velocity of reactionand hence of 119896cat Regardless of the range of values of 119896cat tobe simulated we should be able to represent such enzymedynamics accurately by adjusting the equivalence in timesteps

Figure 2 shows the Lineweaver-Burke plots resultingfrom experiments considering the duration of the reactionconstant and equal to 1 time step representing 10 secondsSince the number of time steps that a reaction takes to beconcluded is considered somewhat equivalent to the velocityof the reaction the Lineweaver-Burke plots should convergeto a similar 119910-intersect Likewise different percentages ofreactive collision should describe different affinities of theenzyme for the substrate and this effect should be reflectedin the slope of the plots Most results were as expected therewas a convergence of the 119910-intersects and the higher thepercentage of reactive collision (ie lower values of 119896

119898) the

lower the value of the slopeFrom the Lineweaver-Burke plots and in particular

considering the linear regression model that approximatesthe equation

1

119881=119870119898

119881maxtimes1

[S]+1

119881max(5)

wewere able to estimate the values of 119896119898and 119896cat described by

the simulation parameters (Table 2) Again it was expectedthat higher percentages of reactive collision would relate tolower values of 119896

119898and vice versa whilst the value of 119896cat

should be less affected The presence of negative values for119896cat and 119896119898 for very low percentages of reactive collisionswas unexpected though This occurs because 119896cat for thosesituations is supposed to be very close to zero As this modelis stochastic small variations may lead the values of 119896cat tobecome negative hence affecting the values of 119896

119898as well

To further validate the approximation of the kineticparameters made by our model we tested them againstexperimentally validated data Six enzyme records fallingwithin the range of kinetic values calculated were randomlyselected from BRENDA database [41]

We selected the simulation scenarios producing themost similar approximation to the experimentally validatedkinetic parameters (Table 3) and compared the correspond-ing Lineweaver-Burke plots (Figure 3) As expected themoresimilar the approximations were to the real values the betterthe simulations performed In particular the number oftime steps stipulated for the duration of the reaction onlyaffects the value of 119896cat and thus can be used to validate thesimulation

42 A Two-Step Enzymatic Reaction After validating ourmodel for situations where only one enzymatic reactionoccurs we then studied the behaviour of our simulator whentwo enzymes are present in a two-stage process

Table 2 Approximation of kinetic parameters by different percent-ages of reactive collision and time steps

reactivecollision Time step 119896

119898(mM) 119896cat (s

minus1)

1 0 minus0850576595 minus00285144535 0 minus2996153951 minus687119864 minus 015 25 minus4656418568 minus977119864 minus 015 50 3439111157 808119864 minus 015 75 2918555171 625119864 minus 015 100 minus2179373575 minus392119864 + 0010 0 minus146001318 minus663194461615 0 1151508927 762333046425 0 087739 108119864 + 0025 5 136829 144119864 + 0025 25 245375 223119864 + 0025 50 120869 106119864 + 0025 75 070036 622119864 minus 0125 100 0531257304 452119864 minus 0134 1 318977 393119864 + 0050 0 071725 127119864 + 0075 0 365866 649119864 + 0075 5 306473 533119864 + 0075 25 113387 201119864 + 0075 50 060205 107119864 + 0075 75 037565 669119864 minus 0175 100 029693544 506119864 minus 0190 0 443222 817119864 + 0095 0 449601 844119864 + 0095 25 1277963717 239662133395 50 056747 111119864 + 0095 75 034196 688119864 minus 0195 100 0237537579 488119864 minus 01100 0 075547 160119864 + 00

Specifically we studied the catalytic activity of twoenzymes commonly present in aromatic aldehyde produc-tion the aryl-alcohol dehydrogenase (EC number 11190)and the benzaldehyde dehydrogenase (EC number 12128)

In particular the model encompasses the following twoequations

benzyl alcohol +NAD+ 997888rarr benzaldehyde +NADH +H+

benzaldehyde+NAD+ +H2O 997888rarr benzoate+NADH + 2H+

(6)

The model represented an area of approximately 1120583m2containing a concentration of 166mM (5119864+03molecules) ofeach type of enzyme 105 obstacles and initial concentrationsof 332119864 + 01mM and 332mM (1119864 + 05 molecules and1119864 + 04 molecules) for NAD+ and NADH respectivelyDuring simulation a concentration of 498119864 minus 01mM(1500 molecules) of benzyl alcohol that is the substrate of

BioMed Research International 7

050

100150200250300350400450500

1 3 5 7 9 11 13 15

1V

(itm

M)

1[S] (mM)

1007550253415

Linear (100)Linear (75)Linear (50)Linear (25)Linear (34)Linear (15)

y = 10596x + 24081

y = 11218x + 33688

y = 13112x + 43521

y = 19657x + 66475

y = 1629x + 5107

R2 = 09999

R2 = 1

R2 = 09999

R2 = 09999

R2 = 09993

R2 = 09993

y = 30326x + 26336

Figure 2 The Lineweaver-Burk plots obtained while simulating different percentages of reactive collision and a time step of 1 The markersrepresent the outputs of simulation and the lines represent the corresponding trend lines based on linear regression (equation also shown)

Table 3 An approximation between experimentally calculated kinetic parameters and the parameters simulated by our model

Enzyme identification Experimental kinetics Simulation parameters Approximated kinetics119896119898

119896cat reactive collision Time step 119896119898(mM) 119896cat (s

minus1)EC 1819mdashglutathione reductase activity 0404 039 25 100 0531257304 452119864 minus 01

EC 41111mdashaspartate 1-decarboxylase 0219 065 75 75 037565 669119864 minus 01

EC 1111mdashalcohol dehydrogenase 041 1 95 75 034196 688119864 minus 01

EC 111205mdashIMP dehydrogenase 17 19 25 25 245375 223119864 + 00

EC 341322mdashD-Ala-D-Ala dipeptidase 1 47 75 25 113387 201119864 + 00

EC 4111mdashpyruvate decarboxylase 18 12 25 5 136829 144119864 + 00

Table 4 The weight size and diffusion rate of the moleculesrepresented in the two-step enzymatic system

Species Molecularweight (gmol)

Particle radius(120583m)

Diffusion rate(120583m2s)

Benzyl alcohol 10814 0323 times 10minus3 4018 times 10minus14

NAD+ 66141 0657 times 10minus3 1975 times 10minus14

NADH 66343 0658 times 10minus3 1973 times 10minus14

Benzaldehyde 106121 0321 times 10minus3 4047 times 10minus14

Benzoate 12112 0338 times 10minus3 3843 times 10minus14

the first reaction was introduced gradually in the environ-ment specifically 10 at every 10 time steps

Agent size and velocity of movement were adjustedaccording to the molecular weight of the biological species(Table 4) Heaviermolecules have a larger radius and a slowerdiffusion rate Proportionally the agents representing benzylalcohol and benzaldehyde molecules should be two times

smaller and faster than the agents representing the moleculesof NAD+ and NADH

To facilitate visual inspection distinct agent types areassociated with different colours and proportional sizes Assuch it is possible to visually observe the evolving of thesimulation and at some extent observe how the agents aremoving and interacting with each other Specifically it ispossible to see how different agents traverse the environmentand how behavioural rules are triggered or take precedenceover each other

As illustrated in Figure 4 although the movement ofthe molecules of benzyl alcohol (green circles) is quite fastthese molecules are unable to interact with the correspond-ing enzyme (aryl-alcohol dehydrogenase named enzymeone and coloured yellow in the figure) unless the enzymehas already bound to a NAD+ molecule (ie creating theholoenzyme 1 coloured in black) Likewise interactions withthe second enzyme benzaldehyde dehydrogenase (magentacircles) are limited to the molecules of NAD+ (red circles)until the first reaction actually occurs and begins producingbenzaldehyde (blue circles) Furthermore it is possible to

8 BioMed Research International

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 20797x + 51479

R2 = 1

R2 = 09994

y = 23614x + 44449

1S (mMminus1)

TheoreticalSimulation

(a)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M) R2 = 1

R2 = 09991

y = 67643x + 30887

y = 11265x + 29988

1S (mMminus1)

TheoreticalSimulation

(b)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 82314x + 20077

y = 9982x + 29191

R2 = 1

R2 = 09984

TheoreticalSimulation

(c)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 17963x + 10567

y = 22109x + 90103

R2 = 1

R2 = 09982

1S (mMminus1)

TheoreticalSimulation

(d)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 42716x + 42716

y = 11353x + 10013

R2 = 1

R2 = 09999

TheoreticalSimulation

(e)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 30115x + 16731

y = 19058x + 13928

R2 = 1

R2 = 09991

1S (mMminus1)

TheoreticalSimulation

(f)

Figure 3The Lineweaver-Burk plots for experimentally calculated kinetic parameters (represented by a solid line) and simulation parameterssimulated by our model (represented by a dash dotted line) From top to bottom and from left to right the plots represent the activity of thefollowing enzymes glutathione reductase aspartate 1-decarboxylase alcohol dehydrogenase IMP dehydrogenase D-Ala-D-Ala dipeptidaseand pyruvate decarboxylase

observe the reconversion of the molecules of NADH (bluecircles) to molecules of NAD+ whenever the first hit thecell membrane (ie boundary of the environment) Likewiseit is possible to observe that obstacles are playing theirpart deflecting the movement of the other agents everyso often A detailed visual documentation of the two-stepenzymatic reaction simulation is available in supplementary

material (see Supplementary Material available online athttpdxdoiorg1011552014769471)

Numeric outputs detail these visual insights and presentdata about the movement of the different species thevelocity at which the reactions are taking place and thebehavioural system as a whole (Figure 5) The number ofagents representing the first substrate benzyl alcohol decays

BioMed Research International 9

NADHEnzyme one

Enzyme two

ObstaclesBenzaldehydeHaloenzyme 1

Haloenzyme 2

Benzyl alcoholBenzoateNAD+

Figure 4 Visual illustration of the evolving of the population of agents during the simulation steps

considerably in the first 2000 steps of simulation togetherwith the disappearance of agents representing NAD+ andthe creation of agents representing the aryl-alcohol dehy-drogenase haloenzyme This leads to the production of agrowing number of agents representing benzaldehyde and anincrease in the number of reactions occurring in the systemAs soon as benzaldehyde agents start to circulate in theenvironment and considering the continuous reconversionofNADHagents intoNAD+ agents the second reaction startsto occur This is reflected in a considerable decrease in thenumber of agents of benzaldehyde and a fairly proportionalincrease in the number of the agents representing benzoatethe product that will be ultimately excreted

43 System Performance This work describes the first phaseof development of the biomolecular simulator That is tosay that focus was set on identifying and implementing

themain biochemical and biophysical laws that would governthe model rather than implementing a realistic picture of themolecular landscape

As far as we know there has not been a previous attemptto simulate the effects of spatial localisation and temporalscales of individuals in the modelling of biomolecular sys-tems So before engaging into more complex scenarios itwas pivotal to take advantage of available experimental dataand ensure that the tool was able to account for basic cellulardynamics such as those governing enzymes adequately Nowthat we obtained a successful proof of concept we will workon system scalability in order to address more complexproblems

For this purpose we run preliminary performance tests tofind out the current scalability of our system Figure 6 sum-marises performance tests using an Intel I7 (2600) 34GHzprocessor with 6GB of RAM and runningWindows 8 64-bitThe tests accounted for three possible scenarios as follows

10 BioMed Research International

100

300

500

700

900

1100

0 5000 10000 15000

NumBenzyl alcohol

Num

ber o

f age

nts

Number of steps

(a)

89100

89300

89500

89700

89900

90100

0 5000 10000 15000

Num

ber o

f age

nts

Number of steps

89100911009310095100

0 16000

Detail

NumNAD+

(b)

Num

ber o

f age

nts

Number of steps

050

100150200250300350

0 5000 10000 15000

NumBenzal

(c)

9900

10100

10300

10500

10700

10900

0 5000 10000 15000

NumNADH

Num

ber o

f age

nts

Number of steps

(d)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 1

1732273237324732

0 10000

Detail

Num

ber o

f age

nts

Number of steps

(e)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 2

267836784678

0 15000

Detail

Num

ber o

f age

nts

Number of steps

(f)

80009000

100001100012000130001400015000

0 5000 10000 15000

NumReactions

40009000

14000

0 16000

Detail

Num

ber o

f age

nts

Number of steps

(g)

0

200

400

600

800

1000

0 5000 10000 15000

NumBenzoate

Num

ber o

f age

nts

Number of steps

(h)

Figure 5 The number of agents of different species interacting in the environment during 15000 simulation steps From top to bottom andfrom left to right the above plots represent the number of agents of benzyl alcohol NAD+ benzaldehyde NADH aryl-alcohol dehydrogenaseholoenzyme and benzaldehyde dehydrogenase holoenzyme At the bottom there is the number of occurring reactions and the number ofmolecules of benzoate excreted the extracellular medium

BioMed Research International 11

0

5000

10000

15000

20000

25000

30000

35000

0 50000 100000 150000 200000

Tim

e (m

s)

Number of agents

Only agentsAgents with movementAgents with movement and reactions

Figure 6 Performance of the tool in scenarios of increasingcomputational complexity

no action that is the agents are created but no diffusion orbehavioural rules are executed without reaction that is theagents are created and diffusion rules are activated but agentsdo not interact among themselves and with reaction thatis agents are created can move and can interact The threescenarios show a similar performance till the system reachesa population of 15119864 + 05 agents That is till this point thephysics governing agent movement and the introduction ofbehavioural rules do not affect simulation time significantlyCost resides on creating the system After that point thetime taken by the simulation of more elaborated scenariosthat is more agents in motion and more rules to manageis somewhat aggravated Over 25119864 + 05 agents the systembecomes computational unviable by a single machine

So in the near future we will investigate the use of dis-tributed and high-performance computing in the simulationofmore complex biomolecular systemsNamely we are inves-tigating the potential of the new distributed environmentof MASON the DMASON (httpwwwisislabitprojectsdmason) and the Biocellion framework [42]

5 Conclusions

ABM is increasingly popular in biology due to its naturalability to represent multiple scales of system decompositionintertwine complicated behaviours and deal with spatial-temporal constraints

The agent-based tool developed in this work aims tosupport biomolecular simulations and most notably provideinsights into catalytic efficiency in scenarios of industrialinterest Hence proof of concept was focused on the approx-imation of kinetic parameters The models correctly sim-ulated known enzymatic characteristics and yielded usefulpredictions that may guide future experimental design Italso provides a simulation variability that may reproduce theexperimental variation observed in lab experiments

Future development of the models presented here willinclude three-dimensional representation metabolic path-way simulation and accounting of extracellular substances

Moreover we plan to take into advantage the new DMA-SON platform to engage into distributed affordable sim-ulation and study more complex scenarios Other recenthigh-performance computing frameworks like Biocellionwill also be evaluated

After consolidation our tool will provide severalresources and services for the investigation of bacterial cellsin benefit of the research and industry communities

Conflict of Interests

The authors do not have any competing interests

Acknowledgments

The authors thank the Agrupamento INBIOMED fromDXPCTSUG-FEDER unha maneira de facer Europa(2012273) The research leading to these results has receivedfunding from the European Unionrsquos Seventh Frame-work Programme FP7REGPOT-2012-20131 under GrantAgreement no 316265 (BIOCAPS) and the [14VI05] Con-tract-Programme from theUniversity ofVigoThis documentreflects only the authorsrsquo views and the European Union isnot liable for any use that may be made of the informationcontained herein

References

[1] D Porro P Branduardi M Sauer and D Mattanovich ldquoOldobstacles and new horizons formicrobial chemical productionrdquoCurrent Opinion in Biotechnology C vol 30 pp 101ndash106 2014

[2] P Jeandet YVasserot T Chastang andECourot ldquoEngineeringmicrobial cells for the biosynthesis of natural compounds ofpharmaceutical significancerdquo BioMed Research Internationalvol 2013 Article ID 780145 13 pages 2013

[3] A Kondo J Ishii K Y Hara T Hasunuma and F Mat-suda ldquoDevelopment of microbial cell factories for bio-refinerythrough synthetic bioengineeringrdquo Journal of Biotechnologyvol 163 no 2 pp 204ndash216 2013

[4] J H Shin H U Kim D I Kim and S Y Lee ldquoProduction ofbulk chemicals via novel metabolic pathways in microorgan-ismsrdquo Biotechnology Advances vol 31 pp 925ndash935 2013

[5] C M Immethun A G Hoynes-OrsquoConnor A Balassy andT S Moon ldquoMicrobial production of isoprenoids enabled bysynthetic biologyrdquo Frontiers in Microbiology vol 4 article 752013

[6] Y Chen and J Nielsen ldquo Advances in metabolic pathway andstrain engineering paving the way for sustainable productionof chemical building blocksrdquo Current Opinion in Biotechnologyvol 24 pp 965ndash972 2013

[7] J W Lee D Na J M Park S Choi and S Y Lee ldquoSystemsmetabolic engineering of microorganisms for natural and non-natural chemicalsrdquo Nature Chemical Biology vol 8 pp 536ndash546 2012

[8] G Stephanopoulos ldquoSynthetic biology andmetabolic engineer-ingrdquo ACS Synthetic Biology vol 1 pp 514ndash525 2012

[9] T-M Lo W S Teo H Ling B Chen A Kang and MW Chang ldquoMicrobial engineering strategies to improve cellviability for biochemical productionrdquo Biotechnology Advancesvol 31 pp 903ndash914 2013

12 BioMed Research International

[10] K M Esvelt and H H Wang ldquoGenome-scale engineering forsystems and synthetic biologyrdquo Molecular Systems Biology vol9 p 641 2013

[11] M K Tiwari R R K Singh I Kim and J-K Lee ldquoCompu-tational approaches for rational design of proteins with novelfunctionalitiesrdquo Computational and Structural BiotechnologyJournal vol 2 Article ID e201209002 2012

[12] M Cvijovic J Almquist J Hagmar et al ldquoBridging the gaps insystems biologyrdquoMolecular Genetics and Genomics vol 289 no5 pp 727ndash734 2014

[13] N Tomar and R K De ldquoComparing methods for metabolicnetwork analysis and an application to metabolic engineeringrdquoGene vol 521 no 1 pp 1ndash14 2013

[14] A Chakrabarti L Miskovic K C Soh and V HatzimanikatisldquoTowards kinetic modeling of genome-scale metabolic net-works without sacrificing stoichiometric thermodynamic andphysiological constraintsrdquo Biotechnology Journal vol 8 no 9pp 1043ndash1057 2013

[15] A F Villaverde and J R Banga ldquoReverse engineering andidentification in systems biology strategies perspectives andchallengesrdquo Journal of the Royal Society Interface vol 11 no 91Article ID 20130505 2014

[16] S Luke C Cioffi-Revilla L Panait K Sullivan and G BalanldquoMASON a multiagent simulation environmentrdquo Simulationvol 81 no 7 pp 517ndash527 2005

[17] R Conte and M Paolucci ldquoOn agent-based modeling andcomputational social sciencerdquo Frontiers in Psychology vol 5article 668 2014

[18] M Wooldridge ldquoAgent-based software engineeringrdquo IEE Pro-ceedings Software vol 144 no 1 pp 26ndash37 1997

[19] E Bonabeau ldquoAgent-based modeling Methods and techniquesfor simulating human systemsrdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 99 no3 pp 7280ndash7287 2002

[20] N Cannata F Corradini E Merelli and L Tesei ldquoAgent-basedmodels of cellular systemsrdquo Methods in Molecular Biology vol930 pp 399ndash426 2013

[21] G An Q Mi J Dutta-Moscato and Y Vodovotz ldquoAgent-basedmodels in translational systems biologyrdquoWiley InterdisciplinaryReviews Systems Biology and Medicine vol 1 no 2 pp 159ndash1712009

[22] J O Dada and P Mendes ldquoMulti-scale modelling and simula-tion in systems biologyrdquo Integrative Biology vol 3 pp 86ndash962011

[23] H Kaul and Y Ventikos ldquoInvestigating biocomplexity throughthe agent-based paradigmrdquo Briefings in Bioinformatics vol 442013

[24] M Holcombe S Adra M Bicak et al ldquoModelling complexbiological systems using an agent-based approachrdquo IntegrativeBiology vol 4 no 1 pp 53ndash64 2012

[25] D CWalker J Southgate GHill et al ldquoThe epitheliome agent-based modelling of the social behaviour of cellsrdquo BioSystemsvol 76 no 1ndash3 pp 89ndash100 2004

[26] M B Biggs and J A Papin ldquoNovel multiscale modeling toolapplied to Pseudomonas aeruginosa biofilm formationrdquo PLoSONE vol 8 no 10 Article ID e78011 2013

[27] S M Stiegelmeyer andM C Giddings ldquoAgent-based modelingof competence phenotype switching in Bacillus subtilisrdquo Theo-retical Biology and Medical Modelling vol 10 article 23 2013

[28] G An and S Kulkarni ldquoAn agent-based modeling frameworklinking inflammation and cancer using evolutionary principles

Description of a generative hierarchy for the hallmarks of cancerand developing a bridge betweenmechanism and epidemiolog-ical datardquoMathematical Biosciences 2014

[29] J Wang L Zhang C Jing et al ldquoMulti-scale agent-basedmodeling on melanoma and its related angiogenesis analysisrdquoTheoretical Biology and Medical Modelling vol 10 article 412013

[30] V Gopalakrishnan M Kim and G An ldquoUsing an agent-basedmodel to examine the role of dynamic bacterial virulence poten-tial in the pathogenesis of surgical site infectionrdquo Advances inWound Care vol 2 no 9 pp 510ndash526 2013

[31] A E Curtin and L Zhou ldquoAn agent-based model of theresponse to angioplasty and bare-metal stent deployment in anatherosclerotic blood vesselrdquo PLoS ONE vol 9 no 4 Article IDe94411 2014

[32] K Bettenbrock H Bai M Ederer et al ldquoChapter Twomdashtowards a systems level understanding of the oxygen responseof Escherichia colirdquo in Advances in Microbial Physiology vol 6pp 65ndash114 2014

[33] A Apte R Senger and S S Fong ldquoDesigning novel cellulasesystems through agent-based modeling and global sensitivityanalysisrdquo Bioengineered vol 5 no 4 pp 243ndash253 2014

[34] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 30 no 21 pp3101ndash3108 2014

[35] S Kang S Kahan and B Momeni ldquoSimulating microbial com-munity patterning using Biocellionrdquo in Methods in MolecularBiology vol 1151 pp 233ndash253 2014

[36] I Millington Game Physics Engine Development How to Builda Robust Commercial-Grade Physics Engine for Your Game CRCPress Boca Raton Fla USA 2010

[37] G Palmer Physics for Game Programmers Apress 2005[38] T Kalwarczyk M Tabaka and R Holyst ldquoBiologisticsmdash

diffusion coefficients for complete proteome of Escherichiacolirdquo Bioinformatics vol 28 no 22 pp 2971ndash2978 2012

[39] K A Johnson and R S Goody ldquoThe original Michaelisconstant translation of the 1913 Michaelis-Menten paperrdquoBiochemistry vol 50 no 39 pp 8264ndash8269 2011

[40] A Cornish-Bowden ldquoThe origins of enzyme kineticsrdquo FEBSLetters vol 587 no 17 pp 2725ndash2730 2013

[41] M Scheer A Grote A Chang et al ldquoBRENDA the enzymeinformation system in 2011rdquo Nucleic Acids Research vol 39 no1 pp D670ndashD676 2011

[42] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 130 no 21 pp3101ndash3108 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

BioMed Research International 3

with computational tractability So far the use of generalpurpose graphical processing unit (GPGPU) technology andmulticore CPU processors are the favoured approaches toparallelise simulation algorithms [34 35]

3 A Novel Agent-Based SpatiotemporalBiomolecular Model

31 Modelling Environment and Overview A multiscaleagent-based model mimicking the biology of biochemicalreactions was developed using MASON version 16 [16] aJava based open source ABM framework that facilitatesmodel developmentThismodel includes agents representingcommon biochemical players such as metabolites cofactorsand enzymes The model also considers one physical barrierrepresenting the cell membrane and a number of geographi-cal hurdles accounting for themolecules known to exist in theintracellular space but not represented individually (to avoidunnecessary computational complexity)

The agent-based model is created on a continuous two-dimensional environment which corresponds to 5120583m2 Thedistance unit is given by the radius of the smallest moleculerepresented in themodel and corresponds to 0323times 10minus3 120583mThis value also establishes the upper limit for the velocity atwhich agents may move such that the smaller the radius ofthe molecule is the faster it will move and vice versa Thecorrespondence between simulation time steps and real timeis configurable and may be used to validate different results

The intracellular environment can be populated byenzymes some metabolites and cofactors (eg NAD+ andNADH) Once the simulation starts other types of agentssuch as other metabolites appear in the model in accordancewith the behavioural rules So the simulation only requiresdefining the particle radius and diffusion coefficient for eachspecies and the initial number of the molecules Agents arethen distributed randomly and may circulate freely

Every agent except obstacles is randomly initialisedwith a given orientation The behaviour of each agent isdetermined by the corresponding set of behavioural rulesand most notably its spatial location (Figure 1) In each timestep the model checks the current situation of the agents anddetermines which rule(s) should be executed and what inputvalues should be used

Given the circular shape of the agents the detection of acollision between agents is based on the Pythagorean Theo-rem for trianglesThat is collision is detected by knowing thatif the distance between the centres of the agents is less thantheir combined radius the agents are to collide

In the event of a collision the simulator identifies thetypes of the agents involved and looks for any behaviouralrules that may apply Either no rule applies and agents shouldbe reoriented or the matching rule should be executed andagents should be affected accordingly Agents are reorientedbased on the angle of collision and the correspondingdiffusion rate [36 37]

Most of the rules applicable in a scenario of collisioninvolve enzymes and metabolites that is the possible occur-rence of an enzymatic reaction (see Section 32)The reaction

Table 1 Agents behavioural rules and interacting agents

Agent Rules Interacts with

Enzyme (apoenzyme) Moving and binding Metabolite andcofactor

Metabolite Moving binding anddeath

Enzyme-cofactorcomplex

Cofactor Moving binding andreconverting

Enzyme and cellmembrane

Enzyme-cofactorcomplex(holoenzyme)

Moving reaction anddecoupling Metabolite

Obstacle Preventing movement All agents inmovement

probability is given by the probability of the collision andthe probability that a reaction occurs given that a collision isoccurringThe claim of the simulation is that it can reproducethe macroscopic enzymatic rate constants 119896

119898and 119896cat (mass

action kinetics) in homogeneous conditionsParticularly the number of agents representing metabo-

lites and enzymes needs to be compared with values reportedin the literature For this purpose at model construction weestablished a conversion mechanism between the numberof agents in the simulation and the number of moles cal-culated in laboratorial experiments In the literature valuesof molecules are typically represented as a concentration(eg mM) Molar concentrations can be modified to numberof molecules per volume unit by simply multiplying theconcentration by the Avogadro number Because this is a2D simulator a height also had to be indicated This wasassumed to be 0005 120583m an approximate typical height ofan enzyme The number of molecules in the simulator canthen be obtained multiplying the previous value by thearea of the simulation space and the estimated height Thediffusion rates and the sizes of the molecules can be generallyobtained directly from the literature or extrapolated usingsome already known correlations In our case diffusion wascalculated based on [38] which estimatesmolecular diffusionbased on the molecular mass of the species

Each type of agent can be tracked continuously in one runof simulation To facilitate the inspection and a dimensionalrepresentation distinct agent types are associated with differ-ent colours and sizes

32 Behavioural Rules of Agents in the Model The behav-ioural rules are twofold interaction of agents with theirenvironment and responses to the presence of other agents(Table 1) Specifically agents interact with the cell membrane(the physical boundary of the cell) and with the obstacles inthe intracellular space The cell is able to retrieve substratesfrom the extracellular space and release products to thisspace Other internally produced metabolites are to remainwithin cell boundaries

The obstacles aim to mimic the presence of other lowerlevel molecules in the intracellular space They are not rep-resented individually to preserve computational tractability(eg a bacterial cell contains approximately 2119864+10molecules

4 BioMed Research International

Start

Create the environment

Create agents and randomly distribute in environment

Set an initial random

movement for agents

For each agent

Calculate new

position

Verify agent within

environment boundaries

Reset position and

reinitiate movement

Verify if new position is

free

Set new position

Resolve collision

Finish loop

Finish simulation

NO

YES

YES

NO

Get neighbours

Finish step

While the agent is

alive or has orders

Figure 1 Decision process for the movement and rotation of an agent during the simulation

of water) but some form of representation was still requiredin order to model the diffusion rate and the orientation of themovement of the simulated molecules adequately

In certain cases the type of agent can be changed andconsequently the corresponding behavioural rules of the newtype would be applied to the agentThis transition is typicallybased on the spatial location of the agent its type and

the local environment One example of agent type reas-signment is the ldquorecyclingrdquo of NADH molecules to NAD+molecules whenever NADH agents collide with the cellmembrane

Regarding agent interaction enzymes interact with cofac-tors and metabolites Many enzymes require the assistance ofcofactors in biochemical transformations When an enzyme

BioMed Research International 5

agent and a cofactor agent collide the enzyme checkswhetherit requires the cofactor to operate If so a new agent represent-ing the enzyme-cofactor complex (holoenzyme) is created inreplacement of the two agents

The interaction between the enzymes (or enzyme-cofactor complexes) and metabolites represents catalysis andwas modelled according to Michaelis-Menten equation (seekinetic parameters section) In general metabolites andenzymes are supposed to react within a certain probabilitywhenever they collide and the enzymatic reaction may beconcluded in the same time step or after a number of timesteps

After the enzymatic reaction takes place that is theenzyme-cofactor complex collides with a substrate the com-plex is destroyed and the agents representing the enzymeand the cofactor are created again Likewise the agentsrepresenting the substrate disappear and new agents arecreated for the products of the reaction

33 Kinetic Parameters The critical part of developing ourmodel was related with incorporating kinetic informationon the cellular dynamics especially on different enzymaticreaction kinetics

Generally the kinetic scheme representing an enzymaticreaction under steady-state conditions is written as

E + S1198701

999448999471119870minus1

ES1198702

999448999471119870minus2

E + P (1)

where E represents the enzyme S is the substrate ES isthe enzyme-substrate complex and P is the product Theassociation rates 1198961 and 1198962 and the dissociation rates 119896 minus 1and 119896minus2 account for the substrate binding andproduct releaseforward and reverse processes respectively

Since the rate constants for the binding and unbindingreactions are either often unknown or difficult to determinemodelling has to rely on approximations also called aggre-gate rate laws such as theMichaelis-Menten kinetics [39 40]

119881 =119881max [S]119870119898+ [S]

(2)

or following the Lineweaver and Burk linear transformation

1

119881=119870119898

119881maxtimes1

[S]+1

119881max(3)

which represents the reaction rate at a substrate concentra-tion [S]119881max is themaximum rate that can be observed in thereaction considering the substrate is in excessTheMichaelisconstant119870

119898is a measure of the concentration of substrate at

which the rate of the reaction is one half its maximum 119881maxThat is 119870

119898is a relative measure of the affinity of the enzyme

for the substrate (how well it binds) Small 119870119898means tight

binding and large 119870119898means weak binding

The turnover number

119896cat =119881max[E]

(4)

where [E] equals total enzyme concentration represents thenumber of moles of product produced per number of molesof enzyme per unit time and is expressed in units of inversetime (119904minus1) That is the rate of the reaction when the enzymeis saturated with substrate

Having inmind the biologicalmeaning of the parameterswe hypothesised that the percentage of reactive collisionsbetween enzyme and metabolite and the number of simu-lation time steps could together be used to mimic the ratesexpressed by 119896

119898and 119896cat To corroborate this hypothesis

we conducted a series of experiments trying out differentpercentages of collision with reaction and number of timesteps and calculating the theoretical values of 119896

119898and 119896cat

The combination of simulation parameters was further vali-dated against experimental values retrieved from the enzymedatabase BRENDA [41]

4 Results and Discussion

To actually demonstrate that our design plan is functionallyplausible we recreated different scenarios of enzymatic activ-ity to show that the constructed model exhibits behavioursthat match those observed in the laboratory experiments

We present results obtained for the simulation of asimple scenario where an enzyme catalyses one substrate andreleases one productThese results are discussed theoreticallyin terms of enzyme affinity to substrate and catalytic effi-ciency and further tested against experimentally calculatedkinetic parameters

Then we show that the tool is able to model biochemicalpathways accounting for biochemical and biophysical lawsadequatelyWe describe the computational costs of represent-ingmore complex biomolecular scenariosWe discuss a num-ber of present commitments and simplifications necessary toensure computational tractability and point out ongoing linesof work

41 Approximation of Kinetic Parameters This process ofanalysis is somewhat similar to that performed in laboratoryexperimentsThat is we studied the behaviour of an identicalamount of enzyme in the presence of increasing concen-trations of substrate and measured the velocity of reactionby determining the rate of product formation Furthermorewe tested different (combinations of) simulation parametersnamely the percentage of collisions producing reaction andthe number of time steps taken by a reaction Based on theinterpretation of the Lineweaver-Burke plot which describesthe Michaelis-Menten laws for kinetic dynamics we calcu-lated the theoretical values of 119896

119898and 119896cat

Substrate concentrations ranged from 664119864 minus 02mMto 664119864 minus 01mM (200 molecules to 2000 moleculesapproximately) and there is a concentration of enzyme of498119864 minus 02mM (150 enzymes approximately) Simulationparameterisation mimicked ldquoextremerdquo scenarios (ie 100immediate reactive collisions very slow reactions and barelyany reactions occurring) as well as more common scenarios(ie midrange percentages of reactive collision and reactionduration) Moreover the experiment was replicated 3 times

6 BioMed Research International

(3 simulation runs for every concentration of substrate) andresults were averaged

The model assumes that a simulation tick correspondsto a configurable specific amount of time in the systemNotably our approach to real time-time step conversionfocused on framing realistic values of velocity of reactionand hence of 119896cat Regardless of the range of values of 119896cat tobe simulated we should be able to represent such enzymedynamics accurately by adjusting the equivalence in timesteps

Figure 2 shows the Lineweaver-Burke plots resultingfrom experiments considering the duration of the reactionconstant and equal to 1 time step representing 10 secondsSince the number of time steps that a reaction takes to beconcluded is considered somewhat equivalent to the velocityof the reaction the Lineweaver-Burke plots should convergeto a similar 119910-intersect Likewise different percentages ofreactive collision should describe different affinities of theenzyme for the substrate and this effect should be reflectedin the slope of the plots Most results were as expected therewas a convergence of the 119910-intersects and the higher thepercentage of reactive collision (ie lower values of 119896

119898) the

lower the value of the slopeFrom the Lineweaver-Burke plots and in particular

considering the linear regression model that approximatesthe equation

1

119881=119870119898

119881maxtimes1

[S]+1

119881max(5)

wewere able to estimate the values of 119896119898and 119896cat described by

the simulation parameters (Table 2) Again it was expectedthat higher percentages of reactive collision would relate tolower values of 119896

119898and vice versa whilst the value of 119896cat

should be less affected The presence of negative values for119896cat and 119896119898 for very low percentages of reactive collisionswas unexpected though This occurs because 119896cat for thosesituations is supposed to be very close to zero As this modelis stochastic small variations may lead the values of 119896cat tobecome negative hence affecting the values of 119896

119898as well

To further validate the approximation of the kineticparameters made by our model we tested them againstexperimentally validated data Six enzyme records fallingwithin the range of kinetic values calculated were randomlyselected from BRENDA database [41]

We selected the simulation scenarios producing themost similar approximation to the experimentally validatedkinetic parameters (Table 3) and compared the correspond-ing Lineweaver-Burke plots (Figure 3) As expected themoresimilar the approximations were to the real values the betterthe simulations performed In particular the number oftime steps stipulated for the duration of the reaction onlyaffects the value of 119896cat and thus can be used to validate thesimulation

42 A Two-Step Enzymatic Reaction After validating ourmodel for situations where only one enzymatic reactionoccurs we then studied the behaviour of our simulator whentwo enzymes are present in a two-stage process

Table 2 Approximation of kinetic parameters by different percent-ages of reactive collision and time steps

reactivecollision Time step 119896

119898(mM) 119896cat (s

minus1)

1 0 minus0850576595 minus00285144535 0 minus2996153951 minus687119864 minus 015 25 minus4656418568 minus977119864 minus 015 50 3439111157 808119864 minus 015 75 2918555171 625119864 minus 015 100 minus2179373575 minus392119864 + 0010 0 minus146001318 minus663194461615 0 1151508927 762333046425 0 087739 108119864 + 0025 5 136829 144119864 + 0025 25 245375 223119864 + 0025 50 120869 106119864 + 0025 75 070036 622119864 minus 0125 100 0531257304 452119864 minus 0134 1 318977 393119864 + 0050 0 071725 127119864 + 0075 0 365866 649119864 + 0075 5 306473 533119864 + 0075 25 113387 201119864 + 0075 50 060205 107119864 + 0075 75 037565 669119864 minus 0175 100 029693544 506119864 minus 0190 0 443222 817119864 + 0095 0 449601 844119864 + 0095 25 1277963717 239662133395 50 056747 111119864 + 0095 75 034196 688119864 minus 0195 100 0237537579 488119864 minus 01100 0 075547 160119864 + 00

Specifically we studied the catalytic activity of twoenzymes commonly present in aromatic aldehyde produc-tion the aryl-alcohol dehydrogenase (EC number 11190)and the benzaldehyde dehydrogenase (EC number 12128)

In particular the model encompasses the following twoequations

benzyl alcohol +NAD+ 997888rarr benzaldehyde +NADH +H+

benzaldehyde+NAD+ +H2O 997888rarr benzoate+NADH + 2H+

(6)

The model represented an area of approximately 1120583m2containing a concentration of 166mM (5119864+03molecules) ofeach type of enzyme 105 obstacles and initial concentrationsof 332119864 + 01mM and 332mM (1119864 + 05 molecules and1119864 + 04 molecules) for NAD+ and NADH respectivelyDuring simulation a concentration of 498119864 minus 01mM(1500 molecules) of benzyl alcohol that is the substrate of

BioMed Research International 7

050

100150200250300350400450500

1 3 5 7 9 11 13 15

1V

(itm

M)

1[S] (mM)

1007550253415

Linear (100)Linear (75)Linear (50)Linear (25)Linear (34)Linear (15)

y = 10596x + 24081

y = 11218x + 33688

y = 13112x + 43521

y = 19657x + 66475

y = 1629x + 5107

R2 = 09999

R2 = 1

R2 = 09999

R2 = 09999

R2 = 09993

R2 = 09993

y = 30326x + 26336

Figure 2 The Lineweaver-Burk plots obtained while simulating different percentages of reactive collision and a time step of 1 The markersrepresent the outputs of simulation and the lines represent the corresponding trend lines based on linear regression (equation also shown)

Table 3 An approximation between experimentally calculated kinetic parameters and the parameters simulated by our model

Enzyme identification Experimental kinetics Simulation parameters Approximated kinetics119896119898

119896cat reactive collision Time step 119896119898(mM) 119896cat (s

minus1)EC 1819mdashglutathione reductase activity 0404 039 25 100 0531257304 452119864 minus 01

EC 41111mdashaspartate 1-decarboxylase 0219 065 75 75 037565 669119864 minus 01

EC 1111mdashalcohol dehydrogenase 041 1 95 75 034196 688119864 minus 01

EC 111205mdashIMP dehydrogenase 17 19 25 25 245375 223119864 + 00

EC 341322mdashD-Ala-D-Ala dipeptidase 1 47 75 25 113387 201119864 + 00

EC 4111mdashpyruvate decarboxylase 18 12 25 5 136829 144119864 + 00

Table 4 The weight size and diffusion rate of the moleculesrepresented in the two-step enzymatic system

Species Molecularweight (gmol)

Particle radius(120583m)

Diffusion rate(120583m2s)

Benzyl alcohol 10814 0323 times 10minus3 4018 times 10minus14

NAD+ 66141 0657 times 10minus3 1975 times 10minus14

NADH 66343 0658 times 10minus3 1973 times 10minus14

Benzaldehyde 106121 0321 times 10minus3 4047 times 10minus14

Benzoate 12112 0338 times 10minus3 3843 times 10minus14

the first reaction was introduced gradually in the environ-ment specifically 10 at every 10 time steps

Agent size and velocity of movement were adjustedaccording to the molecular weight of the biological species(Table 4) Heaviermolecules have a larger radius and a slowerdiffusion rate Proportionally the agents representing benzylalcohol and benzaldehyde molecules should be two times

smaller and faster than the agents representing the moleculesof NAD+ and NADH

To facilitate visual inspection distinct agent types areassociated with different colours and proportional sizes Assuch it is possible to visually observe the evolving of thesimulation and at some extent observe how the agents aremoving and interacting with each other Specifically it ispossible to see how different agents traverse the environmentand how behavioural rules are triggered or take precedenceover each other

As illustrated in Figure 4 although the movement ofthe molecules of benzyl alcohol (green circles) is quite fastthese molecules are unable to interact with the correspond-ing enzyme (aryl-alcohol dehydrogenase named enzymeone and coloured yellow in the figure) unless the enzymehas already bound to a NAD+ molecule (ie creating theholoenzyme 1 coloured in black) Likewise interactions withthe second enzyme benzaldehyde dehydrogenase (magentacircles) are limited to the molecules of NAD+ (red circles)until the first reaction actually occurs and begins producingbenzaldehyde (blue circles) Furthermore it is possible to

8 BioMed Research International

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 20797x + 51479

R2 = 1

R2 = 09994

y = 23614x + 44449

1S (mMminus1)

TheoreticalSimulation

(a)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M) R2 = 1

R2 = 09991

y = 67643x + 30887

y = 11265x + 29988

1S (mMminus1)

TheoreticalSimulation

(b)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 82314x + 20077

y = 9982x + 29191

R2 = 1

R2 = 09984

TheoreticalSimulation

(c)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 17963x + 10567

y = 22109x + 90103

R2 = 1

R2 = 09982

1S (mMminus1)

TheoreticalSimulation

(d)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 42716x + 42716

y = 11353x + 10013

R2 = 1

R2 = 09999

TheoreticalSimulation

(e)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 30115x + 16731

y = 19058x + 13928

R2 = 1

R2 = 09991

1S (mMminus1)

TheoreticalSimulation

(f)

Figure 3The Lineweaver-Burk plots for experimentally calculated kinetic parameters (represented by a solid line) and simulation parameterssimulated by our model (represented by a dash dotted line) From top to bottom and from left to right the plots represent the activity of thefollowing enzymes glutathione reductase aspartate 1-decarboxylase alcohol dehydrogenase IMP dehydrogenase D-Ala-D-Ala dipeptidaseand pyruvate decarboxylase

observe the reconversion of the molecules of NADH (bluecircles) to molecules of NAD+ whenever the first hit thecell membrane (ie boundary of the environment) Likewiseit is possible to observe that obstacles are playing theirpart deflecting the movement of the other agents everyso often A detailed visual documentation of the two-stepenzymatic reaction simulation is available in supplementary

material (see Supplementary Material available online athttpdxdoiorg1011552014769471)

Numeric outputs detail these visual insights and presentdata about the movement of the different species thevelocity at which the reactions are taking place and thebehavioural system as a whole (Figure 5) The number ofagents representing the first substrate benzyl alcohol decays

BioMed Research International 9

NADHEnzyme one

Enzyme two

ObstaclesBenzaldehydeHaloenzyme 1

Haloenzyme 2

Benzyl alcoholBenzoateNAD+

Figure 4 Visual illustration of the evolving of the population of agents during the simulation steps

considerably in the first 2000 steps of simulation togetherwith the disappearance of agents representing NAD+ andthe creation of agents representing the aryl-alcohol dehy-drogenase haloenzyme This leads to the production of agrowing number of agents representing benzaldehyde and anincrease in the number of reactions occurring in the systemAs soon as benzaldehyde agents start to circulate in theenvironment and considering the continuous reconversionofNADHagents intoNAD+ agents the second reaction startsto occur This is reflected in a considerable decrease in thenumber of agents of benzaldehyde and a fairly proportionalincrease in the number of the agents representing benzoatethe product that will be ultimately excreted

43 System Performance This work describes the first phaseof development of the biomolecular simulator That is tosay that focus was set on identifying and implementing

themain biochemical and biophysical laws that would governthe model rather than implementing a realistic picture of themolecular landscape

As far as we know there has not been a previous attemptto simulate the effects of spatial localisation and temporalscales of individuals in the modelling of biomolecular sys-tems So before engaging into more complex scenarios itwas pivotal to take advantage of available experimental dataand ensure that the tool was able to account for basic cellulardynamics such as those governing enzymes adequately Nowthat we obtained a successful proof of concept we will workon system scalability in order to address more complexproblems

For this purpose we run preliminary performance tests tofind out the current scalability of our system Figure 6 sum-marises performance tests using an Intel I7 (2600) 34GHzprocessor with 6GB of RAM and runningWindows 8 64-bitThe tests accounted for three possible scenarios as follows

10 BioMed Research International

100

300

500

700

900

1100

0 5000 10000 15000

NumBenzyl alcohol

Num

ber o

f age

nts

Number of steps

(a)

89100

89300

89500

89700

89900

90100

0 5000 10000 15000

Num

ber o

f age

nts

Number of steps

89100911009310095100

0 16000

Detail

NumNAD+

(b)

Num

ber o

f age

nts

Number of steps

050

100150200250300350

0 5000 10000 15000

NumBenzal

(c)

9900

10100

10300

10500

10700

10900

0 5000 10000 15000

NumNADH

Num

ber o

f age

nts

Number of steps

(d)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 1

1732273237324732

0 10000

Detail

Num

ber o

f age

nts

Number of steps

(e)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 2

267836784678

0 15000

Detail

Num

ber o

f age

nts

Number of steps

(f)

80009000

100001100012000130001400015000

0 5000 10000 15000

NumReactions

40009000

14000

0 16000

Detail

Num

ber o

f age

nts

Number of steps

(g)

0

200

400

600

800

1000

0 5000 10000 15000

NumBenzoate

Num

ber o

f age

nts

Number of steps

(h)

Figure 5 The number of agents of different species interacting in the environment during 15000 simulation steps From top to bottom andfrom left to right the above plots represent the number of agents of benzyl alcohol NAD+ benzaldehyde NADH aryl-alcohol dehydrogenaseholoenzyme and benzaldehyde dehydrogenase holoenzyme At the bottom there is the number of occurring reactions and the number ofmolecules of benzoate excreted the extracellular medium

BioMed Research International 11

0

5000

10000

15000

20000

25000

30000

35000

0 50000 100000 150000 200000

Tim

e (m

s)

Number of agents

Only agentsAgents with movementAgents with movement and reactions

Figure 6 Performance of the tool in scenarios of increasingcomputational complexity

no action that is the agents are created but no diffusion orbehavioural rules are executed without reaction that is theagents are created and diffusion rules are activated but agentsdo not interact among themselves and with reaction thatis agents are created can move and can interact The threescenarios show a similar performance till the system reachesa population of 15119864 + 05 agents That is till this point thephysics governing agent movement and the introduction ofbehavioural rules do not affect simulation time significantlyCost resides on creating the system After that point thetime taken by the simulation of more elaborated scenariosthat is more agents in motion and more rules to manageis somewhat aggravated Over 25119864 + 05 agents the systembecomes computational unviable by a single machine

So in the near future we will investigate the use of dis-tributed and high-performance computing in the simulationofmore complex biomolecular systemsNamely we are inves-tigating the potential of the new distributed environmentof MASON the DMASON (httpwwwisislabitprojectsdmason) and the Biocellion framework [42]

5 Conclusions

ABM is increasingly popular in biology due to its naturalability to represent multiple scales of system decompositionintertwine complicated behaviours and deal with spatial-temporal constraints

The agent-based tool developed in this work aims tosupport biomolecular simulations and most notably provideinsights into catalytic efficiency in scenarios of industrialinterest Hence proof of concept was focused on the approx-imation of kinetic parameters The models correctly sim-ulated known enzymatic characteristics and yielded usefulpredictions that may guide future experimental design Italso provides a simulation variability that may reproduce theexperimental variation observed in lab experiments

Future development of the models presented here willinclude three-dimensional representation metabolic path-way simulation and accounting of extracellular substances

Moreover we plan to take into advantage the new DMA-SON platform to engage into distributed affordable sim-ulation and study more complex scenarios Other recenthigh-performance computing frameworks like Biocellionwill also be evaluated

After consolidation our tool will provide severalresources and services for the investigation of bacterial cellsin benefit of the research and industry communities

Conflict of Interests

The authors do not have any competing interests

Acknowledgments

The authors thank the Agrupamento INBIOMED fromDXPCTSUG-FEDER unha maneira de facer Europa(2012273) The research leading to these results has receivedfunding from the European Unionrsquos Seventh Frame-work Programme FP7REGPOT-2012-20131 under GrantAgreement no 316265 (BIOCAPS) and the [14VI05] Con-tract-Programme from theUniversity ofVigoThis documentreflects only the authorsrsquo views and the European Union isnot liable for any use that may be made of the informationcontained herein

References

[1] D Porro P Branduardi M Sauer and D Mattanovich ldquoOldobstacles and new horizons formicrobial chemical productionrdquoCurrent Opinion in Biotechnology C vol 30 pp 101ndash106 2014

[2] P Jeandet YVasserot T Chastang andECourot ldquoEngineeringmicrobial cells for the biosynthesis of natural compounds ofpharmaceutical significancerdquo BioMed Research Internationalvol 2013 Article ID 780145 13 pages 2013

[3] A Kondo J Ishii K Y Hara T Hasunuma and F Mat-suda ldquoDevelopment of microbial cell factories for bio-refinerythrough synthetic bioengineeringrdquo Journal of Biotechnologyvol 163 no 2 pp 204ndash216 2013

[4] J H Shin H U Kim D I Kim and S Y Lee ldquoProduction ofbulk chemicals via novel metabolic pathways in microorgan-ismsrdquo Biotechnology Advances vol 31 pp 925ndash935 2013

[5] C M Immethun A G Hoynes-OrsquoConnor A Balassy andT S Moon ldquoMicrobial production of isoprenoids enabled bysynthetic biologyrdquo Frontiers in Microbiology vol 4 article 752013

[6] Y Chen and J Nielsen ldquo Advances in metabolic pathway andstrain engineering paving the way for sustainable productionof chemical building blocksrdquo Current Opinion in Biotechnologyvol 24 pp 965ndash972 2013

[7] J W Lee D Na J M Park S Choi and S Y Lee ldquoSystemsmetabolic engineering of microorganisms for natural and non-natural chemicalsrdquo Nature Chemical Biology vol 8 pp 536ndash546 2012

[8] G Stephanopoulos ldquoSynthetic biology andmetabolic engineer-ingrdquo ACS Synthetic Biology vol 1 pp 514ndash525 2012

[9] T-M Lo W S Teo H Ling B Chen A Kang and MW Chang ldquoMicrobial engineering strategies to improve cellviability for biochemical productionrdquo Biotechnology Advancesvol 31 pp 903ndash914 2013

12 BioMed Research International

[10] K M Esvelt and H H Wang ldquoGenome-scale engineering forsystems and synthetic biologyrdquo Molecular Systems Biology vol9 p 641 2013

[11] M K Tiwari R R K Singh I Kim and J-K Lee ldquoCompu-tational approaches for rational design of proteins with novelfunctionalitiesrdquo Computational and Structural BiotechnologyJournal vol 2 Article ID e201209002 2012

[12] M Cvijovic J Almquist J Hagmar et al ldquoBridging the gaps insystems biologyrdquoMolecular Genetics and Genomics vol 289 no5 pp 727ndash734 2014

[13] N Tomar and R K De ldquoComparing methods for metabolicnetwork analysis and an application to metabolic engineeringrdquoGene vol 521 no 1 pp 1ndash14 2013

[14] A Chakrabarti L Miskovic K C Soh and V HatzimanikatisldquoTowards kinetic modeling of genome-scale metabolic net-works without sacrificing stoichiometric thermodynamic andphysiological constraintsrdquo Biotechnology Journal vol 8 no 9pp 1043ndash1057 2013

[15] A F Villaverde and J R Banga ldquoReverse engineering andidentification in systems biology strategies perspectives andchallengesrdquo Journal of the Royal Society Interface vol 11 no 91Article ID 20130505 2014

[16] S Luke C Cioffi-Revilla L Panait K Sullivan and G BalanldquoMASON a multiagent simulation environmentrdquo Simulationvol 81 no 7 pp 517ndash527 2005

[17] R Conte and M Paolucci ldquoOn agent-based modeling andcomputational social sciencerdquo Frontiers in Psychology vol 5article 668 2014

[18] M Wooldridge ldquoAgent-based software engineeringrdquo IEE Pro-ceedings Software vol 144 no 1 pp 26ndash37 1997

[19] E Bonabeau ldquoAgent-based modeling Methods and techniquesfor simulating human systemsrdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 99 no3 pp 7280ndash7287 2002

[20] N Cannata F Corradini E Merelli and L Tesei ldquoAgent-basedmodels of cellular systemsrdquo Methods in Molecular Biology vol930 pp 399ndash426 2013

[21] G An Q Mi J Dutta-Moscato and Y Vodovotz ldquoAgent-basedmodels in translational systems biologyrdquoWiley InterdisciplinaryReviews Systems Biology and Medicine vol 1 no 2 pp 159ndash1712009

[22] J O Dada and P Mendes ldquoMulti-scale modelling and simula-tion in systems biologyrdquo Integrative Biology vol 3 pp 86ndash962011

[23] H Kaul and Y Ventikos ldquoInvestigating biocomplexity throughthe agent-based paradigmrdquo Briefings in Bioinformatics vol 442013

[24] M Holcombe S Adra M Bicak et al ldquoModelling complexbiological systems using an agent-based approachrdquo IntegrativeBiology vol 4 no 1 pp 53ndash64 2012

[25] D CWalker J Southgate GHill et al ldquoThe epitheliome agent-based modelling of the social behaviour of cellsrdquo BioSystemsvol 76 no 1ndash3 pp 89ndash100 2004

[26] M B Biggs and J A Papin ldquoNovel multiscale modeling toolapplied to Pseudomonas aeruginosa biofilm formationrdquo PLoSONE vol 8 no 10 Article ID e78011 2013

[27] S M Stiegelmeyer andM C Giddings ldquoAgent-based modelingof competence phenotype switching in Bacillus subtilisrdquo Theo-retical Biology and Medical Modelling vol 10 article 23 2013

[28] G An and S Kulkarni ldquoAn agent-based modeling frameworklinking inflammation and cancer using evolutionary principles

Description of a generative hierarchy for the hallmarks of cancerand developing a bridge betweenmechanism and epidemiolog-ical datardquoMathematical Biosciences 2014

[29] J Wang L Zhang C Jing et al ldquoMulti-scale agent-basedmodeling on melanoma and its related angiogenesis analysisrdquoTheoretical Biology and Medical Modelling vol 10 article 412013

[30] V Gopalakrishnan M Kim and G An ldquoUsing an agent-basedmodel to examine the role of dynamic bacterial virulence poten-tial in the pathogenesis of surgical site infectionrdquo Advances inWound Care vol 2 no 9 pp 510ndash526 2013

[31] A E Curtin and L Zhou ldquoAn agent-based model of theresponse to angioplasty and bare-metal stent deployment in anatherosclerotic blood vesselrdquo PLoS ONE vol 9 no 4 Article IDe94411 2014

[32] K Bettenbrock H Bai M Ederer et al ldquoChapter Twomdashtowards a systems level understanding of the oxygen responseof Escherichia colirdquo in Advances in Microbial Physiology vol 6pp 65ndash114 2014

[33] A Apte R Senger and S S Fong ldquoDesigning novel cellulasesystems through agent-based modeling and global sensitivityanalysisrdquo Bioengineered vol 5 no 4 pp 243ndash253 2014

[34] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 30 no 21 pp3101ndash3108 2014

[35] S Kang S Kahan and B Momeni ldquoSimulating microbial com-munity patterning using Biocellionrdquo in Methods in MolecularBiology vol 1151 pp 233ndash253 2014

[36] I Millington Game Physics Engine Development How to Builda Robust Commercial-Grade Physics Engine for Your Game CRCPress Boca Raton Fla USA 2010

[37] G Palmer Physics for Game Programmers Apress 2005[38] T Kalwarczyk M Tabaka and R Holyst ldquoBiologisticsmdash

diffusion coefficients for complete proteome of Escherichiacolirdquo Bioinformatics vol 28 no 22 pp 2971ndash2978 2012

[39] K A Johnson and R S Goody ldquoThe original Michaelisconstant translation of the 1913 Michaelis-Menten paperrdquoBiochemistry vol 50 no 39 pp 8264ndash8269 2011

[40] A Cornish-Bowden ldquoThe origins of enzyme kineticsrdquo FEBSLetters vol 587 no 17 pp 2725ndash2730 2013

[41] M Scheer A Grote A Chang et al ldquoBRENDA the enzymeinformation system in 2011rdquo Nucleic Acids Research vol 39 no1 pp D670ndashD676 2011

[42] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 130 no 21 pp3101ndash3108 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

4 BioMed Research International

Start

Create the environment

Create agents and randomly distribute in environment

Set an initial random

movement for agents

For each agent

Calculate new

position

Verify agent within

environment boundaries

Reset position and

reinitiate movement

Verify if new position is

free

Set new position

Resolve collision

Finish loop

Finish simulation

NO

YES

YES

NO

Get neighbours

Finish step

While the agent is

alive or has orders

Figure 1 Decision process for the movement and rotation of an agent during the simulation

of water) but some form of representation was still requiredin order to model the diffusion rate and the orientation of themovement of the simulated molecules adequately

In certain cases the type of agent can be changed andconsequently the corresponding behavioural rules of the newtype would be applied to the agentThis transition is typicallybased on the spatial location of the agent its type and

the local environment One example of agent type reas-signment is the ldquorecyclingrdquo of NADH molecules to NAD+molecules whenever NADH agents collide with the cellmembrane

Regarding agent interaction enzymes interact with cofac-tors and metabolites Many enzymes require the assistance ofcofactors in biochemical transformations When an enzyme

BioMed Research International 5

agent and a cofactor agent collide the enzyme checkswhetherit requires the cofactor to operate If so a new agent represent-ing the enzyme-cofactor complex (holoenzyme) is created inreplacement of the two agents

The interaction between the enzymes (or enzyme-cofactor complexes) and metabolites represents catalysis andwas modelled according to Michaelis-Menten equation (seekinetic parameters section) In general metabolites andenzymes are supposed to react within a certain probabilitywhenever they collide and the enzymatic reaction may beconcluded in the same time step or after a number of timesteps

After the enzymatic reaction takes place that is theenzyme-cofactor complex collides with a substrate the com-plex is destroyed and the agents representing the enzymeand the cofactor are created again Likewise the agentsrepresenting the substrate disappear and new agents arecreated for the products of the reaction

33 Kinetic Parameters The critical part of developing ourmodel was related with incorporating kinetic informationon the cellular dynamics especially on different enzymaticreaction kinetics

Generally the kinetic scheme representing an enzymaticreaction under steady-state conditions is written as

E + S1198701

999448999471119870minus1

ES1198702

999448999471119870minus2

E + P (1)

where E represents the enzyme S is the substrate ES isthe enzyme-substrate complex and P is the product Theassociation rates 1198961 and 1198962 and the dissociation rates 119896 minus 1and 119896minus2 account for the substrate binding andproduct releaseforward and reverse processes respectively

Since the rate constants for the binding and unbindingreactions are either often unknown or difficult to determinemodelling has to rely on approximations also called aggre-gate rate laws such as theMichaelis-Menten kinetics [39 40]

119881 =119881max [S]119870119898+ [S]

(2)

or following the Lineweaver and Burk linear transformation

1

119881=119870119898

119881maxtimes1

[S]+1

119881max(3)

which represents the reaction rate at a substrate concentra-tion [S]119881max is themaximum rate that can be observed in thereaction considering the substrate is in excessTheMichaelisconstant119870

119898is a measure of the concentration of substrate at

which the rate of the reaction is one half its maximum 119881maxThat is 119870

119898is a relative measure of the affinity of the enzyme

for the substrate (how well it binds) Small 119870119898means tight

binding and large 119870119898means weak binding

The turnover number

119896cat =119881max[E]

(4)

where [E] equals total enzyme concentration represents thenumber of moles of product produced per number of molesof enzyme per unit time and is expressed in units of inversetime (119904minus1) That is the rate of the reaction when the enzymeis saturated with substrate

Having inmind the biologicalmeaning of the parameterswe hypothesised that the percentage of reactive collisionsbetween enzyme and metabolite and the number of simu-lation time steps could together be used to mimic the ratesexpressed by 119896

119898and 119896cat To corroborate this hypothesis

we conducted a series of experiments trying out differentpercentages of collision with reaction and number of timesteps and calculating the theoretical values of 119896

119898and 119896cat

The combination of simulation parameters was further vali-dated against experimental values retrieved from the enzymedatabase BRENDA [41]

4 Results and Discussion

To actually demonstrate that our design plan is functionallyplausible we recreated different scenarios of enzymatic activ-ity to show that the constructed model exhibits behavioursthat match those observed in the laboratory experiments

We present results obtained for the simulation of asimple scenario where an enzyme catalyses one substrate andreleases one productThese results are discussed theoreticallyin terms of enzyme affinity to substrate and catalytic effi-ciency and further tested against experimentally calculatedkinetic parameters

Then we show that the tool is able to model biochemicalpathways accounting for biochemical and biophysical lawsadequatelyWe describe the computational costs of represent-ingmore complex biomolecular scenariosWe discuss a num-ber of present commitments and simplifications necessary toensure computational tractability and point out ongoing linesof work

41 Approximation of Kinetic Parameters This process ofanalysis is somewhat similar to that performed in laboratoryexperimentsThat is we studied the behaviour of an identicalamount of enzyme in the presence of increasing concen-trations of substrate and measured the velocity of reactionby determining the rate of product formation Furthermorewe tested different (combinations of) simulation parametersnamely the percentage of collisions producing reaction andthe number of time steps taken by a reaction Based on theinterpretation of the Lineweaver-Burke plot which describesthe Michaelis-Menten laws for kinetic dynamics we calcu-lated the theoretical values of 119896

119898and 119896cat

Substrate concentrations ranged from 664119864 minus 02mMto 664119864 minus 01mM (200 molecules to 2000 moleculesapproximately) and there is a concentration of enzyme of498119864 minus 02mM (150 enzymes approximately) Simulationparameterisation mimicked ldquoextremerdquo scenarios (ie 100immediate reactive collisions very slow reactions and barelyany reactions occurring) as well as more common scenarios(ie midrange percentages of reactive collision and reactionduration) Moreover the experiment was replicated 3 times

6 BioMed Research International

(3 simulation runs for every concentration of substrate) andresults were averaged

The model assumes that a simulation tick correspondsto a configurable specific amount of time in the systemNotably our approach to real time-time step conversionfocused on framing realistic values of velocity of reactionand hence of 119896cat Regardless of the range of values of 119896cat tobe simulated we should be able to represent such enzymedynamics accurately by adjusting the equivalence in timesteps

Figure 2 shows the Lineweaver-Burke plots resultingfrom experiments considering the duration of the reactionconstant and equal to 1 time step representing 10 secondsSince the number of time steps that a reaction takes to beconcluded is considered somewhat equivalent to the velocityof the reaction the Lineweaver-Burke plots should convergeto a similar 119910-intersect Likewise different percentages ofreactive collision should describe different affinities of theenzyme for the substrate and this effect should be reflectedin the slope of the plots Most results were as expected therewas a convergence of the 119910-intersects and the higher thepercentage of reactive collision (ie lower values of 119896

119898) the

lower the value of the slopeFrom the Lineweaver-Burke plots and in particular

considering the linear regression model that approximatesthe equation

1

119881=119870119898

119881maxtimes1

[S]+1

119881max(5)

wewere able to estimate the values of 119896119898and 119896cat described by

the simulation parameters (Table 2) Again it was expectedthat higher percentages of reactive collision would relate tolower values of 119896

119898and vice versa whilst the value of 119896cat

should be less affected The presence of negative values for119896cat and 119896119898 for very low percentages of reactive collisionswas unexpected though This occurs because 119896cat for thosesituations is supposed to be very close to zero As this modelis stochastic small variations may lead the values of 119896cat tobecome negative hence affecting the values of 119896

119898as well

To further validate the approximation of the kineticparameters made by our model we tested them againstexperimentally validated data Six enzyme records fallingwithin the range of kinetic values calculated were randomlyselected from BRENDA database [41]

We selected the simulation scenarios producing themost similar approximation to the experimentally validatedkinetic parameters (Table 3) and compared the correspond-ing Lineweaver-Burke plots (Figure 3) As expected themoresimilar the approximations were to the real values the betterthe simulations performed In particular the number oftime steps stipulated for the duration of the reaction onlyaffects the value of 119896cat and thus can be used to validate thesimulation

42 A Two-Step Enzymatic Reaction After validating ourmodel for situations where only one enzymatic reactionoccurs we then studied the behaviour of our simulator whentwo enzymes are present in a two-stage process

Table 2 Approximation of kinetic parameters by different percent-ages of reactive collision and time steps

reactivecollision Time step 119896

119898(mM) 119896cat (s

minus1)

1 0 minus0850576595 minus00285144535 0 minus2996153951 minus687119864 minus 015 25 minus4656418568 minus977119864 minus 015 50 3439111157 808119864 minus 015 75 2918555171 625119864 minus 015 100 minus2179373575 minus392119864 + 0010 0 minus146001318 minus663194461615 0 1151508927 762333046425 0 087739 108119864 + 0025 5 136829 144119864 + 0025 25 245375 223119864 + 0025 50 120869 106119864 + 0025 75 070036 622119864 minus 0125 100 0531257304 452119864 minus 0134 1 318977 393119864 + 0050 0 071725 127119864 + 0075 0 365866 649119864 + 0075 5 306473 533119864 + 0075 25 113387 201119864 + 0075 50 060205 107119864 + 0075 75 037565 669119864 minus 0175 100 029693544 506119864 minus 0190 0 443222 817119864 + 0095 0 449601 844119864 + 0095 25 1277963717 239662133395 50 056747 111119864 + 0095 75 034196 688119864 minus 0195 100 0237537579 488119864 minus 01100 0 075547 160119864 + 00

Specifically we studied the catalytic activity of twoenzymes commonly present in aromatic aldehyde produc-tion the aryl-alcohol dehydrogenase (EC number 11190)and the benzaldehyde dehydrogenase (EC number 12128)

In particular the model encompasses the following twoequations

benzyl alcohol +NAD+ 997888rarr benzaldehyde +NADH +H+

benzaldehyde+NAD+ +H2O 997888rarr benzoate+NADH + 2H+

(6)

The model represented an area of approximately 1120583m2containing a concentration of 166mM (5119864+03molecules) ofeach type of enzyme 105 obstacles and initial concentrationsof 332119864 + 01mM and 332mM (1119864 + 05 molecules and1119864 + 04 molecules) for NAD+ and NADH respectivelyDuring simulation a concentration of 498119864 minus 01mM(1500 molecules) of benzyl alcohol that is the substrate of

BioMed Research International 7

050

100150200250300350400450500

1 3 5 7 9 11 13 15

1V

(itm

M)

1[S] (mM)

1007550253415

Linear (100)Linear (75)Linear (50)Linear (25)Linear (34)Linear (15)

y = 10596x + 24081

y = 11218x + 33688

y = 13112x + 43521

y = 19657x + 66475

y = 1629x + 5107

R2 = 09999

R2 = 1

R2 = 09999

R2 = 09999

R2 = 09993

R2 = 09993

y = 30326x + 26336

Figure 2 The Lineweaver-Burk plots obtained while simulating different percentages of reactive collision and a time step of 1 The markersrepresent the outputs of simulation and the lines represent the corresponding trend lines based on linear regression (equation also shown)

Table 3 An approximation between experimentally calculated kinetic parameters and the parameters simulated by our model

Enzyme identification Experimental kinetics Simulation parameters Approximated kinetics119896119898

119896cat reactive collision Time step 119896119898(mM) 119896cat (s

minus1)EC 1819mdashglutathione reductase activity 0404 039 25 100 0531257304 452119864 minus 01

EC 41111mdashaspartate 1-decarboxylase 0219 065 75 75 037565 669119864 minus 01

EC 1111mdashalcohol dehydrogenase 041 1 95 75 034196 688119864 minus 01

EC 111205mdashIMP dehydrogenase 17 19 25 25 245375 223119864 + 00

EC 341322mdashD-Ala-D-Ala dipeptidase 1 47 75 25 113387 201119864 + 00

EC 4111mdashpyruvate decarboxylase 18 12 25 5 136829 144119864 + 00

Table 4 The weight size and diffusion rate of the moleculesrepresented in the two-step enzymatic system

Species Molecularweight (gmol)

Particle radius(120583m)

Diffusion rate(120583m2s)

Benzyl alcohol 10814 0323 times 10minus3 4018 times 10minus14

NAD+ 66141 0657 times 10minus3 1975 times 10minus14

NADH 66343 0658 times 10minus3 1973 times 10minus14

Benzaldehyde 106121 0321 times 10minus3 4047 times 10minus14

Benzoate 12112 0338 times 10minus3 3843 times 10minus14

the first reaction was introduced gradually in the environ-ment specifically 10 at every 10 time steps

Agent size and velocity of movement were adjustedaccording to the molecular weight of the biological species(Table 4) Heaviermolecules have a larger radius and a slowerdiffusion rate Proportionally the agents representing benzylalcohol and benzaldehyde molecules should be two times

smaller and faster than the agents representing the moleculesof NAD+ and NADH

To facilitate visual inspection distinct agent types areassociated with different colours and proportional sizes Assuch it is possible to visually observe the evolving of thesimulation and at some extent observe how the agents aremoving and interacting with each other Specifically it ispossible to see how different agents traverse the environmentand how behavioural rules are triggered or take precedenceover each other

As illustrated in Figure 4 although the movement ofthe molecules of benzyl alcohol (green circles) is quite fastthese molecules are unable to interact with the correspond-ing enzyme (aryl-alcohol dehydrogenase named enzymeone and coloured yellow in the figure) unless the enzymehas already bound to a NAD+ molecule (ie creating theholoenzyme 1 coloured in black) Likewise interactions withthe second enzyme benzaldehyde dehydrogenase (magentacircles) are limited to the molecules of NAD+ (red circles)until the first reaction actually occurs and begins producingbenzaldehyde (blue circles) Furthermore it is possible to

8 BioMed Research International

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 20797x + 51479

R2 = 1

R2 = 09994

y = 23614x + 44449

1S (mMminus1)

TheoreticalSimulation

(a)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M) R2 = 1

R2 = 09991

y = 67643x + 30887

y = 11265x + 29988

1S (mMminus1)

TheoreticalSimulation

(b)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 82314x + 20077

y = 9982x + 29191

R2 = 1

R2 = 09984

TheoreticalSimulation

(c)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 17963x + 10567

y = 22109x + 90103

R2 = 1

R2 = 09982

1S (mMminus1)

TheoreticalSimulation

(d)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 42716x + 42716

y = 11353x + 10013

R2 = 1

R2 = 09999

TheoreticalSimulation

(e)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 30115x + 16731

y = 19058x + 13928

R2 = 1

R2 = 09991

1S (mMminus1)

TheoreticalSimulation

(f)

Figure 3The Lineweaver-Burk plots for experimentally calculated kinetic parameters (represented by a solid line) and simulation parameterssimulated by our model (represented by a dash dotted line) From top to bottom and from left to right the plots represent the activity of thefollowing enzymes glutathione reductase aspartate 1-decarboxylase alcohol dehydrogenase IMP dehydrogenase D-Ala-D-Ala dipeptidaseand pyruvate decarboxylase

observe the reconversion of the molecules of NADH (bluecircles) to molecules of NAD+ whenever the first hit thecell membrane (ie boundary of the environment) Likewiseit is possible to observe that obstacles are playing theirpart deflecting the movement of the other agents everyso often A detailed visual documentation of the two-stepenzymatic reaction simulation is available in supplementary

material (see Supplementary Material available online athttpdxdoiorg1011552014769471)

Numeric outputs detail these visual insights and presentdata about the movement of the different species thevelocity at which the reactions are taking place and thebehavioural system as a whole (Figure 5) The number ofagents representing the first substrate benzyl alcohol decays

BioMed Research International 9

NADHEnzyme one

Enzyme two

ObstaclesBenzaldehydeHaloenzyme 1

Haloenzyme 2

Benzyl alcoholBenzoateNAD+

Figure 4 Visual illustration of the evolving of the population of agents during the simulation steps

considerably in the first 2000 steps of simulation togetherwith the disappearance of agents representing NAD+ andthe creation of agents representing the aryl-alcohol dehy-drogenase haloenzyme This leads to the production of agrowing number of agents representing benzaldehyde and anincrease in the number of reactions occurring in the systemAs soon as benzaldehyde agents start to circulate in theenvironment and considering the continuous reconversionofNADHagents intoNAD+ agents the second reaction startsto occur This is reflected in a considerable decrease in thenumber of agents of benzaldehyde and a fairly proportionalincrease in the number of the agents representing benzoatethe product that will be ultimately excreted

43 System Performance This work describes the first phaseof development of the biomolecular simulator That is tosay that focus was set on identifying and implementing

themain biochemical and biophysical laws that would governthe model rather than implementing a realistic picture of themolecular landscape

As far as we know there has not been a previous attemptto simulate the effects of spatial localisation and temporalscales of individuals in the modelling of biomolecular sys-tems So before engaging into more complex scenarios itwas pivotal to take advantage of available experimental dataand ensure that the tool was able to account for basic cellulardynamics such as those governing enzymes adequately Nowthat we obtained a successful proof of concept we will workon system scalability in order to address more complexproblems

For this purpose we run preliminary performance tests tofind out the current scalability of our system Figure 6 sum-marises performance tests using an Intel I7 (2600) 34GHzprocessor with 6GB of RAM and runningWindows 8 64-bitThe tests accounted for three possible scenarios as follows

10 BioMed Research International

100

300

500

700

900

1100

0 5000 10000 15000

NumBenzyl alcohol

Num

ber o

f age

nts

Number of steps

(a)

89100

89300

89500

89700

89900

90100

0 5000 10000 15000

Num

ber o

f age

nts

Number of steps

89100911009310095100

0 16000

Detail

NumNAD+

(b)

Num

ber o

f age

nts

Number of steps

050

100150200250300350

0 5000 10000 15000

NumBenzal

(c)

9900

10100

10300

10500

10700

10900

0 5000 10000 15000

NumNADH

Num

ber o

f age

nts

Number of steps

(d)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 1

1732273237324732

0 10000

Detail

Num

ber o

f age

nts

Number of steps

(e)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 2

267836784678

0 15000

Detail

Num

ber o

f age

nts

Number of steps

(f)

80009000

100001100012000130001400015000

0 5000 10000 15000

NumReactions

40009000

14000

0 16000

Detail

Num

ber o

f age

nts

Number of steps

(g)

0

200

400

600

800

1000

0 5000 10000 15000

NumBenzoate

Num

ber o

f age

nts

Number of steps

(h)

Figure 5 The number of agents of different species interacting in the environment during 15000 simulation steps From top to bottom andfrom left to right the above plots represent the number of agents of benzyl alcohol NAD+ benzaldehyde NADH aryl-alcohol dehydrogenaseholoenzyme and benzaldehyde dehydrogenase holoenzyme At the bottom there is the number of occurring reactions and the number ofmolecules of benzoate excreted the extracellular medium

BioMed Research International 11

0

5000

10000

15000

20000

25000

30000

35000

0 50000 100000 150000 200000

Tim

e (m

s)

Number of agents

Only agentsAgents with movementAgents with movement and reactions

Figure 6 Performance of the tool in scenarios of increasingcomputational complexity

no action that is the agents are created but no diffusion orbehavioural rules are executed without reaction that is theagents are created and diffusion rules are activated but agentsdo not interact among themselves and with reaction thatis agents are created can move and can interact The threescenarios show a similar performance till the system reachesa population of 15119864 + 05 agents That is till this point thephysics governing agent movement and the introduction ofbehavioural rules do not affect simulation time significantlyCost resides on creating the system After that point thetime taken by the simulation of more elaborated scenariosthat is more agents in motion and more rules to manageis somewhat aggravated Over 25119864 + 05 agents the systembecomes computational unviable by a single machine

So in the near future we will investigate the use of dis-tributed and high-performance computing in the simulationofmore complex biomolecular systemsNamely we are inves-tigating the potential of the new distributed environmentof MASON the DMASON (httpwwwisislabitprojectsdmason) and the Biocellion framework [42]

5 Conclusions

ABM is increasingly popular in biology due to its naturalability to represent multiple scales of system decompositionintertwine complicated behaviours and deal with spatial-temporal constraints

The agent-based tool developed in this work aims tosupport biomolecular simulations and most notably provideinsights into catalytic efficiency in scenarios of industrialinterest Hence proof of concept was focused on the approx-imation of kinetic parameters The models correctly sim-ulated known enzymatic characteristics and yielded usefulpredictions that may guide future experimental design Italso provides a simulation variability that may reproduce theexperimental variation observed in lab experiments

Future development of the models presented here willinclude three-dimensional representation metabolic path-way simulation and accounting of extracellular substances

Moreover we plan to take into advantage the new DMA-SON platform to engage into distributed affordable sim-ulation and study more complex scenarios Other recenthigh-performance computing frameworks like Biocellionwill also be evaluated

After consolidation our tool will provide severalresources and services for the investigation of bacterial cellsin benefit of the research and industry communities

Conflict of Interests

The authors do not have any competing interests

Acknowledgments

The authors thank the Agrupamento INBIOMED fromDXPCTSUG-FEDER unha maneira de facer Europa(2012273) The research leading to these results has receivedfunding from the European Unionrsquos Seventh Frame-work Programme FP7REGPOT-2012-20131 under GrantAgreement no 316265 (BIOCAPS) and the [14VI05] Con-tract-Programme from theUniversity ofVigoThis documentreflects only the authorsrsquo views and the European Union isnot liable for any use that may be made of the informationcontained herein

References

[1] D Porro P Branduardi M Sauer and D Mattanovich ldquoOldobstacles and new horizons formicrobial chemical productionrdquoCurrent Opinion in Biotechnology C vol 30 pp 101ndash106 2014

[2] P Jeandet YVasserot T Chastang andECourot ldquoEngineeringmicrobial cells for the biosynthesis of natural compounds ofpharmaceutical significancerdquo BioMed Research Internationalvol 2013 Article ID 780145 13 pages 2013

[3] A Kondo J Ishii K Y Hara T Hasunuma and F Mat-suda ldquoDevelopment of microbial cell factories for bio-refinerythrough synthetic bioengineeringrdquo Journal of Biotechnologyvol 163 no 2 pp 204ndash216 2013

[4] J H Shin H U Kim D I Kim and S Y Lee ldquoProduction ofbulk chemicals via novel metabolic pathways in microorgan-ismsrdquo Biotechnology Advances vol 31 pp 925ndash935 2013

[5] C M Immethun A G Hoynes-OrsquoConnor A Balassy andT S Moon ldquoMicrobial production of isoprenoids enabled bysynthetic biologyrdquo Frontiers in Microbiology vol 4 article 752013

[6] Y Chen and J Nielsen ldquo Advances in metabolic pathway andstrain engineering paving the way for sustainable productionof chemical building blocksrdquo Current Opinion in Biotechnologyvol 24 pp 965ndash972 2013

[7] J W Lee D Na J M Park S Choi and S Y Lee ldquoSystemsmetabolic engineering of microorganisms for natural and non-natural chemicalsrdquo Nature Chemical Biology vol 8 pp 536ndash546 2012

[8] G Stephanopoulos ldquoSynthetic biology andmetabolic engineer-ingrdquo ACS Synthetic Biology vol 1 pp 514ndash525 2012

[9] T-M Lo W S Teo H Ling B Chen A Kang and MW Chang ldquoMicrobial engineering strategies to improve cellviability for biochemical productionrdquo Biotechnology Advancesvol 31 pp 903ndash914 2013

12 BioMed Research International

[10] K M Esvelt and H H Wang ldquoGenome-scale engineering forsystems and synthetic biologyrdquo Molecular Systems Biology vol9 p 641 2013

[11] M K Tiwari R R K Singh I Kim and J-K Lee ldquoCompu-tational approaches for rational design of proteins with novelfunctionalitiesrdquo Computational and Structural BiotechnologyJournal vol 2 Article ID e201209002 2012

[12] M Cvijovic J Almquist J Hagmar et al ldquoBridging the gaps insystems biologyrdquoMolecular Genetics and Genomics vol 289 no5 pp 727ndash734 2014

[13] N Tomar and R K De ldquoComparing methods for metabolicnetwork analysis and an application to metabolic engineeringrdquoGene vol 521 no 1 pp 1ndash14 2013

[14] A Chakrabarti L Miskovic K C Soh and V HatzimanikatisldquoTowards kinetic modeling of genome-scale metabolic net-works without sacrificing stoichiometric thermodynamic andphysiological constraintsrdquo Biotechnology Journal vol 8 no 9pp 1043ndash1057 2013

[15] A F Villaverde and J R Banga ldquoReverse engineering andidentification in systems biology strategies perspectives andchallengesrdquo Journal of the Royal Society Interface vol 11 no 91Article ID 20130505 2014

[16] S Luke C Cioffi-Revilla L Panait K Sullivan and G BalanldquoMASON a multiagent simulation environmentrdquo Simulationvol 81 no 7 pp 517ndash527 2005

[17] R Conte and M Paolucci ldquoOn agent-based modeling andcomputational social sciencerdquo Frontiers in Psychology vol 5article 668 2014

[18] M Wooldridge ldquoAgent-based software engineeringrdquo IEE Pro-ceedings Software vol 144 no 1 pp 26ndash37 1997

[19] E Bonabeau ldquoAgent-based modeling Methods and techniquesfor simulating human systemsrdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 99 no3 pp 7280ndash7287 2002

[20] N Cannata F Corradini E Merelli and L Tesei ldquoAgent-basedmodels of cellular systemsrdquo Methods in Molecular Biology vol930 pp 399ndash426 2013

[21] G An Q Mi J Dutta-Moscato and Y Vodovotz ldquoAgent-basedmodels in translational systems biologyrdquoWiley InterdisciplinaryReviews Systems Biology and Medicine vol 1 no 2 pp 159ndash1712009

[22] J O Dada and P Mendes ldquoMulti-scale modelling and simula-tion in systems biologyrdquo Integrative Biology vol 3 pp 86ndash962011

[23] H Kaul and Y Ventikos ldquoInvestigating biocomplexity throughthe agent-based paradigmrdquo Briefings in Bioinformatics vol 442013

[24] M Holcombe S Adra M Bicak et al ldquoModelling complexbiological systems using an agent-based approachrdquo IntegrativeBiology vol 4 no 1 pp 53ndash64 2012

[25] D CWalker J Southgate GHill et al ldquoThe epitheliome agent-based modelling of the social behaviour of cellsrdquo BioSystemsvol 76 no 1ndash3 pp 89ndash100 2004

[26] M B Biggs and J A Papin ldquoNovel multiscale modeling toolapplied to Pseudomonas aeruginosa biofilm formationrdquo PLoSONE vol 8 no 10 Article ID e78011 2013

[27] S M Stiegelmeyer andM C Giddings ldquoAgent-based modelingof competence phenotype switching in Bacillus subtilisrdquo Theo-retical Biology and Medical Modelling vol 10 article 23 2013

[28] G An and S Kulkarni ldquoAn agent-based modeling frameworklinking inflammation and cancer using evolutionary principles

Description of a generative hierarchy for the hallmarks of cancerand developing a bridge betweenmechanism and epidemiolog-ical datardquoMathematical Biosciences 2014

[29] J Wang L Zhang C Jing et al ldquoMulti-scale agent-basedmodeling on melanoma and its related angiogenesis analysisrdquoTheoretical Biology and Medical Modelling vol 10 article 412013

[30] V Gopalakrishnan M Kim and G An ldquoUsing an agent-basedmodel to examine the role of dynamic bacterial virulence poten-tial in the pathogenesis of surgical site infectionrdquo Advances inWound Care vol 2 no 9 pp 510ndash526 2013

[31] A E Curtin and L Zhou ldquoAn agent-based model of theresponse to angioplasty and bare-metal stent deployment in anatherosclerotic blood vesselrdquo PLoS ONE vol 9 no 4 Article IDe94411 2014

[32] K Bettenbrock H Bai M Ederer et al ldquoChapter Twomdashtowards a systems level understanding of the oxygen responseof Escherichia colirdquo in Advances in Microbial Physiology vol 6pp 65ndash114 2014

[33] A Apte R Senger and S S Fong ldquoDesigning novel cellulasesystems through agent-based modeling and global sensitivityanalysisrdquo Bioengineered vol 5 no 4 pp 243ndash253 2014

[34] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 30 no 21 pp3101ndash3108 2014

[35] S Kang S Kahan and B Momeni ldquoSimulating microbial com-munity patterning using Biocellionrdquo in Methods in MolecularBiology vol 1151 pp 233ndash253 2014

[36] I Millington Game Physics Engine Development How to Builda Robust Commercial-Grade Physics Engine for Your Game CRCPress Boca Raton Fla USA 2010

[37] G Palmer Physics for Game Programmers Apress 2005[38] T Kalwarczyk M Tabaka and R Holyst ldquoBiologisticsmdash

diffusion coefficients for complete proteome of Escherichiacolirdquo Bioinformatics vol 28 no 22 pp 2971ndash2978 2012

[39] K A Johnson and R S Goody ldquoThe original Michaelisconstant translation of the 1913 Michaelis-Menten paperrdquoBiochemistry vol 50 no 39 pp 8264ndash8269 2011

[40] A Cornish-Bowden ldquoThe origins of enzyme kineticsrdquo FEBSLetters vol 587 no 17 pp 2725ndash2730 2013

[41] M Scheer A Grote A Chang et al ldquoBRENDA the enzymeinformation system in 2011rdquo Nucleic Acids Research vol 39 no1 pp D670ndashD676 2011

[42] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 130 no 21 pp3101ndash3108 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

BioMed Research International 5

agent and a cofactor agent collide the enzyme checkswhetherit requires the cofactor to operate If so a new agent represent-ing the enzyme-cofactor complex (holoenzyme) is created inreplacement of the two agents

The interaction between the enzymes (or enzyme-cofactor complexes) and metabolites represents catalysis andwas modelled according to Michaelis-Menten equation (seekinetic parameters section) In general metabolites andenzymes are supposed to react within a certain probabilitywhenever they collide and the enzymatic reaction may beconcluded in the same time step or after a number of timesteps

After the enzymatic reaction takes place that is theenzyme-cofactor complex collides with a substrate the com-plex is destroyed and the agents representing the enzymeand the cofactor are created again Likewise the agentsrepresenting the substrate disappear and new agents arecreated for the products of the reaction

33 Kinetic Parameters The critical part of developing ourmodel was related with incorporating kinetic informationon the cellular dynamics especially on different enzymaticreaction kinetics

Generally the kinetic scheme representing an enzymaticreaction under steady-state conditions is written as

E + S1198701

999448999471119870minus1

ES1198702

999448999471119870minus2

E + P (1)

where E represents the enzyme S is the substrate ES isthe enzyme-substrate complex and P is the product Theassociation rates 1198961 and 1198962 and the dissociation rates 119896 minus 1and 119896minus2 account for the substrate binding andproduct releaseforward and reverse processes respectively

Since the rate constants for the binding and unbindingreactions are either often unknown or difficult to determinemodelling has to rely on approximations also called aggre-gate rate laws such as theMichaelis-Menten kinetics [39 40]

119881 =119881max [S]119870119898+ [S]

(2)

or following the Lineweaver and Burk linear transformation

1

119881=119870119898

119881maxtimes1

[S]+1

119881max(3)

which represents the reaction rate at a substrate concentra-tion [S]119881max is themaximum rate that can be observed in thereaction considering the substrate is in excessTheMichaelisconstant119870

119898is a measure of the concentration of substrate at

which the rate of the reaction is one half its maximum 119881maxThat is 119870

119898is a relative measure of the affinity of the enzyme

for the substrate (how well it binds) Small 119870119898means tight

binding and large 119870119898means weak binding

The turnover number

119896cat =119881max[E]

(4)

where [E] equals total enzyme concentration represents thenumber of moles of product produced per number of molesof enzyme per unit time and is expressed in units of inversetime (119904minus1) That is the rate of the reaction when the enzymeis saturated with substrate

Having inmind the biologicalmeaning of the parameterswe hypothesised that the percentage of reactive collisionsbetween enzyme and metabolite and the number of simu-lation time steps could together be used to mimic the ratesexpressed by 119896

119898and 119896cat To corroborate this hypothesis

we conducted a series of experiments trying out differentpercentages of collision with reaction and number of timesteps and calculating the theoretical values of 119896

119898and 119896cat

The combination of simulation parameters was further vali-dated against experimental values retrieved from the enzymedatabase BRENDA [41]

4 Results and Discussion

To actually demonstrate that our design plan is functionallyplausible we recreated different scenarios of enzymatic activ-ity to show that the constructed model exhibits behavioursthat match those observed in the laboratory experiments

We present results obtained for the simulation of asimple scenario where an enzyme catalyses one substrate andreleases one productThese results are discussed theoreticallyin terms of enzyme affinity to substrate and catalytic effi-ciency and further tested against experimentally calculatedkinetic parameters

Then we show that the tool is able to model biochemicalpathways accounting for biochemical and biophysical lawsadequatelyWe describe the computational costs of represent-ingmore complex biomolecular scenariosWe discuss a num-ber of present commitments and simplifications necessary toensure computational tractability and point out ongoing linesof work

41 Approximation of Kinetic Parameters This process ofanalysis is somewhat similar to that performed in laboratoryexperimentsThat is we studied the behaviour of an identicalamount of enzyme in the presence of increasing concen-trations of substrate and measured the velocity of reactionby determining the rate of product formation Furthermorewe tested different (combinations of) simulation parametersnamely the percentage of collisions producing reaction andthe number of time steps taken by a reaction Based on theinterpretation of the Lineweaver-Burke plot which describesthe Michaelis-Menten laws for kinetic dynamics we calcu-lated the theoretical values of 119896

119898and 119896cat

Substrate concentrations ranged from 664119864 minus 02mMto 664119864 minus 01mM (200 molecules to 2000 moleculesapproximately) and there is a concentration of enzyme of498119864 minus 02mM (150 enzymes approximately) Simulationparameterisation mimicked ldquoextremerdquo scenarios (ie 100immediate reactive collisions very slow reactions and barelyany reactions occurring) as well as more common scenarios(ie midrange percentages of reactive collision and reactionduration) Moreover the experiment was replicated 3 times

6 BioMed Research International

(3 simulation runs for every concentration of substrate) andresults were averaged

The model assumes that a simulation tick correspondsto a configurable specific amount of time in the systemNotably our approach to real time-time step conversionfocused on framing realistic values of velocity of reactionand hence of 119896cat Regardless of the range of values of 119896cat tobe simulated we should be able to represent such enzymedynamics accurately by adjusting the equivalence in timesteps

Figure 2 shows the Lineweaver-Burke plots resultingfrom experiments considering the duration of the reactionconstant and equal to 1 time step representing 10 secondsSince the number of time steps that a reaction takes to beconcluded is considered somewhat equivalent to the velocityof the reaction the Lineweaver-Burke plots should convergeto a similar 119910-intersect Likewise different percentages ofreactive collision should describe different affinities of theenzyme for the substrate and this effect should be reflectedin the slope of the plots Most results were as expected therewas a convergence of the 119910-intersects and the higher thepercentage of reactive collision (ie lower values of 119896

119898) the

lower the value of the slopeFrom the Lineweaver-Burke plots and in particular

considering the linear regression model that approximatesthe equation

1

119881=119870119898

119881maxtimes1

[S]+1

119881max(5)

wewere able to estimate the values of 119896119898and 119896cat described by

the simulation parameters (Table 2) Again it was expectedthat higher percentages of reactive collision would relate tolower values of 119896

119898and vice versa whilst the value of 119896cat

should be less affected The presence of negative values for119896cat and 119896119898 for very low percentages of reactive collisionswas unexpected though This occurs because 119896cat for thosesituations is supposed to be very close to zero As this modelis stochastic small variations may lead the values of 119896cat tobecome negative hence affecting the values of 119896

119898as well

To further validate the approximation of the kineticparameters made by our model we tested them againstexperimentally validated data Six enzyme records fallingwithin the range of kinetic values calculated were randomlyselected from BRENDA database [41]

We selected the simulation scenarios producing themost similar approximation to the experimentally validatedkinetic parameters (Table 3) and compared the correspond-ing Lineweaver-Burke plots (Figure 3) As expected themoresimilar the approximations were to the real values the betterthe simulations performed In particular the number oftime steps stipulated for the duration of the reaction onlyaffects the value of 119896cat and thus can be used to validate thesimulation

42 A Two-Step Enzymatic Reaction After validating ourmodel for situations where only one enzymatic reactionoccurs we then studied the behaviour of our simulator whentwo enzymes are present in a two-stage process

Table 2 Approximation of kinetic parameters by different percent-ages of reactive collision and time steps

reactivecollision Time step 119896

119898(mM) 119896cat (s

minus1)

1 0 minus0850576595 minus00285144535 0 minus2996153951 minus687119864 minus 015 25 minus4656418568 minus977119864 minus 015 50 3439111157 808119864 minus 015 75 2918555171 625119864 minus 015 100 minus2179373575 minus392119864 + 0010 0 minus146001318 minus663194461615 0 1151508927 762333046425 0 087739 108119864 + 0025 5 136829 144119864 + 0025 25 245375 223119864 + 0025 50 120869 106119864 + 0025 75 070036 622119864 minus 0125 100 0531257304 452119864 minus 0134 1 318977 393119864 + 0050 0 071725 127119864 + 0075 0 365866 649119864 + 0075 5 306473 533119864 + 0075 25 113387 201119864 + 0075 50 060205 107119864 + 0075 75 037565 669119864 minus 0175 100 029693544 506119864 minus 0190 0 443222 817119864 + 0095 0 449601 844119864 + 0095 25 1277963717 239662133395 50 056747 111119864 + 0095 75 034196 688119864 minus 0195 100 0237537579 488119864 minus 01100 0 075547 160119864 + 00

Specifically we studied the catalytic activity of twoenzymes commonly present in aromatic aldehyde produc-tion the aryl-alcohol dehydrogenase (EC number 11190)and the benzaldehyde dehydrogenase (EC number 12128)

In particular the model encompasses the following twoequations

benzyl alcohol +NAD+ 997888rarr benzaldehyde +NADH +H+

benzaldehyde+NAD+ +H2O 997888rarr benzoate+NADH + 2H+

(6)

The model represented an area of approximately 1120583m2containing a concentration of 166mM (5119864+03molecules) ofeach type of enzyme 105 obstacles and initial concentrationsof 332119864 + 01mM and 332mM (1119864 + 05 molecules and1119864 + 04 molecules) for NAD+ and NADH respectivelyDuring simulation a concentration of 498119864 minus 01mM(1500 molecules) of benzyl alcohol that is the substrate of

BioMed Research International 7

050

100150200250300350400450500

1 3 5 7 9 11 13 15

1V

(itm

M)

1[S] (mM)

1007550253415

Linear (100)Linear (75)Linear (50)Linear (25)Linear (34)Linear (15)

y = 10596x + 24081

y = 11218x + 33688

y = 13112x + 43521

y = 19657x + 66475

y = 1629x + 5107

R2 = 09999

R2 = 1

R2 = 09999

R2 = 09999

R2 = 09993

R2 = 09993

y = 30326x + 26336

Figure 2 The Lineweaver-Burk plots obtained while simulating different percentages of reactive collision and a time step of 1 The markersrepresent the outputs of simulation and the lines represent the corresponding trend lines based on linear regression (equation also shown)

Table 3 An approximation between experimentally calculated kinetic parameters and the parameters simulated by our model

Enzyme identification Experimental kinetics Simulation parameters Approximated kinetics119896119898

119896cat reactive collision Time step 119896119898(mM) 119896cat (s

minus1)EC 1819mdashglutathione reductase activity 0404 039 25 100 0531257304 452119864 minus 01

EC 41111mdashaspartate 1-decarboxylase 0219 065 75 75 037565 669119864 minus 01

EC 1111mdashalcohol dehydrogenase 041 1 95 75 034196 688119864 minus 01

EC 111205mdashIMP dehydrogenase 17 19 25 25 245375 223119864 + 00

EC 341322mdashD-Ala-D-Ala dipeptidase 1 47 75 25 113387 201119864 + 00

EC 4111mdashpyruvate decarboxylase 18 12 25 5 136829 144119864 + 00

Table 4 The weight size and diffusion rate of the moleculesrepresented in the two-step enzymatic system

Species Molecularweight (gmol)

Particle radius(120583m)

Diffusion rate(120583m2s)

Benzyl alcohol 10814 0323 times 10minus3 4018 times 10minus14

NAD+ 66141 0657 times 10minus3 1975 times 10minus14

NADH 66343 0658 times 10minus3 1973 times 10minus14

Benzaldehyde 106121 0321 times 10minus3 4047 times 10minus14

Benzoate 12112 0338 times 10minus3 3843 times 10minus14

the first reaction was introduced gradually in the environ-ment specifically 10 at every 10 time steps

Agent size and velocity of movement were adjustedaccording to the molecular weight of the biological species(Table 4) Heaviermolecules have a larger radius and a slowerdiffusion rate Proportionally the agents representing benzylalcohol and benzaldehyde molecules should be two times

smaller and faster than the agents representing the moleculesof NAD+ and NADH

To facilitate visual inspection distinct agent types areassociated with different colours and proportional sizes Assuch it is possible to visually observe the evolving of thesimulation and at some extent observe how the agents aremoving and interacting with each other Specifically it ispossible to see how different agents traverse the environmentand how behavioural rules are triggered or take precedenceover each other

As illustrated in Figure 4 although the movement ofthe molecules of benzyl alcohol (green circles) is quite fastthese molecules are unable to interact with the correspond-ing enzyme (aryl-alcohol dehydrogenase named enzymeone and coloured yellow in the figure) unless the enzymehas already bound to a NAD+ molecule (ie creating theholoenzyme 1 coloured in black) Likewise interactions withthe second enzyme benzaldehyde dehydrogenase (magentacircles) are limited to the molecules of NAD+ (red circles)until the first reaction actually occurs and begins producingbenzaldehyde (blue circles) Furthermore it is possible to

8 BioMed Research International

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 20797x + 51479

R2 = 1

R2 = 09994

y = 23614x + 44449

1S (mMminus1)

TheoreticalSimulation

(a)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M) R2 = 1

R2 = 09991

y = 67643x + 30887

y = 11265x + 29988

1S (mMminus1)

TheoreticalSimulation

(b)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 82314x + 20077

y = 9982x + 29191

R2 = 1

R2 = 09984

TheoreticalSimulation

(c)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 17963x + 10567

y = 22109x + 90103

R2 = 1

R2 = 09982

1S (mMminus1)

TheoreticalSimulation

(d)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 42716x + 42716

y = 11353x + 10013

R2 = 1

R2 = 09999

TheoreticalSimulation

(e)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 30115x + 16731

y = 19058x + 13928

R2 = 1

R2 = 09991

1S (mMminus1)

TheoreticalSimulation

(f)

Figure 3The Lineweaver-Burk plots for experimentally calculated kinetic parameters (represented by a solid line) and simulation parameterssimulated by our model (represented by a dash dotted line) From top to bottom and from left to right the plots represent the activity of thefollowing enzymes glutathione reductase aspartate 1-decarboxylase alcohol dehydrogenase IMP dehydrogenase D-Ala-D-Ala dipeptidaseand pyruvate decarboxylase

observe the reconversion of the molecules of NADH (bluecircles) to molecules of NAD+ whenever the first hit thecell membrane (ie boundary of the environment) Likewiseit is possible to observe that obstacles are playing theirpart deflecting the movement of the other agents everyso often A detailed visual documentation of the two-stepenzymatic reaction simulation is available in supplementary

material (see Supplementary Material available online athttpdxdoiorg1011552014769471)

Numeric outputs detail these visual insights and presentdata about the movement of the different species thevelocity at which the reactions are taking place and thebehavioural system as a whole (Figure 5) The number ofagents representing the first substrate benzyl alcohol decays

BioMed Research International 9

NADHEnzyme one

Enzyme two

ObstaclesBenzaldehydeHaloenzyme 1

Haloenzyme 2

Benzyl alcoholBenzoateNAD+

Figure 4 Visual illustration of the evolving of the population of agents during the simulation steps

considerably in the first 2000 steps of simulation togetherwith the disappearance of agents representing NAD+ andthe creation of agents representing the aryl-alcohol dehy-drogenase haloenzyme This leads to the production of agrowing number of agents representing benzaldehyde and anincrease in the number of reactions occurring in the systemAs soon as benzaldehyde agents start to circulate in theenvironment and considering the continuous reconversionofNADHagents intoNAD+ agents the second reaction startsto occur This is reflected in a considerable decrease in thenumber of agents of benzaldehyde and a fairly proportionalincrease in the number of the agents representing benzoatethe product that will be ultimately excreted

43 System Performance This work describes the first phaseof development of the biomolecular simulator That is tosay that focus was set on identifying and implementing

themain biochemical and biophysical laws that would governthe model rather than implementing a realistic picture of themolecular landscape

As far as we know there has not been a previous attemptto simulate the effects of spatial localisation and temporalscales of individuals in the modelling of biomolecular sys-tems So before engaging into more complex scenarios itwas pivotal to take advantage of available experimental dataand ensure that the tool was able to account for basic cellulardynamics such as those governing enzymes adequately Nowthat we obtained a successful proof of concept we will workon system scalability in order to address more complexproblems

For this purpose we run preliminary performance tests tofind out the current scalability of our system Figure 6 sum-marises performance tests using an Intel I7 (2600) 34GHzprocessor with 6GB of RAM and runningWindows 8 64-bitThe tests accounted for three possible scenarios as follows

10 BioMed Research International

100

300

500

700

900

1100

0 5000 10000 15000

NumBenzyl alcohol

Num

ber o

f age

nts

Number of steps

(a)

89100

89300

89500

89700

89900

90100

0 5000 10000 15000

Num

ber o

f age

nts

Number of steps

89100911009310095100

0 16000

Detail

NumNAD+

(b)

Num

ber o

f age

nts

Number of steps

050

100150200250300350

0 5000 10000 15000

NumBenzal

(c)

9900

10100

10300

10500

10700

10900

0 5000 10000 15000

NumNADH

Num

ber o

f age

nts

Number of steps

(d)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 1

1732273237324732

0 10000

Detail

Num

ber o

f age

nts

Number of steps

(e)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 2

267836784678

0 15000

Detail

Num

ber o

f age

nts

Number of steps

(f)

80009000

100001100012000130001400015000

0 5000 10000 15000

NumReactions

40009000

14000

0 16000

Detail

Num

ber o

f age

nts

Number of steps

(g)

0

200

400

600

800

1000

0 5000 10000 15000

NumBenzoate

Num

ber o

f age

nts

Number of steps

(h)

Figure 5 The number of agents of different species interacting in the environment during 15000 simulation steps From top to bottom andfrom left to right the above plots represent the number of agents of benzyl alcohol NAD+ benzaldehyde NADH aryl-alcohol dehydrogenaseholoenzyme and benzaldehyde dehydrogenase holoenzyme At the bottom there is the number of occurring reactions and the number ofmolecules of benzoate excreted the extracellular medium

BioMed Research International 11

0

5000

10000

15000

20000

25000

30000

35000

0 50000 100000 150000 200000

Tim

e (m

s)

Number of agents

Only agentsAgents with movementAgents with movement and reactions

Figure 6 Performance of the tool in scenarios of increasingcomputational complexity

no action that is the agents are created but no diffusion orbehavioural rules are executed without reaction that is theagents are created and diffusion rules are activated but agentsdo not interact among themselves and with reaction thatis agents are created can move and can interact The threescenarios show a similar performance till the system reachesa population of 15119864 + 05 agents That is till this point thephysics governing agent movement and the introduction ofbehavioural rules do not affect simulation time significantlyCost resides on creating the system After that point thetime taken by the simulation of more elaborated scenariosthat is more agents in motion and more rules to manageis somewhat aggravated Over 25119864 + 05 agents the systembecomes computational unviable by a single machine

So in the near future we will investigate the use of dis-tributed and high-performance computing in the simulationofmore complex biomolecular systemsNamely we are inves-tigating the potential of the new distributed environmentof MASON the DMASON (httpwwwisislabitprojectsdmason) and the Biocellion framework [42]

5 Conclusions

ABM is increasingly popular in biology due to its naturalability to represent multiple scales of system decompositionintertwine complicated behaviours and deal with spatial-temporal constraints

The agent-based tool developed in this work aims tosupport biomolecular simulations and most notably provideinsights into catalytic efficiency in scenarios of industrialinterest Hence proof of concept was focused on the approx-imation of kinetic parameters The models correctly sim-ulated known enzymatic characteristics and yielded usefulpredictions that may guide future experimental design Italso provides a simulation variability that may reproduce theexperimental variation observed in lab experiments

Future development of the models presented here willinclude three-dimensional representation metabolic path-way simulation and accounting of extracellular substances

Moreover we plan to take into advantage the new DMA-SON platform to engage into distributed affordable sim-ulation and study more complex scenarios Other recenthigh-performance computing frameworks like Biocellionwill also be evaluated

After consolidation our tool will provide severalresources and services for the investigation of bacterial cellsin benefit of the research and industry communities

Conflict of Interests

The authors do not have any competing interests

Acknowledgments

The authors thank the Agrupamento INBIOMED fromDXPCTSUG-FEDER unha maneira de facer Europa(2012273) The research leading to these results has receivedfunding from the European Unionrsquos Seventh Frame-work Programme FP7REGPOT-2012-20131 under GrantAgreement no 316265 (BIOCAPS) and the [14VI05] Con-tract-Programme from theUniversity ofVigoThis documentreflects only the authorsrsquo views and the European Union isnot liable for any use that may be made of the informationcontained herein

References

[1] D Porro P Branduardi M Sauer and D Mattanovich ldquoOldobstacles and new horizons formicrobial chemical productionrdquoCurrent Opinion in Biotechnology C vol 30 pp 101ndash106 2014

[2] P Jeandet YVasserot T Chastang andECourot ldquoEngineeringmicrobial cells for the biosynthesis of natural compounds ofpharmaceutical significancerdquo BioMed Research Internationalvol 2013 Article ID 780145 13 pages 2013

[3] A Kondo J Ishii K Y Hara T Hasunuma and F Mat-suda ldquoDevelopment of microbial cell factories for bio-refinerythrough synthetic bioengineeringrdquo Journal of Biotechnologyvol 163 no 2 pp 204ndash216 2013

[4] J H Shin H U Kim D I Kim and S Y Lee ldquoProduction ofbulk chemicals via novel metabolic pathways in microorgan-ismsrdquo Biotechnology Advances vol 31 pp 925ndash935 2013

[5] C M Immethun A G Hoynes-OrsquoConnor A Balassy andT S Moon ldquoMicrobial production of isoprenoids enabled bysynthetic biologyrdquo Frontiers in Microbiology vol 4 article 752013

[6] Y Chen and J Nielsen ldquo Advances in metabolic pathway andstrain engineering paving the way for sustainable productionof chemical building blocksrdquo Current Opinion in Biotechnologyvol 24 pp 965ndash972 2013

[7] J W Lee D Na J M Park S Choi and S Y Lee ldquoSystemsmetabolic engineering of microorganisms for natural and non-natural chemicalsrdquo Nature Chemical Biology vol 8 pp 536ndash546 2012

[8] G Stephanopoulos ldquoSynthetic biology andmetabolic engineer-ingrdquo ACS Synthetic Biology vol 1 pp 514ndash525 2012

[9] T-M Lo W S Teo H Ling B Chen A Kang and MW Chang ldquoMicrobial engineering strategies to improve cellviability for biochemical productionrdquo Biotechnology Advancesvol 31 pp 903ndash914 2013

12 BioMed Research International

[10] K M Esvelt and H H Wang ldquoGenome-scale engineering forsystems and synthetic biologyrdquo Molecular Systems Biology vol9 p 641 2013

[11] M K Tiwari R R K Singh I Kim and J-K Lee ldquoCompu-tational approaches for rational design of proteins with novelfunctionalitiesrdquo Computational and Structural BiotechnologyJournal vol 2 Article ID e201209002 2012

[12] M Cvijovic J Almquist J Hagmar et al ldquoBridging the gaps insystems biologyrdquoMolecular Genetics and Genomics vol 289 no5 pp 727ndash734 2014

[13] N Tomar and R K De ldquoComparing methods for metabolicnetwork analysis and an application to metabolic engineeringrdquoGene vol 521 no 1 pp 1ndash14 2013

[14] A Chakrabarti L Miskovic K C Soh and V HatzimanikatisldquoTowards kinetic modeling of genome-scale metabolic net-works without sacrificing stoichiometric thermodynamic andphysiological constraintsrdquo Biotechnology Journal vol 8 no 9pp 1043ndash1057 2013

[15] A F Villaverde and J R Banga ldquoReverse engineering andidentification in systems biology strategies perspectives andchallengesrdquo Journal of the Royal Society Interface vol 11 no 91Article ID 20130505 2014

[16] S Luke C Cioffi-Revilla L Panait K Sullivan and G BalanldquoMASON a multiagent simulation environmentrdquo Simulationvol 81 no 7 pp 517ndash527 2005

[17] R Conte and M Paolucci ldquoOn agent-based modeling andcomputational social sciencerdquo Frontiers in Psychology vol 5article 668 2014

[18] M Wooldridge ldquoAgent-based software engineeringrdquo IEE Pro-ceedings Software vol 144 no 1 pp 26ndash37 1997

[19] E Bonabeau ldquoAgent-based modeling Methods and techniquesfor simulating human systemsrdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 99 no3 pp 7280ndash7287 2002

[20] N Cannata F Corradini E Merelli and L Tesei ldquoAgent-basedmodels of cellular systemsrdquo Methods in Molecular Biology vol930 pp 399ndash426 2013

[21] G An Q Mi J Dutta-Moscato and Y Vodovotz ldquoAgent-basedmodels in translational systems biologyrdquoWiley InterdisciplinaryReviews Systems Biology and Medicine vol 1 no 2 pp 159ndash1712009

[22] J O Dada and P Mendes ldquoMulti-scale modelling and simula-tion in systems biologyrdquo Integrative Biology vol 3 pp 86ndash962011

[23] H Kaul and Y Ventikos ldquoInvestigating biocomplexity throughthe agent-based paradigmrdquo Briefings in Bioinformatics vol 442013

[24] M Holcombe S Adra M Bicak et al ldquoModelling complexbiological systems using an agent-based approachrdquo IntegrativeBiology vol 4 no 1 pp 53ndash64 2012

[25] D CWalker J Southgate GHill et al ldquoThe epitheliome agent-based modelling of the social behaviour of cellsrdquo BioSystemsvol 76 no 1ndash3 pp 89ndash100 2004

[26] M B Biggs and J A Papin ldquoNovel multiscale modeling toolapplied to Pseudomonas aeruginosa biofilm formationrdquo PLoSONE vol 8 no 10 Article ID e78011 2013

[27] S M Stiegelmeyer andM C Giddings ldquoAgent-based modelingof competence phenotype switching in Bacillus subtilisrdquo Theo-retical Biology and Medical Modelling vol 10 article 23 2013

[28] G An and S Kulkarni ldquoAn agent-based modeling frameworklinking inflammation and cancer using evolutionary principles

Description of a generative hierarchy for the hallmarks of cancerand developing a bridge betweenmechanism and epidemiolog-ical datardquoMathematical Biosciences 2014

[29] J Wang L Zhang C Jing et al ldquoMulti-scale agent-basedmodeling on melanoma and its related angiogenesis analysisrdquoTheoretical Biology and Medical Modelling vol 10 article 412013

[30] V Gopalakrishnan M Kim and G An ldquoUsing an agent-basedmodel to examine the role of dynamic bacterial virulence poten-tial in the pathogenesis of surgical site infectionrdquo Advances inWound Care vol 2 no 9 pp 510ndash526 2013

[31] A E Curtin and L Zhou ldquoAn agent-based model of theresponse to angioplasty and bare-metal stent deployment in anatherosclerotic blood vesselrdquo PLoS ONE vol 9 no 4 Article IDe94411 2014

[32] K Bettenbrock H Bai M Ederer et al ldquoChapter Twomdashtowards a systems level understanding of the oxygen responseof Escherichia colirdquo in Advances in Microbial Physiology vol 6pp 65ndash114 2014

[33] A Apte R Senger and S S Fong ldquoDesigning novel cellulasesystems through agent-based modeling and global sensitivityanalysisrdquo Bioengineered vol 5 no 4 pp 243ndash253 2014

[34] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 30 no 21 pp3101ndash3108 2014

[35] S Kang S Kahan and B Momeni ldquoSimulating microbial com-munity patterning using Biocellionrdquo in Methods in MolecularBiology vol 1151 pp 233ndash253 2014

[36] I Millington Game Physics Engine Development How to Builda Robust Commercial-Grade Physics Engine for Your Game CRCPress Boca Raton Fla USA 2010

[37] G Palmer Physics for Game Programmers Apress 2005[38] T Kalwarczyk M Tabaka and R Holyst ldquoBiologisticsmdash

diffusion coefficients for complete proteome of Escherichiacolirdquo Bioinformatics vol 28 no 22 pp 2971ndash2978 2012

[39] K A Johnson and R S Goody ldquoThe original Michaelisconstant translation of the 1913 Michaelis-Menten paperrdquoBiochemistry vol 50 no 39 pp 8264ndash8269 2011

[40] A Cornish-Bowden ldquoThe origins of enzyme kineticsrdquo FEBSLetters vol 587 no 17 pp 2725ndash2730 2013

[41] M Scheer A Grote A Chang et al ldquoBRENDA the enzymeinformation system in 2011rdquo Nucleic Acids Research vol 39 no1 pp D670ndashD676 2011

[42] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 130 no 21 pp3101ndash3108 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

6 BioMed Research International

(3 simulation runs for every concentration of substrate) andresults were averaged

The model assumes that a simulation tick correspondsto a configurable specific amount of time in the systemNotably our approach to real time-time step conversionfocused on framing realistic values of velocity of reactionand hence of 119896cat Regardless of the range of values of 119896cat tobe simulated we should be able to represent such enzymedynamics accurately by adjusting the equivalence in timesteps

Figure 2 shows the Lineweaver-Burke plots resultingfrom experiments considering the duration of the reactionconstant and equal to 1 time step representing 10 secondsSince the number of time steps that a reaction takes to beconcluded is considered somewhat equivalent to the velocityof the reaction the Lineweaver-Burke plots should convergeto a similar 119910-intersect Likewise different percentages ofreactive collision should describe different affinities of theenzyme for the substrate and this effect should be reflectedin the slope of the plots Most results were as expected therewas a convergence of the 119910-intersects and the higher thepercentage of reactive collision (ie lower values of 119896

119898) the

lower the value of the slopeFrom the Lineweaver-Burke plots and in particular

considering the linear regression model that approximatesthe equation

1

119881=119870119898

119881maxtimes1

[S]+1

119881max(5)

wewere able to estimate the values of 119896119898and 119896cat described by

the simulation parameters (Table 2) Again it was expectedthat higher percentages of reactive collision would relate tolower values of 119896

119898and vice versa whilst the value of 119896cat

should be less affected The presence of negative values for119896cat and 119896119898 for very low percentages of reactive collisionswas unexpected though This occurs because 119896cat for thosesituations is supposed to be very close to zero As this modelis stochastic small variations may lead the values of 119896cat tobecome negative hence affecting the values of 119896

119898as well

To further validate the approximation of the kineticparameters made by our model we tested them againstexperimentally validated data Six enzyme records fallingwithin the range of kinetic values calculated were randomlyselected from BRENDA database [41]

We selected the simulation scenarios producing themost similar approximation to the experimentally validatedkinetic parameters (Table 3) and compared the correspond-ing Lineweaver-Burke plots (Figure 3) As expected themoresimilar the approximations were to the real values the betterthe simulations performed In particular the number oftime steps stipulated for the duration of the reaction onlyaffects the value of 119896cat and thus can be used to validate thesimulation

42 A Two-Step Enzymatic Reaction After validating ourmodel for situations where only one enzymatic reactionoccurs we then studied the behaviour of our simulator whentwo enzymes are present in a two-stage process

Table 2 Approximation of kinetic parameters by different percent-ages of reactive collision and time steps

reactivecollision Time step 119896

119898(mM) 119896cat (s

minus1)

1 0 minus0850576595 minus00285144535 0 minus2996153951 minus687119864 minus 015 25 minus4656418568 minus977119864 minus 015 50 3439111157 808119864 minus 015 75 2918555171 625119864 minus 015 100 minus2179373575 minus392119864 + 0010 0 minus146001318 minus663194461615 0 1151508927 762333046425 0 087739 108119864 + 0025 5 136829 144119864 + 0025 25 245375 223119864 + 0025 50 120869 106119864 + 0025 75 070036 622119864 minus 0125 100 0531257304 452119864 minus 0134 1 318977 393119864 + 0050 0 071725 127119864 + 0075 0 365866 649119864 + 0075 5 306473 533119864 + 0075 25 113387 201119864 + 0075 50 060205 107119864 + 0075 75 037565 669119864 minus 0175 100 029693544 506119864 minus 0190 0 443222 817119864 + 0095 0 449601 844119864 + 0095 25 1277963717 239662133395 50 056747 111119864 + 0095 75 034196 688119864 minus 0195 100 0237537579 488119864 minus 01100 0 075547 160119864 + 00

Specifically we studied the catalytic activity of twoenzymes commonly present in aromatic aldehyde produc-tion the aryl-alcohol dehydrogenase (EC number 11190)and the benzaldehyde dehydrogenase (EC number 12128)

In particular the model encompasses the following twoequations

benzyl alcohol +NAD+ 997888rarr benzaldehyde +NADH +H+

benzaldehyde+NAD+ +H2O 997888rarr benzoate+NADH + 2H+

(6)

The model represented an area of approximately 1120583m2containing a concentration of 166mM (5119864+03molecules) ofeach type of enzyme 105 obstacles and initial concentrationsof 332119864 + 01mM and 332mM (1119864 + 05 molecules and1119864 + 04 molecules) for NAD+ and NADH respectivelyDuring simulation a concentration of 498119864 minus 01mM(1500 molecules) of benzyl alcohol that is the substrate of

BioMed Research International 7

050

100150200250300350400450500

1 3 5 7 9 11 13 15

1V

(itm

M)

1[S] (mM)

1007550253415

Linear (100)Linear (75)Linear (50)Linear (25)Linear (34)Linear (15)

y = 10596x + 24081

y = 11218x + 33688

y = 13112x + 43521

y = 19657x + 66475

y = 1629x + 5107

R2 = 09999

R2 = 1

R2 = 09999

R2 = 09999

R2 = 09993

R2 = 09993

y = 30326x + 26336

Figure 2 The Lineweaver-Burk plots obtained while simulating different percentages of reactive collision and a time step of 1 The markersrepresent the outputs of simulation and the lines represent the corresponding trend lines based on linear regression (equation also shown)

Table 3 An approximation between experimentally calculated kinetic parameters and the parameters simulated by our model

Enzyme identification Experimental kinetics Simulation parameters Approximated kinetics119896119898

119896cat reactive collision Time step 119896119898(mM) 119896cat (s

minus1)EC 1819mdashglutathione reductase activity 0404 039 25 100 0531257304 452119864 minus 01

EC 41111mdashaspartate 1-decarboxylase 0219 065 75 75 037565 669119864 minus 01

EC 1111mdashalcohol dehydrogenase 041 1 95 75 034196 688119864 minus 01

EC 111205mdashIMP dehydrogenase 17 19 25 25 245375 223119864 + 00

EC 341322mdashD-Ala-D-Ala dipeptidase 1 47 75 25 113387 201119864 + 00

EC 4111mdashpyruvate decarboxylase 18 12 25 5 136829 144119864 + 00

Table 4 The weight size and diffusion rate of the moleculesrepresented in the two-step enzymatic system

Species Molecularweight (gmol)

Particle radius(120583m)

Diffusion rate(120583m2s)

Benzyl alcohol 10814 0323 times 10minus3 4018 times 10minus14

NAD+ 66141 0657 times 10minus3 1975 times 10minus14

NADH 66343 0658 times 10minus3 1973 times 10minus14

Benzaldehyde 106121 0321 times 10minus3 4047 times 10minus14

Benzoate 12112 0338 times 10minus3 3843 times 10minus14

the first reaction was introduced gradually in the environ-ment specifically 10 at every 10 time steps

Agent size and velocity of movement were adjustedaccording to the molecular weight of the biological species(Table 4) Heaviermolecules have a larger radius and a slowerdiffusion rate Proportionally the agents representing benzylalcohol and benzaldehyde molecules should be two times

smaller and faster than the agents representing the moleculesof NAD+ and NADH

To facilitate visual inspection distinct agent types areassociated with different colours and proportional sizes Assuch it is possible to visually observe the evolving of thesimulation and at some extent observe how the agents aremoving and interacting with each other Specifically it ispossible to see how different agents traverse the environmentand how behavioural rules are triggered or take precedenceover each other

As illustrated in Figure 4 although the movement ofthe molecules of benzyl alcohol (green circles) is quite fastthese molecules are unable to interact with the correspond-ing enzyme (aryl-alcohol dehydrogenase named enzymeone and coloured yellow in the figure) unless the enzymehas already bound to a NAD+ molecule (ie creating theholoenzyme 1 coloured in black) Likewise interactions withthe second enzyme benzaldehyde dehydrogenase (magentacircles) are limited to the molecules of NAD+ (red circles)until the first reaction actually occurs and begins producingbenzaldehyde (blue circles) Furthermore it is possible to

8 BioMed Research International

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 20797x + 51479

R2 = 1

R2 = 09994

y = 23614x + 44449

1S (mMminus1)

TheoreticalSimulation

(a)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M) R2 = 1

R2 = 09991

y = 67643x + 30887

y = 11265x + 29988

1S (mMminus1)

TheoreticalSimulation

(b)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 82314x + 20077

y = 9982x + 29191

R2 = 1

R2 = 09984

TheoreticalSimulation

(c)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 17963x + 10567

y = 22109x + 90103

R2 = 1

R2 = 09982

1S (mMminus1)

TheoreticalSimulation

(d)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 42716x + 42716

y = 11353x + 10013

R2 = 1

R2 = 09999

TheoreticalSimulation

(e)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 30115x + 16731

y = 19058x + 13928

R2 = 1

R2 = 09991

1S (mMminus1)

TheoreticalSimulation

(f)

Figure 3The Lineweaver-Burk plots for experimentally calculated kinetic parameters (represented by a solid line) and simulation parameterssimulated by our model (represented by a dash dotted line) From top to bottom and from left to right the plots represent the activity of thefollowing enzymes glutathione reductase aspartate 1-decarboxylase alcohol dehydrogenase IMP dehydrogenase D-Ala-D-Ala dipeptidaseand pyruvate decarboxylase

observe the reconversion of the molecules of NADH (bluecircles) to molecules of NAD+ whenever the first hit thecell membrane (ie boundary of the environment) Likewiseit is possible to observe that obstacles are playing theirpart deflecting the movement of the other agents everyso often A detailed visual documentation of the two-stepenzymatic reaction simulation is available in supplementary

material (see Supplementary Material available online athttpdxdoiorg1011552014769471)

Numeric outputs detail these visual insights and presentdata about the movement of the different species thevelocity at which the reactions are taking place and thebehavioural system as a whole (Figure 5) The number ofagents representing the first substrate benzyl alcohol decays

BioMed Research International 9

NADHEnzyme one

Enzyme two

ObstaclesBenzaldehydeHaloenzyme 1

Haloenzyme 2

Benzyl alcoholBenzoateNAD+

Figure 4 Visual illustration of the evolving of the population of agents during the simulation steps

considerably in the first 2000 steps of simulation togetherwith the disappearance of agents representing NAD+ andthe creation of agents representing the aryl-alcohol dehy-drogenase haloenzyme This leads to the production of agrowing number of agents representing benzaldehyde and anincrease in the number of reactions occurring in the systemAs soon as benzaldehyde agents start to circulate in theenvironment and considering the continuous reconversionofNADHagents intoNAD+ agents the second reaction startsto occur This is reflected in a considerable decrease in thenumber of agents of benzaldehyde and a fairly proportionalincrease in the number of the agents representing benzoatethe product that will be ultimately excreted

43 System Performance This work describes the first phaseof development of the biomolecular simulator That is tosay that focus was set on identifying and implementing

themain biochemical and biophysical laws that would governthe model rather than implementing a realistic picture of themolecular landscape

As far as we know there has not been a previous attemptto simulate the effects of spatial localisation and temporalscales of individuals in the modelling of biomolecular sys-tems So before engaging into more complex scenarios itwas pivotal to take advantage of available experimental dataand ensure that the tool was able to account for basic cellulardynamics such as those governing enzymes adequately Nowthat we obtained a successful proof of concept we will workon system scalability in order to address more complexproblems

For this purpose we run preliminary performance tests tofind out the current scalability of our system Figure 6 sum-marises performance tests using an Intel I7 (2600) 34GHzprocessor with 6GB of RAM and runningWindows 8 64-bitThe tests accounted for three possible scenarios as follows

10 BioMed Research International

100

300

500

700

900

1100

0 5000 10000 15000

NumBenzyl alcohol

Num

ber o

f age

nts

Number of steps

(a)

89100

89300

89500

89700

89900

90100

0 5000 10000 15000

Num

ber o

f age

nts

Number of steps

89100911009310095100

0 16000

Detail

NumNAD+

(b)

Num

ber o

f age

nts

Number of steps

050

100150200250300350

0 5000 10000 15000

NumBenzal

(c)

9900

10100

10300

10500

10700

10900

0 5000 10000 15000

NumNADH

Num

ber o

f age

nts

Number of steps

(d)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 1

1732273237324732

0 10000

Detail

Num

ber o

f age

nts

Number of steps

(e)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 2

267836784678

0 15000

Detail

Num

ber o

f age

nts

Number of steps

(f)

80009000

100001100012000130001400015000

0 5000 10000 15000

NumReactions

40009000

14000

0 16000

Detail

Num

ber o

f age

nts

Number of steps

(g)

0

200

400

600

800

1000

0 5000 10000 15000

NumBenzoate

Num

ber o

f age

nts

Number of steps

(h)

Figure 5 The number of agents of different species interacting in the environment during 15000 simulation steps From top to bottom andfrom left to right the above plots represent the number of agents of benzyl alcohol NAD+ benzaldehyde NADH aryl-alcohol dehydrogenaseholoenzyme and benzaldehyde dehydrogenase holoenzyme At the bottom there is the number of occurring reactions and the number ofmolecules of benzoate excreted the extracellular medium

BioMed Research International 11

0

5000

10000

15000

20000

25000

30000

35000

0 50000 100000 150000 200000

Tim

e (m

s)

Number of agents

Only agentsAgents with movementAgents with movement and reactions

Figure 6 Performance of the tool in scenarios of increasingcomputational complexity

no action that is the agents are created but no diffusion orbehavioural rules are executed without reaction that is theagents are created and diffusion rules are activated but agentsdo not interact among themselves and with reaction thatis agents are created can move and can interact The threescenarios show a similar performance till the system reachesa population of 15119864 + 05 agents That is till this point thephysics governing agent movement and the introduction ofbehavioural rules do not affect simulation time significantlyCost resides on creating the system After that point thetime taken by the simulation of more elaborated scenariosthat is more agents in motion and more rules to manageis somewhat aggravated Over 25119864 + 05 agents the systembecomes computational unviable by a single machine

So in the near future we will investigate the use of dis-tributed and high-performance computing in the simulationofmore complex biomolecular systemsNamely we are inves-tigating the potential of the new distributed environmentof MASON the DMASON (httpwwwisislabitprojectsdmason) and the Biocellion framework [42]

5 Conclusions

ABM is increasingly popular in biology due to its naturalability to represent multiple scales of system decompositionintertwine complicated behaviours and deal with spatial-temporal constraints

The agent-based tool developed in this work aims tosupport biomolecular simulations and most notably provideinsights into catalytic efficiency in scenarios of industrialinterest Hence proof of concept was focused on the approx-imation of kinetic parameters The models correctly sim-ulated known enzymatic characteristics and yielded usefulpredictions that may guide future experimental design Italso provides a simulation variability that may reproduce theexperimental variation observed in lab experiments

Future development of the models presented here willinclude three-dimensional representation metabolic path-way simulation and accounting of extracellular substances

Moreover we plan to take into advantage the new DMA-SON platform to engage into distributed affordable sim-ulation and study more complex scenarios Other recenthigh-performance computing frameworks like Biocellionwill also be evaluated

After consolidation our tool will provide severalresources and services for the investigation of bacterial cellsin benefit of the research and industry communities

Conflict of Interests

The authors do not have any competing interests

Acknowledgments

The authors thank the Agrupamento INBIOMED fromDXPCTSUG-FEDER unha maneira de facer Europa(2012273) The research leading to these results has receivedfunding from the European Unionrsquos Seventh Frame-work Programme FP7REGPOT-2012-20131 under GrantAgreement no 316265 (BIOCAPS) and the [14VI05] Con-tract-Programme from theUniversity ofVigoThis documentreflects only the authorsrsquo views and the European Union isnot liable for any use that may be made of the informationcontained herein

References

[1] D Porro P Branduardi M Sauer and D Mattanovich ldquoOldobstacles and new horizons formicrobial chemical productionrdquoCurrent Opinion in Biotechnology C vol 30 pp 101ndash106 2014

[2] P Jeandet YVasserot T Chastang andECourot ldquoEngineeringmicrobial cells for the biosynthesis of natural compounds ofpharmaceutical significancerdquo BioMed Research Internationalvol 2013 Article ID 780145 13 pages 2013

[3] A Kondo J Ishii K Y Hara T Hasunuma and F Mat-suda ldquoDevelopment of microbial cell factories for bio-refinerythrough synthetic bioengineeringrdquo Journal of Biotechnologyvol 163 no 2 pp 204ndash216 2013

[4] J H Shin H U Kim D I Kim and S Y Lee ldquoProduction ofbulk chemicals via novel metabolic pathways in microorgan-ismsrdquo Biotechnology Advances vol 31 pp 925ndash935 2013

[5] C M Immethun A G Hoynes-OrsquoConnor A Balassy andT S Moon ldquoMicrobial production of isoprenoids enabled bysynthetic biologyrdquo Frontiers in Microbiology vol 4 article 752013

[6] Y Chen and J Nielsen ldquo Advances in metabolic pathway andstrain engineering paving the way for sustainable productionof chemical building blocksrdquo Current Opinion in Biotechnologyvol 24 pp 965ndash972 2013

[7] J W Lee D Na J M Park S Choi and S Y Lee ldquoSystemsmetabolic engineering of microorganisms for natural and non-natural chemicalsrdquo Nature Chemical Biology vol 8 pp 536ndash546 2012

[8] G Stephanopoulos ldquoSynthetic biology andmetabolic engineer-ingrdquo ACS Synthetic Biology vol 1 pp 514ndash525 2012

[9] T-M Lo W S Teo H Ling B Chen A Kang and MW Chang ldquoMicrobial engineering strategies to improve cellviability for biochemical productionrdquo Biotechnology Advancesvol 31 pp 903ndash914 2013

12 BioMed Research International

[10] K M Esvelt and H H Wang ldquoGenome-scale engineering forsystems and synthetic biologyrdquo Molecular Systems Biology vol9 p 641 2013

[11] M K Tiwari R R K Singh I Kim and J-K Lee ldquoCompu-tational approaches for rational design of proteins with novelfunctionalitiesrdquo Computational and Structural BiotechnologyJournal vol 2 Article ID e201209002 2012

[12] M Cvijovic J Almquist J Hagmar et al ldquoBridging the gaps insystems biologyrdquoMolecular Genetics and Genomics vol 289 no5 pp 727ndash734 2014

[13] N Tomar and R K De ldquoComparing methods for metabolicnetwork analysis and an application to metabolic engineeringrdquoGene vol 521 no 1 pp 1ndash14 2013

[14] A Chakrabarti L Miskovic K C Soh and V HatzimanikatisldquoTowards kinetic modeling of genome-scale metabolic net-works without sacrificing stoichiometric thermodynamic andphysiological constraintsrdquo Biotechnology Journal vol 8 no 9pp 1043ndash1057 2013

[15] A F Villaverde and J R Banga ldquoReverse engineering andidentification in systems biology strategies perspectives andchallengesrdquo Journal of the Royal Society Interface vol 11 no 91Article ID 20130505 2014

[16] S Luke C Cioffi-Revilla L Panait K Sullivan and G BalanldquoMASON a multiagent simulation environmentrdquo Simulationvol 81 no 7 pp 517ndash527 2005

[17] R Conte and M Paolucci ldquoOn agent-based modeling andcomputational social sciencerdquo Frontiers in Psychology vol 5article 668 2014

[18] M Wooldridge ldquoAgent-based software engineeringrdquo IEE Pro-ceedings Software vol 144 no 1 pp 26ndash37 1997

[19] E Bonabeau ldquoAgent-based modeling Methods and techniquesfor simulating human systemsrdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 99 no3 pp 7280ndash7287 2002

[20] N Cannata F Corradini E Merelli and L Tesei ldquoAgent-basedmodels of cellular systemsrdquo Methods in Molecular Biology vol930 pp 399ndash426 2013

[21] G An Q Mi J Dutta-Moscato and Y Vodovotz ldquoAgent-basedmodels in translational systems biologyrdquoWiley InterdisciplinaryReviews Systems Biology and Medicine vol 1 no 2 pp 159ndash1712009

[22] J O Dada and P Mendes ldquoMulti-scale modelling and simula-tion in systems biologyrdquo Integrative Biology vol 3 pp 86ndash962011

[23] H Kaul and Y Ventikos ldquoInvestigating biocomplexity throughthe agent-based paradigmrdquo Briefings in Bioinformatics vol 442013

[24] M Holcombe S Adra M Bicak et al ldquoModelling complexbiological systems using an agent-based approachrdquo IntegrativeBiology vol 4 no 1 pp 53ndash64 2012

[25] D CWalker J Southgate GHill et al ldquoThe epitheliome agent-based modelling of the social behaviour of cellsrdquo BioSystemsvol 76 no 1ndash3 pp 89ndash100 2004

[26] M B Biggs and J A Papin ldquoNovel multiscale modeling toolapplied to Pseudomonas aeruginosa biofilm formationrdquo PLoSONE vol 8 no 10 Article ID e78011 2013

[27] S M Stiegelmeyer andM C Giddings ldquoAgent-based modelingof competence phenotype switching in Bacillus subtilisrdquo Theo-retical Biology and Medical Modelling vol 10 article 23 2013

[28] G An and S Kulkarni ldquoAn agent-based modeling frameworklinking inflammation and cancer using evolutionary principles

Description of a generative hierarchy for the hallmarks of cancerand developing a bridge betweenmechanism and epidemiolog-ical datardquoMathematical Biosciences 2014

[29] J Wang L Zhang C Jing et al ldquoMulti-scale agent-basedmodeling on melanoma and its related angiogenesis analysisrdquoTheoretical Biology and Medical Modelling vol 10 article 412013

[30] V Gopalakrishnan M Kim and G An ldquoUsing an agent-basedmodel to examine the role of dynamic bacterial virulence poten-tial in the pathogenesis of surgical site infectionrdquo Advances inWound Care vol 2 no 9 pp 510ndash526 2013

[31] A E Curtin and L Zhou ldquoAn agent-based model of theresponse to angioplasty and bare-metal stent deployment in anatherosclerotic blood vesselrdquo PLoS ONE vol 9 no 4 Article IDe94411 2014

[32] K Bettenbrock H Bai M Ederer et al ldquoChapter Twomdashtowards a systems level understanding of the oxygen responseof Escherichia colirdquo in Advances in Microbial Physiology vol 6pp 65ndash114 2014

[33] A Apte R Senger and S S Fong ldquoDesigning novel cellulasesystems through agent-based modeling and global sensitivityanalysisrdquo Bioengineered vol 5 no 4 pp 243ndash253 2014

[34] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 30 no 21 pp3101ndash3108 2014

[35] S Kang S Kahan and B Momeni ldquoSimulating microbial com-munity patterning using Biocellionrdquo in Methods in MolecularBiology vol 1151 pp 233ndash253 2014

[36] I Millington Game Physics Engine Development How to Builda Robust Commercial-Grade Physics Engine for Your Game CRCPress Boca Raton Fla USA 2010

[37] G Palmer Physics for Game Programmers Apress 2005[38] T Kalwarczyk M Tabaka and R Holyst ldquoBiologisticsmdash

diffusion coefficients for complete proteome of Escherichiacolirdquo Bioinformatics vol 28 no 22 pp 2971ndash2978 2012

[39] K A Johnson and R S Goody ldquoThe original Michaelisconstant translation of the 1913 Michaelis-Menten paperrdquoBiochemistry vol 50 no 39 pp 8264ndash8269 2011

[40] A Cornish-Bowden ldquoThe origins of enzyme kineticsrdquo FEBSLetters vol 587 no 17 pp 2725ndash2730 2013

[41] M Scheer A Grote A Chang et al ldquoBRENDA the enzymeinformation system in 2011rdquo Nucleic Acids Research vol 39 no1 pp D670ndashD676 2011

[42] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 130 no 21 pp3101ndash3108 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

BioMed Research International 7

050

100150200250300350400450500

1 3 5 7 9 11 13 15

1V

(itm

M)

1[S] (mM)

1007550253415

Linear (100)Linear (75)Linear (50)Linear (25)Linear (34)Linear (15)

y = 10596x + 24081

y = 11218x + 33688

y = 13112x + 43521

y = 19657x + 66475

y = 1629x + 5107

R2 = 09999

R2 = 1

R2 = 09999

R2 = 09999

R2 = 09993

R2 = 09993

y = 30326x + 26336

Figure 2 The Lineweaver-Burk plots obtained while simulating different percentages of reactive collision and a time step of 1 The markersrepresent the outputs of simulation and the lines represent the corresponding trend lines based on linear regression (equation also shown)

Table 3 An approximation between experimentally calculated kinetic parameters and the parameters simulated by our model

Enzyme identification Experimental kinetics Simulation parameters Approximated kinetics119896119898

119896cat reactive collision Time step 119896119898(mM) 119896cat (s

minus1)EC 1819mdashglutathione reductase activity 0404 039 25 100 0531257304 452119864 minus 01

EC 41111mdashaspartate 1-decarboxylase 0219 065 75 75 037565 669119864 minus 01

EC 1111mdashalcohol dehydrogenase 041 1 95 75 034196 688119864 minus 01

EC 111205mdashIMP dehydrogenase 17 19 25 25 245375 223119864 + 00

EC 341322mdashD-Ala-D-Ala dipeptidase 1 47 75 25 113387 201119864 + 00

EC 4111mdashpyruvate decarboxylase 18 12 25 5 136829 144119864 + 00

Table 4 The weight size and diffusion rate of the moleculesrepresented in the two-step enzymatic system

Species Molecularweight (gmol)

Particle radius(120583m)

Diffusion rate(120583m2s)

Benzyl alcohol 10814 0323 times 10minus3 4018 times 10minus14

NAD+ 66141 0657 times 10minus3 1975 times 10minus14

NADH 66343 0658 times 10minus3 1973 times 10minus14

Benzaldehyde 106121 0321 times 10minus3 4047 times 10minus14

Benzoate 12112 0338 times 10minus3 3843 times 10minus14

the first reaction was introduced gradually in the environ-ment specifically 10 at every 10 time steps

Agent size and velocity of movement were adjustedaccording to the molecular weight of the biological species(Table 4) Heaviermolecules have a larger radius and a slowerdiffusion rate Proportionally the agents representing benzylalcohol and benzaldehyde molecules should be two times

smaller and faster than the agents representing the moleculesof NAD+ and NADH

To facilitate visual inspection distinct agent types areassociated with different colours and proportional sizes Assuch it is possible to visually observe the evolving of thesimulation and at some extent observe how the agents aremoving and interacting with each other Specifically it ispossible to see how different agents traverse the environmentand how behavioural rules are triggered or take precedenceover each other

As illustrated in Figure 4 although the movement ofthe molecules of benzyl alcohol (green circles) is quite fastthese molecules are unable to interact with the correspond-ing enzyme (aryl-alcohol dehydrogenase named enzymeone and coloured yellow in the figure) unless the enzymehas already bound to a NAD+ molecule (ie creating theholoenzyme 1 coloured in black) Likewise interactions withthe second enzyme benzaldehyde dehydrogenase (magentacircles) are limited to the molecules of NAD+ (red circles)until the first reaction actually occurs and begins producingbenzaldehyde (blue circles) Furthermore it is possible to

8 BioMed Research International

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 20797x + 51479

R2 = 1

R2 = 09994

y = 23614x + 44449

1S (mMminus1)

TheoreticalSimulation

(a)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M) R2 = 1

R2 = 09991

y = 67643x + 30887

y = 11265x + 29988

1S (mMminus1)

TheoreticalSimulation

(b)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 82314x + 20077

y = 9982x + 29191

R2 = 1

R2 = 09984

TheoreticalSimulation

(c)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 17963x + 10567

y = 22109x + 90103

R2 = 1

R2 = 09982

1S (mMminus1)

TheoreticalSimulation

(d)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 42716x + 42716

y = 11353x + 10013

R2 = 1

R2 = 09999

TheoreticalSimulation

(e)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 30115x + 16731

y = 19058x + 13928

R2 = 1

R2 = 09991

1S (mMminus1)

TheoreticalSimulation

(f)

Figure 3The Lineweaver-Burk plots for experimentally calculated kinetic parameters (represented by a solid line) and simulation parameterssimulated by our model (represented by a dash dotted line) From top to bottom and from left to right the plots represent the activity of thefollowing enzymes glutathione reductase aspartate 1-decarboxylase alcohol dehydrogenase IMP dehydrogenase D-Ala-D-Ala dipeptidaseand pyruvate decarboxylase

observe the reconversion of the molecules of NADH (bluecircles) to molecules of NAD+ whenever the first hit thecell membrane (ie boundary of the environment) Likewiseit is possible to observe that obstacles are playing theirpart deflecting the movement of the other agents everyso often A detailed visual documentation of the two-stepenzymatic reaction simulation is available in supplementary

material (see Supplementary Material available online athttpdxdoiorg1011552014769471)

Numeric outputs detail these visual insights and presentdata about the movement of the different species thevelocity at which the reactions are taking place and thebehavioural system as a whole (Figure 5) The number ofagents representing the first substrate benzyl alcohol decays

BioMed Research International 9

NADHEnzyme one

Enzyme two

ObstaclesBenzaldehydeHaloenzyme 1

Haloenzyme 2

Benzyl alcoholBenzoateNAD+

Figure 4 Visual illustration of the evolving of the population of agents during the simulation steps

considerably in the first 2000 steps of simulation togetherwith the disappearance of agents representing NAD+ andthe creation of agents representing the aryl-alcohol dehy-drogenase haloenzyme This leads to the production of agrowing number of agents representing benzaldehyde and anincrease in the number of reactions occurring in the systemAs soon as benzaldehyde agents start to circulate in theenvironment and considering the continuous reconversionofNADHagents intoNAD+ agents the second reaction startsto occur This is reflected in a considerable decrease in thenumber of agents of benzaldehyde and a fairly proportionalincrease in the number of the agents representing benzoatethe product that will be ultimately excreted

43 System Performance This work describes the first phaseof development of the biomolecular simulator That is tosay that focus was set on identifying and implementing

themain biochemical and biophysical laws that would governthe model rather than implementing a realistic picture of themolecular landscape

As far as we know there has not been a previous attemptto simulate the effects of spatial localisation and temporalscales of individuals in the modelling of biomolecular sys-tems So before engaging into more complex scenarios itwas pivotal to take advantage of available experimental dataand ensure that the tool was able to account for basic cellulardynamics such as those governing enzymes adequately Nowthat we obtained a successful proof of concept we will workon system scalability in order to address more complexproblems

For this purpose we run preliminary performance tests tofind out the current scalability of our system Figure 6 sum-marises performance tests using an Intel I7 (2600) 34GHzprocessor with 6GB of RAM and runningWindows 8 64-bitThe tests accounted for three possible scenarios as follows

10 BioMed Research International

100

300

500

700

900

1100

0 5000 10000 15000

NumBenzyl alcohol

Num

ber o

f age

nts

Number of steps

(a)

89100

89300

89500

89700

89900

90100

0 5000 10000 15000

Num

ber o

f age

nts

Number of steps

89100911009310095100

0 16000

Detail

NumNAD+

(b)

Num

ber o

f age

nts

Number of steps

050

100150200250300350

0 5000 10000 15000

NumBenzal

(c)

9900

10100

10300

10500

10700

10900

0 5000 10000 15000

NumNADH

Num

ber o

f age

nts

Number of steps

(d)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 1

1732273237324732

0 10000

Detail

Num

ber o

f age

nts

Number of steps

(e)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 2

267836784678

0 15000

Detail

Num

ber o

f age

nts

Number of steps

(f)

80009000

100001100012000130001400015000

0 5000 10000 15000

NumReactions

40009000

14000

0 16000

Detail

Num

ber o

f age

nts

Number of steps

(g)

0

200

400

600

800

1000

0 5000 10000 15000

NumBenzoate

Num

ber o

f age

nts

Number of steps

(h)

Figure 5 The number of agents of different species interacting in the environment during 15000 simulation steps From top to bottom andfrom left to right the above plots represent the number of agents of benzyl alcohol NAD+ benzaldehyde NADH aryl-alcohol dehydrogenaseholoenzyme and benzaldehyde dehydrogenase holoenzyme At the bottom there is the number of occurring reactions and the number ofmolecules of benzoate excreted the extracellular medium

BioMed Research International 11

0

5000

10000

15000

20000

25000

30000

35000

0 50000 100000 150000 200000

Tim

e (m

s)

Number of agents

Only agentsAgents with movementAgents with movement and reactions

Figure 6 Performance of the tool in scenarios of increasingcomputational complexity

no action that is the agents are created but no diffusion orbehavioural rules are executed without reaction that is theagents are created and diffusion rules are activated but agentsdo not interact among themselves and with reaction thatis agents are created can move and can interact The threescenarios show a similar performance till the system reachesa population of 15119864 + 05 agents That is till this point thephysics governing agent movement and the introduction ofbehavioural rules do not affect simulation time significantlyCost resides on creating the system After that point thetime taken by the simulation of more elaborated scenariosthat is more agents in motion and more rules to manageis somewhat aggravated Over 25119864 + 05 agents the systembecomes computational unviable by a single machine

So in the near future we will investigate the use of dis-tributed and high-performance computing in the simulationofmore complex biomolecular systemsNamely we are inves-tigating the potential of the new distributed environmentof MASON the DMASON (httpwwwisislabitprojectsdmason) and the Biocellion framework [42]

5 Conclusions

ABM is increasingly popular in biology due to its naturalability to represent multiple scales of system decompositionintertwine complicated behaviours and deal with spatial-temporal constraints

The agent-based tool developed in this work aims tosupport biomolecular simulations and most notably provideinsights into catalytic efficiency in scenarios of industrialinterest Hence proof of concept was focused on the approx-imation of kinetic parameters The models correctly sim-ulated known enzymatic characteristics and yielded usefulpredictions that may guide future experimental design Italso provides a simulation variability that may reproduce theexperimental variation observed in lab experiments

Future development of the models presented here willinclude three-dimensional representation metabolic path-way simulation and accounting of extracellular substances

Moreover we plan to take into advantage the new DMA-SON platform to engage into distributed affordable sim-ulation and study more complex scenarios Other recenthigh-performance computing frameworks like Biocellionwill also be evaluated

After consolidation our tool will provide severalresources and services for the investigation of bacterial cellsin benefit of the research and industry communities

Conflict of Interests

The authors do not have any competing interests

Acknowledgments

The authors thank the Agrupamento INBIOMED fromDXPCTSUG-FEDER unha maneira de facer Europa(2012273) The research leading to these results has receivedfunding from the European Unionrsquos Seventh Frame-work Programme FP7REGPOT-2012-20131 under GrantAgreement no 316265 (BIOCAPS) and the [14VI05] Con-tract-Programme from theUniversity ofVigoThis documentreflects only the authorsrsquo views and the European Union isnot liable for any use that may be made of the informationcontained herein

References

[1] D Porro P Branduardi M Sauer and D Mattanovich ldquoOldobstacles and new horizons formicrobial chemical productionrdquoCurrent Opinion in Biotechnology C vol 30 pp 101ndash106 2014

[2] P Jeandet YVasserot T Chastang andECourot ldquoEngineeringmicrobial cells for the biosynthesis of natural compounds ofpharmaceutical significancerdquo BioMed Research Internationalvol 2013 Article ID 780145 13 pages 2013

[3] A Kondo J Ishii K Y Hara T Hasunuma and F Mat-suda ldquoDevelopment of microbial cell factories for bio-refinerythrough synthetic bioengineeringrdquo Journal of Biotechnologyvol 163 no 2 pp 204ndash216 2013

[4] J H Shin H U Kim D I Kim and S Y Lee ldquoProduction ofbulk chemicals via novel metabolic pathways in microorgan-ismsrdquo Biotechnology Advances vol 31 pp 925ndash935 2013

[5] C M Immethun A G Hoynes-OrsquoConnor A Balassy andT S Moon ldquoMicrobial production of isoprenoids enabled bysynthetic biologyrdquo Frontiers in Microbiology vol 4 article 752013

[6] Y Chen and J Nielsen ldquo Advances in metabolic pathway andstrain engineering paving the way for sustainable productionof chemical building blocksrdquo Current Opinion in Biotechnologyvol 24 pp 965ndash972 2013

[7] J W Lee D Na J M Park S Choi and S Y Lee ldquoSystemsmetabolic engineering of microorganisms for natural and non-natural chemicalsrdquo Nature Chemical Biology vol 8 pp 536ndash546 2012

[8] G Stephanopoulos ldquoSynthetic biology andmetabolic engineer-ingrdquo ACS Synthetic Biology vol 1 pp 514ndash525 2012

[9] T-M Lo W S Teo H Ling B Chen A Kang and MW Chang ldquoMicrobial engineering strategies to improve cellviability for biochemical productionrdquo Biotechnology Advancesvol 31 pp 903ndash914 2013

12 BioMed Research International

[10] K M Esvelt and H H Wang ldquoGenome-scale engineering forsystems and synthetic biologyrdquo Molecular Systems Biology vol9 p 641 2013

[11] M K Tiwari R R K Singh I Kim and J-K Lee ldquoCompu-tational approaches for rational design of proteins with novelfunctionalitiesrdquo Computational and Structural BiotechnologyJournal vol 2 Article ID e201209002 2012

[12] M Cvijovic J Almquist J Hagmar et al ldquoBridging the gaps insystems biologyrdquoMolecular Genetics and Genomics vol 289 no5 pp 727ndash734 2014

[13] N Tomar and R K De ldquoComparing methods for metabolicnetwork analysis and an application to metabolic engineeringrdquoGene vol 521 no 1 pp 1ndash14 2013

[14] A Chakrabarti L Miskovic K C Soh and V HatzimanikatisldquoTowards kinetic modeling of genome-scale metabolic net-works without sacrificing stoichiometric thermodynamic andphysiological constraintsrdquo Biotechnology Journal vol 8 no 9pp 1043ndash1057 2013

[15] A F Villaverde and J R Banga ldquoReverse engineering andidentification in systems biology strategies perspectives andchallengesrdquo Journal of the Royal Society Interface vol 11 no 91Article ID 20130505 2014

[16] S Luke C Cioffi-Revilla L Panait K Sullivan and G BalanldquoMASON a multiagent simulation environmentrdquo Simulationvol 81 no 7 pp 517ndash527 2005

[17] R Conte and M Paolucci ldquoOn agent-based modeling andcomputational social sciencerdquo Frontiers in Psychology vol 5article 668 2014

[18] M Wooldridge ldquoAgent-based software engineeringrdquo IEE Pro-ceedings Software vol 144 no 1 pp 26ndash37 1997

[19] E Bonabeau ldquoAgent-based modeling Methods and techniquesfor simulating human systemsrdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 99 no3 pp 7280ndash7287 2002

[20] N Cannata F Corradini E Merelli and L Tesei ldquoAgent-basedmodels of cellular systemsrdquo Methods in Molecular Biology vol930 pp 399ndash426 2013

[21] G An Q Mi J Dutta-Moscato and Y Vodovotz ldquoAgent-basedmodels in translational systems biologyrdquoWiley InterdisciplinaryReviews Systems Biology and Medicine vol 1 no 2 pp 159ndash1712009

[22] J O Dada and P Mendes ldquoMulti-scale modelling and simula-tion in systems biologyrdquo Integrative Biology vol 3 pp 86ndash962011

[23] H Kaul and Y Ventikos ldquoInvestigating biocomplexity throughthe agent-based paradigmrdquo Briefings in Bioinformatics vol 442013

[24] M Holcombe S Adra M Bicak et al ldquoModelling complexbiological systems using an agent-based approachrdquo IntegrativeBiology vol 4 no 1 pp 53ndash64 2012

[25] D CWalker J Southgate GHill et al ldquoThe epitheliome agent-based modelling of the social behaviour of cellsrdquo BioSystemsvol 76 no 1ndash3 pp 89ndash100 2004

[26] M B Biggs and J A Papin ldquoNovel multiscale modeling toolapplied to Pseudomonas aeruginosa biofilm formationrdquo PLoSONE vol 8 no 10 Article ID e78011 2013

[27] S M Stiegelmeyer andM C Giddings ldquoAgent-based modelingof competence phenotype switching in Bacillus subtilisrdquo Theo-retical Biology and Medical Modelling vol 10 article 23 2013

[28] G An and S Kulkarni ldquoAn agent-based modeling frameworklinking inflammation and cancer using evolutionary principles

Description of a generative hierarchy for the hallmarks of cancerand developing a bridge betweenmechanism and epidemiolog-ical datardquoMathematical Biosciences 2014

[29] J Wang L Zhang C Jing et al ldquoMulti-scale agent-basedmodeling on melanoma and its related angiogenesis analysisrdquoTheoretical Biology and Medical Modelling vol 10 article 412013

[30] V Gopalakrishnan M Kim and G An ldquoUsing an agent-basedmodel to examine the role of dynamic bacterial virulence poten-tial in the pathogenesis of surgical site infectionrdquo Advances inWound Care vol 2 no 9 pp 510ndash526 2013

[31] A E Curtin and L Zhou ldquoAn agent-based model of theresponse to angioplasty and bare-metal stent deployment in anatherosclerotic blood vesselrdquo PLoS ONE vol 9 no 4 Article IDe94411 2014

[32] K Bettenbrock H Bai M Ederer et al ldquoChapter Twomdashtowards a systems level understanding of the oxygen responseof Escherichia colirdquo in Advances in Microbial Physiology vol 6pp 65ndash114 2014

[33] A Apte R Senger and S S Fong ldquoDesigning novel cellulasesystems through agent-based modeling and global sensitivityanalysisrdquo Bioengineered vol 5 no 4 pp 243ndash253 2014

[34] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 30 no 21 pp3101ndash3108 2014

[35] S Kang S Kahan and B Momeni ldquoSimulating microbial com-munity patterning using Biocellionrdquo in Methods in MolecularBiology vol 1151 pp 233ndash253 2014

[36] I Millington Game Physics Engine Development How to Builda Robust Commercial-Grade Physics Engine for Your Game CRCPress Boca Raton Fla USA 2010

[37] G Palmer Physics for Game Programmers Apress 2005[38] T Kalwarczyk M Tabaka and R Holyst ldquoBiologisticsmdash

diffusion coefficients for complete proteome of Escherichiacolirdquo Bioinformatics vol 28 no 22 pp 2971ndash2978 2012

[39] K A Johnson and R S Goody ldquoThe original Michaelisconstant translation of the 1913 Michaelis-Menten paperrdquoBiochemistry vol 50 no 39 pp 8264ndash8269 2011

[40] A Cornish-Bowden ldquoThe origins of enzyme kineticsrdquo FEBSLetters vol 587 no 17 pp 2725ndash2730 2013

[41] M Scheer A Grote A Chang et al ldquoBRENDA the enzymeinformation system in 2011rdquo Nucleic Acids Research vol 39 no1 pp D670ndashD676 2011

[42] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 130 no 21 pp3101ndash3108 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

8 BioMed Research International

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 20797x + 51479

R2 = 1

R2 = 09994

y = 23614x + 44449

1S (mMminus1)

TheoreticalSimulation

(a)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M) R2 = 1

R2 = 09991

y = 67643x + 30887

y = 11265x + 29988

1S (mMminus1)

TheoreticalSimulation

(b)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 82314x + 20077

y = 9982x + 29191

R2 = 1

R2 = 09984

TheoreticalSimulation

(c)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 17963x + 10567

y = 22109x + 90103

R2 = 1

R2 = 09982

1S (mMminus1)

TheoreticalSimulation

(d)

1S (mMminus1)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 42716x + 42716

y = 11353x + 10013

R2 = 1

R2 = 09999

TheoreticalSimulation

(e)

0

100

200

300

400

2 4 6 8 10 12 14 16

1V

(itm

M)

y = 30115x + 16731

y = 19058x + 13928

R2 = 1

R2 = 09991

1S (mMminus1)

TheoreticalSimulation

(f)

Figure 3The Lineweaver-Burk plots for experimentally calculated kinetic parameters (represented by a solid line) and simulation parameterssimulated by our model (represented by a dash dotted line) From top to bottom and from left to right the plots represent the activity of thefollowing enzymes glutathione reductase aspartate 1-decarboxylase alcohol dehydrogenase IMP dehydrogenase D-Ala-D-Ala dipeptidaseand pyruvate decarboxylase

observe the reconversion of the molecules of NADH (bluecircles) to molecules of NAD+ whenever the first hit thecell membrane (ie boundary of the environment) Likewiseit is possible to observe that obstacles are playing theirpart deflecting the movement of the other agents everyso often A detailed visual documentation of the two-stepenzymatic reaction simulation is available in supplementary

material (see Supplementary Material available online athttpdxdoiorg1011552014769471)

Numeric outputs detail these visual insights and presentdata about the movement of the different species thevelocity at which the reactions are taking place and thebehavioural system as a whole (Figure 5) The number ofagents representing the first substrate benzyl alcohol decays

BioMed Research International 9

NADHEnzyme one

Enzyme two

ObstaclesBenzaldehydeHaloenzyme 1

Haloenzyme 2

Benzyl alcoholBenzoateNAD+

Figure 4 Visual illustration of the evolving of the population of agents during the simulation steps

considerably in the first 2000 steps of simulation togetherwith the disappearance of agents representing NAD+ andthe creation of agents representing the aryl-alcohol dehy-drogenase haloenzyme This leads to the production of agrowing number of agents representing benzaldehyde and anincrease in the number of reactions occurring in the systemAs soon as benzaldehyde agents start to circulate in theenvironment and considering the continuous reconversionofNADHagents intoNAD+ agents the second reaction startsto occur This is reflected in a considerable decrease in thenumber of agents of benzaldehyde and a fairly proportionalincrease in the number of the agents representing benzoatethe product that will be ultimately excreted

43 System Performance This work describes the first phaseof development of the biomolecular simulator That is tosay that focus was set on identifying and implementing

themain biochemical and biophysical laws that would governthe model rather than implementing a realistic picture of themolecular landscape

As far as we know there has not been a previous attemptto simulate the effects of spatial localisation and temporalscales of individuals in the modelling of biomolecular sys-tems So before engaging into more complex scenarios itwas pivotal to take advantage of available experimental dataand ensure that the tool was able to account for basic cellulardynamics such as those governing enzymes adequately Nowthat we obtained a successful proof of concept we will workon system scalability in order to address more complexproblems

For this purpose we run preliminary performance tests tofind out the current scalability of our system Figure 6 sum-marises performance tests using an Intel I7 (2600) 34GHzprocessor with 6GB of RAM and runningWindows 8 64-bitThe tests accounted for three possible scenarios as follows

10 BioMed Research International

100

300

500

700

900

1100

0 5000 10000 15000

NumBenzyl alcohol

Num

ber o

f age

nts

Number of steps

(a)

89100

89300

89500

89700

89900

90100

0 5000 10000 15000

Num

ber o

f age

nts

Number of steps

89100911009310095100

0 16000

Detail

NumNAD+

(b)

Num

ber o

f age

nts

Number of steps

050

100150200250300350

0 5000 10000 15000

NumBenzal

(c)

9900

10100

10300

10500

10700

10900

0 5000 10000 15000

NumNADH

Num

ber o

f age

nts

Number of steps

(d)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 1

1732273237324732

0 10000

Detail

Num

ber o

f age

nts

Number of steps

(e)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 2

267836784678

0 15000

Detail

Num

ber o

f age

nts

Number of steps

(f)

80009000

100001100012000130001400015000

0 5000 10000 15000

NumReactions

40009000

14000

0 16000

Detail

Num

ber o

f age

nts

Number of steps

(g)

0

200

400

600

800

1000

0 5000 10000 15000

NumBenzoate

Num

ber o

f age

nts

Number of steps

(h)

Figure 5 The number of agents of different species interacting in the environment during 15000 simulation steps From top to bottom andfrom left to right the above plots represent the number of agents of benzyl alcohol NAD+ benzaldehyde NADH aryl-alcohol dehydrogenaseholoenzyme and benzaldehyde dehydrogenase holoenzyme At the bottom there is the number of occurring reactions and the number ofmolecules of benzoate excreted the extracellular medium

BioMed Research International 11

0

5000

10000

15000

20000

25000

30000

35000

0 50000 100000 150000 200000

Tim

e (m

s)

Number of agents

Only agentsAgents with movementAgents with movement and reactions

Figure 6 Performance of the tool in scenarios of increasingcomputational complexity

no action that is the agents are created but no diffusion orbehavioural rules are executed without reaction that is theagents are created and diffusion rules are activated but agentsdo not interact among themselves and with reaction thatis agents are created can move and can interact The threescenarios show a similar performance till the system reachesa population of 15119864 + 05 agents That is till this point thephysics governing agent movement and the introduction ofbehavioural rules do not affect simulation time significantlyCost resides on creating the system After that point thetime taken by the simulation of more elaborated scenariosthat is more agents in motion and more rules to manageis somewhat aggravated Over 25119864 + 05 agents the systembecomes computational unviable by a single machine

So in the near future we will investigate the use of dis-tributed and high-performance computing in the simulationofmore complex biomolecular systemsNamely we are inves-tigating the potential of the new distributed environmentof MASON the DMASON (httpwwwisislabitprojectsdmason) and the Biocellion framework [42]

5 Conclusions

ABM is increasingly popular in biology due to its naturalability to represent multiple scales of system decompositionintertwine complicated behaviours and deal with spatial-temporal constraints

The agent-based tool developed in this work aims tosupport biomolecular simulations and most notably provideinsights into catalytic efficiency in scenarios of industrialinterest Hence proof of concept was focused on the approx-imation of kinetic parameters The models correctly sim-ulated known enzymatic characteristics and yielded usefulpredictions that may guide future experimental design Italso provides a simulation variability that may reproduce theexperimental variation observed in lab experiments

Future development of the models presented here willinclude three-dimensional representation metabolic path-way simulation and accounting of extracellular substances

Moreover we plan to take into advantage the new DMA-SON platform to engage into distributed affordable sim-ulation and study more complex scenarios Other recenthigh-performance computing frameworks like Biocellionwill also be evaluated

After consolidation our tool will provide severalresources and services for the investigation of bacterial cellsin benefit of the research and industry communities

Conflict of Interests

The authors do not have any competing interests

Acknowledgments

The authors thank the Agrupamento INBIOMED fromDXPCTSUG-FEDER unha maneira de facer Europa(2012273) The research leading to these results has receivedfunding from the European Unionrsquos Seventh Frame-work Programme FP7REGPOT-2012-20131 under GrantAgreement no 316265 (BIOCAPS) and the [14VI05] Con-tract-Programme from theUniversity ofVigoThis documentreflects only the authorsrsquo views and the European Union isnot liable for any use that may be made of the informationcontained herein

References

[1] D Porro P Branduardi M Sauer and D Mattanovich ldquoOldobstacles and new horizons formicrobial chemical productionrdquoCurrent Opinion in Biotechnology C vol 30 pp 101ndash106 2014

[2] P Jeandet YVasserot T Chastang andECourot ldquoEngineeringmicrobial cells for the biosynthesis of natural compounds ofpharmaceutical significancerdquo BioMed Research Internationalvol 2013 Article ID 780145 13 pages 2013

[3] A Kondo J Ishii K Y Hara T Hasunuma and F Mat-suda ldquoDevelopment of microbial cell factories for bio-refinerythrough synthetic bioengineeringrdquo Journal of Biotechnologyvol 163 no 2 pp 204ndash216 2013

[4] J H Shin H U Kim D I Kim and S Y Lee ldquoProduction ofbulk chemicals via novel metabolic pathways in microorgan-ismsrdquo Biotechnology Advances vol 31 pp 925ndash935 2013

[5] C M Immethun A G Hoynes-OrsquoConnor A Balassy andT S Moon ldquoMicrobial production of isoprenoids enabled bysynthetic biologyrdquo Frontiers in Microbiology vol 4 article 752013

[6] Y Chen and J Nielsen ldquo Advances in metabolic pathway andstrain engineering paving the way for sustainable productionof chemical building blocksrdquo Current Opinion in Biotechnologyvol 24 pp 965ndash972 2013

[7] J W Lee D Na J M Park S Choi and S Y Lee ldquoSystemsmetabolic engineering of microorganisms for natural and non-natural chemicalsrdquo Nature Chemical Biology vol 8 pp 536ndash546 2012

[8] G Stephanopoulos ldquoSynthetic biology andmetabolic engineer-ingrdquo ACS Synthetic Biology vol 1 pp 514ndash525 2012

[9] T-M Lo W S Teo H Ling B Chen A Kang and MW Chang ldquoMicrobial engineering strategies to improve cellviability for biochemical productionrdquo Biotechnology Advancesvol 31 pp 903ndash914 2013

12 BioMed Research International

[10] K M Esvelt and H H Wang ldquoGenome-scale engineering forsystems and synthetic biologyrdquo Molecular Systems Biology vol9 p 641 2013

[11] M K Tiwari R R K Singh I Kim and J-K Lee ldquoCompu-tational approaches for rational design of proteins with novelfunctionalitiesrdquo Computational and Structural BiotechnologyJournal vol 2 Article ID e201209002 2012

[12] M Cvijovic J Almquist J Hagmar et al ldquoBridging the gaps insystems biologyrdquoMolecular Genetics and Genomics vol 289 no5 pp 727ndash734 2014

[13] N Tomar and R K De ldquoComparing methods for metabolicnetwork analysis and an application to metabolic engineeringrdquoGene vol 521 no 1 pp 1ndash14 2013

[14] A Chakrabarti L Miskovic K C Soh and V HatzimanikatisldquoTowards kinetic modeling of genome-scale metabolic net-works without sacrificing stoichiometric thermodynamic andphysiological constraintsrdquo Biotechnology Journal vol 8 no 9pp 1043ndash1057 2013

[15] A F Villaverde and J R Banga ldquoReverse engineering andidentification in systems biology strategies perspectives andchallengesrdquo Journal of the Royal Society Interface vol 11 no 91Article ID 20130505 2014

[16] S Luke C Cioffi-Revilla L Panait K Sullivan and G BalanldquoMASON a multiagent simulation environmentrdquo Simulationvol 81 no 7 pp 517ndash527 2005

[17] R Conte and M Paolucci ldquoOn agent-based modeling andcomputational social sciencerdquo Frontiers in Psychology vol 5article 668 2014

[18] M Wooldridge ldquoAgent-based software engineeringrdquo IEE Pro-ceedings Software vol 144 no 1 pp 26ndash37 1997

[19] E Bonabeau ldquoAgent-based modeling Methods and techniquesfor simulating human systemsrdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 99 no3 pp 7280ndash7287 2002

[20] N Cannata F Corradini E Merelli and L Tesei ldquoAgent-basedmodels of cellular systemsrdquo Methods in Molecular Biology vol930 pp 399ndash426 2013

[21] G An Q Mi J Dutta-Moscato and Y Vodovotz ldquoAgent-basedmodels in translational systems biologyrdquoWiley InterdisciplinaryReviews Systems Biology and Medicine vol 1 no 2 pp 159ndash1712009

[22] J O Dada and P Mendes ldquoMulti-scale modelling and simula-tion in systems biologyrdquo Integrative Biology vol 3 pp 86ndash962011

[23] H Kaul and Y Ventikos ldquoInvestigating biocomplexity throughthe agent-based paradigmrdquo Briefings in Bioinformatics vol 442013

[24] M Holcombe S Adra M Bicak et al ldquoModelling complexbiological systems using an agent-based approachrdquo IntegrativeBiology vol 4 no 1 pp 53ndash64 2012

[25] D CWalker J Southgate GHill et al ldquoThe epitheliome agent-based modelling of the social behaviour of cellsrdquo BioSystemsvol 76 no 1ndash3 pp 89ndash100 2004

[26] M B Biggs and J A Papin ldquoNovel multiscale modeling toolapplied to Pseudomonas aeruginosa biofilm formationrdquo PLoSONE vol 8 no 10 Article ID e78011 2013

[27] S M Stiegelmeyer andM C Giddings ldquoAgent-based modelingof competence phenotype switching in Bacillus subtilisrdquo Theo-retical Biology and Medical Modelling vol 10 article 23 2013

[28] G An and S Kulkarni ldquoAn agent-based modeling frameworklinking inflammation and cancer using evolutionary principles

Description of a generative hierarchy for the hallmarks of cancerand developing a bridge betweenmechanism and epidemiolog-ical datardquoMathematical Biosciences 2014

[29] J Wang L Zhang C Jing et al ldquoMulti-scale agent-basedmodeling on melanoma and its related angiogenesis analysisrdquoTheoretical Biology and Medical Modelling vol 10 article 412013

[30] V Gopalakrishnan M Kim and G An ldquoUsing an agent-basedmodel to examine the role of dynamic bacterial virulence poten-tial in the pathogenesis of surgical site infectionrdquo Advances inWound Care vol 2 no 9 pp 510ndash526 2013

[31] A E Curtin and L Zhou ldquoAn agent-based model of theresponse to angioplasty and bare-metal stent deployment in anatherosclerotic blood vesselrdquo PLoS ONE vol 9 no 4 Article IDe94411 2014

[32] K Bettenbrock H Bai M Ederer et al ldquoChapter Twomdashtowards a systems level understanding of the oxygen responseof Escherichia colirdquo in Advances in Microbial Physiology vol 6pp 65ndash114 2014

[33] A Apte R Senger and S S Fong ldquoDesigning novel cellulasesystems through agent-based modeling and global sensitivityanalysisrdquo Bioengineered vol 5 no 4 pp 243ndash253 2014

[34] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 30 no 21 pp3101ndash3108 2014

[35] S Kang S Kahan and B Momeni ldquoSimulating microbial com-munity patterning using Biocellionrdquo in Methods in MolecularBiology vol 1151 pp 233ndash253 2014

[36] I Millington Game Physics Engine Development How to Builda Robust Commercial-Grade Physics Engine for Your Game CRCPress Boca Raton Fla USA 2010

[37] G Palmer Physics for Game Programmers Apress 2005[38] T Kalwarczyk M Tabaka and R Holyst ldquoBiologisticsmdash

diffusion coefficients for complete proteome of Escherichiacolirdquo Bioinformatics vol 28 no 22 pp 2971ndash2978 2012

[39] K A Johnson and R S Goody ldquoThe original Michaelisconstant translation of the 1913 Michaelis-Menten paperrdquoBiochemistry vol 50 no 39 pp 8264ndash8269 2011

[40] A Cornish-Bowden ldquoThe origins of enzyme kineticsrdquo FEBSLetters vol 587 no 17 pp 2725ndash2730 2013

[41] M Scheer A Grote A Chang et al ldquoBRENDA the enzymeinformation system in 2011rdquo Nucleic Acids Research vol 39 no1 pp D670ndashD676 2011

[42] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 130 no 21 pp3101ndash3108 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

BioMed Research International 9

NADHEnzyme one

Enzyme two

ObstaclesBenzaldehydeHaloenzyme 1

Haloenzyme 2

Benzyl alcoholBenzoateNAD+

Figure 4 Visual illustration of the evolving of the population of agents during the simulation steps

considerably in the first 2000 steps of simulation togetherwith the disappearance of agents representing NAD+ andthe creation of agents representing the aryl-alcohol dehy-drogenase haloenzyme This leads to the production of agrowing number of agents representing benzaldehyde and anincrease in the number of reactions occurring in the systemAs soon as benzaldehyde agents start to circulate in theenvironment and considering the continuous reconversionofNADHagents intoNAD+ agents the second reaction startsto occur This is reflected in a considerable decrease in thenumber of agents of benzaldehyde and a fairly proportionalincrease in the number of the agents representing benzoatethe product that will be ultimately excreted

43 System Performance This work describes the first phaseof development of the biomolecular simulator That is tosay that focus was set on identifying and implementing

themain biochemical and biophysical laws that would governthe model rather than implementing a realistic picture of themolecular landscape

As far as we know there has not been a previous attemptto simulate the effects of spatial localisation and temporalscales of individuals in the modelling of biomolecular sys-tems So before engaging into more complex scenarios itwas pivotal to take advantage of available experimental dataand ensure that the tool was able to account for basic cellulardynamics such as those governing enzymes adequately Nowthat we obtained a successful proof of concept we will workon system scalability in order to address more complexproblems

For this purpose we run preliminary performance tests tofind out the current scalability of our system Figure 6 sum-marises performance tests using an Intel I7 (2600) 34GHzprocessor with 6GB of RAM and runningWindows 8 64-bitThe tests accounted for three possible scenarios as follows

10 BioMed Research International

100

300

500

700

900

1100

0 5000 10000 15000

NumBenzyl alcohol

Num

ber o

f age

nts

Number of steps

(a)

89100

89300

89500

89700

89900

90100

0 5000 10000 15000

Num

ber o

f age

nts

Number of steps

89100911009310095100

0 16000

Detail

NumNAD+

(b)

Num

ber o

f age

nts

Number of steps

050

100150200250300350

0 5000 10000 15000

NumBenzal

(c)

9900

10100

10300

10500

10700

10900

0 5000 10000 15000

NumNADH

Num

ber o

f age

nts

Number of steps

(d)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 1

1732273237324732

0 10000

Detail

Num

ber o

f age

nts

Number of steps

(e)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 2

267836784678

0 15000

Detail

Num

ber o

f age

nts

Number of steps

(f)

80009000

100001100012000130001400015000

0 5000 10000 15000

NumReactions

40009000

14000

0 16000

Detail

Num

ber o

f age

nts

Number of steps

(g)

0

200

400

600

800

1000

0 5000 10000 15000

NumBenzoate

Num

ber o

f age

nts

Number of steps

(h)

Figure 5 The number of agents of different species interacting in the environment during 15000 simulation steps From top to bottom andfrom left to right the above plots represent the number of agents of benzyl alcohol NAD+ benzaldehyde NADH aryl-alcohol dehydrogenaseholoenzyme and benzaldehyde dehydrogenase holoenzyme At the bottom there is the number of occurring reactions and the number ofmolecules of benzoate excreted the extracellular medium

BioMed Research International 11

0

5000

10000

15000

20000

25000

30000

35000

0 50000 100000 150000 200000

Tim

e (m

s)

Number of agents

Only agentsAgents with movementAgents with movement and reactions

Figure 6 Performance of the tool in scenarios of increasingcomputational complexity

no action that is the agents are created but no diffusion orbehavioural rules are executed without reaction that is theagents are created and diffusion rules are activated but agentsdo not interact among themselves and with reaction thatis agents are created can move and can interact The threescenarios show a similar performance till the system reachesa population of 15119864 + 05 agents That is till this point thephysics governing agent movement and the introduction ofbehavioural rules do not affect simulation time significantlyCost resides on creating the system After that point thetime taken by the simulation of more elaborated scenariosthat is more agents in motion and more rules to manageis somewhat aggravated Over 25119864 + 05 agents the systembecomes computational unviable by a single machine

So in the near future we will investigate the use of dis-tributed and high-performance computing in the simulationofmore complex biomolecular systemsNamely we are inves-tigating the potential of the new distributed environmentof MASON the DMASON (httpwwwisislabitprojectsdmason) and the Biocellion framework [42]

5 Conclusions

ABM is increasingly popular in biology due to its naturalability to represent multiple scales of system decompositionintertwine complicated behaviours and deal with spatial-temporal constraints

The agent-based tool developed in this work aims tosupport biomolecular simulations and most notably provideinsights into catalytic efficiency in scenarios of industrialinterest Hence proof of concept was focused on the approx-imation of kinetic parameters The models correctly sim-ulated known enzymatic characteristics and yielded usefulpredictions that may guide future experimental design Italso provides a simulation variability that may reproduce theexperimental variation observed in lab experiments

Future development of the models presented here willinclude three-dimensional representation metabolic path-way simulation and accounting of extracellular substances

Moreover we plan to take into advantage the new DMA-SON platform to engage into distributed affordable sim-ulation and study more complex scenarios Other recenthigh-performance computing frameworks like Biocellionwill also be evaluated

After consolidation our tool will provide severalresources and services for the investigation of bacterial cellsin benefit of the research and industry communities

Conflict of Interests

The authors do not have any competing interests

Acknowledgments

The authors thank the Agrupamento INBIOMED fromDXPCTSUG-FEDER unha maneira de facer Europa(2012273) The research leading to these results has receivedfunding from the European Unionrsquos Seventh Frame-work Programme FP7REGPOT-2012-20131 under GrantAgreement no 316265 (BIOCAPS) and the [14VI05] Con-tract-Programme from theUniversity ofVigoThis documentreflects only the authorsrsquo views and the European Union isnot liable for any use that may be made of the informationcontained herein

References

[1] D Porro P Branduardi M Sauer and D Mattanovich ldquoOldobstacles and new horizons formicrobial chemical productionrdquoCurrent Opinion in Biotechnology C vol 30 pp 101ndash106 2014

[2] P Jeandet YVasserot T Chastang andECourot ldquoEngineeringmicrobial cells for the biosynthesis of natural compounds ofpharmaceutical significancerdquo BioMed Research Internationalvol 2013 Article ID 780145 13 pages 2013

[3] A Kondo J Ishii K Y Hara T Hasunuma and F Mat-suda ldquoDevelopment of microbial cell factories for bio-refinerythrough synthetic bioengineeringrdquo Journal of Biotechnologyvol 163 no 2 pp 204ndash216 2013

[4] J H Shin H U Kim D I Kim and S Y Lee ldquoProduction ofbulk chemicals via novel metabolic pathways in microorgan-ismsrdquo Biotechnology Advances vol 31 pp 925ndash935 2013

[5] C M Immethun A G Hoynes-OrsquoConnor A Balassy andT S Moon ldquoMicrobial production of isoprenoids enabled bysynthetic biologyrdquo Frontiers in Microbiology vol 4 article 752013

[6] Y Chen and J Nielsen ldquo Advances in metabolic pathway andstrain engineering paving the way for sustainable productionof chemical building blocksrdquo Current Opinion in Biotechnologyvol 24 pp 965ndash972 2013

[7] J W Lee D Na J M Park S Choi and S Y Lee ldquoSystemsmetabolic engineering of microorganisms for natural and non-natural chemicalsrdquo Nature Chemical Biology vol 8 pp 536ndash546 2012

[8] G Stephanopoulos ldquoSynthetic biology andmetabolic engineer-ingrdquo ACS Synthetic Biology vol 1 pp 514ndash525 2012

[9] T-M Lo W S Teo H Ling B Chen A Kang and MW Chang ldquoMicrobial engineering strategies to improve cellviability for biochemical productionrdquo Biotechnology Advancesvol 31 pp 903ndash914 2013

12 BioMed Research International

[10] K M Esvelt and H H Wang ldquoGenome-scale engineering forsystems and synthetic biologyrdquo Molecular Systems Biology vol9 p 641 2013

[11] M K Tiwari R R K Singh I Kim and J-K Lee ldquoCompu-tational approaches for rational design of proteins with novelfunctionalitiesrdquo Computational and Structural BiotechnologyJournal vol 2 Article ID e201209002 2012

[12] M Cvijovic J Almquist J Hagmar et al ldquoBridging the gaps insystems biologyrdquoMolecular Genetics and Genomics vol 289 no5 pp 727ndash734 2014

[13] N Tomar and R K De ldquoComparing methods for metabolicnetwork analysis and an application to metabolic engineeringrdquoGene vol 521 no 1 pp 1ndash14 2013

[14] A Chakrabarti L Miskovic K C Soh and V HatzimanikatisldquoTowards kinetic modeling of genome-scale metabolic net-works without sacrificing stoichiometric thermodynamic andphysiological constraintsrdquo Biotechnology Journal vol 8 no 9pp 1043ndash1057 2013

[15] A F Villaverde and J R Banga ldquoReverse engineering andidentification in systems biology strategies perspectives andchallengesrdquo Journal of the Royal Society Interface vol 11 no 91Article ID 20130505 2014

[16] S Luke C Cioffi-Revilla L Panait K Sullivan and G BalanldquoMASON a multiagent simulation environmentrdquo Simulationvol 81 no 7 pp 517ndash527 2005

[17] R Conte and M Paolucci ldquoOn agent-based modeling andcomputational social sciencerdquo Frontiers in Psychology vol 5article 668 2014

[18] M Wooldridge ldquoAgent-based software engineeringrdquo IEE Pro-ceedings Software vol 144 no 1 pp 26ndash37 1997

[19] E Bonabeau ldquoAgent-based modeling Methods and techniquesfor simulating human systemsrdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 99 no3 pp 7280ndash7287 2002

[20] N Cannata F Corradini E Merelli and L Tesei ldquoAgent-basedmodels of cellular systemsrdquo Methods in Molecular Biology vol930 pp 399ndash426 2013

[21] G An Q Mi J Dutta-Moscato and Y Vodovotz ldquoAgent-basedmodels in translational systems biologyrdquoWiley InterdisciplinaryReviews Systems Biology and Medicine vol 1 no 2 pp 159ndash1712009

[22] J O Dada and P Mendes ldquoMulti-scale modelling and simula-tion in systems biologyrdquo Integrative Biology vol 3 pp 86ndash962011

[23] H Kaul and Y Ventikos ldquoInvestigating biocomplexity throughthe agent-based paradigmrdquo Briefings in Bioinformatics vol 442013

[24] M Holcombe S Adra M Bicak et al ldquoModelling complexbiological systems using an agent-based approachrdquo IntegrativeBiology vol 4 no 1 pp 53ndash64 2012

[25] D CWalker J Southgate GHill et al ldquoThe epitheliome agent-based modelling of the social behaviour of cellsrdquo BioSystemsvol 76 no 1ndash3 pp 89ndash100 2004

[26] M B Biggs and J A Papin ldquoNovel multiscale modeling toolapplied to Pseudomonas aeruginosa biofilm formationrdquo PLoSONE vol 8 no 10 Article ID e78011 2013

[27] S M Stiegelmeyer andM C Giddings ldquoAgent-based modelingof competence phenotype switching in Bacillus subtilisrdquo Theo-retical Biology and Medical Modelling vol 10 article 23 2013

[28] G An and S Kulkarni ldquoAn agent-based modeling frameworklinking inflammation and cancer using evolutionary principles

Description of a generative hierarchy for the hallmarks of cancerand developing a bridge betweenmechanism and epidemiolog-ical datardquoMathematical Biosciences 2014

[29] J Wang L Zhang C Jing et al ldquoMulti-scale agent-basedmodeling on melanoma and its related angiogenesis analysisrdquoTheoretical Biology and Medical Modelling vol 10 article 412013

[30] V Gopalakrishnan M Kim and G An ldquoUsing an agent-basedmodel to examine the role of dynamic bacterial virulence poten-tial in the pathogenesis of surgical site infectionrdquo Advances inWound Care vol 2 no 9 pp 510ndash526 2013

[31] A E Curtin and L Zhou ldquoAn agent-based model of theresponse to angioplasty and bare-metal stent deployment in anatherosclerotic blood vesselrdquo PLoS ONE vol 9 no 4 Article IDe94411 2014

[32] K Bettenbrock H Bai M Ederer et al ldquoChapter Twomdashtowards a systems level understanding of the oxygen responseof Escherichia colirdquo in Advances in Microbial Physiology vol 6pp 65ndash114 2014

[33] A Apte R Senger and S S Fong ldquoDesigning novel cellulasesystems through agent-based modeling and global sensitivityanalysisrdquo Bioengineered vol 5 no 4 pp 243ndash253 2014

[34] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 30 no 21 pp3101ndash3108 2014

[35] S Kang S Kahan and B Momeni ldquoSimulating microbial com-munity patterning using Biocellionrdquo in Methods in MolecularBiology vol 1151 pp 233ndash253 2014

[36] I Millington Game Physics Engine Development How to Builda Robust Commercial-Grade Physics Engine for Your Game CRCPress Boca Raton Fla USA 2010

[37] G Palmer Physics for Game Programmers Apress 2005[38] T Kalwarczyk M Tabaka and R Holyst ldquoBiologisticsmdash

diffusion coefficients for complete proteome of Escherichiacolirdquo Bioinformatics vol 28 no 22 pp 2971ndash2978 2012

[39] K A Johnson and R S Goody ldquoThe original Michaelisconstant translation of the 1913 Michaelis-Menten paperrdquoBiochemistry vol 50 no 39 pp 8264ndash8269 2011

[40] A Cornish-Bowden ldquoThe origins of enzyme kineticsrdquo FEBSLetters vol 587 no 17 pp 2725ndash2730 2013

[41] M Scheer A Grote A Chang et al ldquoBRENDA the enzymeinformation system in 2011rdquo Nucleic Acids Research vol 39 no1 pp D670ndashD676 2011

[42] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 130 no 21 pp3101ndash3108 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

10 BioMed Research International

100

300

500

700

900

1100

0 5000 10000 15000

NumBenzyl alcohol

Num

ber o

f age

nts

Number of steps

(a)

89100

89300

89500

89700

89900

90100

0 5000 10000 15000

Num

ber o

f age

nts

Number of steps

89100911009310095100

0 16000

Detail

NumNAD+

(b)

Num

ber o

f age

nts

Number of steps

050

100150200250300350

0 5000 10000 15000

NumBenzal

(c)

9900

10100

10300

10500

10700

10900

0 5000 10000 15000

NumNADH

Num

ber o

f age

nts

Number of steps

(d)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 1

1732273237324732

0 10000

Detail

Num

ber o

f age

nts

Number of steps

(e)

4900

4920

4940

4960

4980

5000

0 5000 10000 15000

Haloenzyme 2

267836784678

0 15000

Detail

Num

ber o

f age

nts

Number of steps

(f)

80009000

100001100012000130001400015000

0 5000 10000 15000

NumReactions

40009000

14000

0 16000

Detail

Num

ber o

f age

nts

Number of steps

(g)

0

200

400

600

800

1000

0 5000 10000 15000

NumBenzoate

Num

ber o

f age

nts

Number of steps

(h)

Figure 5 The number of agents of different species interacting in the environment during 15000 simulation steps From top to bottom andfrom left to right the above plots represent the number of agents of benzyl alcohol NAD+ benzaldehyde NADH aryl-alcohol dehydrogenaseholoenzyme and benzaldehyde dehydrogenase holoenzyme At the bottom there is the number of occurring reactions and the number ofmolecules of benzoate excreted the extracellular medium

BioMed Research International 11

0

5000

10000

15000

20000

25000

30000

35000

0 50000 100000 150000 200000

Tim

e (m

s)

Number of agents

Only agentsAgents with movementAgents with movement and reactions

Figure 6 Performance of the tool in scenarios of increasingcomputational complexity

no action that is the agents are created but no diffusion orbehavioural rules are executed without reaction that is theagents are created and diffusion rules are activated but agentsdo not interact among themselves and with reaction thatis agents are created can move and can interact The threescenarios show a similar performance till the system reachesa population of 15119864 + 05 agents That is till this point thephysics governing agent movement and the introduction ofbehavioural rules do not affect simulation time significantlyCost resides on creating the system After that point thetime taken by the simulation of more elaborated scenariosthat is more agents in motion and more rules to manageis somewhat aggravated Over 25119864 + 05 agents the systembecomes computational unviable by a single machine

So in the near future we will investigate the use of dis-tributed and high-performance computing in the simulationofmore complex biomolecular systemsNamely we are inves-tigating the potential of the new distributed environmentof MASON the DMASON (httpwwwisislabitprojectsdmason) and the Biocellion framework [42]

5 Conclusions

ABM is increasingly popular in biology due to its naturalability to represent multiple scales of system decompositionintertwine complicated behaviours and deal with spatial-temporal constraints

The agent-based tool developed in this work aims tosupport biomolecular simulations and most notably provideinsights into catalytic efficiency in scenarios of industrialinterest Hence proof of concept was focused on the approx-imation of kinetic parameters The models correctly sim-ulated known enzymatic characteristics and yielded usefulpredictions that may guide future experimental design Italso provides a simulation variability that may reproduce theexperimental variation observed in lab experiments

Future development of the models presented here willinclude three-dimensional representation metabolic path-way simulation and accounting of extracellular substances

Moreover we plan to take into advantage the new DMA-SON platform to engage into distributed affordable sim-ulation and study more complex scenarios Other recenthigh-performance computing frameworks like Biocellionwill also be evaluated

After consolidation our tool will provide severalresources and services for the investigation of bacterial cellsin benefit of the research and industry communities

Conflict of Interests

The authors do not have any competing interests

Acknowledgments

The authors thank the Agrupamento INBIOMED fromDXPCTSUG-FEDER unha maneira de facer Europa(2012273) The research leading to these results has receivedfunding from the European Unionrsquos Seventh Frame-work Programme FP7REGPOT-2012-20131 under GrantAgreement no 316265 (BIOCAPS) and the [14VI05] Con-tract-Programme from theUniversity ofVigoThis documentreflects only the authorsrsquo views and the European Union isnot liable for any use that may be made of the informationcontained herein

References

[1] D Porro P Branduardi M Sauer and D Mattanovich ldquoOldobstacles and new horizons formicrobial chemical productionrdquoCurrent Opinion in Biotechnology C vol 30 pp 101ndash106 2014

[2] P Jeandet YVasserot T Chastang andECourot ldquoEngineeringmicrobial cells for the biosynthesis of natural compounds ofpharmaceutical significancerdquo BioMed Research Internationalvol 2013 Article ID 780145 13 pages 2013

[3] A Kondo J Ishii K Y Hara T Hasunuma and F Mat-suda ldquoDevelopment of microbial cell factories for bio-refinerythrough synthetic bioengineeringrdquo Journal of Biotechnologyvol 163 no 2 pp 204ndash216 2013

[4] J H Shin H U Kim D I Kim and S Y Lee ldquoProduction ofbulk chemicals via novel metabolic pathways in microorgan-ismsrdquo Biotechnology Advances vol 31 pp 925ndash935 2013

[5] C M Immethun A G Hoynes-OrsquoConnor A Balassy andT S Moon ldquoMicrobial production of isoprenoids enabled bysynthetic biologyrdquo Frontiers in Microbiology vol 4 article 752013

[6] Y Chen and J Nielsen ldquo Advances in metabolic pathway andstrain engineering paving the way for sustainable productionof chemical building blocksrdquo Current Opinion in Biotechnologyvol 24 pp 965ndash972 2013

[7] J W Lee D Na J M Park S Choi and S Y Lee ldquoSystemsmetabolic engineering of microorganisms for natural and non-natural chemicalsrdquo Nature Chemical Biology vol 8 pp 536ndash546 2012

[8] G Stephanopoulos ldquoSynthetic biology andmetabolic engineer-ingrdquo ACS Synthetic Biology vol 1 pp 514ndash525 2012

[9] T-M Lo W S Teo H Ling B Chen A Kang and MW Chang ldquoMicrobial engineering strategies to improve cellviability for biochemical productionrdquo Biotechnology Advancesvol 31 pp 903ndash914 2013

12 BioMed Research International

[10] K M Esvelt and H H Wang ldquoGenome-scale engineering forsystems and synthetic biologyrdquo Molecular Systems Biology vol9 p 641 2013

[11] M K Tiwari R R K Singh I Kim and J-K Lee ldquoCompu-tational approaches for rational design of proteins with novelfunctionalitiesrdquo Computational and Structural BiotechnologyJournal vol 2 Article ID e201209002 2012

[12] M Cvijovic J Almquist J Hagmar et al ldquoBridging the gaps insystems biologyrdquoMolecular Genetics and Genomics vol 289 no5 pp 727ndash734 2014

[13] N Tomar and R K De ldquoComparing methods for metabolicnetwork analysis and an application to metabolic engineeringrdquoGene vol 521 no 1 pp 1ndash14 2013

[14] A Chakrabarti L Miskovic K C Soh and V HatzimanikatisldquoTowards kinetic modeling of genome-scale metabolic net-works without sacrificing stoichiometric thermodynamic andphysiological constraintsrdquo Biotechnology Journal vol 8 no 9pp 1043ndash1057 2013

[15] A F Villaverde and J R Banga ldquoReverse engineering andidentification in systems biology strategies perspectives andchallengesrdquo Journal of the Royal Society Interface vol 11 no 91Article ID 20130505 2014

[16] S Luke C Cioffi-Revilla L Panait K Sullivan and G BalanldquoMASON a multiagent simulation environmentrdquo Simulationvol 81 no 7 pp 517ndash527 2005

[17] R Conte and M Paolucci ldquoOn agent-based modeling andcomputational social sciencerdquo Frontiers in Psychology vol 5article 668 2014

[18] M Wooldridge ldquoAgent-based software engineeringrdquo IEE Pro-ceedings Software vol 144 no 1 pp 26ndash37 1997

[19] E Bonabeau ldquoAgent-based modeling Methods and techniquesfor simulating human systemsrdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 99 no3 pp 7280ndash7287 2002

[20] N Cannata F Corradini E Merelli and L Tesei ldquoAgent-basedmodels of cellular systemsrdquo Methods in Molecular Biology vol930 pp 399ndash426 2013

[21] G An Q Mi J Dutta-Moscato and Y Vodovotz ldquoAgent-basedmodels in translational systems biologyrdquoWiley InterdisciplinaryReviews Systems Biology and Medicine vol 1 no 2 pp 159ndash1712009

[22] J O Dada and P Mendes ldquoMulti-scale modelling and simula-tion in systems biologyrdquo Integrative Biology vol 3 pp 86ndash962011

[23] H Kaul and Y Ventikos ldquoInvestigating biocomplexity throughthe agent-based paradigmrdquo Briefings in Bioinformatics vol 442013

[24] M Holcombe S Adra M Bicak et al ldquoModelling complexbiological systems using an agent-based approachrdquo IntegrativeBiology vol 4 no 1 pp 53ndash64 2012

[25] D CWalker J Southgate GHill et al ldquoThe epitheliome agent-based modelling of the social behaviour of cellsrdquo BioSystemsvol 76 no 1ndash3 pp 89ndash100 2004

[26] M B Biggs and J A Papin ldquoNovel multiscale modeling toolapplied to Pseudomonas aeruginosa biofilm formationrdquo PLoSONE vol 8 no 10 Article ID e78011 2013

[27] S M Stiegelmeyer andM C Giddings ldquoAgent-based modelingof competence phenotype switching in Bacillus subtilisrdquo Theo-retical Biology and Medical Modelling vol 10 article 23 2013

[28] G An and S Kulkarni ldquoAn agent-based modeling frameworklinking inflammation and cancer using evolutionary principles

Description of a generative hierarchy for the hallmarks of cancerand developing a bridge betweenmechanism and epidemiolog-ical datardquoMathematical Biosciences 2014

[29] J Wang L Zhang C Jing et al ldquoMulti-scale agent-basedmodeling on melanoma and its related angiogenesis analysisrdquoTheoretical Biology and Medical Modelling vol 10 article 412013

[30] V Gopalakrishnan M Kim and G An ldquoUsing an agent-basedmodel to examine the role of dynamic bacterial virulence poten-tial in the pathogenesis of surgical site infectionrdquo Advances inWound Care vol 2 no 9 pp 510ndash526 2013

[31] A E Curtin and L Zhou ldquoAn agent-based model of theresponse to angioplasty and bare-metal stent deployment in anatherosclerotic blood vesselrdquo PLoS ONE vol 9 no 4 Article IDe94411 2014

[32] K Bettenbrock H Bai M Ederer et al ldquoChapter Twomdashtowards a systems level understanding of the oxygen responseof Escherichia colirdquo in Advances in Microbial Physiology vol 6pp 65ndash114 2014

[33] A Apte R Senger and S S Fong ldquoDesigning novel cellulasesystems through agent-based modeling and global sensitivityanalysisrdquo Bioengineered vol 5 no 4 pp 243ndash253 2014

[34] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 30 no 21 pp3101ndash3108 2014

[35] S Kang S Kahan and B Momeni ldquoSimulating microbial com-munity patterning using Biocellionrdquo in Methods in MolecularBiology vol 1151 pp 233ndash253 2014

[36] I Millington Game Physics Engine Development How to Builda Robust Commercial-Grade Physics Engine for Your Game CRCPress Boca Raton Fla USA 2010

[37] G Palmer Physics for Game Programmers Apress 2005[38] T Kalwarczyk M Tabaka and R Holyst ldquoBiologisticsmdash

diffusion coefficients for complete proteome of Escherichiacolirdquo Bioinformatics vol 28 no 22 pp 2971ndash2978 2012

[39] K A Johnson and R S Goody ldquoThe original Michaelisconstant translation of the 1913 Michaelis-Menten paperrdquoBiochemistry vol 50 no 39 pp 8264ndash8269 2011

[40] A Cornish-Bowden ldquoThe origins of enzyme kineticsrdquo FEBSLetters vol 587 no 17 pp 2725ndash2730 2013

[41] M Scheer A Grote A Chang et al ldquoBRENDA the enzymeinformation system in 2011rdquo Nucleic Acids Research vol 39 no1 pp D670ndashD676 2011

[42] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 130 no 21 pp3101ndash3108 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

BioMed Research International 11

0

5000

10000

15000

20000

25000

30000

35000

0 50000 100000 150000 200000

Tim

e (m

s)

Number of agents

Only agentsAgents with movementAgents with movement and reactions

Figure 6 Performance of the tool in scenarios of increasingcomputational complexity

no action that is the agents are created but no diffusion orbehavioural rules are executed without reaction that is theagents are created and diffusion rules are activated but agentsdo not interact among themselves and with reaction thatis agents are created can move and can interact The threescenarios show a similar performance till the system reachesa population of 15119864 + 05 agents That is till this point thephysics governing agent movement and the introduction ofbehavioural rules do not affect simulation time significantlyCost resides on creating the system After that point thetime taken by the simulation of more elaborated scenariosthat is more agents in motion and more rules to manageis somewhat aggravated Over 25119864 + 05 agents the systembecomes computational unviable by a single machine

So in the near future we will investigate the use of dis-tributed and high-performance computing in the simulationofmore complex biomolecular systemsNamely we are inves-tigating the potential of the new distributed environmentof MASON the DMASON (httpwwwisislabitprojectsdmason) and the Biocellion framework [42]

5 Conclusions

ABM is increasingly popular in biology due to its naturalability to represent multiple scales of system decompositionintertwine complicated behaviours and deal with spatial-temporal constraints

The agent-based tool developed in this work aims tosupport biomolecular simulations and most notably provideinsights into catalytic efficiency in scenarios of industrialinterest Hence proof of concept was focused on the approx-imation of kinetic parameters The models correctly sim-ulated known enzymatic characteristics and yielded usefulpredictions that may guide future experimental design Italso provides a simulation variability that may reproduce theexperimental variation observed in lab experiments

Future development of the models presented here willinclude three-dimensional representation metabolic path-way simulation and accounting of extracellular substances

Moreover we plan to take into advantage the new DMA-SON platform to engage into distributed affordable sim-ulation and study more complex scenarios Other recenthigh-performance computing frameworks like Biocellionwill also be evaluated

After consolidation our tool will provide severalresources and services for the investigation of bacterial cellsin benefit of the research and industry communities

Conflict of Interests

The authors do not have any competing interests

Acknowledgments

The authors thank the Agrupamento INBIOMED fromDXPCTSUG-FEDER unha maneira de facer Europa(2012273) The research leading to these results has receivedfunding from the European Unionrsquos Seventh Frame-work Programme FP7REGPOT-2012-20131 under GrantAgreement no 316265 (BIOCAPS) and the [14VI05] Con-tract-Programme from theUniversity ofVigoThis documentreflects only the authorsrsquo views and the European Union isnot liable for any use that may be made of the informationcontained herein

References

[1] D Porro P Branduardi M Sauer and D Mattanovich ldquoOldobstacles and new horizons formicrobial chemical productionrdquoCurrent Opinion in Biotechnology C vol 30 pp 101ndash106 2014

[2] P Jeandet YVasserot T Chastang andECourot ldquoEngineeringmicrobial cells for the biosynthesis of natural compounds ofpharmaceutical significancerdquo BioMed Research Internationalvol 2013 Article ID 780145 13 pages 2013

[3] A Kondo J Ishii K Y Hara T Hasunuma and F Mat-suda ldquoDevelopment of microbial cell factories for bio-refinerythrough synthetic bioengineeringrdquo Journal of Biotechnologyvol 163 no 2 pp 204ndash216 2013

[4] J H Shin H U Kim D I Kim and S Y Lee ldquoProduction ofbulk chemicals via novel metabolic pathways in microorgan-ismsrdquo Biotechnology Advances vol 31 pp 925ndash935 2013

[5] C M Immethun A G Hoynes-OrsquoConnor A Balassy andT S Moon ldquoMicrobial production of isoprenoids enabled bysynthetic biologyrdquo Frontiers in Microbiology vol 4 article 752013

[6] Y Chen and J Nielsen ldquo Advances in metabolic pathway andstrain engineering paving the way for sustainable productionof chemical building blocksrdquo Current Opinion in Biotechnologyvol 24 pp 965ndash972 2013

[7] J W Lee D Na J M Park S Choi and S Y Lee ldquoSystemsmetabolic engineering of microorganisms for natural and non-natural chemicalsrdquo Nature Chemical Biology vol 8 pp 536ndash546 2012

[8] G Stephanopoulos ldquoSynthetic biology andmetabolic engineer-ingrdquo ACS Synthetic Biology vol 1 pp 514ndash525 2012

[9] T-M Lo W S Teo H Ling B Chen A Kang and MW Chang ldquoMicrobial engineering strategies to improve cellviability for biochemical productionrdquo Biotechnology Advancesvol 31 pp 903ndash914 2013

12 BioMed Research International

[10] K M Esvelt and H H Wang ldquoGenome-scale engineering forsystems and synthetic biologyrdquo Molecular Systems Biology vol9 p 641 2013

[11] M K Tiwari R R K Singh I Kim and J-K Lee ldquoCompu-tational approaches for rational design of proteins with novelfunctionalitiesrdquo Computational and Structural BiotechnologyJournal vol 2 Article ID e201209002 2012

[12] M Cvijovic J Almquist J Hagmar et al ldquoBridging the gaps insystems biologyrdquoMolecular Genetics and Genomics vol 289 no5 pp 727ndash734 2014

[13] N Tomar and R K De ldquoComparing methods for metabolicnetwork analysis and an application to metabolic engineeringrdquoGene vol 521 no 1 pp 1ndash14 2013

[14] A Chakrabarti L Miskovic K C Soh and V HatzimanikatisldquoTowards kinetic modeling of genome-scale metabolic net-works without sacrificing stoichiometric thermodynamic andphysiological constraintsrdquo Biotechnology Journal vol 8 no 9pp 1043ndash1057 2013

[15] A F Villaverde and J R Banga ldquoReverse engineering andidentification in systems biology strategies perspectives andchallengesrdquo Journal of the Royal Society Interface vol 11 no 91Article ID 20130505 2014

[16] S Luke C Cioffi-Revilla L Panait K Sullivan and G BalanldquoMASON a multiagent simulation environmentrdquo Simulationvol 81 no 7 pp 517ndash527 2005

[17] R Conte and M Paolucci ldquoOn agent-based modeling andcomputational social sciencerdquo Frontiers in Psychology vol 5article 668 2014

[18] M Wooldridge ldquoAgent-based software engineeringrdquo IEE Pro-ceedings Software vol 144 no 1 pp 26ndash37 1997

[19] E Bonabeau ldquoAgent-based modeling Methods and techniquesfor simulating human systemsrdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 99 no3 pp 7280ndash7287 2002

[20] N Cannata F Corradini E Merelli and L Tesei ldquoAgent-basedmodels of cellular systemsrdquo Methods in Molecular Biology vol930 pp 399ndash426 2013

[21] G An Q Mi J Dutta-Moscato and Y Vodovotz ldquoAgent-basedmodels in translational systems biologyrdquoWiley InterdisciplinaryReviews Systems Biology and Medicine vol 1 no 2 pp 159ndash1712009

[22] J O Dada and P Mendes ldquoMulti-scale modelling and simula-tion in systems biologyrdquo Integrative Biology vol 3 pp 86ndash962011

[23] H Kaul and Y Ventikos ldquoInvestigating biocomplexity throughthe agent-based paradigmrdquo Briefings in Bioinformatics vol 442013

[24] M Holcombe S Adra M Bicak et al ldquoModelling complexbiological systems using an agent-based approachrdquo IntegrativeBiology vol 4 no 1 pp 53ndash64 2012

[25] D CWalker J Southgate GHill et al ldquoThe epitheliome agent-based modelling of the social behaviour of cellsrdquo BioSystemsvol 76 no 1ndash3 pp 89ndash100 2004

[26] M B Biggs and J A Papin ldquoNovel multiscale modeling toolapplied to Pseudomonas aeruginosa biofilm formationrdquo PLoSONE vol 8 no 10 Article ID e78011 2013

[27] S M Stiegelmeyer andM C Giddings ldquoAgent-based modelingof competence phenotype switching in Bacillus subtilisrdquo Theo-retical Biology and Medical Modelling vol 10 article 23 2013

[28] G An and S Kulkarni ldquoAn agent-based modeling frameworklinking inflammation and cancer using evolutionary principles

Description of a generative hierarchy for the hallmarks of cancerand developing a bridge betweenmechanism and epidemiolog-ical datardquoMathematical Biosciences 2014

[29] J Wang L Zhang C Jing et al ldquoMulti-scale agent-basedmodeling on melanoma and its related angiogenesis analysisrdquoTheoretical Biology and Medical Modelling vol 10 article 412013

[30] V Gopalakrishnan M Kim and G An ldquoUsing an agent-basedmodel to examine the role of dynamic bacterial virulence poten-tial in the pathogenesis of surgical site infectionrdquo Advances inWound Care vol 2 no 9 pp 510ndash526 2013

[31] A E Curtin and L Zhou ldquoAn agent-based model of theresponse to angioplasty and bare-metal stent deployment in anatherosclerotic blood vesselrdquo PLoS ONE vol 9 no 4 Article IDe94411 2014

[32] K Bettenbrock H Bai M Ederer et al ldquoChapter Twomdashtowards a systems level understanding of the oxygen responseof Escherichia colirdquo in Advances in Microbial Physiology vol 6pp 65ndash114 2014

[33] A Apte R Senger and S S Fong ldquoDesigning novel cellulasesystems through agent-based modeling and global sensitivityanalysisrdquo Bioengineered vol 5 no 4 pp 243ndash253 2014

[34] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 30 no 21 pp3101ndash3108 2014

[35] S Kang S Kahan and B Momeni ldquoSimulating microbial com-munity patterning using Biocellionrdquo in Methods in MolecularBiology vol 1151 pp 233ndash253 2014

[36] I Millington Game Physics Engine Development How to Builda Robust Commercial-Grade Physics Engine for Your Game CRCPress Boca Raton Fla USA 2010

[37] G Palmer Physics for Game Programmers Apress 2005[38] T Kalwarczyk M Tabaka and R Holyst ldquoBiologisticsmdash

diffusion coefficients for complete proteome of Escherichiacolirdquo Bioinformatics vol 28 no 22 pp 2971ndash2978 2012

[39] K A Johnson and R S Goody ldquoThe original Michaelisconstant translation of the 1913 Michaelis-Menten paperrdquoBiochemistry vol 50 no 39 pp 8264ndash8269 2011

[40] A Cornish-Bowden ldquoThe origins of enzyme kineticsrdquo FEBSLetters vol 587 no 17 pp 2725ndash2730 2013

[41] M Scheer A Grote A Chang et al ldquoBRENDA the enzymeinformation system in 2011rdquo Nucleic Acids Research vol 39 no1 pp D670ndashD676 2011

[42] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 130 no 21 pp3101ndash3108 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

12 BioMed Research International

[10] K M Esvelt and H H Wang ldquoGenome-scale engineering forsystems and synthetic biologyrdquo Molecular Systems Biology vol9 p 641 2013

[11] M K Tiwari R R K Singh I Kim and J-K Lee ldquoCompu-tational approaches for rational design of proteins with novelfunctionalitiesrdquo Computational and Structural BiotechnologyJournal vol 2 Article ID e201209002 2012

[12] M Cvijovic J Almquist J Hagmar et al ldquoBridging the gaps insystems biologyrdquoMolecular Genetics and Genomics vol 289 no5 pp 727ndash734 2014

[13] N Tomar and R K De ldquoComparing methods for metabolicnetwork analysis and an application to metabolic engineeringrdquoGene vol 521 no 1 pp 1ndash14 2013

[14] A Chakrabarti L Miskovic K C Soh and V HatzimanikatisldquoTowards kinetic modeling of genome-scale metabolic net-works without sacrificing stoichiometric thermodynamic andphysiological constraintsrdquo Biotechnology Journal vol 8 no 9pp 1043ndash1057 2013

[15] A F Villaverde and J R Banga ldquoReverse engineering andidentification in systems biology strategies perspectives andchallengesrdquo Journal of the Royal Society Interface vol 11 no 91Article ID 20130505 2014

[16] S Luke C Cioffi-Revilla L Panait K Sullivan and G BalanldquoMASON a multiagent simulation environmentrdquo Simulationvol 81 no 7 pp 517ndash527 2005

[17] R Conte and M Paolucci ldquoOn agent-based modeling andcomputational social sciencerdquo Frontiers in Psychology vol 5article 668 2014

[18] M Wooldridge ldquoAgent-based software engineeringrdquo IEE Pro-ceedings Software vol 144 no 1 pp 26ndash37 1997

[19] E Bonabeau ldquoAgent-based modeling Methods and techniquesfor simulating human systemsrdquo Proceedings of the NationalAcademy of Sciences of the United States of America vol 99 no3 pp 7280ndash7287 2002

[20] N Cannata F Corradini E Merelli and L Tesei ldquoAgent-basedmodels of cellular systemsrdquo Methods in Molecular Biology vol930 pp 399ndash426 2013

[21] G An Q Mi J Dutta-Moscato and Y Vodovotz ldquoAgent-basedmodels in translational systems biologyrdquoWiley InterdisciplinaryReviews Systems Biology and Medicine vol 1 no 2 pp 159ndash1712009

[22] J O Dada and P Mendes ldquoMulti-scale modelling and simula-tion in systems biologyrdquo Integrative Biology vol 3 pp 86ndash962011

[23] H Kaul and Y Ventikos ldquoInvestigating biocomplexity throughthe agent-based paradigmrdquo Briefings in Bioinformatics vol 442013

[24] M Holcombe S Adra M Bicak et al ldquoModelling complexbiological systems using an agent-based approachrdquo IntegrativeBiology vol 4 no 1 pp 53ndash64 2012

[25] D CWalker J Southgate GHill et al ldquoThe epitheliome agent-based modelling of the social behaviour of cellsrdquo BioSystemsvol 76 no 1ndash3 pp 89ndash100 2004

[26] M B Biggs and J A Papin ldquoNovel multiscale modeling toolapplied to Pseudomonas aeruginosa biofilm formationrdquo PLoSONE vol 8 no 10 Article ID e78011 2013

[27] S M Stiegelmeyer andM C Giddings ldquoAgent-based modelingof competence phenotype switching in Bacillus subtilisrdquo Theo-retical Biology and Medical Modelling vol 10 article 23 2013

[28] G An and S Kulkarni ldquoAn agent-based modeling frameworklinking inflammation and cancer using evolutionary principles

Description of a generative hierarchy for the hallmarks of cancerand developing a bridge betweenmechanism and epidemiolog-ical datardquoMathematical Biosciences 2014

[29] J Wang L Zhang C Jing et al ldquoMulti-scale agent-basedmodeling on melanoma and its related angiogenesis analysisrdquoTheoretical Biology and Medical Modelling vol 10 article 412013

[30] V Gopalakrishnan M Kim and G An ldquoUsing an agent-basedmodel to examine the role of dynamic bacterial virulence poten-tial in the pathogenesis of surgical site infectionrdquo Advances inWound Care vol 2 no 9 pp 510ndash526 2013

[31] A E Curtin and L Zhou ldquoAn agent-based model of theresponse to angioplasty and bare-metal stent deployment in anatherosclerotic blood vesselrdquo PLoS ONE vol 9 no 4 Article IDe94411 2014

[32] K Bettenbrock H Bai M Ederer et al ldquoChapter Twomdashtowards a systems level understanding of the oxygen responseof Escherichia colirdquo in Advances in Microbial Physiology vol 6pp 65ndash114 2014

[33] A Apte R Senger and S S Fong ldquoDesigning novel cellulasesystems through agent-based modeling and global sensitivityanalysisrdquo Bioengineered vol 5 no 4 pp 243ndash253 2014

[34] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 30 no 21 pp3101ndash3108 2014

[35] S Kang S Kahan and B Momeni ldquoSimulating microbial com-munity patterning using Biocellionrdquo in Methods in MolecularBiology vol 1151 pp 233ndash253 2014

[36] I Millington Game Physics Engine Development How to Builda Robust Commercial-Grade Physics Engine for Your Game CRCPress Boca Raton Fla USA 2010

[37] G Palmer Physics for Game Programmers Apress 2005[38] T Kalwarczyk M Tabaka and R Holyst ldquoBiologisticsmdash

diffusion coefficients for complete proteome of Escherichiacolirdquo Bioinformatics vol 28 no 22 pp 2971ndash2978 2012

[39] K A Johnson and R S Goody ldquoThe original Michaelisconstant translation of the 1913 Michaelis-Menten paperrdquoBiochemistry vol 50 no 39 pp 8264ndash8269 2011

[40] A Cornish-Bowden ldquoThe origins of enzyme kineticsrdquo FEBSLetters vol 587 no 17 pp 2725ndash2730 2013

[41] M Scheer A Grote A Chang et al ldquoBRENDA the enzymeinformation system in 2011rdquo Nucleic Acids Research vol 39 no1 pp D670ndashD676 2011

[42] S Kang S Kahan J McDermott N Flann and I ShmulevichldquoBiocellion accelerating computer simulation of multicellularbiological system modelsrdquo Bioinformatics vol 130 no 21 pp3101ndash3108 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Anatomy Research International

PeptidesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

Volume 2014

Zoology

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Molecular Biology International

GenomicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioinformaticsAdvances in

Marine BiologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Signal TransductionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

Evolutionary BiologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Biochemistry Research International

ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Genetics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Virolog y

Hindawi Publishing Corporationhttpwwwhindawicom

Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Enzyme Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Microbiology