Univerzita Karlova v Praze

Prırodovedecka fakulta

Katedra fyzikalnı a makromolekularnı chemie

Modelovanı chemickych vlastnostı nano- a biostruktur

Mgr. et Mgr. Jan Heyda

Ion-Protein InteractionsInterakce iontu s proteiny

Disertacnı prace

Ustav organicke chemie a biochemie, AV CR v.v.i.

Centrum biomolekul a komplexnıch molekulovych systemu

Skolitel: Prof. Pavel Jungwirth, DSc.

Praha 2011

The completion of my dissertation thesis would have not been possible without

the support of many people.

Firstly, I would like to express my deep thanks to all my colleagues who I have

had a chance to meet during my four years of doctoral studies. They have been

creating the friendly environment in which it is a pleasure for me to work and study.

Special thanks belong to my advisor, Pavel Jungwirth, who has introduced me kindly

into the world of computational mysteries and has offered invaluable assistance and

guidance.

Next, I thank my parents, my sister Jitka and my future mother-in-law for sup-

porting me throughout all my studies.

Lastly, I wish to express my deepest love and gratitude to Radka.

Prohlasenı:

Prohlasuji, ze jsem zaverecnou praci zpracoval samostatne a ze jsem uvedl vsechny

pouzite informacnı zdroje a literaturu. Tato prace ani jejı podstatna cast nebyla

predlozena k zıskanı jineho nebo stejneho akademickeho titulu.

V Praze, v cervenci 2011 Jan Heyda

Contents

List of Figures ii

List of Abbreviations iv

1 Introduction 1

2 Advanced Techniques in Modern Molecular Dynamics Simulations 7

2.1 Simulation Protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Analytical Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 Spatial distribution function . . . . . . . . . . . . . . . . . . . 10

2.2.2 Proximal distribution functions . . . . . . . . . . . . . . . . . 14

3 Amino Acid Proxies 16

3.1 Model of the peptide bond . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Getting larger, getting hydrophobic . . . . . . . . . . . . . . . . . . . 18

4 Single Amino Acids and Short Oligopeptides 22

4.1 Positively charged amino acids . . . . . . . . . . . . . . . . . . . . . . 23

4.2 Side-chain interactions in dipeptides . . . . . . . . . . . . . . . . . . . 23

4.3 Ammonium moieties in the context of amino acids . . . . . . . . . . . 28

4.4 Ion-specific effects on electrophoretic mobility . . . . . . . . . . . . . 31

4.5 Surface propensities of β-amyloid 1-16 fragment at varying pH . . . . 34

5 Peptides and Proteins 39

5.1 Ion specific effects on catalytic activity of HIV-1 protease . . . . . . . 39

5.2 LinB enzyme – an example of a dehalogenase . . . . . . . . . . . . . 40

5.3 Denaturating and stabilizing effects of molecular cations . . . . . . . 44

5.4 Denaturation of TrpCage miniprotein . . . . . . . . . . . . . . . . . . 45

6 Conclusion 49

CONTENTS ii

Bibliography 52

List of Attached Publications 64

Attached Publications 66

List of Figures

1.1 Schematic picture of environment around globular peptide . . . . . . 4

2.1 Construction of the spatially resolved distribution function . . . . . . 13

2.2 Example of surface decomposition . . . . . . . . . . . . . . . . . . . . 14

2.3 Proximal and radial distribution functions . . . . . . . . . . . . . . . 15

3.1 Functional groups occuring in amino acids . . . . . . . . . . . . . . . 17

3.2 N-methylacetamide in salt solutions . . . . . . . . . . . . . . . . . . . 18

3.3 Summary of alkylated ammonium cations . . . . . . . . . . . . . . . 20

4.1 Distribution of water molecules around histidine side chain . . . . . . 24

4.2 Guanidinium stacking vs. ammonium repulsion . . . . . . . . . . . . 25

4.3 Interaction between charged and neutral histidine side chains . . . . . 26

4.4 Effect of electrostatics and dispersion on conformational sampling of

diARG and diLYS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.5 Ammonium moieties . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.6 Ammonium moieties – local charge and local density . . . . . . . . . 30

4.7 Electrophoretic mobilities in Na2SO4 and NaCl for mLYS, tLYS, mARG,

tARG peptides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.8 Mobility of tARG as a function of molar fraction of GdmCl . . . . . . 34

4.9 Sampling of bulk and interfacial region during the simulation . . . . . 37

4.10 Surface propensities of individual amino acids . . . . . . . . . . . . . 38

5.1 Spatial distribution of cations around HIV-1 protease . . . . . . . . . 41

5.2 Affinity of alkali cations to surface of enzyme LinB . . . . . . . . . . 42

5.3 Spatial distribution of sodium cation around LinB enzyme . . . . . . 43

5.4 Structure, environment and global coordinates along the denaturation

process in urea solution . . . . . . . . . . . . . . . . . . . . . . . . . . 47

List of Abbreviations

Arg arginine amino acid

Asp aspartic amino acid

CD circular dichroism

CM center of mass

DSC differential scanning calorimetry

EWALD Ewald summation method for effective calculation of electrostatics

FES free energy surface

FF force field

GAFF generalized AMBER force field

Gdm guanidinium cation

Glu glutamic amino acid

Gly glycine amino acid

GTFE group transfer free energy

His histidine amino acid

HIV Human Immunodeficiency Virus

Lys lysine amino acid

MC Monte Carlo

MD molecular dynamics

MM molecular mechanics

NMA N-methylacetamide

NMR nuclear magnetic resonance

PBC periodic boundary conditions

PMEMD solver of Newtonian equations with effective implementation of EWALD

QM quantum mechanics

QM/MM combination of QM and MM methods

RDF radial distribution function

REMD replica exchange molecular dynamics

RESP restrained electrostatic potential

RMSD root mean square deviation

LIST OF FIGURES v

SANDER traditional solver of Newtonian equations of motion in AMBER

SAS(A) solvent accessible surface (area)

SHAKE method for effective constraining of bond lengths during dynamics

SHG second harmonic generation

TAA tetraalkylammonium

TBA tetrabutylammonium

TEA tetraethylammonium

TMA tetramethylammonium

TPA tetrapropylammonium

TPS transition path sampling

TrpCage TrpCage minipeptide (PDB code 1L2Y)

TrpZip TrpZip minipeptide (PDB code 1HRW)

VMD visualization molecular dynamics software

Title: Ion-Protein Interactions

Author: Mgr. et Mgr. Jan Heyda

Department: Physical and Macromoleculer Chemistry

Advisor: Prof. Pavel Jungwirth, DSc., IOCB AS CR, v.v.i.

Advisor’s e-mail address: pavel.jungwirth@uochb.cas.cz

Abstract: Conventional molecular dynamics simulations in combination with ad-

vanced methods of analyses were used to improve the understanding of the interac-

tion between ions and proteins in salt solutions. Thus systems of diverse complexity

and size were investigated, starting with simple (and molecular) salt solutions with

small fragments that mimic the various functional groups of amino acids such as

N-methylacetamide representing the peptide bond or alkylated ammonium cations.

Continuing with individual positively charged amino acids (arginine, histidine, ly-

sine) a strong binding interaction with small fluoride anion that is significantly weak-

ened for larger halides (Cl−, Br−, I−) was described. This observation was extended

by detecting the strong sensitivity of fluoride to charge distribution on ammonium,

lysine side chain, and the N-terminal of glycine while sensitivity of iodide was found

to be low. Later it was shown that the attractive side chain-side chain interactions

are significant for short positively charged peptide fragments in polyarginine and

dihistidine, while they are not present at all in case of polylysine.

Considering the qualitative difference in the origin of ion-specific interactions,

electrophoretic mobility measurements (for mono- and tetra- amino acids) were

employed in tandem with MD simulations. The ion-specific arginine-sulphate and

arginine-guanidinium interactions were proved, both pronounced as the specific de-

crease or increase in electrophoretic mobility in contrast to observations for lysine,

chloride anion, and sodium cation.

Cation-specific interaction was found, both experimentally and computationally,

to be responsible for specific affecting of the enzymatic activity of HIV-1 protease

and LinB enzyme from dehalogenase family. In both cases the general salting out

effect was experimentally observed (pronounced as the increase of the enzymatic ac-

tivity). Finally, the denaturant-specific unfolding pathway of TrpCage minipeptide

was identified by comparing the denaturation process in urea and guanidinium chlo-

ride solution. In all the studies the aim was to shed more light on complex behaviour

caused by ion-specific effects such as ordering in Hofmeister series, speeding up the

enzymatic activity, preferential interactions with functional groups or the osmolyte

specific denaturation pathways.

Keywords: molecular dynamics, proteins, denaturation, salts, osmolytes.

Nazev prace: Interakce iontu s proteiny

Autor: Mgr. et Mgr. Jan Heyda

Katedra: Fyzikalnı a makromolekularnı chemie

Vedoucı doktorske prace: Prof. Pavel Jungwirth, DSc., UOCHB AV CR, v.v.i.

E-mail vedoucıho: pavel.jungwirth@uochb.cas.cz

Abstrakt: V predkladane praci byly pouzity metody molekulove dynamiky v kom-

binaci s pokrocilymi technikami analyzy k zıskanı detailnıch informacı a pro hlubsı

pochopenı interakcı mezi ionty a proteiny v roztocıch. Proto byly zkoumany systemy

o ruznem stupni komplexity, pocınaje roztoky molekularnıch solı s drobnymi frag-

menty, podobajıcımi se funkcnım skupinam aminokyselin, jako napr. N-methylacetamid

reprezentujıcı peptidovou vazbu nebo alkylovane amonne kationty.

Dale se predmetem naseho studia staly jednotlive kladne nabite aminokyseliny,

u nichz byla popsana silna interakce s malym fluoridovym aniontem, jez je vsak pro

vetsı halogenidy (Cl−, Br−, I−) vyrazne zeslabena. Toto pozorovanı bylo prohloubeno

objevem vysoke citlivosti fluoridu na rozlozenı naboje na amonne skupine, bocnım

retezci lysinu a N-konci glycinu, zatımco jodid zde vykazoval pouze velice nızkou

citlivost. Nasledne bylo prokazano, ze u kratkych kladne nabitych peptidovych useku

v polyargininu a dihistidinu jsou preferovane pritazlive interakce mezi bocnımi retezci,

naopak v prıpade polylysinu prıtomny nejsou.

Na zaklade existence kvalitativnıho rozdılu v puvodu iontove specifickych inter-

akcı bylo spolecne s MD simulacemi provedeno merenı elektroforetickych pohyblivostı

(pro mono- a tetra aminokyseliny). Tımto zpusobem byly odhaleny iontove specificke

interakce mezi arigininem a sulfatem, a mezi argininem a guanidnym kationtem –

oba efekty se projevily jako charakteristicke zvysenı ci snızenı elektroforeticke po-

hyblivosti ve srovnanı s lysinem, chloridovym aniontem a sodıkovym kationtem.

Dale bylo experimentalne i vypocetne zjisteno, ze enzymaticka aktivita HIV-1

proteazy a enzymu LinB z rodiny dehalogenaz souvisı s kationtove specifickou inter-

akcı, ktera vysvetluje nektere zmeny v aktivite. V obou prıpadech byl experimentalne

pozorovan i efekt vysolovanı (v podobe zvysenı enzymaticke aktivity). V neposlednı

rade byly srovnany denaturacnı procesy probıhajıcı v roztocıch mocoviny a chloridu

guanidneho a identifikovany dva ruzne zpusoby rozbalenı minipeptidu TrpCage.

Ve vsech zmınenych studiıch bylo snahou vıce osvetlit komplexnı chovanı vyse

uvedenych systemu, a to zejmena objasnit iontove charakteristicke jevy, jako napr.

poradı v Hofmeisterove rade iontu, urychlenı enzymaticke aktivity, favorizovane in-

terakce nebo prubeh denaturace zavisly na danem osmolytu.

Klıcova slova: molekulova dynamika, proteiny, denaturace, soli, osmolyty.

Chapter 1

Introduction

Complex systems are arguably the most popular research targets in contemporary

computational science [1–7]. The number and quality of publications rise in hand

with increasing and persuading evidence of which effects are robust and which are

not. In simple systems – such as binary or ternary solutions of non-electrolytes –

it is becoming increasingly difficult to provide so needed novelty for high-quality

publications. Note, however, that recent achievements do to some extent disprove

this claim; for example Laage [8], who studied water reorientation and hydrogen-

bond cleavage, Sedlmeier [9], who critically compared water models with structure

factors from neutron scattering experiment, or Dzubiella [10], who introduced a new

generation of implicit solvents. In any case once the complex species, either polymer,

peptide or even a pair of large spheres, is introduced into the simple solution, the

number of study opportunities quickly increases [2, 11–14]. Not only the general

presence and evidence of an effect, but rather its absolute strength is important.

It is typically the detailed balance between competing interactions that makes this

research relevant for biological systems.

The new point of view gives rise in turn to questions about robustness and sensi-

tivity of previously observed effects, encourages development of new force-fields (FF),

and looks for alternative explanations and new concepts. We can state that in some

areas the computational machinery is established and operative. Examples such as:

explaining effects of thermodynamic stability of proteins [15–18] providing a con-

sistent picture for a hydrophobic-hydrophilic effect on absorption behaviour [19] or

gathering information about the quality of water models by comparison with neutron

diffraction experiments; appear more frequently and are provided with the highest

possible accuracy (often very close to numerically exact solutions) [9].

On the other hand, there are areas that were encountered on the way and are still

2

far from being completely understood. Good examples may be the dynamic aspects

of peptide folding [20–23] or the efficient methods for hopping over barriers on the

free energy surfaces (FES) that would enable us to explore lengthy bio-relevant

processes on diverse timescales [24]. Here we contributed to the understanding of

peptide dynamics, focusing on TrpCage minipeptide when exposed to denaturating

conditions. A brief summary is given in Part 5.4 and complete results are in our

publication [25].

These exhaustive calculations reveal apparent drawbacks, such as significantly

stronger force-field dependence than previously assumed. This situation takes place

more and more often, as microsecond timescale simulations and therefore almost

complete sampling becomes increasingly available [7,15,18,26,27]. The positive out-

come is understanding of the limitations of molecular dynamics (MD) calculations

of complex systems.

Inevitably, from time to time an apparent inconsistency between two diverse

approaches appears, either in connection with two different points of view or better

framing of validity limits for the conflicting theories.

Tanford’s model of transfer free energy is a nice illustration of such a contro-

versy [28–32]. In a nutshell, it has been assumed that the stability of a protein,

for instance in its native buffered solution compared to solution of either stabiliz-

ing or destabilizing osmolyte, can be to a large extent estimated based on the so

called group transfer free energies (GTFE) of individual amino acids side chains.

The thermodynamic cycle is described in the scheme below.

Naqueous

∆ G◦unfolding, H2O−−−−−−−−−−→ Uaqueous

∆ G◦transfer, native

y y∆ G◦transfer, unfolded

N1M osmolyte −−−−−−−−−−−−−−→∆ G◦unfolding, 1M osmolyte

U1M osmolyte

The simplest amino acid (glycine that lacks a side chain) was proposed to be the

ideal reference (∆Gapparenttr, Gly = 0) [28]. The first observation was quickly supported by

several experimental measurements and the key contributions such as the GTFE of

amino acids and the peptide bond were extracted from the results [33,34].

∆G◦tr, i = RT ln

ai, water

ai, urea

= RT lnsi, water

si, urea

+ RT lnγi, water

γi, urea

(1.1)

where ai, water/urea is the activity of amino acid i in water or urea solution, and

si, water/urea, γi, water/urea are the corresponding solubility and activity coefficient. The

3

∆G◦tr, i stays for the thermodynamic transfer free energy. Neglecting the second term

results in apparent ∆Gapptr, i

∆Gapptr, i = RT ln

si, water

si, urea

(1.2)

Subtracting glycine contribution, ∆G◦tr, Gly, from Eq. 1.1 results in group (side

chain) transfer free energy (GTFE◦tr, j)

GTFE◦, ?, apptr, i = RT

[ln

si, water

si, urea

+ lnγi, water

γi, urea

− lnsGly, water

sGly, urea

+ lnγGly, water

γGly, urea

](1.3)

where we distinguish three types of GTFE: 1) apparent (GTFEapptr, j) when only

the first and the third terms are available, 2) referenced to the glycine standard

state (GTFE?tr, j) when also the fourth term is accessible, 3) thermodynamically

exact (GTFE◦tr, j) when all four terms are known.

However, it became evident that predictions based on this ‘amino acid dictionary’

were not in good agreement with the exactly measured transfer free energies of tested

proteins. As was realized later, the limitations of the Tanford’s model were not mainly

due to the assumed separability into contributions of individual amino acids (being

obviously the first suspect), but much more due to the lack of knowledge of protein

structures; the native, the expanded, and the ensemble of denatured states. Therefore

the poor quality of information such as solvent accessible surface areas (SASA) of the

porous structure (random coil in good solvent) or internally dry structure (a compact

denatured state) resulted in large errors that essentially disfavour Tanford’s model

when compared with much simpler denaturant-binding and extrapolation models

[35,36].

The key experimental value, describing a protein in osmolyte solution, became the

so called m-value, which is the change in free energy related to transfer of protein from

water to 1M osmolyte solution. Experimentally, the transfer free energy is measured

for a series of concentration and the m-value is equal to the limiting slope at zero

concentration. In this way Tanford’s model can predict the m-value based only on

the protein composition and the structure in water and 1M osmolyte.

The extensive work of Schellman [37–39] should be acknowledged here, as it

has brought a lot of thermodynamic insight into this field. The approach based on

the calculation of the so called preferential binding, schematically drawn in Figure

1.1, can be seen as the next generation of methods, however, the computational

and experimental requirements limit its wider use. The equation for evaluation of a

preferential binding coefficient is provided in 1.4.

4

Figure 1.1. Competition of water (blue spheres) and cosolvent (yellow ellipses)

molecules for the vicinity of the protein (a large gray sphere). The preferential binding

of cosolvent (excess of cosolvent, Γ > 0 – the left figure), and preferential hydration

(depletion of cosolvent, Γ < 0 – the right figure).

Γ =

⟨N local

cosolvent −N bulk

cosolvent

N bulksolvent

N localsolvent

⟩(1.4)

where the 〈·〉 represents the ensemble average.

A breakthrough appeared again in 2007, when Auton, Holthauzen and Bolen [40]

redid the analysis of the original experimental data, taking into account the ther-

modynamic reference state of glycine [41] ∆G0tr, Gly = 0 instead of the apparent one

as mentioned in Equation 1.3. This brought a completely new insight into interpre-

tation of protein denaturation and reestablished the validity of the transfer model.

The outcome can be summarized in two main points:

1. The protein backbone contributes to newly exposed SASA only by 25%, while

side chains contribute by 75%.

2. The backbone contributes dominantly to the transfer free energy of protein,

while the contribution of side chains is only modest.

Soon before, Street et al. [31] noticed the strong correlation between the m-value

and fractional polar surface of osmolyte. When combined with the dominant role

of protein backbone for denaturation, they proposed the so called osmolyte induced

denaturation model.

Therefore the key interaction is the one with the peptide bond. This would obvi-

ously explain the underlying similarity of all proteins, as the average SAS is roughly

in 40% created by the exposed peptide bonds. The striking statistically supported

5

(by scans over protein databases) consistency of this observation motivated both

experimental [42–44] and theoretical [4,32,45–48] communities to provide a detailed

atomistic explanation of this general effect.

To this subject, we contributed by a detailed study of N-methylacetamide (NMA)

[55], which is widely used as a model of the peptide bond [49, 50] being exposed to

alkali-halide salt solutions at moderate concentrations. The question was, whether

the direct binding of cations or anions is responsible for the stabilizing effect of cations

and destabilizing effect of anions, i.e., whether or not the ions stabilize/destabilize

peptides in the same manner as osmolytes do. The main outcome, i.e., the difference

between cations and anions observed together with the robust difference between

anions (traditionally assumed as potential destabilizers) and destabilizing osmolytes

is summarized in Part 3.1.

Even though we would like to deal with problems in their full complexity, there

is usually no other way to proceed further than to use approximations. Therefore

the reductionist approach is often used with advantage and a system is divided into

pieces using the best accessible knowledge, or by an approach that has shown to be

recently the most successful and promising.

The usual approach towards the understanding of ion-protein interactions would

start with ion-ion, ion-amino acid proxy, ion-amino acid, and ion-peptide complexes

so as to naturally reach the ion-protein system. Even though from the theoretical

point of view this approach is the best one, as the first two steps capture most of

the essence, the practical aspects force us to start the work in parallel.

We started with ion-protein studies [25, 51] from the very beginning, having in

mind that these systems with their wide range of interactions are a challenging task.

The effects of sodium and potassium cations were investigated, and following the

protocol of Vrbka et al. [2], we quantified the sodium preference when compared to

potassium. However, the simulation data provided us with much more. The complex-

ity encountered was another goal of these studies. In this way we faced the upcoming

obstacles and learned which effects need to be carefully treated.

While the ion-protein projects took long time, putting in front of us new obstacles

and challenges, both of the methodological and fundamental origin, it supplied us

continuously by new phenomena and effects that were itself of an interest and many

smaller projects consequently arose.

The following text will be organized so that it follows the complexity of systems

under study, therefore not necessarily the time-line.

1. Ion-proxy interaction, where proxy stays for a functional group of a relevant

6

biomolecule. Examples are peptide bond models or models of amino acid side

chains, or even molecules of a partially hydrophobic partially hydrophilic char-

acter.

2. Ion-amino acid interaction, with dominant, but not exclusive, focus on posi-

tively charged amino acids.

3. Ion-peptide and ion-protein interaction. This part shows the diversity that is

a genuine property of complex systems.

Chapter 2

Advanced Techniques in Modern

Molecular Dynamics Simulations

The increase in power and accessibility of computational resources has led to an

employment of a whole set of simulation methods that were not affordable a decade

ago. The main reason was that an accurate evaluation of key properties could not

be attained within available resources and therefore there was a lack of motivation

for further development of principally attractive but practically limited methods.

The situation has changed (mainly due to massive parallelization) and, e.g., the

family of REMD (Replica Exchange Molecular Dynamics) techniques were developed

[52–54]. These methods are based on parallel (but semi-independent) evolution of the

same system at wide range of temperatures (typically 270K-450K), where the system

is allowed to jump from one temperature to another in a Monte Carlo (MC) fashion.

The presence of high temperature replicas guarantees that even high potential energy

barriers can be overcome. That is crucial for equilibrium sampling of the free energy

landscape and therefore for the evaluation of underlying thermodynamics. The price

for using REMD is that the ability to describe time evolution of the system is lost,

let alone larger computational resources which are needed.

Even though in certain cases such special methods are advantageous, I focused

on extensive direct classical MD calculations, since my projects were quite suited for

this technique. Also, in some of my studies the time-evolution was an important as-

pect [55], or even a key factor if the effect was dynamic [25]. The ensembles employed

were also conventional. Mainly, the canonical ensemble either at constant pressure

and constant temperature (NpT), or in some cases at constant volume and constant

temperature (NVT), served best for our purpose. In cases where the explicit tem-

perature dependence or system size effects were investigated, a corresponding set of

2.1 Simulation Protocols 8

systems was calculated.

The classical molecular dynamics ensembles and protocols used were introduced

above, however, important technical details remain to be determined. The standard

protocol used in our simulations can be described as follows:

1. Preparation of the system – the mixture of salt(s) with water and with peptide

is created and to some extent randomized. Periodic boundary conditions (PBC)

are applied in most cases as the modelled system should mimic (through the

infinite number of periodic images) either bulk or interface.

2. The system is quickly energy-minimized to avoid close contacts and other arte-

facts from preparation.

3. Velocity generations (from Maxwell-Boltzmann distribution) follows by gradual

heating towards the designed temperature, usually run at constant volume.

4. In case of constant pressure calculations (NpT ensemble) a short compression

is performed, which leads to desired density.

5. Equilibration run – typically of 1 ns length, follows.

6. Finally, the production run with length that depends on the timescale of the

process, typically 10 ns – 1µs, is performed.

The integration step was usually 1 fs or, in cases of large proteins, 2 fs, with all bonds

constrained by the SHAKE algorithm.

One rather important issue should be stressed here. Although in studies of salt

or other (non-)electrolyte solutions the initial conditions are of little importance (if

starting from a roughly homogeneous system), the situation changes dramatically for

peptides and proteins in particular. Here, the initial structure has a good justification

(typically a crystal or nuclear magnetic resonance (NMR) structure), so it should

not be perturbed during the preparation steps. Therefore it is advisable to keep

initially the protein restrained, which enables the independent relaxation of water

and protein. A golden rule is to do everything more slowly and with more care,

otherwise one can simulate for many weeks “bio-irrelevant” structures.

2.1 Simulation Protocols

Our calculations were performed with the AMBER package [56], the polariz-

able calculations were done using the program SANDER (with induced dipoles con-

2.1 Simulation Protocols 9

verged in every timestep), and nonpolarizable simulations were performed using the

PMEMD code.

Both programs can be viewed as implementations of the Verlet propagator, i.e.,

solvers of Newtonian equations of motion. The systems were constructed in the LEAP

module, and basic analyses were done by the PTRAJ toolbox. Both of these are freely

available as a part of AMBERTOOLS [56]. More advanced analyses were coded as

Python scripts. The two most widely used quantities – the spatial distribution func-

tion and the proximal distribution function are introduced in the following section.

The parametrization for amino acids is taken from the AMBER force-field parm99

[57], in some cases from its updated versions parm03 [58] or parm99SB [56]. Less

commonly the GAFF (generalized Amber force-field) [59] library was used together

with partial charges (evaluated by RESP, i.e., the restrained electrostatic poten-

tial) that were calculated following the recommended procedure using the quantum

chemistry package Gaussian09 [60]. Widely used parametrizations for cations and

anions [61–65] were applied. In most of our projects, sensitivity to parametrization

was tested by employing different force-fields.

Berendsen weak temperature and pressure coupling scheme [66] was employed,

even though it is known that it does not strictly generate a canonical ensemble

[67, 68]. However, the robustness and the wide spread in community still more than

overcome this marginal limitation. The particle mesh EWALD [69] is used to treat

the electrostatics beyond the cutoff of 9 –12 A.

Although we employ the molecular dynamics (therefore obtaining the time evolu-

tion explicitly), it is still mainly a method for sampling of independent configurations.

In recent years two below described approaches were relatively often used, usually

in connection with complex systems [70]. The complexity of current force-fields pre-

clude the use of these approaches for quantitative results, nevertheless, their relative

simplicity and easy applicability is valuable for qualitative trends.

1. The force-field of a given system is typically complex, however, if we suspect

any intermolecular term (electrostatics, dispersion) of playing a dominant role,

we can tune this interaction, or even switch it off completely. This obviously

influences other interactions as well, but in the first approximation the direct

impact should be the major one. Especially in comparative studies this may

be a useful tool. This method can directly probe, for instance, the effect of

dispersive interaction or the distribution of charges inside the molecule.

2. Gas phase (or implicit solvent) simulations of a single amino acid or peptides

can provide the complete ensemble of conformations. This can be used in com-

2.2 Analytical Tools 10

bination with switching on/off terms (electrostatics, dispersion) of potential

energy. Apparently the second method is more invasive, but on the other hand

it only aims to produce the conformational ensemble, and for that purpose it

may still be suitable.

2.2 Analytical Tools

Already at the point of project planning one has to have in mind the goal of

the computation. There can be very different requirements on both the size of the

system and the length of the time propagation. Basic properties, especially those of

a local character and of a low dimensionality, converge quickly (surprisingly even for

a small system size). A typical example is the short-range structure of the radial

distribution function (RDF). Properties which are predominantly dictated by the

solvent molecules sampling benefit from their huge amount and consequently a rapid

improvement of statistics.

In contrast, there are rare events in complex biorelevant systems (with either

energetic or entropic bottlenecks [71]) or simulations that aim for excess properties

[72]. In this case, the long tails of the distribution functions have to be well converged.

An example is the activity derivative (directly related to excess chemical potential)

or the excess number of ions at the interface (related to the derivative of surface

tension with respect to the solute activity).

2.2.1 Spatial distribution function

The power of present-day computers allows to collect large amounts of data.

RDFs, which are directly connected to the excess free energy (F (r) = −kT ln g(r),

with F (r) = 0 for r → ∞), are of primary interest due to their descriptive nature.

Nevertheless, we have to keep in mind that the spherical symmetry was implicitly

assumed and employed. The applicability of RDFs to more complex species (typ-

ically characterized by several sites or by the center of mass (CM) only) is thus

questionable.

The straightforward derivation [73] of the RDF is performed below. We started

from the so called N-particle probability (with norm equal to unity), PN(r1, r2, . . . rN ),

which is directly related through the Boltzmann distribution to the potential energy

of the system U(r1, r2, . . . , rN ) via

2.2 Analytical Tools 11

PN(r1, r2, . . . rN ) =1

ZN

e

−U(r1, r2, . . . , rN )

kT

ZN =

∫V N

e

−U(r1, r2, . . . , rN )

kT dr1dr2 . . . drN

where ri are position vectors, k is the Boltzmann constant, T is the absolute

temperature, and ZN is a normalization constant (also called configuration integral).

The RDF is now obtained in four steps – 2.1 – 2.4.

n2(r1, r2) ≡N !

(N − 2)!P2(r1, r2) = N(N − 1)P2(r1, r2) (2.1)

= N(N − 1)

∫V N−2

PN(r1, r2, . . . , rN )dr3dr4 . . . drN

where we introduced n2(r1, r2), the two particle density (norm equal to N(N−1)). In

homogeneous systems not the positions of two particles, but only the relative vector,

r = r1 − r2, is important, therefore two particle density n2(r1, r2) simplifies to

n2(r1 − r2, r2), from which r2 can be integrated out. In many cases it is convenient

to introduce the pair distribution function g(r) (later called spatial distribution

function).

n2(r1 − r2) =1

N

∫V

n2(r1 − r2, r2)dr2 (2.2)

g(r) =n2(r)

ρbulk(2.3)

In case of spherical particles not the relative position, but only the relative distance

is important, and the introduction of spherical coordinates, as done in Eq. 2.4, leads

to the definition of the RDF, g(r)

g(r) =1

4πr2

∫ 2π

0

∫ π

0

g(r, ϕ, θ) r2 dϕ dθ (2.4)

For this reason I have developed a code for calculation of the three dimensional

spatial distribution function g(r) that is closely related to more conventional g(r)

(Equation 2.4). If the function is homogeneous in space, it is difficult to visualize its

values (as it is hard to look through a filled cube). Luckily the spatial distribution

function typically exhibits even sharper peaks than RDF, and thus enables us to

draw probability clouds for chosen iso-levels.

2.2 Analytical Tools 12

The iso-level is equivalent to the iso-contour in the 2D situation. The spatial

distribution functions can be easily plotted in graphical software for MD, such as

VMD [74]. At this stage, one can, by varying iso-levels, monitor the regions of dif-

ferent probability, locate maxima, minima and barriers between them.

The spatial distribution is constructed in the process that is displayed in Figure

2.1. First, a reference frame (i.e., a position and orientation of the central molecule) is

defined (left). In the second step, all equivalent molecules are aligned to the reference

one (middle) and the whole system is, thus, translated and rotated. Already at this

point the preferred and avoided locations are visible. The last step is the projection of

coordinates of mapped atoms to a three dimensional grid together with normalization

to the bulk density (right).

Clearly, the spatial distribution function is superior in information content to

the RDF. In case of complex systems the large amount of closely located interaction

sites gives rise to a large number of correlations between neighbouring points on the

g(r) curve, and it leads to large correlations between g(r) around neighbouring sites.

Even though this is not a problem from a statistical-mechanical point of view, it

introduces difficulties when interpretation of g(r) in terms of structures and sites is

carried out.

Although it may seem that the use of spatially resolved distribution function is

restricted only to rigid molecules, we have shown that it can also shed more light

on flexible structures, such as preferred side-chain conformations of di- and poly-

peptides, on protein folding, or even on the affinity of cations to the surface of

HIV-1 protease [51, 75] or LinB enzyme of dehalogenase family [76], i.e., systems

with hundreds of residues. This is possible only due to the fact that we do not

insist on sampling around a single structure (for that information one would have to

run a restrained MD simulation), but we allow the system to span a basin of close

conformations.

In cases when the system passes through millions of conformations, still clus-

tering techniques can provide the so called centroids. Such conformations are quite

distinguishable from each other and at the same time they can cover majority of all

appeared structures. With these centroids, as a set of reference structures, we can

reasonably well sample the spatial distribution function by averaging over structures

that are located in the basin of these references. In this way, we have efficiently coarse

grained the information, while still preserving access to most of the details.

2.2 Analytical Tools 13

Figure 2.1. Construction of the spatially resolved distribution function, for a guani-

dinium (cyan dots) chloride (orange dots) solution, can be seen in three steps. In the

first step (left), the central molecule (blue) is aligned (that means translated and

rotated) to a defined reference frame (red molecule) with a fixed position and ori-

entation. In the second step (middle) all equivalent molecules from all realizations

of the system are aligned, together with the translation and rotation of the rest of

the system (regions with higher probability appear). In the last step (right), a three

dimensional grid is employed resulting in local density, which after normalization to

the bulk value provides the spatially resolved distribution function.

2.2 Analytical Tools 14

Figure 2.2. Whole spatial neighbourhood is prescribed to parts of a molecule based

on proximity criteria [77]. The small rigid organic molecule NMA that contains a

carbonyl group (red), an amide group (blue) and methyl groups (gray) is shown on

left, and TrpCage minipeptide in an unfolded conformation on right, showing the

2 A(top), and 4 A(bottom) proximity of backbone (black) and side chains (yellow).

2.2.2 Proximal distribution functions

In the connection with spatial distribution function, it is often useful to define

the so called proximal distribution function [77], where a set of atoms is taken as a

center and the distance to the freely mobile molecule is calculated as the shortest

one. In some cases we may aim to completely divide the whole complex molecule in

such sets.

An example is given in Figure 2.2 for a simple molecule, NMA, which is de-

composed into polar and ‘hydrophobic’ pieces, and for TrpCage minipeptide in the

unfolded structure which was divided into the backbone and side-chain contribution.

Then the ‘uncorrelated’ proximal distribution functions are obtained such that

the closest distance between a mobile ion and every set is measured and the mobile

ion falls into the distribution function of the closest set only as it is shown on the left

in Figure 2.3. The ‘correlated’ ones are calculated by employing the closest distance

2.2 Analytical Tools 15

Figure 2.3. Illustration of three basic distribution functions, described in an exam-

ple of a molecule with two sites (red and black) and two types of a mobile ion (cyan

and yellow). In case of the uncorrelated proximal distribution function only the clos-

est distance to the closest set is used (left). In the correlated proximal distribution

function, only the shortest distance to every set is used (middle), while in case of the

standard RDF, all ion-site distances are used (right).

for every set as shown in the middle of Figure 2.3. The standard radial distribution

function is shown for comparison (right).

Probably the biggest advantage of proximal distribution functions is the access

to excess coordination numbers which are directly related to preferential binding

parameters, as described in Eq. 1.4, and a family of activity derivatives, all of them

directly connected to excess chemical potentials [39, 47,48,72].

Chapter 3

Amino Acid Proxies

If the aim is to understand the complex behaviour of a protein that is full of

complicated groups and motifs, it is advantageous to start with the building blocks

– amino acids. One can push this approach even further and focuses at first on the

functional groups that may be essential for the subsequent understanding of the

corresponding amino acids. Those systems are described in more detail in the next

chapter.

The crudest approximation is to assign all the relevancy to the functional groups,

shown in Figure 3.1, and neglect everything else. This leads to study of charged

groups (carboxyl, ammonium, imidazolium, guanidinium), polar groups (alcohols,

thiols, carboxamide), and also the peptide bond.

This should evoke exactly the approach of Tanford that was described in the intro-

duction. Recently Horinek et al. performed a calculation directly providing transfer

free energies for transfer from pure water to urea solutions, from all atom MD simu-

lations [48]. The results were directly and critically compared with the experimental

values. In contrast to the experimental measurements, their analysis of simulation

data allows to divide the total effect into two direct and one indirect contributions:

1. Direct binding to polar parts of the protein surface

2. Direct binding to nonpolar parts of the protein surface

3. Indirect effect mediated by modifications of the bulk water properties

However, even though the simulations were performed with great care and all

available knowledge about advantages and disadvantages of urea and amino acid

force-fields, the results showed that the total effect of urea can be recovered well

only due to cancellation of errors. Such a result is without doubt more disturbing

3.1 Model of the peptide bond 17

Figure 3.1. The functional groups that are supposed to be crucial for local inter-

action of salts and solvent with proteins and peptides. A charged carboxyl group of

aspartate, glutamate and C-terminal (A), ammonium moiety of lysine or N-terminal

(B), guanidinium moiety of arginine (C), imidazolium moiety of histidine (D), alco-

hols and thiols (E), carboxamide group of asparagine and glutamine (E), and the

peptide bond (H).

than promising, demonstrating that the increasing complexity of tasks approached by

MD puts more and more requirements on force-field quality. It is no longer sufficient

that the water model behaves appropriately. Today’s needs go much further and ask

for more general transferability and robustness across various complex systems.

3.1 Model of the peptide bond

In our case, the ultimate goal is to understand the interaction between ions and

proteins. As a first step, we investigated how the sodium/potassium halides solutions

affect N-methylacetamide – i.e., the proxy of the peptide bond. This model system is

worth a deeper exploration mainly due to the recent results of Bolen and Rose [30,31].

Owing to the fact that NMA contains a polar part (the peptide bond) and also

hydrophobic pieces (methyl groups) we conducted also polarizable simulations [55].

Simulations were analyzed not only in terms of spatial and radial distribution

functions, but also the distribution of residence times was estimated together with

mean times of interaction that were calculated based on the first order kinetic as-

sumptions. The spatial distribution functions in Figure 3.2 clearly show that the

polar groups are the most prominent sites for both cations (carbonyl oxygen) and

anions (amide hydrogen). However, since the accessible volume is rather limited,

the corresponding radial distribution functions carry this preference only for cations

(height of the peak is roughly 4 for potassium and 6 for sodium), while being around

unity for anions. The second very important observation is the smeared, but in total

strong and robust, preference of softer anions for the methyl groups (peak ranging

3.2 Getting larger, getting hydrophobic 18

Figure 3.2. Spatial distribution (left) of iodide (top, in violet) and chloride (bottom,

in gold) anion and sodium cation (green) around N-methylacetamide complemented

by partial contributions (of carbonyl (red), amide (blue), and methyl groups (black))

of the proximal distribution function (right).

from ∼1 for chloride to ∼2 for iodide). This fact leads to an exclusion of fluoride,

neutral behaviour of chloride, and to attraction of bromide and iodide to NMA.

3.2 Getting larger, getting hydrophobic

In the previous part we learned how specific with respect to interaction with ions

the peptide bond is. Another case study we performed was that of ammonium and

tetraalkyl ammonium species, the former being the functional group model for the

side chain of lysine. Based on Collins law of matching water affinities [78–81], the

ammonium is already a large cation, therefore it should prefer iodide over fluoride

or chloride. Here we found that it is not the size of the molecule, but a possibility

and accessibility of hydrogen bonding together with the charge density that dictates

which anion binds more strongly.

Using the spatial distribution functions, it was found that fluoride binds very

strongly and locally to acidic hydrogens of ammonium, trimethylammonium, and

even tripropylammonium, however, the larger burial of acidic hydrogen lowers the

3.2 Getting larger, getting hydrophobic 19

strength of binding. As halide anions get bigger, the presence of acidic hydrogen is

of a lesser importance. Iodide as the largest anion tends to prefer a flatter and larger

region of alkyl groups.

This can be partially explained if we realize that the anions compete with water

(water oxygen) for the surface of positively charged alkylated-ammonium. With a

certain size of anion it is more favourable that the hydrogen bond to the positively

charged hydrogen of alkyl-ammonium is donated by water molecule, while the larger

halide occupies other sites on the surface. In Figure 3.3 these trends are captured.

While the hydrogen accessibility and degree of anion desolvation is crucial for fluo-

ride, for iodide it is the competition with water for direct binding to hydrogen and its

low charge density that drives it to the charge hidden/buried under the ‘hydrophobic’

alkyl chains.

The MD results have been in detail described in our article [92], and for that

reason I present there only the trend in preference for small halides – ammonium,

trimethyl-ammonium, tripropyl-ammonium, and tetrapropyl-ammonium – and com-

pare the extremes – fluoride and iodide vs. water as the neutral species that compete

with anions.

To further rationalize our observations, we calculated the excess chemical poten-

tials, µex, based on Widom [82, 83] particle insertion technique (Equation 3.1) that

was evaluated by a MC calculation within the Faunus software framework [84]. The

excess chemical potential is equivalent (related via 3.2) to the mean activity coeffi-

cient, γ± – the property which was measured for tetraalkyl ammonium chlorides and

iodides [85,86].

β µex = − ln 〈exp [−β∆U ]〉 (3.1)

γ± = exp (βµex/2) (3.2)

where the 〈·〉 represents the ensemble average.

The effective potentials that need to be supplied for the MC calculations – cation-

cation, cation-anion, and anion-anion – were extracted from RDFs (related to po-

tentials of mean force) from all atom MD simulations according to Equation 3.3. In

this way the effective potential captures the short range specificity (ion-pairing) and

the long range part is an unspecific Debye-Huckel potential. This technique is well

known [87–89], but is not as widely used as one might expect. The reason is the sig-

nificant sensitivity to the accuracy (convergence of long tails) and quality (properly

described populations and positions of ion-pair, solvent shared minima, etc.) of the

RDF that should be ideally obtained from simulations at low concentrations.

3.2 Getting larger, getting hydrophobic 20

Figure 3.3. Spatial distribution of fluoride anion (left, coloured black), water oxygen

(middle, red), and iodide anion (right, violet) around ammonium, trimethylammo-

nium, tripropylammonium, and tetrapropylammonium cations. Note the sensitivity

of fluoride to the presence and exposure of acidic hydrogen(s).

3.2 Getting larger, getting hydrophobic 21

β w(r) = − ln g(r) + [1 − exp (−κr)] lBz1z2/r (3.3)

The calculated excess chemical potentials are in accordance almost quantita-

tively with experimental data. The last test of validity was based on the calculation

of apparent association constants K?A which are defined in Equation 3.4. The results

were compared with dielectric relaxation spectroscopy measurements [90,91]. Alter-

natively Equation 3.5 provides the more rigorous derivation based on Kirkwood-Buff

integral that is, however, more difficult to converge.

K?A =

V · [TAAX]

[TAA+] [X−](3.4)

KA =

∫ ∞

contact

(g(r) − 1) 4πr2dr (3.5)

The definition of an ion-pair is particularly difficult in the experiment, which is

documented by the fact that various techniques provide slightly different values. On

the other hand, in the analysis of MD trajectory the separation distances or other

criteria of contact must be defined. Obviously the unique definition is missing here

as well. The set of cation-anion distances used for tetraalkyl ammonium halides can

be found in our article [92].

Chapter 4

Single Amino Acids and Short

Oligopeptides

At a certain point, there is nothing substantial left that can be extracted from

the simple systems. Of course the small system can always be studied further to

understand in every detail. But one has to keep in mind the original goal of this

project – the real protein, and for this purpose everything crucial has been done on

a small system.

We focused almost exclusively on the effect of anions, halide anions in particular.

We were primarily interested in positively charged amino acids [93], because this topic

was complementary to interaction of Na+/K+ with carboxyl and carbonyl moieties

at the protein surfaces or model polypeptides [2]. Next, we moved to dipeptides (in

some cases also decapeptides) in several studies of positively charged amino acids,

where the side chain-side chain interactions were investigated thoroughly.

The study of the ammonium moiety that occurs in various functionalities in

proteins found this moiety to be highly specific in the sense of interaction with

fluoride vs. iodide anions. This establishes a link to ammonium salts studied in the

previous chapter. The aim was to perform calculations on systems containing fluoride

or iodide together with ammonium ion or ammonium moiety, which can be treated by

neutron scattering. Direct measurements of ammonium floride solutions are hardly

feasible due to release of hydrofluoric acid that damages the cuvette.

The lysine amino acid may be the next experimental target, but the large size

would complicate the measured structure factor. This is the reason why the sig-

nificantly smaller and simpler glycine amino acid was chosen to be experimentally

investigated. At ambient conditions glycine is present in the zwitterionic form, so

the N-terminal itself is the ammonium moiety.

4.1 Positively charged amino acids 23

4.1 Positively charged amino acids

Due to the fact that this part of the story was already mentioned in my master

thesis I would like to only briefly summarize the major results. The ion-specific effects

were proposed for egg white protein at the end of 19th century [94, 95]. Following

the successful approach for cations, which were shown to be attracted dominantly

by negatively charged aspartate and glutamate on protein surface [2, 51, 96–98], we

focused on anions interacting with positively charged amino acids.

Using both polarizable and nonpolarizable simulations we observed anion-specific

binding to positively charged groups of arginine, histidine, and lysine. Fluoride ex-

hibits the strongest and the most spatially localized interaction, while binding of

larger anions is weaker, but accompanied with more smeared spatial preference.

Next to the charged moiety anions always followed the order in 4.1, together with

the fact that all anions preferred charged moieties in the order 4.2.

Positively charged moiety: F− > Cl− > Br− > I− (4.1)

X−: guanidinium > imidazolium > ammonium (4.2)

The results are summarized in our publication [93] in terms of spatial distribution

functions (i.e., the most detailed information), distribution functions (that smear out

the angle-resolution) and analysis of residence times in the vicinity of amino acid.

An example of the approach for information concentration is given for water around

side chain of histidine in Figure 4.1. In this way the binding strength, characterized

by a single number, is extended to the distribution function (providing the value for

any given distance) and even with the spatial resolution.

4.2 Side-chain interactions in dipeptides

The Tanford’s model [28] assumes additivity and the Bolen’s approach invokes ef-

fective additivity with residues exposed to solvent in a native and denatured/unfolded

state [31]. Experimental results [99] show, however, that the effects are to a great

extent cooperative, and therefore it matters what the environment of the amino acid

of interest is. This dramatically complicates the picture, as it is equivalent to say

that the amino acid property is environment dependent – therefore not only pH and

ionic strength, but also the organic/inorganic species present in the surroundings

must be taken into account.

4.2 Side-chain interactions in dipeptides 24

Figure 4.1. The distribution of water oxygen (red) around charged moiety of his-

tidine amino acid (left), followed by a cumulative number (dotted line) with the

proximal distribution function (full line, middle) and expressed with a number of

water molecules in the first solvent shell (i.e., within 3 A, right).

Fortunately, the protein structures and folds tend to exhibit general features, i.e.,

hydrophobic residues are typically buried, polar residues are found mostly at the

interface, but also as buried, while charged residues are almost exclusively present

at the protein surface.

Similarly the intuition indicates that two charged side chains of the same polarity

will not be observed in contact, unless stabilized by a counter charge in their vicinity,

or due to steric hindrances.

In the first study [100] we compared polyarginine and polylysine (actually di-

and decamers) and found that they follow the behaviour of their charged moieties

guanidinium and ammonium. Namely, no close contacts of side chains, but rather

electrostatic repulsion was observed for polylysine, while surprisingly a substantial

amount of direct contacts between guanidinium moieties in case of polyarginine was

detected.

The explanation on QM level of guanidinium-guanidinium stacking was intro-

duced, clearly showing that it is the combination of several effects which attract

the two guanidiniums to each other. It is mainly the cavitation and ion-ion disper-

sion that stabilize the guanidinium cations in a stacked orientation, while none of

those interactions can stabilize the tetraedrally shaped ammonium pair, which is

thus repelled similarly to a pair of sodium cations.

In the case of polyarginine this attraction is presumably even stronger than in the

Gdm+-Gdm+ pair due to the additional attractive hydrophobic interaction between

4.2 Side-chain interactions in dipeptides 25

Figure 4.2. Closely stacked conformation of diarginine and a pair of guanidinium

cations (left side), and the most probable orientation of dilysine and a pair of am-

monium cations bridged by chlorides (right side).

hydrocarbon parts of side chains. Further support for this pairing comes from the

search in the protein database [cite] where such arginine stacking motifs were found,

either inside a single protein or stabilizing protein dimers.

Our study was extended in the work of Vazdar et al. [101] – we investigated in

more detail the protein databases [102,103], in parallel with exploration of sensitivity

of guanidinium-guanidinium stacking to the parametrization of dihedral torsions of

the peptide backbone.

This sensitivity study is very important, because backbone torsions are often

changed in new generations of force-fields. The reason is that backbone torsions are

known to be responsible for preferences for secondary structure elements (α vs. β).

However, the fact that the side chain-side chain interactions are also affected is

probably not fully appreciated.

Last, but not least, the QM calculations on an explicitly solvated (with up to 14

water molecules) guanidinium dimer yielded very stable minima employing networks

of water-guanidinium and water-water hydrogen bonds that stabilize the dimer in

contact. Very stable structures were identified for a cluster with six water molecules.

The structure with twelve water molecules was found to be a global minimum.

The rather strong stacking of guanidinium moieties of arginine motivated us to

explore the aromatic imidazolium cation in chloride solution and as a unit of a

4.2 Side-chain interactions in dipeptides 26

Figure 4.3. Spatial distribution function (left) between centers of imidazolium moi-

eties of histidine dipeptide, with one side chain charged and another neutral. Further

analyzed with angle-resolved radial distribution function (middle) and standard ra-

dial distribution function (right). Representative conformations are assigned to three

pronounced peaks in the radial distribution function based on cluster analysis [56].

dipeptide with formula ACE-XXX-YYY-NME (where ACE means acetyl, NME N-

methyl and XXX, YYY stays for histidine, lysine, arginine). The pKa∼ 6 enables

simple protonation/deprotonation of histidine, therefore it is often engaged in active

sites of enzymes. For that reason we investigated both neutral (singly protonated)

and charged (doubly protonated) forms of histidine.

The imidazolium chloride (pKb =7) [104] solutions were studied also in mixtures

of different charged states, primarily to verify that the orientations observed for

peptides are not entirely due to the limited number of accessible side-chain con-

formations. The spatially resolved distributions, together with the RDFs provide

stacked structures for imidazole-imidazole, imidazolium-imidazole, and imidazolium-

imidazolium pairs. Additional T-shaped configurations (with a N-H. . .N hydrogen

bond ) were found for the imidazole-imidazolium pairs.

The results were characterized [105] by spatial distributions between the centers

of mass of charged moieties, combined with orientationally resolved and standard

RDFs. Interactions between neighbouring positively charged and neutral histidine

side chain in Figure 4.3 can serve as an example of this. Based on the spatially

and angularly resolved distributions there is an evidence of a significant preference

for parallel orientation of side chains for near contacts for both histidine-histidine

and histidine-arginine pairs. In contrast, the ammonium group of lysine avoids the

cation-π interaction with imidazolium moiety, and prefers structures with aligned

hydrocarbon chain (mimicking the orientations of aliphatic amino acid, i.e., nor-

4.2 Side-chain interactions in dipeptides 27

Figure 4.4. Side chain-side chain RDFs obtained from variants of gas phase con-

formation sampling of diLYS (black) and diARG (red) at 350K. Three increas-

ingly simplified cases are compared, namely: with electrostatics included (left), with

switched-off electrostatics but full Lennard-Jones potential (middle), and switched-

off both electrostatics and Lennard-Jones terms that included hydrogens of ammo-

nium or guanidinium (right). The arginine and lysine side chain structures are shown

for clarity.

leucine).

The cases illustrated above call for a method that is able to capture and dis-

tinguish the effects that come from bonding (bonds, angles and dihedrals) and non-

bonding (Van der Waals and electrostatics) contributions. The approach from section

2.2.1. is particularly useful here, especially in cases where the number of configura-

tions is restricted. Below in Figure 4.4 we see the resulting RDFs from gas phase

conformational sampling with switched on, or off electrostatics. All the calculations

were conducted at 350K.

As expected, the unscreened electrostatics is strongly repulsive (the left figure).

When the electrostatic contribution is subtracted, dispersion leads to a strong pair-

ing in diarginine, however, only a modest pairing is observed for dilysine (the middle

figure). This effect can be understood when the shape of functional groups is com-

pared. While guanidinium is flat, the ammonium moiety is tetrahedral and larger

in volume (the middle figure inset structures). If the hydrogen atoms are removed

from the functional groups (the result being a stick-like ammonium vs. a triangle-

like shaped guanidinium), the RDFs become similar (the right figure). The series

4.3 Ammonium moieties in the context of amino acids 28

in Figure 4.4 strongly support the notion that the key interaction is the dispersion

force and the key property is the shape of guanidinium vs. ammonium group.

4.3 Ammonium moieties in the context of amino

acids

The next section is devoted to the problem of transferability and additivity that

is widely assumed (also by us). The functional groups scrutinized are the ammonium

cation and the ammonium moieties in lysine and in the zwitterionic form of glycine.

The apparent similarity between them was studied in detail. The motivation is both

experimental and theoretical.

Experimentally, using neutron diffraction (small or wide angle), it is difficult

to study fluoride anion in water solutions with species that contain acidic hydro-

gens, due to its partial conversion into hydrofluoric acid which destroys the cuvette.

Therefore careful preparation of the experiment is imperative. The measured total

structure factor, F (Q), is connected to the RDFs extracted from MD simulations

via Equations 4.3, 4.4, where cα is the atomic concentration, bα is the coherent scat-

tering length [106]. With this connection in hand, a series of isotope substituted

experiments must be performed in order to divide the total structure factor into

the partial structure factors Sαβ(Q) that correspond (via Fourier transformation) to

RDFs gαβ(r) of species α and β.

F (Q) =∑

α

∑β

cαcβbαbβ (Sαβ(Q)− 1) (4.3)

gαβ(r) =1

2π2ρr

∫ (Sαβ(Q)− 1

)sin(Qr) QdQ + 1 (4.4)

The goal, i.e., probing the law of matching hydrating affinities [78,81] and finding

out whether ammonium is “weakly hydrated” cation that likes “weakly hydrated”

iodide against fluoride or vice versa, must be approached indirectly. The lysine amino

acid is the next candidate, however, its large size and the resulting complicated

structure factor favours glycine amino acid that is both simple and soluble. In water

it is present in its zwitterionic form, therefore the ammonium moiety is present and

can interact with fluoride and iodide.

Computationally, all three systems are easily accessible and create a nice test

for the widely used transferability assumption. A 2.5M glycine solution was put in

contact with 3M KF or KI solutions. In case of lysine or ammonium no extra salt

4.3 Ammonium moieties in the context of amino acids 29

Figure 4.5. Spatial distribution of fluoride (black) and iodide (violet) anion around

ammonium moiety in glycine (left), lysine (middle), and ammonium (right). The

contour level is the same in all cases and corresponds to 10× the bulk density.

is needed, nevertheless, in case of lysine, both variants only with fluoride or iodide

counterions and with extra KF resp. KI salt were considered. To get a direct link to

experimental structure factors for glycine solutions, the densities in simulations were

modified to reproduce the experimental values. Therefore in that case both constant

pressure [NpT] and constant volume [NVT] simulations were performed.

In Figure 4.5 we see the structures of individual solutions, together with the

structures of studied species. The exact compositions are summarized in the attached

article [106] The results were analyzed in terms of spatial distribution functions, the

RDFs and, most importantly, the total charge within the first solvent shell and local

concentrations of fluoride or iodide (defined in Equation 4.5 and evaluated for a

distance that corresponds to the first solvent shell of fluoride or iodide). In case of

glycine a semiquantitative agreement with neutron scattering was achieved for KF

vs. KI solution, with the dominant source of error coming from the questionable

quality of the fluoride force-field.

ρα(r) =Nα(r)

Nwat(r)(4.5)

ρbulkα =

Nα

Nwat(4.6)

The quite disturbing difference is apparent in the number of coordinated water

molecules in the first solvent shell of fluoride that is given consistently among force-

fields to be 6, while QM calculations provide a lower value, typically ∼ 5. Additional

4.3 Ammonium moieties in the context of amino acids 30

Figure 4.6. The local concentration of fluoride (black) and iodide (violet) anions

(left Y axis) and the total effective charge in the vicinity of ammonium moiety (right

Y axis) as a function of the charge of the ammonium moieties of glycine, lysine, and

ammonium cation (X axis).

simulations were performed with a newly developed force-field [107] that quantita-

tively agreed with our results, still being unable to decrease the number of water

molecules in the first solvent shell of fluoride.

The main result – the fact that ammonium moiety is far from being the same in

these three cases – is captured in Figure 4.6. It is shown how the local concentration

(based on the composition within the first solvent shell) and the effective charge

inside the first solvent shell (i.e., the charge of the ammonium moiety − average

number of anions) vary for these three moieties. The preference for fluoride is large

in case of ammonium cation, where we even see the ‘apparent overcharging’, but it

is lowered for the ammonium moiety of lysine. In contrast, the ammonium moiety

of glycine shows the preference for iodide (which exhibits roughly the same local

concentration around all ammonium moieties) over fluoride. The observation for

glycine is in semiquantitative agreement with neutron scattering experiments, as

provided in our article [106].

4.4 Ion-specific effects on electrophoretic mobility 31

4.4 Ion-specific effects on electrophoretic mobility

The ion-specific effects discussed in previous sections and chapters are present

already for low concentrations of simple monovalent salts. This feature is very im-

portant because it guarantees the almost ideal solution properties, such as an almost

complete dissociation, an activity coefficient being close to unity, no perturbation

of solution density and so on. Having this under control, one can design a series of

experiments that can distinguish between specific and general effects. For charged

species a very suitable technique is the capillary electrophoresis which provides the

mobilities of dissolved species.

For monovalent salts at low concentrations and neutral pH, already Fuoss and On-

sager [108] in the 1930s showed that the mobility is dependent on the ionic strength

of solution. However, already in their linear approximation, both mobilities of coions

and counterions, and even relaxation time of the ionic atmospheres have to be known

to evaluate corrections to ideal behaviour. One can more or less quantitatively esti-

mate the effect of ion-association, but the estimates of relaxation time ask for further

approximations, which are not easily available from MD calculation.

Even though the law of limiting behaviour guarantees that the mobilities of in-

dividual species are independent at infinite dilution, this is violated already for rel-

atively low concentrations of divalent salts (in our case we used sodium sulphate).

Bjerrum suggested an ion-pairing model to address this issue [109]. Using series of

equilibrium relations (4.7) – such as those presented below, with equilibrium con-

stants K1, K2, . . . – and assuming that all species interact only via electrostatics one

can estimate the extent of ion-pairing (4.8), as we did in the publication.

AνA+ + BνB− ABνA−νB (4.7)

ABνA−νB + BνB− ABνA−2·νB2

...

Ki = 4π

∫ d

a

r2 exp

{[zA − (i− 1)zB] zBlB

r

}dr (4.8)

where zA, zB are charges of species A and B, lB =e20

4πεε0kTis the Bjerrum length,

and a, and b are cation-anion distances that define the ion-pairing.

4.4 Ion-specific effects on electrophoretic mobility 32

Figure 4.7. Figure 5 (adopted) from our article [110]. The left figure shows the

mobility of monopeptides, mARG (blue), mLYS (red) in NaCl (dashed line) and

Na2SO4 (full line). The middle one describes tertapeptides similarly, and finally,

the right figure provides the ratio of mobilities in two salts (red are amino acids,

and blue are tetrapeptides, + symbolizes arginine and × the lysine). The green line

is the prediction based on Onsager-Fuoss theory [108], as implemented in program

PeakMaster [111].

In the first article [110] we dealt with the situation when the interaction is no

longer general, but starts to be specific. To this end, we probed the mono-, and tetra-

lysine and arginine in NaCl and Na2SO4 solutions. The experimental measurements

were complemented by MD that provided the atomistic resolution.

Figure 4.7 shows the relative mobility for mono- and tetra-peptides in the presence

of Na2SO4 and NaCl. Several trends are quite clearly observed:

1. The limiting mobility behaviour (a mobility of a molecule in its infinite dilution

and in infinite dilution of the background electrolyte) is easily reached in the

case of single amino acids (the mobilities at low concentrations of NaCl and

Na2SO4 are close). Even though this trend is observed for tetrapeptides as well,

it starts to be violated already for the smallest concentrations measured.

2. The behaviour of chloride is rather regular and does not any show ion-specificity

for mono- or tetra- arginine, or lysine.

3. Sulphate evidently exhibits a preference for guanidinium moiety of arginine

compared to that of ammonium moiety of lysine (the right figure – ratio of

arginines are always smaller when compared to lysines). This preference is

significantly stronger for tetrapeptides. MD simulations provide the specific

character of interaction (ammonium moiety vs. guanidinium moiety), while

4.4 Ion-specific effects on electrophoretic mobility 33

Table 4.1. Experimentally measured electrophoretic mobilities µ (e.u.) of tARG

and tLYS in 50mM NaCl and GdmCl aqueous solutions.

GdmCl NaCl

tetra-arginine 34.13±0.06 31.89 ±0.09

tetra-lysine 35.31±0.10 35.27±0.06

predictions based on Bjerrum theory are able to explain the purely Coulombic

part of the ion-pairing effect, and so the step from mono- to tetra-peptides.

The second investigation goes deeper to the background of theory of electrolytes.

The GdmCl and NaCl solutions are expected to behave very similarly in terms of

thermodynamic properties and the way they affect water. Even the limiting mobilities

[112] are very close to each other (µNa+ = 55 e.u., µGdm+ = 52 e.u., electrophoretic

units (e.u.), 1 e.u. = 10−9 m2·V−1·s−1) as well as the activity coefficients for a wide

range of concentrations [104]. Due to the presence of the same counterion the classical

theory which omits any specific interactions must predict the very same mobilities

of any species migrating in GdmCl or NaCl solutions.

However, inspired by MD calculations and neutron scattering experiments for

GdmCl solution [100, 113, 114] we anticipated the like-charge stacking interaction

of guanidinium cations. The difference between arginine (with limiting mobility of

µARG =26.9 e.u.) and lysine (µLY S =27.6 e.u.) [111] amino acids is only due to the

functional group of the side chain (guanidinium vs. ammonium moiety). Due to the

very similar size (C6H14N4O2, C6H14N2O2) and molecular mass (Mr(ARG)=174.2 g·mol−1

vs. Mr(LYS)=146.19 g·mol−1 ) the short peptides suit as a perfect test to verify the

stacking hypothesis not only qualitatively (presence of stacking interaction), but also

quantitatively (strength of this interaction in terms of association constant).

Measuring the mobility of tARG in 50mM GdmCl or 50mM NaCl, and tLYS

in 50mM GdmCl or 50mM NaCl we observed an interesting effect. The mobility of

tetra-peptide is slowed down by counter-ion binding and screening, but it is sped-up

by co-ion binding. The results summarized in Table 4.1 show clearly that in the

case of tLYS the mobility is the same in the two salts (only slightly faster in NaCl

– exactly as predicted by classical theory [108]), but there is a sufficiently strong

specific Gdm+ effect observed for tARG.

To quantitatively unravel the strength of the Gdm+ stacking interaction, the

mobilities in various molar fraction mixtures of NaCl and GdmCl were measured

4.5 Surface propensities of β-amyloid 1-16 fragment at varying pH 34

Figure 4.8. Experimentally, the ionic strength was kept constant at I = 50mM, and

NaCl was gradually replaced by GdmCl. The effect is clearly nonlinear and suits

perfectly to Langmuir adsorption. Fitted values show weak, but pronounced bind-

ing KGdm+ , and maximum mobility increment ∆µmax. The responsible guanidinium

binding interaction – stacking with arginine side chain is displayed in red, the Cl−

binding in gold.

(keeping ionic strength constant). The data obtained together with the Langmuir-

like fit are provided in Figure 4.8. The curved shape strongly suggest that the effect

has a binding character, since it tends to saturate.

All the measurements are very well reproducible, the error bars are very small

(typically 0.1 e.u.), and we can exclude major experimental/instrumental errors. Due

to the design of the experiment that was performed on two analytes (tARG, tLYS)

and two co-cations (Na+, Gdm+) with the same chloride counterion, all interpreta-

tions based on two-species interaction can be rejected, except for the specific attrac-

tive interaction of Gdm+ with tARG, but not tLYS.

4.5 Surface propensities of β-amyloid 1-16 frag-

ment at varying pH

The last contribution in this chapter takes under detailed investigation the pH

dependent surface affinity of the β-amyloid 1-16 fragment. The pH sensitivity is a

very general and important feature for all proteins. The classically assumed ther-

4.5 Surface propensities of β-amyloid 1-16 fragment at varying pH 35

modynamic pKa constants [104] are listed in Table 4.2. Within pH=6 to 8, i.e., in

the most usually used pH window, histidine is the only amino acid that can undergo

protonation/deprotonation process, therefore quickly responds to small pH changes.

Due to this fact, it may be quite difficult to perform a simulation of a protein that

has several histidine residues simply as the number of all possible protonation com-

binations quickly increases.

Table 4.2. Model pKa (pKModel) values for functional groups of relevant amino acids

side chains as used in PROPKA software [115].

residue C-terminal Asp Glu His N-terminal Cys Typ Lys Arg

pKModel 3.2 3.8 4.5 6.5 8.0 9.0 10.0 10.5 12.5

Luckily there are more [116] or less [117, 118] sophisticated methods how to es-

timate the protonation state, mainly based on the quality of the environment that

surrounds the amino acid. However, as the classical MD setup does not allow to

break bonds, the protonation state is the same during the whole simulation. This

approach is quite well justified assuming the probabilities that can be estimated from

free energies obtained from pKa constants.

Nevertheless, in some cases special techniques must be used [116,119]. The worst

situation takes place when the apparent pKa is structure-dependent. That is often the

case for medium sized peptides that do not have a priori known and stable secondary

and tertiary structures, therefore the definition of surface and buried residues is ill

defined, because the exposure of amino acids vary during the dynamics.

For an illustration a few empirical penalties used in pKa prediction software

PROPKA [115] are shown in Table 4.3. Obviously the electrostatics, H-bonding,

burial or exposure have a substantial effect. The resulting apparent pKa value is

then:

pK?a = pKModel+∆pKGlobalDes+∆pKLocalDes+∆pKSDC-HB+∆pKBKB-HB+∆pKchgchg

As in the experiment, three different pH conditions were simulated. The acidic

(pH=3), neutral (pH=7), and basic (pH=10) conditions were investigated, pro-

tonated in line with the PROPKA software predictions [118]. We have to stress

here that in some cases the apparent pKa is close to the pH studied. The fact that

experimentally observed total charge agrees with the computed one supports the pro-

tonation state we employed. However, we cannot exclude the possibility of a charge

4.5 Surface propensities of β-amyloid 1-16 fragment at varying pH 36

Table 4.3. The contributions to apparent pKa values, as used in PROPKA software

[115]. In desolvation effects, N is the number of nonhydrogen atoms within a certain

distance (differs for a local and global effect) from the ionizable group. In other three

cases, these maximal values are scaled by a distance-related factor to obtain the final

contribution.

Magnitude Description of the effect

∆pKGlobalDes 0.01·N Desolvation effect

∆pKLocalDes 0.07·N Local desolvation effect

∆pKSDC-HB 0.8–1.6 H-bonding to side chain

∆pKBKB-HB ∼1.2 H-bonding to backbone

∆pKchgchg ∼2.4 Electrostatic interaction

fluctuation and its effect on the simulation, but we assume that the general behaviour

remains the same.

Charges vary with pH quite significantly (+5 at pH=3, -2 at pH=7, -5 at

pH=10) due to a large polarity of the β-amyloid 1-16 fragment. This has a ma-

jor consequence on the surface propensity. Time evolution at three pH values in

Figure 4.9 shows clearly the anticorrelation between charge and surface adsorption.

The results thus support the experimental evidence at pH=7, but display roughly

the same effect at pH=3 and pH =10, while in the experiment the pH=3 displays

surface adsorption and pH =10 does not.

The total charge is the same for pH=3 and pH =10, which means that the

difference in presence or depletion from the air/water interface comes entirely from

the difference in solvation of charged groups. Conformational flexibility of β-amyloid

1-16 fragment prohibit a quantitative conclusion from available simulation data.

Nevertheless, we speculate that while ASP, GLU, and LYS amino acids are surface

active only in their neutral states and avoid the surface when charged, HIS, and

ARG are much less sensitive and exhibit surface presence (or even preference) even

when charged.

This hypothesis is supported by the observation in Figure 4.10 where charged

side chains exhibit (or do not) the surface activity as speculated above. Further

support comes from our studies of diARG, diHIS, and diLYS revealing that a charge

has only a marginal effect for cation-cation contact in first two cases, however, it

is prohibitive in case of diLYS. Finally, in the upcoming publication (Wernerson et

al. in preparation), we observed the adsorption of Gdm+ cation at the air/water

4.5 Surface propensities of β-amyloid 1-16 fragment at varying pH 37

Figure 4.9. Time evolution of z-position (colour shows the mass distribution pro-

jected to z-axis) of β-amyloid 1-16 fragment at pH=3 (left), pH =7 (middle), and

pH=10 (right), together with radius of gyration (on top of individual figures). The

air/water interface (dashed line) and middle of the box (full line) are marked in blue.

interface which is consistent with the hypothesis.

Obviously extended and more focused studies are needed to reach more solid

conclusions.

4.5 Surface propensities of β-amyloid 1-16 fragment at varying pH 38

Figure 4.10. The sequence of β-amyloid (in an extended conformation) on the

top clearly shows the polar character of peptide. At pH =10, however, hydropho-

bic residues (most left) exhibit dominantly surface activity (compared to the CM-

position – black line) and the polar residues (second from left) are mainly hydrated,

as well as negatively charged side chains (second from right). The opposite behaviour

is observed for the only positively charged residue ARG that is close to CM-position

and definitely not extensively hydrated. HIS and LYS residues are present in their

neutral forms.

Chapter 5

Peptides and Proteins

5.1 Ion specific effects on catalytic activity of HIV-1

protease

Renewed interest in the Hofmeister series during the last decade has resulted in a

deeper understanding of the ion-protein interaction. Furthermore thorough informa-

tion has been gathered about issues such as what the origin of their behaviour at the

interface is and which qualities may lie behind the ion-specificity. Most of the studies

show that in case of simple (atomic) cations the crucial interaction sites are almost

exclusively carbonyl and carboxyl moieties, which makes the study more tractable

than that of the more complex ions.

HIV-1 protease has an indispensable role in the maturation of HIV particles,

and therefore as an important target for the anti-HIV drugs was extensively exper-

imentally studied [120–122]. Several groups analyzed the dependence of kinetics on

salt concentration, observing the “salting out” effect which results in an increased

substrate binding [123,124].

Several theories [125,126] were suggested in literature to explain how the protease

recognizes the substrate. Due to the electrostatic nature behind this recognition and

a large number (8 groups on monomer, 16 groups on HIV-1 protease) of negatively

charged amino acids (ASP and GLU) on the protease surface, the direct binding

mechanism was proposed and tested via MD simulations.

As later observed, the protonation state of the catalytic dyad is rather unclear,

however, the experimentally predicted pKa values of <2.5 and >6.2 [127] evoke that

the two aspartates share at pH=6 (experimental condition) a single proton. If and

how the situation does change when a cation approaches the aspartic dyad is yet

5.2 LinB enzyme – an example of a dehalogenase 40

unknown. The MD calculations were, therefore performed in parallel on systems

with both possible protonation scenarios.

Not only the enzyme, but also the substrate which displayed the highest difference

in measured activity, were studied by MD simulations in NaCl and KCl solutions.

Irrespective to the protonation state of catalytic dyad, sodium always showed roughly

two to three times higher preference (in terms of a number of ions) for the protein

surface compared to potassium. A quantitatively similar trend was observed for the

substrate.

v =vmax[S]

KM + [S]=

kcat[E0][S]

KM + [S](5.1)

where [S] and [E0] are the substrate and initial enzyme concentration, v and vmax

are the reaction rate and its maximum, KM is the so called Michaelis constant, and

kcat is the catalytic rate [128].

Using the Michaelis-Menten kinetics [128], described by Equation 5.1, the ex-

periments targeted not only the catalytic efficiencies, kcat

KM, but also provided the

individual contributions, namely the binding affinity of substrate-enzyme (KM), and

the catalytic rate (kcat). Significantly higher catalytic efficiency (up to 100%) in hand

with overall higher enzymatic activity (∼ 20%) in KCl was observed compared to

NaCl.

The results of MD simulations showed (in terms of RDFs and numbers of ions in

the first solvent shell) the overall stronger affinity of Na+ compared to K+ towards

the enzyme and substrate. The spatially resolved plot, shown in Figure 5.1, evokes

the following picture. While the ratio of binding of Na+ vs. K+ to isolated negatively

charged amino acids at the surface is roughly 2-3, the difference increases in situations

where two negatively charged amino acids are located close to each other and point

with carboxyl groups to the same spot. There are few “hot spots” on HIV-1 protease,

the most striking one being the catalytic dyad.

On top of the general salting out effect, we observed the cation specific attraction

to the catalytic dyad in the active site and to the region located close to the entrance

to the active site. This may lead to a partial reduction in accessibility of substrate,

therefore it lowers the enzymatic activity, when replacing K+ with Na+.

5.2 LinB enzyme – an example of a dehalogenase

The HIV-1 protease was our first project where the connection of MD and ex-

periment was established for Hofmeister salts. All what we learned there was used

5.2 LinB enzyme – an example of a dehalogenase 41

Figure 5.1. Spatial distribution of sodium (green) and potassium (cyan) around

the HIV-1 protease (coloured according to the polarity; blue is negative, and red is

positive). The contours correspond to the value of 10 times the bulk density (left).

A detail look on the aspartic dyad for two possible protonations (left, insets). The

coarse grained RDFs (right) show clearly the larger attraction of Na+ compared to

K+ to all parts of the enzyme surface.

as a background in a more complex project that scrutinizes the enzymes from a de-

halogenase family [129,130]. The haloalkane dehalogenases might be used for decon-

tamination of polluted areas, therefore their crystal structure, the enzymatic cycle,

optimal pH window of stability and enzymatic activity are well established [131–133].

The QM/MM and MD modelling were successfully employed in recent studies, in

connection with mutagenesis and substrate specific studies [134,135].

The generic feature of members of dehalogenase family is the presence of buried

active site. The active site always consists of enzymatic triad (two carboxylic acids

and one histidine), two halogen-stabilizing residues (tryptophane and asparagine, or

glutamine) and is accessible through a tunnel, in some cases a dynamically open-

ning/closing slot is also present. This constitution results in a substantial substrate-

selectivity [136,137].

In the current project, in progress, activation/deactivation of enzymatic activity

in salt solution has been studied. Experimentally, the enzymatic activity as a function

of salt concentration was measured for a wide range of salts (alkali halides, Ca2+,

NH+4 , and others) for two enzymes, DbjA and LinB.

MD simulations were performed for LinB enzyme, which carries a large negative

charge (∼ −10). The enzyme was exposed to 0.5M concentration of the alkali chloride

solutions (lithium chloride was omitted), as that was experimentally found to be the

5.2 LinB enzyme – an example of a dehalogenase 42

Figure 5.2. The contributions to proximal distribution function (most left) were

calculated between carboxylic groups (left), carbonyl groups (middle), and polar

groups of the peptide bond (right) and alkali cations – sodium (green), potassium

(blue), rubidium (red), cesium (violet). Note that the total charge of protein is -10.

most sensitive concentration.

In our case, the experimentally observed effects of salts on enzymatic activity are

small (up to tens of percent) and data did not follow direct nor reverse Hofmeister

series, namely: K < Na < Cs < Rb. In apparent contrast, MD calculations revealed

that the cations are ordered in direct Hofmeister series (Na+ > K+ > Rb+ > Cs+)

according to the affinity of cations to the LinB surface, as measured by proximal

distribution function. Figure 5.2 shows that not only the overall affinity, but all

hydrophilic parts of protein surface (charged groups, polar groups and the peptide

bonds) exhibit the direct Hofmeister ordering.

Enzymatic activity is only a single number behind a series of rather complex pro-

cesses (solubility of substrate, enzyme, product, protein dynamics, tunnel dynamics,

enzymatic cycle, etc.) many of which may be affected by the presence of salt.

Salt effects can always be imagined as either direct (noncovalent binding – due

to electrostatics or dispersion forces) or indirect (a change in activity of species,

marginal pH shift, etc.). From the theoretical point of view the interpretation of

indirect mechanism is usually computationally demanding and technical, but still

tractabl. However, experimental proof is only rarely accessible, because it is very

5.2 LinB enzyme – an example of a dehalogenase 43

Figure 5.3. Spatial distribution of sodium (the most attracted cation), in green,

around surface of LinB enzyme. The isocontours correspond to regions with 10 times

higher sodium probability. Even though the regions of high probability are unequally

distributed around protein surface, they follows the same trend for all cations. The

picture shows two opposite sides of LinB enzyme, with tunnel entrance on the top

in both cases. Note that the total charge of protein is -10. The inset shows the

space-filling representation of LinB.

complicated to extract the partial contributions of the complex effect from the mea-

sured data.

Our simulation data do not seem to be able to explain, solely on the basis of an

ion affinity, the experimental observed cationic ordering. Based on the spatial dis-

tribution, shown in Figure 5.3, we proposed several sites near the tunnel entrance,

which are highly occupied by cations. The enhanced presence of cations will influ-

ence entering of substrate, releasing of product, and can even induce a mild local

conformational changes (i.e., affecting orientation of polar groups). All these options

must be taken into account and quantitatively analyzed one after another, using both

theoretical predictions for further experiments (mutations in or close to preferential

binding sites) and experimental observations for upcoming theoretical work.

Spatial maps resolved further the distribution of cations around LinB enzyme,

however, even the most promising binding sites follow always the direct Hofmeister

series. The work is still in progress and we expect the first publication on this topic

in a year time.

5.3 Denaturating and stabilizing effects of molecular cations 44

5.3 Denaturating and stabilizing effects of molec-

ular cations

The backbone based theory for protein denaturation and stabilization was in-

troduced in the first chapter. Here we focus on the tetrapropyl ammonium cation

(TPA+) and the guanidinium cation (Gdm+) as chloride and sulphate salts. The

question was how these neighbours in the Hofmeiester series act at protein surfaces

in the current study on the melitin peptide. The resulting denaturation or stabilizing

effect of these salts is interpreted at the level of pair-interactions introduced below:

• homoion pairing

• heteroion pairing

• interaction with charged and polar groups of protein

• interaction with hydrophobic groups of protein

Following the known homo- and hetero-ion pairing of guanidinium chloride and

sulphate [114], we performed a simulation of TPA2SO4 to obtain information about

its ion-pairing properties. Low and evenly distributed charge density of TPA results

in unlocalized ion-pairing with sulphate. It may be found a bit surprising that homo-

cation pairing of flat TPA surfaces was not observed.

The major outcome of the work is summarized in Table 5.1 that describes partial

effects of denaturants under study. The balance of ion-ion, ion-hydrophobes, ion-

hydrophiles, and hydrogen bonding properties is essential and may be used to predict

the overall stabilizing/denaturing effect. The predictions stated in 2009 in Table 4

of our publication [138] were experimentally verified in 2011 [139].

It is only due to cation-anion pairing in solution that the action of strong de-

naturant GdmCl can be significantly weakened when used as Gdm2SO4, therefore

exemplifying the counterion effect. The counterion effect is not observed for TPA

cation, which does not effectively pair with sulphate. Also its inability to create

hydrogen bonds leads to an unbalanced denaturating effect, i.e., TPA+ is a strong

denaturant of the Trpzip peptide (where it can exhibit its stacking interaction with

flat surfaces, i.e., tryptophane), while it is only a mild denaturant of alahel peptide

that is stabilized by backbone hydrogen bonds.

Further detailed interpretations and predictions can be found in the attached

publication [138].

5.4 Denaturation of TrpCage miniprotein 45

Table 5.1. Observed or deduced effects of GdmCl, Gdm2SO4, TPACl, and TPA2SO4

in solutions and at protein surfaces. Numbers represent the interaction strength

(magnitude of the effect). Adapted from Mason et al. [138]

salt GdmCl Gdm2SO4 TPACl TPA2SO4

Interaction between ions

homocation pairing 40% <20% 0% 0%

homoanion pairing 0% 0% 0% 0%

hetero-ion pairing 60% 100% 0% 0%

Interaction of ions with groups in proteins

cation with cationic side chains 40% 20% 0% 0%

anion with cationic side chains 60% 100% 60% 100%

cation with anionic side chains 100% 80% 0% 0%

anion with anionic side chains 0% 0% 0% 0%

cation with hydrophobic groups 40% 20% 80% 80%

anion with hydrophobic groups 20% 0% 20% 0%

5.4 Denaturation of TrpCage miniprotein

The TrpCage minipeptide [140] was for the first time synthesized in 2002 from

peptide extendin-4 (from the oral secretion of a lizard) to become the fastest folder

that mimics the protein. Its native structure shown in Figure 5.4 (left top) rational-

izes that it is considered and studied as an ideal model-protein. It manifests the rapid

(∼4µs) native fold around hydrophobic core with the central tryptophane residue

(origin of the name TrpCage). Its small size and fast fold perfectly suits the MD mod-

elling, therefore TrpCage miniprotein become a widely studied target with implicit

and explicit solvation, and enabled to employ a large variety of techniques (i.e., direct

MD, REMD, transition path sampling (TPS) techniques) [15,17,18,46,47,141–143].

But TrpCage minipeptide does not serve only to the computational community,

it is a perfect target for experimental studies as well. Point mutations [144,145] carry

the information about the importance of particular amino acids and lead to targeted

design of more stable species [146]. The fluorescence uses the tryptophane and reveals

the folding times [147]. NMR techniques can easily monitor the shift of equilibrium

from folded to unfolded state, or in combination with ultrafast spectroscop [148]

even to trace the dynamics of folding event, and the circular dichroism (CD) and

5.4 Denaturation of TrpCage miniprotein 46

differential scanning calorimetry (DSC) reveal the underlying thermodynamics [149,

150].

Together with beta-hairpin [151], Trpzip [152], Vilin-headpiece and Protein-G

[153], TrpCage is a member of test set for development of new amino acid force-fields

(aiming the proper balance between α and β structures) and for demonstration of

new methods for enhanced sampling [54].

We focused on the action of two common denaturants, urea and guanidinium

chloride, and investigated the unfolding during the denaturating process. REMD

calculations provide information about the shape of the free energy surface, but

they lack the time resolution due to the MC steps that are part of the procedure.

TPS consists of thousands of short trajectories that start from a border-region on

the FES (i.e., between native and unfolded). In this way, it provides great dynamic

information about these border-region(s), however, connection of these regions is

absent. Finally, the elevated temperature MD would be advantageous (as it speeds

up all processes), however, the effect of the denaturant is inevitably contaminated

by that of the temperature.

For these reasons the direct MD simulations were proposed to be the most suitable

for exploration of the microsecond denaturation event in its full complexity. For

description of complex species, such as proteins, whole branche of global coordinates

was proposed. The need is obvious – the large number of degrees of freedom prohibit

analysis in full detail, unless such an ideal coordinate is known a priori. In our case we

used, in line with other studies, the root mean square deviation (RMSD) and root

mean square deviation of the helical part (RMSDhelix) as a measure of deviation

from the native conformation. As a measure of the compactness, we chose radius of

gyration (Rg) and the hydrophobic core around TrpCage-motif was monitored using

the conveniently defined core-coordinate (mean distance of the tyrosine, and prolines

to the tryptophane residue). It should be stressed that many other global but also

local coordinates were tested, but the above described have been found to be the

most suitable.

Figure 5.4 depicts an example of the time evolution of minipeptide’s structure,

together with temporary composition of the first solvent shell and the history of four

above described coordinates with two dimensional FESs constructed from those. The

way from the native to the extended conformation is described below, and may be

viewed as the main outcome of the work, as well as the comparison of actions of urea

and guanidinium chloride.

5.4 Denaturation of TrpCage miniprotein 47

Figure 5.4. The time evolution of the system in 2M urea solution. The miniprotein

conformation (top three figures), solution composition inside the first solvent shell

with red waters, and yellow urea molecules (middle) is captured at times t= 0 ns

(left column), t= 500 ns (middle), and t=1000 ns (right). The time evolution of

four global coordinates (RMSD (black) and Rg (red); core-coordinate (green) and

RMSDhelix (blue)), and their two dimensional free energy surfaces (RMSD-Rg, core-

coordinate-RMSDhelix) at the bottom.

5.4 Denaturation of TrpCage miniprotein 48

native structure �

� proline shift � ASP-ARG saltbridge destabilization �

� enhanced flexibility and increased solvent accessible surface area �

� denatured state

All these steps are reversible, but sensitive to the presence of cosolvent. Quan-

titative difference was observed in our calculations for conformations sampled in

denaturating solutions compared to those in neat water. The difference in action

of urea and guanidinium were found in the sites that were occupied, and in the

magnitude to which they destabilize the secondary structure elements (helix and

loop).

Urea was homogeneously distributed around minipeptide, either creating hydro-

gen bonds to carbonyl oxygens of peptide and polar groups, or just surrounding

hydrophobic residues. On the contrary, guanidinium cation was dominantly found

close to the loop region, where it took advantage of solvent exposed dangling car-

bonyl oxygens, creating double hydrogen bond with negatively charged aspartic acid,

and stacking to flat surfaces of TRP, ARG, and TYR. The uniformness of urea and

selectivity of guanidinium binding leads to differences in action to native, misfolded,

partially unfolded and denatured states.

As mentioned above, even though the mode of action of urea and guanidinium

differ, both routes go through the same set of key steps and both lead the minipeptide

towards the denatured states. The detailed analyses were performed and those that

were found being robust are published in our paper.

Chapter 6

Conclusion

This thesis consists of 13 articles in which we have investigated ion-specific effects

in solutions, with focus on interactions of ions with peptide and protein surfaces,

by means of molecular dynamics simulations. The objects of our interest range from

solutions of molecular salts, followed by the action of salts on small organic fragments,

and amino acids, to the effect on surfaces of peptides and proteins.

All of the projects have common aims. Namely:

• Understanding of ion-specific effects, and consequent ordering in Hofmeister

series for cations, anions, and osmolytes.

• Interaction of ions with organic molecules and biomolecules.

• Rationalization of the reductionistic approach and understanding of its limita-

tions.

Molecular dynamics, employing nonpolarizable or polarizable force-fields, was

used as the most convenient method providing us with the data that were sub-

sequently analyzed. To understand the ion-specific effects in different contexts we

needed methods descriptive enough to capture both quantitative and qualitative

pictures, i.e.:

• Radial and proximal distribution functions and related thermodynamic prop-

erties

• Spatial distribution function, clearly highlighting the hot-spots for interaction

• Time evolution of the system on the free energy surface employing suitable

coordinates (e.g., ion-ion distance or collective coordinates for peptides, such

as radius of gyration)

50

Based on above mentioned techniques, we were able to interpret and propose a

mechanism by which anions affect the peptide bonds in proteins [55], or to probe

the Collins concept of matching water affinities [81] for ammonium cation. For the

latter we took in one case the advantage of combined MC-MD approach [92] and in

another case neutron scattering experiments linked with MD [106].

Furthermore, we characterized the behaviour and organization of small (F−) and

large (I−) anions in the vicinity of positively charged amino acids [93].

Next we described the side-chain conformational freedom for positively charged

amino acids in dipeptides [100, 101, 105]. This revealed the qualitative and to some

extent surprising difference between flat faces of guanidinium or imidazolium moieties

(in arginine and histidine respectively), compared to that of tetraedrally shaped

ammonium moiety of lysine.

Motivated by mounting evidence of specific behaviour of guanidinium (cation-

cation stacking, strong pairing with sulphate, etc.), we succesfully combined the

MD framework with measurements of electrophoretic mobilities [110, 154]. While

MD provided the initial motivation and atomistic insight, capillary electrophoresis

provided hard experimental data, placing the proposed effects on solid ground.

In tandem with surface sensitive experimental techniques (second harmonic gen-

eration (SHG) spectroscopy) we explored the pH dependent surface activity of the

β-amyloid 1-16 fragment, charge of which varies dramatically from +6 at pH=3,

through +2 at pH=7 to -6 at pH=11. The results captured the dominant role of

total charge and sketched the surface behaviour of positively and negatively charged

groups [155].

While other research groups concentrated on the thermodynamical description of

peptide folding [47, 141], we focused on the dynamics of peptide denaturation. Two

widely used denaturants (urea and guanidinium chloride) were investigated when

acting on the TrpCage minipeptide [25]. Two different (denaturant-specific) path-

ways of unfolding were observed, however, with a similar result – i.e., the ensemble

of denatured states which were characterized by three independent experimental

techniques (CD, DSC, NMR).

We managed to provide a very detailed explanation of different denaturating ef-

fect of neighbouring cations in Hofmeister series, tetrapropyl ammonium and guani-

dinium. It was rationalized based on the pair interactions, taking into acount both

the ion-specific interactions in salt solution and the ion-specific interaction with the

protein surface [138]. The predictions we made in 2009 came true in 2011, when they

were experimentally verified [139].

The Hofmeister series for cations was tested in two studies employing very rel-

51

evant enzymes. In the first case, the enzymatic activity assay (within Michaelis-

Menten kinetics) of HIV-1 protease was performed in sodium chloride and potassium

chloride, observing the activity consistently higher by 20% in the latter case. MD

calculations found generally a twice higher affinity of sodium cation to the enzyme

surface, and on top of that, particular spatially resolved maxima around the active

site [51]. The second study, which is still under progress, targets the catalytic activity

of the LinB dehalogenase, in a large set of salt solutions at various concentrations.

From the computational side, we aimed at alkali chloride salts where we found to a

large extent direct Hofmeister ordering.

To summarize, in this thesis I demonstrated the wide range of applications for

MD simulations for biologically relevant systems at various level of complexity. The

all-atom description allowed to obtain information about ion-specific effects in all

studied contexts. Due to the fact that proteins are always exposed to solvents and

salty solutions this work has potential applications to many different fields, such as

biophysics, biochemistry, biology or biotechnology.

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[155] A. E. Miller, P. B. Petersen, C. W. Hollars, R. J. Saykally, J. Heyda, and P. Jungwirth,“Behavior of beta-amyloid 1-16 at the air-water interface at varying ph by nonlinear spec-troscopy and molecular dynamics simulations”, Journal of Physical Chemistry A 115(23),pp. 5873–5880 (2011).

List of Attached Publications

1. J. Heyda, T. Hrobarik, and P. Jungwirth, “Ion-specific interactions between halides and basicamino acids in water”, Journal of Physical Chemistry A 113(10), pp. 1969–1975 (2009).

2. P. E. Mason, C. E. Dempsey, L. Vrbka, J. Heyda, J. W. Brady, and P. Jungwirth, “Specificityof ion-protein interactions: Complementary and competitive effects of tetrapropylammonium,guanidinium, sulfate, and chloride ions”, Journal of Physical Chemistry B 113(10), pp. 3227–3234 (2009).

3. J. Vondrasek, P. E. Mason, J. Heyda, K. D. Collins, and P. Jungwirth, “The molecular originof like-charge arginine-arginine pairing in water”, Journal of Physical Chemistry B 113(27),pp. 9041–9045 (2009).

4. J. Heyda, J. Pokorna, L. Vrbka, R. Vacha, B. Jagoda-Cwiklik, J. Konvalinka, P. Jungwirth,and J. Vondrasek, “Ion specific effects of sodium and potassium on the catalytic activity ofHIV-1 protease”, Physical Chemistry Chemical Physics 11(35), pp. 7599–7604 (2009).

5. J. Heyda, J. C. Vincent, D. J. Tobias, J. Dzubiella, and P. Jungwirth, “Ion specificity atthe peptide bond: Molecular dynamics simulations of N-methylacetamide in aqueous saltsolutions”, Journal of Physical Chemistry B 114(2), pp. 1213–1220 (2010).

6. J. Heyda, P. E. Mason, and P. Jungwirth, “Attractive interactions between side chainsof histidine-histidine and histidine-arginine-based cationic dipeptides in water”, Journal ofPhysical Chemistry B 114(26), pp. 8744–8749 (2010).

7. J. Heyda, M. Lund, M. Oncak, P. Slavıcek, and P. Jungwirth, “Reversal of hofmeisterordering for pairing of NH+

4 vs alkylated ammonium cations with halide anions in water”,Journal of Physical Chemistry B 114(33), pp. 10843–10852 (2010).

8. E. Wernersson, J. Heyda, A. Kubıckova, T. Krızek, P. Coufal, and P. Jungwirth, “Effectof association with sulfate on the electrophoretic mobility of polyarginine and polylysine”,Journal of Physical Chemistry B 114(36), pp. 11934–11941 (2010).

9. P. E. Mason, J. Heyda, H. E. Fischer, and P. Jungwirth, “Specific interactions of ammo-nium functionalities in amino acids with aqueous fluoride and iodide”, Journal of PhysicalChemistry B 114(43), pp. 13853–13860 (2010).

10. Anna Kubıckova, Tomas Krızek, Pavel Coufal, Erik Wernersson, Jan Heyda, and PavelJungwirth, “Guanidinium cations pair with positively charged arginine side chains in water”,The Journal of Physical Chemistry Letters 2(12), pp. 1387–1389 (2011).

BIBLIOGRAPHY 65

11. A. E. Miller, P. B. Petersen, C. W. Hollars, R. J. Saykally, J. Heyda, and P. Jungwirth,“Behavior of beta-amyloid 1-16 at the air-water interface at varying pH by nonlinear spec-troscopy and molecular dynamics simulations”, Journal of Physical Chemistry A 115(23),pp. 5873–5880 (2011).

12. J. Heyda, M. Kozısek, L. Bednarova, G. Thompson, J. Konvalinka, J. Vondrasek, andP. Jungwirth, “Urea and guanidinium induced denaturation of a trp-cage miniprotein”,The Journal of Physical Chemistry B (2011), doi: 10.1021/jp200790h.

13. Mario Vazdar, Jirı Vymetal, Jan Heyda, Jirı Vondrasek, and Pavel Jungwirth, “Like-chargeguanidinium pairing from molecular dynamics and ab initio calculations”, The Journal ofPhysical Chemistry A (2011), doi: 10.1021/jp203519p.

Attached Publications