Modeling the Biochemical Network of APP-C99: Dimerization and Interactions with Cholesterol

Longjiaxin Zhong and John E. Straub Boston University, Chemistry Department, 590 Commonwealth Avenue, Boston, MA 02215

Abstract

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(1996).

Introduction

Methods

Mathematical Model for Reaction Network Conclusions

Future Direction

References

Acknowledgements

Alzheimer's Disease (AD) constitutes one of the leading causes of death in the elderly. The goal of this work is to explore the nature of homodimer formation of the amyloid precursor protein (APP-C99), and APP-C99 binding to cholesterol, which is believed to play a critical role in the etiology of AD. The model takes the form of a set of non-linear ordinary differential equations describing the conception of C99 dimerization and binding to cholesterol. The rate of homodimerization of APP-C99 was determined by theoretical calculation, computer simulation, and Gillespie stochastic simulation. The computational association rates were generated using a particle-based random walk and collision model written in python. Preliminary results suggest that this simple theoretical model can capture essential aspects of the association of APP-C99 and cholesterol in a cellular environment. In the future, our network model may be further generalized to include more detailed models, including two lipid domains (liquid-ordered and liquid-disordered) and additional lipids (sphingomyelin) that may bind cholesterol.

Amyloid Precursor Protein (APP) is a transmembrane protein that undergoes a series of proteolytic processing steps involving secretase enzymes, ultimately leading to the formation of amyloid beta (Aβ) protein. Processing of APP produces the 99 amino acid fragment known as APP-C99. APP-C99 contains a single transmembrane helical domain that is subsequently cleaved by the γ-secretase enzyme to produce the Aβ protein. Aβ protein aggregates are believed to act as pathogenic agents in AD. Fig 1. Model of C99 subdomains

imbedded in cell membrane and the Aβ amyloid fragment produced from cleavage by γ-secretase. 1

Fig 3. Depiction of C99 dimer in a POPC lipid bilayer (left) and in a DPC micelle (right) .2

1. Sanderson, J. M. Resolving the kinetics of lipid, protein and peptide diffusion in membranes. Mol. Membr. Biol. 29, 118–143 (2012).2. Dominguez, L; Foster L; Straub,J.E.; Thirumalai, D, J. Am. Chem. Soc., 136 , 9619–9626 (2014)3. Panahi,A; Bandara, A; Pantelopulos ,G; Straub, J.E., J. Phys. Chem. Lett., 7, 3535–3541 (2016)

A complete understanding of the kinetics of processing of APP-C99 by γ-secretase must include detailed knowledge of the distribution of APP-C99 substrates available for cleavage, and how that distribution depends on APP-C99 protein sequence and concentration of cholesterol.

The goal of this research is to develop the first detailed kinetic model of the network of reactions that determine the equilibrium concentrations of APP-C99 in its various forms - monomer, homodimer, and monomer bound to cholesterol. Our model consists of kinetic equations that capture the association and dissociation of the key molecular species APP-C99 and cholesterol.

Thanks to my advisor Professor John Straub for scientific instruction, my colleagues in the lab for helping me with SCC and programing, and Doctor Ryo Urano for coding up the Gillespie Algorithm.

This work was supported by Undergraduate Research Opportunities Program (UROP).

The goal of this work is to explore the nature of APP-C99 homodimer formation, and its role in Alzheimer's Disease (AD), as well as the role of APP-C99 in sensing cholesterol.

1. BUILDING BIOCHEMICAL REACTION NETWORK: A novel biochemical reaction network has been developed and used to explore cholesterol's influence on APP-C99 homodimerization

2. PARAMETERIZING THE REACTION NETWORK MODEL: The biochemical reaction network has been parameterized using results of experiment (equilibrium constants for APP-C99 dimerization) and simulation (rates of APP-C99 and cholesterol diffusion). The model explores realistic concentrations of peptide and cholesterol that are found in in vitro experiments as well as in vivo conditions.

3. SOLUTION OF REACTION NETWORK MODEL: Two approaches are used identify solutions of the biochemical reaction network: (1) particle-based simulation models involving diffusion and reaction and (2) stochastic simulation of the reaction kinetics.

In our model, [A] is the concentration of C99 monomer, [A2] is the concentration of C99 dimer, and [C] and [C2] are concentrations of cholesterol monomer and cholesterol dimer.

The basic kinetic model is

Fig 2. Representation of C99-cholesterol complex. Cholesterol molecules are marked in blue, lipid molecules are in gray, and peptides are shown as blue cylinders.3

Expressed in differential equation form

Additional Background

In the lipids of biomembranes, phosphatidylcholine–based lipids with cholesterol can adopt the two coexisting fluid phases that are Liquid-Disordered phase (Ld) and Liquid-Ordered phase (Lo). Lo phase domains, high in cholesterol are known as “raft”.

The reaction network can be further generalized to include two lipid domains (liquid ordered and liquid disordered) and additional lipids (sphingomyelin) that may bind cholesterol. Following the validation of our model, a broad range of "initial conditions" for the concentrations of APP-C99 and cholesterol (and later sphingomyelin) might be studied. Our ultimate goal is to develop a detailed understanding of the predominant species expected for each range of concentration of protein and cholesterol. This knowledge will be used to address critical questions regarding the state of the APP-C99 protein, namely: "Is APP-C99 predominantly a monomer or a dimer?" and "Is APP-C99 free or bound to cholesterol?" Addressing these open questions will represent a fundamental contribution to AD research.

Fig5. Representation of ripple phase, solid-ordered phase, liquid-disordered phase, and liquid-ordered phase. Eeman, M; Deleu, M, Base, 14(4), 2010(2009)

Represented of Lo and Ld domains may be included as

Fig 4. Another representation of Ld and Lo domains.Meer, G; Voelker,D ; Feigenson, G, Nature Reviews Molecular Cell Biology , 9, 112-124 (2008)

Fig 6. Liquid-ordered phase is on the left of the origin and the Liquid-disorder is on the right. There are two C99 monomers which marked in red and blue. (Left) moving trajectory of the particles. (Right) change of number of particles. Red line represents the monomer, and blue line represents the dimer.

A = C99 monomer= C99 dimer C = cholesterol monomer = cholesterol dimerAC = C99 – cholesterol heterodimer = Association rate of two C99 monomers = Dissociation rate of C99 dimer = Association rate of C99 monomer and cholesterol monomer = Dissociation rate of C99 – cholesterol heterodimer = Association rate of two cholesterol monomers = Dissociation rate of cholesterol dimer

We used diffusion rates, encounter radii, and dissociation constants of C99 and cholesterol in POPC lipid bilayer.

Temperature: 29.85 degree CelsiusTime span: 50 – 200 nanosecondsLiquid disordered phase: Diffusion rate of C99 (POPC): Diffusion rate of Cholesterol (POPC): Encounter radii of C99 homo-dimerization: 9.3 AngstromEncounter radii of cholesterol homo-dimerization: 6.9 AngstromEncounter radii of C99 - cholesterol hetero-dimerization: 9.5 Angstrom

There is no experimental study for the diffusion rate of the C99 dimer. Following Saffman and Delbruck (1975) we assumed the diffusion rate of the homodimer is twice as fast as the monomer.

The particle-based numerical model includes a continuous time random walk model and Brownian motion. The continuous time random walk model approximates diffusive motion of the protein in a lipid membrane.

1. Modeling the diffusion in liquid ordered phase and disordered phases By programing in python, the simplest model with two phases that separated from the origin was built up. Particles in the model are set at random positions at the beginning and then do random walks in certain time steps. We can observe from the trajectory that particles move faster in the disordered phase than in the ordered phase.

Fig 7. (Left)There are 10 C99 monomers marked in different colors in the system. (Right) the system includes association and dissociation.

2. Simulating the association of C99 and Cholesterol Homo-dimerization We ignored the dissociation of the dimer and assumed the concentration of the C99 or cholesterol in the system doesn’t change in the process of dimerization. The association rate of C99 and cholesterol dimerization was then calculated. According to the stochastic model, the association rate for C99 is and the association rate for cholesterol is 1.41.

Fig 8. Inverse number of C99 versus time (seconds) where the slope will give us the association rate in units of 1/s. The blue line is the data generated from the stochastic model with the standard deviation in blue. The red line and red region are data from Gillespie algorithm.