Reversible Interacting-Particle Reaction Dynamics.

Interacting-particle reaction dynamics (iPRD) simulates the spatiotemporal evolution of particles that experience interaction forces and can react with one another. The combination of interaction forces and reactions enables a wide range of complex reactive systems in biology and chemistry to be simulated, but gives rise to new questions such as how to evolve the dynamical equations in a computationally efficient and statistically correct manner. Here we consider reversible reactions such as A + B ⇄ C with interacting particles and derive expressions for the microscopic iPRD simulation parameters such that desired values for the equilibrium constant and the dissociation rate are obtained in the dilute limit. We then introduce a Monte Carlo algorithm that ensures detailed balance in the iPRD time-evolution (iPRD-DB). iPRD-DB guarantees the correct thermodynamics at all concentrations and maintains the desired kinetics in the dilute limit, where chemical rates are well-defined and kinetic measurement experiments usually operate. We show that in dense particle systems, the incorporation of detailed balance is essential to obtain physically realistic solutions. iPRD-DB is implemented in ReaDDy 2.

[1]  C. Schütte,et al.  MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations. , 2017, The Journal of chemical physics.

[2]  Esam T Abualrous,et al.  Protein-peptide association kinetics beyond the seconds timescale from atomistic simulations , 2017, Nature Communications.

[3]  F. Noé,et al.  An efficient multi-scale Green's function reaction dynamics scheme. , 2017, The Journal of chemical physics.

[4]  Frank Noé,et al.  Particle-based membrane model for mesoscopic simulation of cellular dynamics. , 2017, The Journal of chemical physics.

[5]  Aleksandar Donev,et al.  Efficient reactive Brownian dynamics. , 2017, The Journal of chemical physics.

[6]  Frank Noé,et al.  Lipid-mediated PX-BAR domain recruitment couples local membrane constriction to endocytic vesicle fission , 2017, Nature Communications.

[7]  F. Noé,et al.  Complete protein–protein association kinetics in atomic detail revealed by molecular dynamics simulations and Markov modelling , 2017, Nature Chemistry.

[8]  V. Haucke,et al.  mTORC1 activity repression by late endosomal phosphatidylinositol 3,4-bisphosphate , 2017, Science.

[9]  Steven S. Andrews,et al.  Smoldyn: particle‐based simulation with rule‐based modeling, improved molecular interaction and a library interface , 2017, Bioinform..

[10]  P. R. ten Wolde,et al.  Multiscale simulations of anisotropic particles combining molecular dynamics and Green's function reaction dynamics. , 2016, The Journal of chemical physics.

[11]  S. Sadiq.  Reaction–diffusion basis of retroviral infectivity , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[12]  D. Scott,et al.  Small molecules, big targets: drug discovery faces the protein–protein interaction challenge , 2016, Nature Reviews Drug Discovery.

[13]  H. Ewers,et al.  Nanoscopic compartmentalization of membrane protein motion at the axon initial segment , 2016, bioRxiv.

[14]  Colleen E. Clancy,et al.  Mechanisms Restricting Diffusion of Intracellular cAMP , 2016, Scientific Reports.

[15]  P. R. ten Wolde,et al.  Combining molecular dynamics with mesoscopic Green's function reaction dynamics simulations. , 2015, The Journal of chemical physics.

[16]  H. Qian,et al.  A Discrete Stochastic Formulation for Reversible Bimolecular Reactions via Diffusion Encounter , 2015, 1511.08798.

[17]  Frank Noé,et al.  Dynamical Organization of Syntaxin-1A at the Presynaptic Active Zone , 2015, PLoS Comput. Biol..

[18]  Frank Noé,et al.  Higher-order architecture of rhodopsin in intact photoreceptors and its implication for phototransduction kinetics. , 2015, Structure.

[19]  Frank Noé,et al.  ReaDDyMM: Fast interacting particle reaction-diffusion simulations using graphical processing units. , 2015, Biophysical journal.

[20]  Frank Noé,et al.  Simulation tools for particle-based reaction-diffusion dynamics in continuous space , 2014, BMC biophysics.

[21]  Margaret E. Johnson,et al.  Free-Propagator Reweighting Integrator for Single-Particle Dynamics in Reaction-Diffusion Models of Heterogeneous Protein-Protein Interaction Systems , 2014, Physical review. X.

[22]  F. Noé,et al.  Explicit spatiotemporal simulation of receptor-G protein coupling in rod cell disk membranes. , 2014, Biophysical journal.

[23]  Peter G Bolhuis,et al.  Sampling the equilibrium kinetic network of Trp-cage in explicit solvent. , 2014, The Journal of chemical physics.

[24]  U. Schwarz,et al.  Studying protein assembly with reversible Brownian dynamics of patchy particles. , 2014, The Journal of chemical physics.

[25]  Max Hoffmann,et al.  Oscillations of Min-proteins in micropatterned environments: a three-dimensional particle-based stochastic simulation approach. , 2014, Soft matter.

[26]  Frank Noé,et al.  ReaDDy - A Software for Particle-Based Reaction-Diffusion Dynamics in Crowded Cellular Environments , 2013, PloS one.

[27]  Frank Noé,et al.  Spatiotemporal control of endocytosis by phosphatidylinositol-3,4-bisphosphate , 2013, Nature.

[28]  T. Franosch,et al.  Anomalous transport in the crowded world of biological cells , 2013, Reports on progress in physics. Physical Society.

[29]  P. R. ten Wolde,et al.  Spatio-temporal correlations can drastically change the response of a MAPK pathway , 2009, Proceedings of the National Academy of Sciences.

[30]  H. McMahon,et al.  Mechanisms of endocytosis. , 2009, Annual review of biochemistry.

[31]  Aleksandar Donev,et al.  A First-Passage Kinetic Monte Carlo algorithm for complex diffusion-reaction systems , 2009, J. Comput. Phys..

[32]  R. Erban,et al.  Stochastic modelling of reaction–diffusion processes: algorithms for bimolecular reactions , 2009, Physical biology.

[33]  P. R. ten Wolde,et al.  Reaction Brownian dynamics and the effect of spatial fluctuations on the gain of a push-pull network. , 2008, The Journal of chemical physics.

[34]  M. Armand,et al.  Building better batteries , 2008, Nature.

[35]  M. Kalos,et al.  First-passage Monte Carlo algorithm: diffusion without all the hops. , 2006, Physical review letters.

[36]  J. Tarascon,et al.  FeP: Another Attractive Anode for the Li-Ion Battery Enlisting a Reversible Two-Step Insertion/Conversion Process , 2006 .

[37]  P. R. ten Wolde,et al.  Green's-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space. , 2005, The Journal of chemical physics.

[38]  U. Bhalla.  Signaling in small subcellular volumes. I. Stochastic and diffusion effects on individual pathways. , 2004, Biophysical journal.

[39]  J. Lippincott-Schwartz,et al.  Development and Use of Fluorescent Protein Markers in Living Cells , 2003, Science.

[40]  P. Swain,et al.  Stochastic Gene Expression in a Single Cell , 2002, Science.

[41]  C. Nobes,et al.  Rho GTPases: molecular switches that control the organization and dynamics of the actin cytoskeleton. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[42]  N. Agmon,et al.  Theory of reversible diffusion‐influenced reactions , 1990 .

[43]  M. Doi.  Stochastic theory of diffusion-controlled reaction , 1976 .

[44]  Masao Doi,et al.  Theory of diffusion-controlled reaction between non-simple molecules. II , 1975 .

[45]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[46]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[47]  George E. Kimball,et al.  Diffusion-controlled reaction rates , 1949 .

[48]  M. Smoluchowski.  Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen , 1918 .

[49]  P. R. ten Wolde,et al.  Green's-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space. , 2005, The Journal of chemical physics.

[50]  P. R. ten Wolde,et al.  Simulating biochemical networks at the particle level and in time and space: Green's function reaction dynamics. , 2005, Physical review letters.

[51]  T. Pollard,et al.  Cellular Motility Driven by Assembly and Disassembly of Actin Filaments , 2003, Cell.

[52]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[53]  W. Balch,et al.  GTPases: multifunctional molecular switches regulating vesicular traffic. , 1994, Annual review of biochemistry.

[54]  C. Brooks.  Computer simulation of liquids , 1989 .

[55]  N. Shigesada,et al.  Theory of Bimolecular Reaction Processes in Liquids , 1967 .