A framework for discrete stochastic simulation on 3D moving boundary domains

We have developed a method for modeling spatial stochastic biochemical reactions in complex, three-dimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. We demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formation during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical.

[1]  J. Segall,et al.  Polarization of yeast cells in spatial gradients of alpha mating factor. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[2]  D. Bray,et al.  Stochastic simulation of chemical reactions with spatial resolution and single molecule detail , 2004, Physical biology.

[3]  L. Christophorou.  Science , 2018, Emerging Dynamics: Science, Energy, Society and Values.

[4]  T. Newman,et al.  Modeling multicellular systems using subcellular elements. , 2005, Mathematical biosciences and engineering : MBE.

[5]  E. Montroll,et al.  Random Walks on Lattices. II , 1965 .

[6]  M. Thattai,et al.  Intrinsic noise in gene regulatory networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Elliott W. Montroll,et al.  Random Walks on Lattices. III. Calculation of First‐Passage Times with Application to Exciton Trapping on Photosynthetic Units , 1969 .

[8]  Scott B. Baden,et al.  Fast Monte Carlo Simulation Methods for Biological Reaction-Diffusion Systems in Solution and on Surfaces , 2008, SIAM J. Sci. Comput..

[9]  Michael A. Gibson,et al.  Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels , 2000 .

[10]  H. Meinhardt,et al.  A theory of biological pattern formation , 1972, Kybernetik.

[11]  L. Petzold,et al.  Reaction-diffusion master equation in the microscopic limit. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Timm Wilke,et al.  Chemie , 2014 .

[13]  H. Kitano,et al.  A quantitative characterization of the yeast heterotrimeric G protein cycle , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[14]  J. Elf,et al.  Stochastic reaction-diffusion kinetics in the microscopic limit , 2010, Proceedings of the National Academy of Sciences.

[15]  J. Elf,et al.  Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases. , 2004, Systems biology.

[16]  M. Ehrenberg,et al.  Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[17]  C. Lumsden,et al.  Stochastic Simulation of Coupled Reaction-Diffusion Processes , 1996 .

[18]  J W Sedat,et al.  Polarization of chemoattractant receptor signaling during neutrophil chemotaxis. , 2000, Science.

[19]  L. Petzold,et al.  Reaction rates for mesoscopic reaction-diffusion kinetics. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  A. Verkman,et al.  Photobleaching recovery and anisotropy decay of green fluorescent protein GFP-S65T in solution and cells: cytoplasmic viscosity probed by green fluorescent protein translational and rotational diffusion. , 1997, Biophysical journal.

[21]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[22]  David Fange,et al.  Noise-Induced Min Phenotypes in E. coli , 2006, PLoS Comput. Biol..

[23]  Christian A Yates,et al.  Discrete and continuous models for tissue growth and shrinkage. , 2014, Journal of theoretical biology.

[24]  Ruth E. Baker,et al.  From Microscopic to Macroscopic Descriptions of Cell Migration on Growing Domains , 2010, Bulletin of mathematical biology.

[25]  Brian Drawert,et al.  Spatial Stochastic Dynamics Enable Robust Cell Polarization , 2013, PLoS Comput. Biol..

[26]  Erwin Frey,et al.  Geometry-induced protein pattern formation , 2016, Proceedings of the National Academy of Sciences.

[27]  P. T. Wolde,et al.  Simulating biochemical networks at the particle level and in time and space: Green's function reaction dynamics. , 2005 .

[28]  Andrew B Goryachev,et al.  Dynamics of Cdc42 network embodies a Turing‐type mechanism of yeast cell polarity , 2008, FEBS letters.

[29]  David Bernstein,et al.  Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithm. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Andreas Hellander,et al.  MOLNs: A cloud platform for interactive, reproducible and scalable spatial stochastic computational experiments in systems biology using PyURDME , 2015, SIAM J. Sci. Comput..

[31]  Radek Erban,et al.  Going from microscopic to macroscopic on nonuniform growing domains. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  C. Gardiner.  Handbook of Stochastic Methods , 1983 .

[33]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[34]  Anders Logg,et al.  DOLFIN: Automated finite element computing , 2010, TOMS.

[35]  P. T. Saunders,et al.  Tip Growth of Fungal Hyphae , 1977 .

[36]  Roger Brent,et al.  Detailed Simulations of Cell Biology with Smoldyn 2.1 , 2010, PLoS Comput. Biol..

[37]  Stefan Hellander,et al.  Reaction rates for a generalized reaction-diffusion master equation. , 2015, Physical review. E.

[38]  Erwin Frey,et al.  GDI-Mediated Cell Polarization in Yeast Provides Precise Spatial and Temporal Control of Cdc42 Signaling , 2013, PLoS Comput. Biol..

[39]  Per Lötstedt,et al.  Flexible single molecule simulation of reaction-diffusion processes , 2011, J. Comput. Phys..

[40]  Heinz Zemanek,et al.  Kybernetik , 1964, Elektron. Rechenanlagen.

[41]  Qing Nie,et al.  Noise filtering tradeoffs in spatial gradient sensing and cell polarization response , 2011, BMC Systems Biology.

[42]  S. Leibler,et al.  Biological rhythms: Circadian clocks limited by noise , 2000, Nature.

[43]  D. Gillespie.  A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .

[44]  Brian Drawert,et al.  The diffusive finite state projection algorithm for efficient simulation of the stochastic reaction-diffusion master equation. , 2010, The Journal of chemical physics.

[45]  Andreas Hellander,et al.  URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries , 2012, BMC Systems Biology.

[46]  Andreas Hellander,et al.  Simulation of Stochastic Reaction-Diffusion Processes on Unstructured Meshes , 2008, SIAM J. Sci. Comput..

[47]  N. Wingreen,et al.  Dynamic structures in Escherichia coli: Spontaneous formation of MinE rings and MinD polar zones , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[48]  A. Bretscher,et al.  Polarization of cell growth in yeast. I. Establishment and maintenance of polarity states. , 2000, Journal of cell science.

[49]  Alexandra Jilkine,et al.  A Density-Dependent Switch Drives Stochastic Clustering and Polarization of Signaling Molecules , 2011, PLoS Comput. Biol..

[50]  Qing Nie,et al.  Robust Spatial Sensing of Mating Pheromone Gradients by Yeast Cells , 2008, PloS one.

[51]  T. Marquez-Lago,et al.  Simulating Stochastic Reaction-Diffusion Systems on and within Moving Boundaries , 2014, PloS one.