Title Stochastic modelling of reaction-diffusion processes / Radek Erban (University of Oxford), S. Jonathan Chapman (University of Oxford)

Published Cambridge ; New York, NY : Cambridge University Press, [2020] ©2020

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Description 1 online resource Series Cambridge texts in applied mathematics Cambridge texts in applied mathematics. Contents Cover -- Half-title page -- Series page -- Title page -- Copyright page -- Contents -- Preface -- 1 Stochastic Simulation of Chemical Reactions -- 1.1 Stochastic Simulation of Degradation -- 1.2 Stochastic Simulation of Production and Degradation -- 1.3 Higher-Order Chemical Reactions -- 1.4 Stochastic Simulation of Dimerization -- 1.5 Gillespie Algorithm -- Exercises -- 2 Deterministic versus Stochastic Modelling -- 2.1 Systems with Multiple Favourable States -- 2.2 Self-Induced Stochastic Resonance -- 2.3 Stochastic Focusing -- 2.4 Designing Stochastic Chemical Systems -- Exercises 3 Stochastic Differential Equations -- 3.1 A Computational Definition of SDE -- 3.2 Examples of SDEs -- 3.3 Fokker-Planck Equation -- 3.4 Boundary Conditions on the Fokker-Planck Equation -- 3.5 Kolmogorov Backward Equation -- 3.6 SDEs with Multiple Favourable States -- 3.7 Chemical Fokker-Planck Equation -- 3.8 Analysis of Problem from Section 2.1 -- 3.9 Analysis of Problem from Section 2.2 -- Exercises -- 4 Diffusion -- 4.1 Diffusion Modelled by SDEs -- 4.2 Compartment-Based Approach to Diffusion -- 4.3 Diffusion and Velocity-Jump Processes -- 4.4 Diffusion to Adsorbing Surfaces 4.5 Reactive Boundary Conditions -- 4.6 Einstein-Smoluchowski Relation -- Exercises -- 5 Efficient Stochastic Modelling of Chemical Reactions -- 5.1 A Simple Multiscale Problem -- 5.2 Multiscale SSA with Partial Equilibrium Assumption -- 5.3 Multiscale Modelling -- 5.4 First-Reaction SSA -- 5.5 Exact Efficient SSAs -- Exercises -- 6 Stochastic Reaction-Diffusion Models -- 6.1 A Compartment-Based Reaction-Diffusion Algorithm -- 6.2 A Reaction-Diffusion SSA Based on the SDE Model of Diffusion -- 6.3 Compartment-Based SSA for Higher-Order Reactions -- 6.4 A Choice of Compartment Size h 6.5 Molecular-Based Approaches for Second-Order Reactions -- 6.6 Reaction Radius and Reaction Probability -- 6.7 Modelling Reversible Reactions -- 6.8 Biological Pattern Formation -- Exercises -- 7 SSAs for Reaction-Diffusion-Advection Processes -- 7.1 SSAs for Diffusion-Advection Processes -- 7.2 Reaction-Diffusion-Advection SSAs -- 7.3 Bacterial Chemotaxis -- 7.4 Collective Behaviour of Locusts -- 7.5 Ions and Ion Channels -- 7.6 Metropolis-Hastings Algorithm -- Exercises -- 8 Microscopic Models of Brownian Motion -- 8.1 One-Particle Solvent Model -- 8.2 Generalized Langevin Equation 8.3 Solvent as Harmonic Oscillators -- 8.4 Solvent as Points Colliding with the Diffusing Particle -- 8.5 Forces Between Atoms and Molecules -- 8.6 Molecular Dynamics -- Exercises -- 9 Multiscale and Multi-Resolution Methods -- 9.1 Coupling SDE-Based and Compartment-Based Models -- 9.2 Coupling Molecular Dynamics with Langevin Dynamics -- 9.3 Multi-Resolution Molecular and Brownian Dynamics -- Exercises -- Appendix -- Appendix A Deterministic Modelling of Chemical Reactions -- Appendix B Discrete Probability Distributions -- Appendix C Continuous Probability Distributions -- References -- Index Summary This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models Bibliography Includes bibliographical references and index Notes Online resource; title from digital title page (viewed on November 26, 2019) Subject Stochastic processes -- Textbooks Reaction-diffusion equations -- Textbooks Reaction-diffusion equations Stochastic processes Genre/Form Textbooks Form Electronic book Author Chapman, Jon, author. ISBN 9781108628389 1108628389

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