Stochastic Dynamics in Computational Biology

1. Front Matter

   Pages I-XVIII

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2. Well-Mixed Stochastic Reaction Kinetics

   • Stefanie Winkelmann, Christof Schütte

   Pages 1-36

3. Population Scaling

   • Stefanie Winkelmann, Christof Schütte

   Pages 37-104

4. Temporal Scaling

   • Stefanie Winkelmann, Christof Schütte

   Pages 105-129

5. Spatial Scaling

   • Stefanie Winkelmann, Christof Schütte

   Pages 131-182

6. Back Matter

   Pages 183-272

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The aim of this book is to provide a well-structured and coherent overview of existing mathematical modeling approaches for biochemical reaction systems, investigating relations between both the conventional models and several types of deterministic-stochastic hybrid model recombinations. Another main objective is to illustrate and compare diverse numerical simulation schemes and their computational effort. Unlike related works, this book presents a broad scope in its applications, from offering a detailed introduction to hybrid approaches for the case of multiple population scales to discussing the setting of time-scale separation resulting from widely varying firing rates of reaction channels. Additionally, it also addresses modeling approaches for non well-mixed reaction-diffusion dynamics, including deterministic and stochastic PDEs and spatiotemporal master equations. Finally, by translating and incorporating complex theory to a level accessible to non-mathematicians, this book effectively bridges the gap between mathematical research in computational biology and its practical use in biological, biochemical, and biomedical systems.

• Hybrid models
• Chemical reaction network
• reaction-diffusion process
• Chemical master equation
• Stochastic simulation
• Reaction rate equation
• Gene expression
• enzyme kinetics
• hybrid models
• multi-scale systems

“The primary audience is graduate students and researchers. … content would have to be selected and formatted for lectures carefully. It is most suitable for independent study, and is especially useful as a reference text for the foundations of techniques used in current research. The choice of references are excellent and very current: it is a good survey of both the relevant foundations and current state of research … and would be a useful starting point for a literature review.” (Chay Paterson, zbMATH 1467.92005, 2021)

• Zuse Institute Berlin, Berlin, Germany

  Stefanie Winkelmann

• Institute of Mathematics, Freie Universität Berlin, Berlin, Germany, Zuse Institute Berlin, Berlin, Germany

  Christof Schütte

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