Stochastic Chemical Reaction Systems in Biology

图书简介

This book provides an introduction to the analysis of stochastic dynamic models in biology and medicine. The main aim is to offer a coherent set of probabilistic techniques and mathematical tools which can be used for the simulation and analysis of various biological phenomena. These tools are illustrated on a number of examples. For each example, the biological background is described, and mathematical models are developed following a unified set of principles. These models are then analyzed and, finally, the biological implications of the mathematical results are interpreted. The biological topics covered include gene expression, biochemistry, cellular regulation, and cancer biology. The book will be accessible to graduate students who have a strong background in differential equations, the theory of nonlinear dynamical systems, Markovian stochastic processes, and both discrete and continuous state spaces, and who are familiar with the basic concepts of probability theory.

1. Introduction.- Part I Essentials of Deterministic and Stochastic Chemical Kinetics: 2. Kinetic Rate Equations and the Law of Mass Action.- 3. Probability Distribution and Stochastic Processes.- 4. Large Deviations and Kramers’ rate formula.- 5. The Probabilistic Basis of Chemical Kinetics.- 6. Mesoscopic Thermodynamics of Markov Processes.- 7. Emergent Macroscopic Chemical Thermodynamics.- 8. Phase Transition and Mesoscopic Nonlinear Bistability.- Part III Stochastic Kinetics of Biochemical Systems and Processes: 9. Classic Enzyme Kinetics—The Michaelis-Menten and Briggs-Haldane Theories.- 10. Single-Molecule Enzymology and Driven Biochemical Kinetics with Chemostat.- 11. Stochastic Linear Reaction Kinetic Systems.- 12. Nonlinear Stochastic Reaction Systems with Simple Examples.- 13. Kinetics of the Central Dogma of Molecular Cell Biology.- 14. Stochastic Macromolecular Mechanics and Mechanochemistry.- Part IV Epilogue: Beyond Chemical Reaction Kinetics: 15. Landscape, Attractor-State Switching, and Differentiation.- 16. Nonlinear Stochastic Dynamics: New Paradigm and Syntheses.- References.- Index.

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Stochastic Chemical Reaction Systems in Biology（Lecture Notes on Mathematical Modelling in the Life Sciences） 生物学中的随机化学反应系统 数学史

Stochastic Chemical Reaction Systems in Biology（Lecture Notes on Mathematical Modelling in the Life Sciences）

生物学中的随机化学反应系统
数学史