Stochastic Dynamics for Systems Biology Chapman & Hall/CRC Mathematical Biology Series
Auteurs : Mazza Christian, Benaim Michel
Stochastic Dynamics for Systems Biology is one of the first books to provide a systematic study of the many stochastic models used in systems biology. The book shows how the mathematical models are used as technical tools for simulating biological processes and how the models lead to conceptual insights on the functioning of the cellular processing system. Most of the text should be accessible to scientists with basic knowledge in calculus and probability theory.
The authors illustrate the relevant Markov chain theory using realistic models from systems biology, including signaling and metabolic pathways, phosphorylation processes, genetic switches, and transcription. A central part of the book presents an original and up-to-date treatment of cooperativity. The book defines classical indexes, such as the Hill coefficient, using notions from statistical mechanics. It explains why binding curves often have S-shapes and why cooperative behaviors can lead to ultrasensitive genetic switches. These notions are then used to model transcription rates. Examples cover the phage lambda genetic switch and eukaryotic gene expression.
The book then presents a short course on dynamical systems and describes stochastic aspects of linear noise approximation. This mathematical framework enables the simplification of complex stochastic dynamics using Gaussian processes and nonlinear ODEs. Simple examples illustrate the technique in noise propagation in gene networks and the effects of network structures on multistability and gene expression noise levels. The last chapter provides up-to-date results on stochastic and deterministic mass action kinetics with applications to enzymatic biochemical reactions and metabolic pathways.
Dynamics of Reaction Networks: Markov Processes: Reaction Networks: Introduction. Continuous-Time Markov Chains. Illustrations from Systems Biology: First-Order Chemical Reaction Networks. Biochemical Pathways. Binding Processes and Transcription Rates. Kinetics of Binding Processes. Transcription Factor Binding at Nucleosomal DNA. Signalling Switches. A Short Course on Dynamical Systems: Differential Equations, Flows, and Vector Fields. Equilibria, Periodic Orbits and Limit Cycles. Linearization. Linear Noise Approximation: Density-Dependent Population Processes and the Linear Noise Approximation. Mass Action Kinetics. Appendix: Self-Regulated Genes. Asymptotic Behavior of the Solutions to Time-Continuous Lyapunov Equations. Bibliography. Index.
Date de parution : 03-2014
15.6x23.4 cm
Thèmes de Stochastic Dynamics for Systems Biology :
Mots-clés :
Stochastic Models Used In Systems Biology; Functioning Of The Cellular Processing System; Stochastic Aspects Of Linear Noise Approximation; Noise Propagation In Gene Networks; Stochastic And Deterministic Mass Action Kinetics; Simulating Biological Processes; Cooperativity And Ultrasensitive Genetic Switches; Simplification Of Complex Stochastic Dynamics Using Gaussian Processes And Nonlinear Odes; Unique Invariant Probability Measure; Enzymatic Biochemical Reactions And Metabolic Pathways; Ordinary Differential Equation; Time Continuous Markov Chains; Nucleosomal DNA; Vice Versa; Steady State Distribution; Gene Networks; Mass Action Kinetics; Invariant Probability Measure; Chemical Reaction Networks; Matrix Tree Theorem; Markov Chain; Gibbs Boltzmann Distribution; Hill Coefficient; Mass Action Principle; Mass Action; Phase Portrait; Detailed Balance Equation; Free Energy Function; Hill Sense; Binding Sites; Invariant Measure; Propensity Functions; Ligand Molecule; Omega Limit Set