Stochastic dynamics for systems biology. (2016)

• Record Type: Book
• Further Information: Note: By Christian Mazza, Michel Benaim.
• Authors: Mazza, Christian; Benaim, Michel
• Contents: Dynamics of Reaction Networks: Markov Processes; Reaction Networks: Introduction; Introduction to modelling: a self-regulated gene; Birth and death processes to model basic chemical reactions; Some results on the self-regulated gene Continuous-Time Markov Chains; Introduction; General time-continuous Markov chains; Some important Markov chains; Two-time-scale stochastic simulations Illustrations from Systems Biology; First-Order Chemical Reaction Networks; Reaction networks; Linear first-order reaction networks; Statistical descriptors for linear rate functions; Open and closed conversion systems; Illustration: Intrinsic noise in gene regulatory networks Biochemical Pathways; Stochastic fluctuations in metabolic pathways; Signalling networks Binding Processes and Transcription Rates; Positive and negative control; Binding probabilities; Gibbs-Boltzmann distributions; Local Hill coefficients; Cooperativity in the microstate; The sigmoidal nature of the binding curve; Cooperativity in the Hill sense; ηH(v) as an indicator of cooperativity; The cooperativity index; Macroscopic cooperativity; The case N = 3; Transcription rates for basic models; A genetic switch: regulation by λ phage repressor Kinetics of Binding Processes; A mathematical model of eukaryotic gene activation; Steady state distribution of more general binding processes Transcription Factor Binding at Nucleosomal DNA; Competition between nucleosomes and TF; Nucleosome-mediated cooperativity between TF Signalling Switches; Ordered phosphorylation; Unordered phosphorylation A Short Course on Dynamical Systems; Differential Equations, Flows, and Vector Fields; Some examples; Vector fields and differential equations; Existence and uniqueness theorems; Higher order and nonautonomous equations; Flow and phase portrait Equilibria, Periodic Orbits and Limit Cycles; Equilibria, periodic orbits and invariant sets; Alpha and omega limit sets; The Poincaré-Bendixson theorem; Chaos; Lyapunov functions; Attractors; Stability in autonomous systems; Application to Lotka-Volterra equations Linearisation; Linear differential equations; Linearization and stable manifolds Linear Noise Approximation; Density-Dependent Population Processes and the Linear Noise Approximation; A law of large numbers; Illustration: bistable behaviour of self-regulated genes; Epigenetics and multistationarity; Gaussian approximation; Illustration: attenuation of noise using negative feedback loops in prokaryotic transcription Mass Action Kinetics; Deterministic mass action kinetics and the deficiency zero theorem; Stochastic mass action kinetics; Extension to more general dynamics Appendix; Self-Regulated Genes; Dimerisation ; Transcription with fast dimerisation Asymptotic Behaviour of the Solutions to Time-Continuous Lyapunov Equations; Time-continuous Lyapunov equations; Asymptotically autonomous dynamical systems Bibliography Index
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2016
• Extent: 1 online resource (274 pages), (9 illustrations)
• Subjects: 572.8650151828; Gene expression -- Statistical methods; Systems biology -- Statistical methods
• Languages: English
• ISBNs: 9781466514942; 1466514949
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.