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Stochastic processes, multiscale modeling, and numerical methods for computational cellular biology

Author: David Holcman
Publisher: Cham, Switzerland : Springer Nature, [2017]
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology.
Springer Verlag 2017
(DLC) 2017952704
(OCoLC)989966603
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: David Holcman
ISBN: 9783319626277 3319626272
OCLC Number: 1005850974
Description: 1 online resource (xiii, 377 pages) : color illustrations
Contents: Part I: Stochastic Chemical Reactions.- Test Models for Statistical Inference: Two-Dimensional Reaction Systems Displaying Limit Cycle Bifurcations and Bistability.- Importance Sampling for Metastable and Multiscale Dynamical Systems.- Multiscale Simulation of Stochastic Reaction-diffusion Networks.- Part II: Stochastic Numerical Approaches, Algorithms and Coarse-Grained Simulations.- Numerical Methods for Ergodic SDEs: When Stochastic Integration Meets Geometric Integration.- Stability and Strong Convergence for Spatial Stochastic Kinetics.- The T cells in an Ageing Virtual Mouse.- Part III: Analysis of Stochastic Dynamical Systems for Modeling Cell Biology.- Model reduction for Stochastic Reaction Systems.- ZI-closure Scheme: A Method to Solve and Study Stochastic Reaction Networks.- Deterministic and Stochastic Becker-Döring Equations: Past and Recent Mathematical Developments.- Coagulation-Fragmentation with a Finite Number of Particles: Models, Stochastic Analysis and Applications to Telomere Clustering and Viral Capsid Assembly.- A Review of Stochastic and Delay Simulation Approaches in both Time and Space in Computational Cell Biology --
Part IV: Diffusion Processes and Stochastic Modeling.- Recent Mathematical Models of Axonal Transport --
Stochastic Models for Evolving Cellular Populations of Mitochondria: Disease, Development, and Ageing.- Modeling and Stochastic Analysis of the Single Photon Response --
A Phenomenological Spatial Model for Macro-ecological Patterns in Species-rich Ecosystems.
Responsibility: David Holcman, editor.

Abstract:

"This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of stochastic reaction-diffusion models, while in the latter, one can describe the processes by adopting the framework of Markov jump processes and stochastic differential equations. Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology will appeal to graduate students and researchers in the fields of applied mathematics, biophysics, and cellular biology."--Provided by publisher.

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