Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology
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Beschreibung
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, oneneeds 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.
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, oneneeds 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.
Provides a collection of organized reviews on fundamental topics, not necessarily covered by classical text books, due to the interdisciplinary nature of the subject Features new mathematical-physics research in biology, biophysics, and covers stochastic processes in cellular biology Investigates current problems and trends within mathematical biology and how these are described using dynamical systems approaches Includes supplementary material: sn.pub/extras
Autor*in
David Holcman
Themen in »Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology«
Chemical master equation Stochastic integration Numerical methods Modeling cell biology Stochastic Coagulation Fragmentation Exact reduction of chemical reaction networks Asymptotic analysis Fokker-Planck equation Monte Carlo Methods for Multiscale Problems Stochastic analysis Stochastic algorithms for macromolecular simulations systems biology