Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology

Description

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. Front Matter ....Pages i-xiii Front Matter ....Pages 1-1 Test Models for Statistical Inference: Two-Dimensional Reaction Systems Displaying Limit Cycle Bifurcations and Bistability (Tomislav Plesa, Tomáš Vejchodský, Radek Erban)....Pages 3-27 Importance Sampling for Metastable and Multiscale Dynamical Systems (K. Spiliopoulos)....Pages 29-53 Multiscale Simulation of Stochastic Reaction-Diffusion Networks (Stefan Engblom, Andreas Hellander, Per Lötstedt)....Pages 55-79 Front Matter ....Pages 81-81 Numerical Methods for Stochastic Simulation: When Stochastic Integration Meets Geometric Numerical Integration (Assyr Abdulle)....Pages 83-107 Stability and Strong Convergence for Spatial Stochastic Kinetics (Stefan Engblom)....Pages 109-125 The T Cells in an Ageing Virtual Mouse (Mario Castro, Grant Lythe, Carmen Molina-París)....Pages 127-140 Front Matter ....Pages 141-141 Model Reduction for Stochastic Reaction Systems (Stephen Smith, Ramon Grima)....Pages 143-158 ZI-Closure Scheme: A Method to Solve and Study Stochastic Reaction Networks (M. Vlysidis, P. H. Constantino, Y. N. Kaznessis)....Pages 159-174 Deterministic and Stochastic Becker–Döring Equations: Past and Recent Mathematical Developments (E. Hingant, R. Yvinec)....Pages 175-204 Coagulation-Fragmentation with a Finite Number of Particles: Models, Stochastic Analysis, and Applications to Telomere Clustering and Viral Capsid Assembly (Nathanael Hoze, David Holcman)....Pages 205-239 A Review of Stochastic and Delay Simulation Approaches in Both Time and Space in Computational Cell Biology (Kevin Burrage, Pamela Burrage, Andre Leier, Tatiana Marquez-Lago)....Pages 241-261 Front Matter ....Pages 263-263 Recent Mathematical Models of Axonal Transport (Chuan Xue, Gregory Jameson)....Pages 265-285 Stochastic Models for Evolving Cellular Populations of Mitochondria: Disease, Development, and Ageing (Hanne Hoitzing, Iain G. Johnston, Nick S. Jones)....Pages 287-314 Modeling and Stochastic Analysis of the Single Photon Response (Jürgen Reingruber, David Holcman)....Pages 315-348 A Phenomenological Spatial Model for Macro-Ecological Patterns in Species-Rich Ecosystems (Fabio Peruzzo, Sandro Azaele)....Pages 349-368 Back Matter ....Pages 369-377