This book focuses on the modeling and mathematical analysis of shastic 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, shasticity 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 shastic 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 shastic reaction-diffusion models, while in the latter, one can describe the processes by adopting the framework of Markov jump processes and shastic differential equations.
Shastic 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.