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

  • David Holcman

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Stochastic Chemical Reactions

    1. Front Matter
      Pages 1-1
    2. Stefan Engblom, Andreas Hellander, Per Lötstedt
      Pages 55-79
  3. Stochastic Numerical Approaches, Algorithms and Coarse-Grained Simulations

    1. Front Matter
      Pages 81-81
    2. Mario Castro, Grant Lythe, Carmen Molina-París
      Pages 127-140
  4. Analysis of Stochastic Dynamical Systems for Modeling Cell Biology

  5. Diffusion Processes and Stochastic Modeling

    1. Front Matter
      Pages 263-263
    2. Chuan Xue, Gregory Jameson
      Pages 265-285
    3. Jürgen Reingruber, David Holcman
      Pages 315-348
  6. Back Matter
    Pages 369-377

About this book


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.


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

Editors and affiliations

  • David Holcman
    • 1
  1. 1.Institute for Biology École Normale SupérieureApplied Mathematics and Computational BiologyParisFrance

Bibliographic information