Stochastic Narrow Escape in Molecular and Cellular Biology

Analysis and Applications

  • David Holcman
  • Zeev Schuss

Table of contents

  1. Front Matter
    Pages i-xix
  2. David Holcman, Zeev Schuss
    Pages 1-44
  3. David Holcman, Zeev Schuss
    Pages 45-94
  4. David Holcman, Zeev Schuss
    Pages 95-112
  5. David Holcman, Zeev Schuss
    Pages 113-134
  6. David Holcman, Zeev Schuss
    Pages 135-141
  7. David Holcman, Zeev Schuss
    Pages 143-168
  8. David Holcman, Zeev Schuss
    Pages 169-182
  9. David Holcman, Zeev Schuss
    Pages 183-201
  10. David Holcman, Zeev Schuss
    Pages 203-245
  11. Back Matter
    Pages 247-259

About this book

Introduction

This book covers recent developments in the non-standard asymptotics of the mathematical narrow escape problem in stochastic theory, as well as applications of the narrow escape problem in cell biology. The first part of the book concentrates on mathematical methods, including advanced asymptotic methods in partial equations, and is aimed primarily at applied mathematicians and theoretical physicists who are interested in biological applications. The second part of the book is intended for computational biologists, theoretical chemists, biochemists, biophysicists, and physiologists. It includes a summary of output formulas from the mathematical portion of the book and concentrates on their applications in modeling specific problems in theoretical molecular and cellular biology.

Critical biological processes, such as synaptic plasticity and transmission, activation of genes by transcription factors, or double-strained DNA break repair, are controlled by diffusion in structures that have both large and small spatial scales. These may be small binding sites inside or on the surface of the cell, or narrow passages between subcellular compartments. The great disparity in spatial scales is the key to controlling cell function by structure. This volume reports recent progress on resolving analytical and numerical difficulties in extracting properties from experimental data, biophysical models, and from Brownian dynamics simulations of diffusion in multi-scale structures.

Keywords

Neumann-Dirichlet boundary cellular biology and modeling cellular microdomains mathematical biology movement through cell membrane neurobiology and modeling stochastic narrow escape applications

Authors and affiliations

  • David Holcman
    • 1
  • Zeev Schuss
    • 2
  1. 1.Ecole Normale SuperieureGroup of Applied Mathematics and ComputaParisFrance
  2. 2.Department of MathematicsTel Aviv University School of MathematicTel AvivIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-3103-3
  • Copyright Information Springer Science+Business Media New York 2015
  • Publisher Name Springer, New York, NY
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-1-4939-3102-6
  • Online ISBN 978-1-4939-3103-3
  • About this book