Simple Mathematical Models of Gene Regulatory Dynamics

  • Michael C. Mackey
  • Moisés Santillán
  • Marta Tyran-Kamińska
  • Eduardo S. Zeron

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Deterministic Modeling Techniques

    1. Front Matter
      Pages 1-1
    2. Michael C. Mackey, Moisés Santillán, Marta Tyran-Kamińska, Eduardo S. Zeron
      Pages 3-6
    3. Michael C. Mackey, Moisés Santillán, Marta Tyran-Kamińska, Eduardo S. Zeron
      Pages 7-27
  3. Dealing with Noise

    1. Front Matter
      Pages 29-30
    2. Michael C. Mackey, Moisés Santillán, Marta Tyran-Kamińska, Eduardo S. Zeron
      Pages 31-47
    3. Michael C. Mackey, Moisés Santillán, Marta Tyran-Kamińska, Eduardo S. Zeron
      Pages 49-69
  4. Specific Examples

    1. Front Matter
      Pages 71-71
    2. Michael C. Mackey, Moisés Santillán, Marta Tyran-Kamińska, Eduardo S. Zeron
      Pages 73-85
    3. Michael C. Mackey, Moisés Santillán, Marta Tyran-Kamińska, Eduardo S. Zeron
      Pages 87-97
    4. Michael C. Mackey, Moisés Santillán, Marta Tyran-Kamińska, Eduardo S. Zeron
      Pages 99-114
  5. Back Matter
    Pages 115-124

About this book

Introduction

This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dynamics. The notes commence with an introduction to the deterministic modeling of gene-networks, with extensive reference to applicable results coming from dynamical systems theory. The second part of the notes treats extensively several approaches to the study of gene-network dynamics in the presence of noise—either arising from low numbers of molecules involved, or due to noise external to the regulatory process.  The third and final part of the notes gives a detailed treatment of three well studied and concrete examples of gene-network dynamics by considering the lactose operon, the tryptophan operon, and the lysis-lysogeny switch.  The notes contain an index for easy location of particular topics as well as an extensive bibliography of the current literature. The target audience of these notes are mainly graduates students and young researchers with a solid mathematical background (calculus, ordinary differential equations, and probability theory at a minimum), as well as with basic notions of biochemistry, cell biology, and molecular biology. They are meant to serve as a readable and brief entry point into a field that is currently highly active, and will allow the reader to grasp the current state of research and so prepare them for defining and tackling new research problems.

Keywords

92-XX, 37-XX gene regulation mathematical modeling operon dynamical systems stochastic systems

Authors and affiliations

  • Michael C. Mackey
    • 1
  • Moisés Santillán
    • 2
  • Marta Tyran-Kamińska
    • 3
  • Eduardo S. Zeron
    • 4
  1. 1.Department of PhysiologyMcGill UniversityMontreal, QCCanada
  2. 2.Unidad MonterreyCinvestav del IPNApodaca, NLMexico
  3. 3.Institute of MathematicsUniversity of SilesiaKatowicePoland
  4. 4.Departamento de MatemáticasCinvestav del IPN Ciudad de MéxicoMexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-45318-7
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-45317-0
  • Online ISBN 978-3-319-45318-7
  • Series Print ISSN 2193-4789
  • Series Online ISSN 2193-4797
  • About this book