Advertisement

Analysis of Deterministic Cyclic Gene Regulatory Network Models with Delays

  • Mehmet Eren Ahsen
  • Hitay Özbay
  • Silviu-Iulian Niculescu

Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)

Also part of the SpringerBriefs in Control, Automation and Robotics book sub series (BRIEFSCONTROL)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Mehmet Eren Ahsen, Hitay Özbay, Silviu-Iulian Niculescu
    Pages 1-11
  3. Mehmet Eren Ahsen, Hitay Özbay, Silviu-Iulian Niculescu
    Pages 13-23
  4. Mehmet Eren Ahsen, Hitay Özbay, Silviu-Iulian Niculescu
    Pages 25-42
  5. Mehmet Eren Ahsen, Hitay Özbay, Silviu-Iulian Niculescu
    Pages 43-51
  6. Mehmet Eren Ahsen, Hitay Özbay, Silviu-Iulian Niculescu
    Pages 53-72
  7. Mehmet Eren Ahsen, Hitay Özbay, Silviu-Iulian Niculescu
    Pages 73-85
  8. Mehmet Eren Ahsen, Hitay Özbay, Silviu-Iulian Niculescu
    Pages 87-88
  9. Back Matter
    Pages 89-94

About this book

Introduction

This brief examines a deterministic, ODE-based model for gene regulatory networks (GRN) that incorporates nonlinearities and time-delayed feedback. An introductory chapter provides some insights into molecular biology and GRNs. The mathematical tools necessary for studying the GRN model are then reviewed, in particular Hill functions and Schwarzian derivatives. One chapter is devoted to the analysis of GRNs under negative feedback with time delays and a special case of a homogenous GRN is considered. Asymptotic stability analysis of GRNs under positive feedback is then considered in a separate chapter, in which conditions leading to bi-stability are derived. Graduate and advanced undergraduate students and researchers in control engineering, applied mathematics, systems biology and synthetic biology will find this brief to be a clear and concise introduction to the modeling and analysis of GRNs.

Keywords

Asymptotic Stability Bi-stability Gene regulatory network Hill functions Negative Schwarzian derivative Ordinary differential networks

Authors and affiliations

  • Mehmet Eren Ahsen
    • 1
  • Hitay Özbay
    • 2
  • Silviu-Iulian Niculescu
    • 3
  1. 1.Department of BioengineeringUniversity of Texas at DallasRichardsonUSA
  2. 2.Electrical & Electronics EngineeringBilkent UniversityAnkaraTurkey
  3. 3.Laboratoire des Signaux et SystèmesCNRS - Centrale Supelec - Université Paris-SudGif sur YvetteFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-15606-4
  • Copyright Information The Author(s) 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-15605-7
  • Online ISBN 978-3-319-15606-4
  • Series Print ISSN 2191-8112
  • Series Online ISSN 2191-8120
  • Buy this book on publisher's site
Industry Sectors
Aerospace
Oil, Gas & Geosciences
Engineering