Overview
- Includes a concise introduction to the necessary molecular biology for mathematicians
- Focuses on a deterministic, ODE-based model of GRNs, rather than the more difficult-to-analyze models based on Boolean and Bayesian networks
- Contains exercises to allow use with graduate-level courses
Part of the book series: SpringerBriefs in Electrical and Computer Engineering (BRIEFSELECTRIC)
Part of the book sub series: SpringerBriefs in Control, Automation and Robotics (BRIEFSCONTROL)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Analysis of Deterministic Cyclic Gene Regulatory Network Models with Delays
Authors: Mehmet Eren Ahsen, Hitay Özbay, Silviu-Iulian Niculescu
Series Title: SpringerBriefs in Electrical and Computer Engineering
DOI: https://doi.org/10.1007/978-3-319-15606-4
Publisher: Birkhäuser Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: The Author(s) 2015
Softcover ISBN: 978-3-319-15605-7Published: 24 March 2015
eBook ISBN: 978-3-319-15606-4Published: 25 February 2015
Series ISSN: 2191-8112
Series E-ISSN: 2191-8120
Edition Number: 1
Number of Pages: XIII, 94
Number of Illustrations: 15 illustrations in colour
Topics: Systems Theory, Control, Mathematical and Computational Biology, Gene Expression, Control, Robotics, Mechatronics