Feedback Control in Systems Biology

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ISBN 9781439816905
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  • Explains how feedback control theory can be used to quantitatively characterize biological circuitry
  • Delivers a sound theoretical basis in control engineering for biologists with no previous knowledge of the field
  • Uses research-based examples to illustrate concepts and techniques
  • Focuses on applications, without too much complicated math
  • Emphasizes fundamental concepts and ideas used to analyze, rather than design, feedback systems
  • Discusses nonlinear systems, an understanding of which is crucial for systems biologists
  • Includes extensive references to aid with comprehension
  • Contains more than 100 illustrations


Like engineering systems, biological systems must also operate effectively in the presence of internal and external uncertainty—such as genetic mutations or temperature changes, for example. It is not surprising, then, that evolution has resulted in the widespread use of feedback, and research in systems biology over the past decade has shown that feedback control systems are widely found in biology. As an increasing number of researchers in the life sciences become interested in control-theoretic ideas such as feedback, stability, noise and disturbance attenuation, and robustness, there is a need for a text that explains feedback control as it applies to biological systems.

Written by established researchers in both control engineering and systems biology, Feedback Control in Systems Biology explains how feedback control concepts can be applied to systems biology. Filling the need for a text on control theory for systems biologists, it provides an overview of relevant ideas and methods from control engineering and illustrates their application to the analysis of biological systems with case studies in cellular and molecular biology.

Control Theory for Systems Biologists

The book focuses on the fundamental concepts used to analyze the effects of feedback in biological control systems, rather than the control system design methods that form the core of most control textbooks. In addition, the authors do not assume that readers are familiar with control theory. They focus on "control applications" such as metabolic and gene-regulatory networks rather than aircraft, robots, or engines, and on mathematical models derived from classical reaction kinetics rather than classical mechanics. Another significant feature of the book is that it discusses nonlinear systems, an understanding of which is crucial for systems biologists because of the highly nonlinear nature of biological systems.

The authors cover tools and techniques for the analysis of linear and nonlinear systems; negative and positive feedback; robustness analysis methods; techniques for the reverse-engineering of biological interaction networks; and the analysis of stochastic biological control systems. They also identify new research directions for control theory inspired by the dynamic characteristics of biological systems. A valuable reference for researchers, this text offers a sound starting point for scientists entering this fascinating and rapidly developing field.

Table of Contents

What is feedback control?
Feedback control in biological systems
Application of control theory to biological systems: a historical perspective

Linear systems
State-space models
Linear time-invariant systems and the frequency response
Fourier analysis
Transfer functions and the Laplace transform
Change of state variables and canonical representations
Characterising system dynamics in the time domain
Characterising system dynamics in the frequency domain
Block diagram representations of interconnected systems
Case Study I: Characterising the frequency dependence of osmo–adaptation in Saccharomyces cerevisiae
Case Study II: Characterising the dynamics of the Dictyostelium external signal receptor network

Nonlinear systems
Equilibrium points
Linearisation around equilibrium points
Stability and regions of attractions
Optimisation methods for nonlinear systems
Case study III: Stability analysis of tumor dormancy equilibrium
Case study IV: Global optimisation of a model of the tryptophan control system against multiple experiment data

Negative feedback systems
Stability of negative feedback systems
Performance of negative feedback systems
Fundamental tradeoffs with negative feedback
Case Study V: Analysis of stability and oscillations in the p53-Mdm2 feedback system
Case Study VI: Perfect adaptation via integral feedback control in bacterial chemotaxis

Positive feedback systems
Bifurcations, bistability and limit cycles
Monotone systems
Chemical reaction network theory
Case Study VII: Positive feedback leads to multistability, bifurcations and hysteresis in a MAPK cascade
Case Study VIII: Coupled positive and negative feedback loops in the yeast galactose pathway

Model validation using robustness analysis
Robustness analysis tools for model validation
New robustness analysis tools for biological systems
Case Study IX: Validating models of cAMP oscillations in aggregating Dictyostelium cells
Case Study X: Validating models of the p53-Mdm2 System

Reverse engineering biomolecular networks
Inferring network interactions using linear models
Least squares
Exploiting prior knowledge
Dealing with measurement noise
Exploiting time-varying models
Case Study XI: Inferring regulatory interactions in the innate immune system from noisy measurements
Case Study XII: Reverse engineering a cell cycle regulatory subnetwork of Saccharomyces cerevisiae from experimental microarray data

Stochastic effects in biological control systems
Stochastic modelling and simulation
A framework for analysing the effect of stochastic noise on stability
Case Study XIII: Stochastic effects on the stability of cAMP oscillations in aggregating Dictyostelium cells
Case Study XIV: Stochastic effects on the robustness of cAMP oscillations in aggregating Dictyostelium cells


Author Bio(s)

Editorial Reviews

... sets out the powerful engineering perspective on biological systems in all of its glory. Comprehensive, thoughtful and accessible, this is one of the best books in the field.
—Prof. Michael Stumpf, Division of Molecular Biosciences, Imperial College London

This is an excellent book which will be enjoyed by biologists and theoreticians alike. The authors skilfully combine key concepts from control theory with real cases studies in order to show how the theory can be used both to study and to gain insight into biological networks.
—Prof. Helen Byrne, Centre for Collaborative Applied Mathematics, University of Oxford

Cosentino and Bates address one of the great educational challenges for systems biology—namely the inaccessibility of control theory to life scientists. As so many researchers have demonstrated, control theory has profound relevance for the study of biophysical systems, but Cosentino and Bates are the first to address this topic in a self contained manner for the uninitiated. This book is an essential resource for life scientists interested in the principles of feedback control and nonlinear dynamics.
—Prof. Frank Doyle, Department of Chemical Engineering, University of California at Santa Barbara

Systems biology is an inherently interdisciplinary endeavor, and Cosentino and Bates seamlessly interweave these perspectives into an engaging and comprehensive text that is equally accessible to biologists, computational scientists, and engineers. Through their detailed examination of case studies, the authors develop a general conceptual framework for using quantitative analysis to better understand biological systems. This book is an excellent introduction for researchers new to the field, and it provides compelling and contemporary content for engineering courses on dynamics and control.
—Prof. Joshua Leonard, Department of Chemical and Biological Engineering, Northwestern University

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