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.
Author(s): Carlo Cosentino, Declan Bates
Edition: 1
Publisher: CRC Press
Year: 2011
Language: English
Pages: 296
Tags: Биологические дисциплины;Матметоды и моделирование в биологии;
Feedback Control in Systems Biology......Page 2
Dedication......Page 4
Contents......Page 6
Preface......Page 10
Acknowledgements......Page 12
Epigraph......Page 14
1.1 What is feedback control?......Page 15
1.2 Feedback control in biological systems......Page 18
1.2.1 The tryptophan operon feedback control system......Page 19
1.2.2 The polyamine feedback control system......Page 20
1.2.3 The heat shock feedback control system......Page 21
1.3 Application of control theory to biological systems:A historical perspective......Page 24
References......Page 25
2.1 Introduction......Page 31
2.2 State-space models......Page 32
2.3 Linear time-invariant systems and the frequency re-sponse......Page 34
2.4 Fourier analysis......Page 40
2.5 Transfer functions and the Laplace transform......Page 44
2.6 Stability......Page 47
2.7 Change of state variables and canonical representa-tions......Page 49
2.8 Characterising system dynamics in the time domain......Page 50
2.9 Characterising system dynamics in the frequencydomain......Page 54
2.10 Block diagram representations of interconnected sys-tems......Page 56
2.11 Case Study I: Characterising the frequency depen-dence of osmo-adaptation in Saccharomyces cere-visiae......Page 61
2.11.2 Frequency domain analysis......Page 62
2.11.3 Time domain analysis......Page 64
2.12 Case Study II: Characterising the dynamics of theDictyostelium external signal receptor network......Page 68
2.12.2 A generic structure for ligand–receptor interactionnetworks......Page 69
2.12.3 Structure of the ligand–receptor interaction networkin aggregating Dictyostelium cells......Page 71
2.12.4 Dynamic response of the ligand–receptor interactionnetwork in Dictyostelium......Page 74
References......Page 77
3.1 Introduction......Page 81
3.2 Equilibrium points......Page 83
3.3 Linearisation around equilibrium points......Page 86
3.4.1 Lyapunov stability......Page 92
3.4.2 Region of attraction......Page 95
3.5 Optimisation methods for nonlinear systems......Page 99
3.5.1 Local optimisation methods......Page 101
3.5.2 Global optimisation methods......Page 103
3.5.3 Linear matrix inequalities......Page 105
3.6 Case Study III: Stability analysis of tumour dor-mancy equilibrium......Page 107
3.6.1 Introduction......Page 108
3.6.2 Model of cancer development......Page 109
3.6.3 Stability of the equilibrium points......Page 110
3.6.4 Checking inclusion in the region of attraction......Page 111
3.6.5 Analysis of the tumour dormancy equilibrium......Page 114
3.7 Case Study IV: Global optimisation of a model ofthe tryptophan control system against multiple ex-periment data......Page 119
3.7.2 Model of the tryptophan control system......Page 120
3.7.3 Model analysis using global optimisation......Page 123
References......Page 124
4.1 Introduction......Page 129
4.2 Stability of negative feedback systems......Page 133
4.3 Performance of negative feedback systems......Page 136
4.4 Fundamental tradeoffs with negative feedback......Page 141
4.5 Case Study V: Analysis of stability and oscillationsin the p53-Mdm2 feedback system......Page 146
4.6 Case Study VI: Perfect adaptation via integral feed-back control in bacterial chemotaxis......Page 151
4.6.1 A mathematical model of bacterial chemotaxis......Page 152
4.6.2 Analysis of the perfect adaptation mechanism......Page 156
4.6.3 Perfect adaptation requires demethylation of active onlyreceptors......Page 159
References......Page 162
5.2.1 Bifurcations and bistability......Page 165
5.2.2 Limit cycles......Page 168
5.3 Monotone systems......Page 172
5.4 Chemical reaction network theory......Page 175
5.4.1 Preliminaries on reaction network structure......Page 176
5.4.2 Networks of deficiency zero......Page 178
5.4.3 Networks of deficiency one......Page 180
5.5 Case Study VII: Positive feedback leads to multista-bility, bifurcations and hysteresis in a MAPK cas-cade......Page 182
5.6 Case Study VIII: Coupled positive and negative feed-back loops in the yeast galactose pathway......Page 189
References......Page 196
6.1 Introduction......Page 199
6.2.1 Bifurcation diagrams......Page 201
6.2.2 Sensitivity analysis......Page 202
6.2.3 μ-analysis......Page 206
6.2.4 Optimisation-based robustness analysis......Page 209
6.2.5 Sum-of-squares polynomials......Page 210
6.2.6 Monte Carlo simulation......Page 212
6.3 New robustness analysis tools for biological systems......Page 213
6.4 Case Study IX: Validating models of cAMP oscilla-tions in aggregating Dictyostelium cells......Page 216
6.5 Case Study X: Validating models of the p53-Mdm2System......Page 218
References......Page 220
7.2 Inferring network interactions using linear models......Page 225
7.2.1 Discrete-time vs continuous-time model......Page 227
7.3 Least squares......Page 230
7.3.1 Least squares for dynamical systems......Page 234
7.3.2 Methods based on least squares regression......Page 237
7.4 Exploiting prior knowledge......Page 240
7.4.1 Network inference via LMI-based optimisation......Page 241
7.4.2 MAX-PARSE: An algorithm for pruning a fully con-nected network according to maximum parsimony......Page 243
7.5 Dealing with measurement noise......Page 245
7.5.1 Total least squares......Page 246
7.5.2 Constrained total least squares......Page 247
7.6 Exploiting time-varying models......Page 250
7.7 Case Study XI: Inferring regulatory interactions inthe innate immune system from noisy measurements......Page 253
7.8 Case Study XII: Reverse engineering a cell cycleregulatory subnetwork of Saccharomyces cerevisiaefrom experimental microarray data......Page 257
7.8.1 PACTLS: An algorithm for reverse engineering par-tially known networks from noisy data......Page 258
7.8.2 Results......Page 261
References......Page 264
8.1 Introduction......Page 269
8.2 Stochastic modelling and simulation......Page 270
8.3 A framework for analysing the effect of stochasticnoise on stability......Page 273
8.3.1 The effective stability approximation......Page 274
8.3.2 A computationally efficient approximation of the dom-inant stochastic perturbation......Page 275
8.3.3 Analysis using the Nyquist stability criterion......Page 277
8.4 Case Study XIII: Stochastic effects on the stabilityof cAMP oscillations in aggregating Dictyosteliumcells......Page 280
8.5 Case Study XIV: Stochastic effects on the robustnessof cAMP oscillations in aggregating Dictyosteliumcells......Page 285
References......Page 290
Index......Page 293
