Feedback Control in Systems Biology 1st Edition by Carlo Cosentino, Declan Bates ISBN 9781040056592 1040056598

1 Introduction

1.1 What is feedback control?

1.2 Feedback control in biological systems

1.2.1 The tryptophan operon feedback control system

1.2.2 The polyamine feedback control system

1.2.3 The heat shock feedback control system

1.3 Application of control theory to biological systems: A historical perspective

References

2 Linear syst ems

2.1 Introduction

2.2 State-space models

2.3 Linear time-invariant systems and the frequency response

2.4 Fourier analysis

2.5 Transfer functions and the Laplace transform

2.6 Stability

2.7 Change of state variables and canonical representations

2.8 Characterising system dynamics in the time domain

2.9 Characterising system dynamics in the frequency domain

2.10 Block diagram representations of interconnected systems

2.11 Case Study I: Characterising the frequency dependence of osmo-adaptation in Saccharomyces cere-visiae

2.11.1 Introduction

2.11.2 Frequency domain analysis

2.11.3 Time domain analysis

2.12 Case Study II: Characterising the dynamics of the Dictyostelium external signal receptor network

2.12.1 Introduction

2.12.2 A generic structure for ligand-receptor interaction networks

2.12.3 Structure of the ligand-receptor interaction network in aggregating Dictyostelium cells

2.12.4 Dynamic response of the ligand-receptor interaction network in Dictyostelium

References

3 Nonlinear s ystems

3.1 Introduction

3.2 Equilibrium points

3.3 Linearisation around equilibrium points

3.4 Stability and regions of attractions

3.4.1 Lyapunov stability

3.4.2 Region of attraction

3.5 Optimisation methods for nonlinear systems

3.5.1 Local optimisation methods

3.5.2 Global optimisation methods

3.5.3 Linear matrix inequalities

3.6 Case Study III: Stability analysis of tumour dormancy equilibrium

3.6.1 Introduction

3.6.2 Model of cancer development

3.6.3 Stability of the equilibrium points

3.6.4 Checking inclusion in the region of attraction

3.6.5 Analysis of the tumour dormancy equilibrium Validation of the proposed technique

3.7 Case Study IV: Global optimisation of a model of the tryptophan control system against multiple experiment data

3.7.1 Introduction

3.7.2 Model of the tryptophan control system

3.7.3 Model analysis using global optimisation

References

4 Negative fee dback systems

4.1 Introduction

4.2 Stability of negative feedback systems

4.3 Performance of negative feedback systems

4.4 Fundamental tradeoffs with negative feedback

4.5 Case Study V: Analysis of stability and oscillations in the p53-Mdm2 feedback system

4.6 Case Study VI: Perfect adaptation via integral feedback control in bacterial chemotaxis

4.6.1 A mathematical model of bacterial chemotaxis

4.6.2 Analysis of the perfect adaptation mechanism

4.6.3 Perfect adaptation requires demethylation of active only receptors

References

5 Positive fee dback systems

5.1 Introduction

5.2 Bifurcations, bistability and limit cycles

5.2.1 Bifurcations and bistability

5.2.2 Limit cycles

5.3 Monotone systems

5.4 Chemical reaction network theory

5.4.1 Preliminaries on reaction network structure

5.4.2 Networks of deficiency zero

5.4.3 Networks of deficiency one

5.5 Case Study VII: Positive feedback leads to multista bility, bifurcations and hysteresis in a MAPK cas cade

5.6 Case Study VIII: Coupled positive and negative feed back loops in the yeast galactose pathway

References

6 Model valid ation using robustness analysis

6.1 Introduction

6.2 Robustness analysis tools for model validation

6.2.1 Bifurcation diagrams

6.2.2 Sensitivity analysis

6.2.3 μ-analysis

6.2.4 Optimisation-based robustness analysis

6.2.5 Sum-of-squares polynomials

6.2.6 Monte Carlo simulation

6.3 New robustness analysis tools for biological systems

6.4 Case Study IX: Validating models of cAMP oscillations in aggregating Dictyostelium cells

6.5 Case Study X: Validating models of the p53-Mdm2 System

References

7 Reverse eng ineering biomolecular networks

7.1 Introduction

7.2 Inferring network interactions using linear models

7.2.1 Discrete-time vs continuous-time model

7.3 Least squares

7.3.1 Least squares for dynamical systems

7.3.2 Methods based on least squares regression

7.4 Exploiting prior knowledge

7.4.1 Network inference via LMI-based optimisation

7.4.2 MAX-PARSE: An algorithm for pruning a fully connected network according to maximum parsimony

7.4.3 CORE-Net: A network growth algorithm using preferential attachment

7.5 Dealing with measurement noise

7.5.1 Total least squares

7.5.2 Constrained total least squares

7.6 Exploiting time-varying models

7.7 Case Study XI: Inferring regulatory interactions in the innate immune system from noisy measurements

7.8 Case Study XII: Reverse engineering a cell cycle regulatory subnetwork of Saccharomyces cerevisiae from experimental microarray data

7.8.1 PACTLS: An algorithm for reverse engineering partially known networks from noisy data

7.8.2 Results

References

8 Stochastic effects in biological control systems

8.1 Introduction

8.2 Stochastic modelling and simulation

8.3 A framework for analysing the effect of stochastic noise on stability

8.3.1 The effective stability approximation

8.3.2 A computationally efficient approximation of the dominant stochastic perturbation

8.3.3 Analysis using the Nyquist stability criterion

8.4 Case Study XIII: Stochastic effects on the stability of cAMP oscillations in aggregating Dictyostelium cells

8.5 Case Study XIV: Stochastic effects on the robustness of cAMP oscillations in aggregating Dictyostelium cells

References

Index