Feedback Control in Systems Biology

Introduction What is feedback control? Feedback control in biological systems Application of control theory to biological systems: a historical perspective References Linear systems Introduction State-space models Linear time-invariant systems and the frequency response Fourier analysis Transfer functions and the Laplace transform Stability 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 References Nonlinear systems Introduction 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 References Negative feedback systems Introduction 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 References Positive feedback systems Introduction 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 References Model validation using robustness analysis Introduction 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 References Reverse engineering biomolecular networks Introduction 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 References Stochastic effects in biological control systems Introduction 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 References Index