The
Department of Electrical and Computer Engineering
520.636 – Feedback Control of Biological Signaling Pathways – Fall 2011
Information Sheet
(updated: August 31,
2011)
Lecturer: Pablo A. Iglesias, Barton
226A, pi@jhu.edu
Lectures: MW 3:00-4:15, Hackerman 209
Prerequisites: Differential equations, control theory. The latter is not strictly speaking necessary, but useful. Some knowledge of biology is also useful, but I hope to be able to provide you as much as you need.
Grading: Homeworks (20%), Final (60%), Project (20%)
Required text: None. Notes will be supplied.
Recommended texts:
Computational Cell Biology: An Introductory Text on Computer Modeling in Molecular and Cell Biology, Christopher Fall, Eric Marland, John Wagner, John Tyson Springer; ISBN: 0387953698; 1st edition, 2002
Mathematical Physiology. James P. Keener, James Sneyd Springer Verlag; ISBN: 0387983813; 1st edition, 1998
Mathematical Models in Biology. by Leah Edelstein-Keshet McGraw Hill Text; ISBN: 0075549506, 1988
Receptors: Models for Binding, Trafficking, and Signaling by Douglas A. Lauffenburger, Jennifer J. Linderman, Oxford University Press; ISBN: 0195106636 1996
Introduction: To a large extent, signal transduction pathways are nothing but biological feedback controllers. In this course we will look at examples of the use of feedback control in engineering systems and look for counterparts in biological signaling networks. To do this will require some knowledge of mathematical modeling techniques in biology, so a part of the course will be devoted to this.
Final project: Students will be asked to find a signaling pathway in the literature, to design a model of this system and to analyse its control properties.
1. Introduction
2. Modeling biochemical reactions
2.1. Mass action
2.2. Enzyme kinetics
2.3. Enzyme inhibitors
2.4. Cooperativity
3. Stochastic modeling
3.1. The Chemical Master Equation (CME)
3.2. Mean levels of proteins
3.3. Stochastic simulation algorithm (SSA)
3.4. The chemical Langevin equation
3.5. Fokker-Planck equation
3.6. Finite-state projection method
4. Negative feedback: Reducing sensitivity
4.1. Sensitivity
4.2. Feedback inhibition
4.3. Growth factor signaling
4.4. G-protein signaling
4.5. Zero order ultrasensitivity
5. Negative feedback: Regulation and robustness
5.1. Bacterial chemotaxis: Background
5.2. Adaptation
5.3. Temporal sensing
5.4. Internal model principle
6. Negative feedback: Noise suppression
7. Positive feedback: Switching behavior
7.1. Monostable switches
7.2. Bistable switches
8. Positive feedback: Biological oscillators
8.1. An example
8.2. Types of oscillations in biological circuits
8.3. Substrate-depletion oscillator
8.4. Activator-inhibitor oscillator
8.5. Poincare-Bendixson theorem
8.6. Hopf bifurcation
8.7. The Brusselator
8.8. Oscillators without positive feedback
8.9. Relaxation oscillators
9. Spatial modeling
9.1. Modeling diffusion
9.2. Solving diffusion equations
9.3. Diffusion in greater dimensions
9.4. Reaction-diffusion equations
9.5. Reaction-diffusion equations with nonlinear reactions
9.6. Turing instabilities in reaction-diffusion equations
A. Background on dynamical systems theory and control (this will be covered as needed during the rest of the semester)
1.1. Ordinary differential equations
1.2. Equilibrium points
1.3. First order systems – stability, potentials
1.4. Phase plane analysis – second order systems
1.5. Bifurcations (Saddle-node, transcritical and pitchfork)
1.6. Stability – Lyapunov stability, attractivity, asymptotic stability
1.7. Local analysis – linearization, Lyapunov’s indirect method