IMA Tutorial

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					                                    IMA Tutorial
                                          Day 1
Lecture 1:     Cell physiology, molecular biology and mathematical modeling
               John Tyson

An introduction to cell growth and division, programmed cell death, cell differentiation,
motility, and signaling. Basic molecular mechanisms governing these processes.
Modeling molecular mechanisms with ordinary differential equations.

Lecture 2:     Network motifs: sniffers, buzzers, toggles and blinkers
               John Tyson

Simple models of regulatory motifs. Positive and negative feedback. Signal-response
curves and bifurcation diagrams. Adaptation. Ultrasensitivity. Bistability and oscillations.
Simple bifurcations: saddle-node and Hopf. Homoclinic bifurcations.

Comp Lab 1: Phase planes, vector fields, nullclines, bifurcations
            John Tyson and Daniel Forger

How to use WinPP and XPP. Models of bistability and oscillations. Drawing phase plane
portraits. How portraits depend on parameter values. One-parameter bifurcation
diagrams.

Lecture 3:     Cell cycle regulation
               John Tyson

Physiological characteristics of the cell division cycle. Molecular biology of cyclin-
dependent kinases. Simple model of bistability and oscillations in the CDK control
system of frog eggs. More complex models of yeast cell cycles. Mammalian cell cycle
and cancer.

Comp Lab 2: Modeling exercises
            John Tyson and Daniel Forger

Building simple models of cell cycle, circadian rhythm, programmed cell death,
glycolysis, Ca2+ oscillations, etc.
                                        Day 2
Lecture 4:    Stochastic modeling of molecular regulatory networks
              Daniel Forger

Relation between stochastic and deterministic formalisms. Two discrete simulation
methods proposed by Gillespie. 1/N relationship. Noise induced oscillations. Chemical
Langevin equations and hybrid methods. Introduction to simulation packages.

Comp Lab 3: Stochastic Simulation
            Daniel Forger and John Tyson

Simulations of simple models of genetic networks using the Gillespie Method.
Comparison of behavior for small and large number of chemical events.

Lecture 5:    Models of Circadian Rhythms
              Daniel Forger

Basic properties of circadian clocks. Goodwin and early models. More realistic models.
Model predictions and their experimental validation. Temperature Compensation.
Unanswered questions.

Lecture 6:    Synchronization and Phase Resetting
              Daniel Forger

Phase Response Curves, Phase Transition Curves and Winfree’s Type 0 vs. Type 1
distinction. Global vs. local coupling. Pulse vs. sustained coupling. Coupling induced
rhythmicity. Relationship between phase resetting and coupling.