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.