April 17-18, 2008
Computer Lab 1: Phase planes, vector fields, nullclines, bifurcationsApril 17, 2008 1:15 pm - 2:30 pm
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.
Computer Lab 2: Modeling exercises
April 17, 2008 4:00 pm - 5:00 pm
Building simple models of cell cycle, circadian rhythm, programmed cell death, glycolysis, Ca2+ oscillations, etc.
Computer Lab 3: Stochastic Simulation
April 18, 2008 1:15 pm - 2:30 pm
Simulations of simple models of genetic networks using the Gillespie Method. Comparison of behavior for small and large number of chemical events.
Lecture 4: Stochastic modeling of molecular regulatory networksApril 18, 2008 9:00 am - 9:00 am
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.
Lecture 5: Models of circadian rhythms April 18, 2008 10:30 am - 11:30 am
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 resettingApril 18, 2008 3:00 pm - 4:00 pm
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.
Lecture 1: Cell physiology, molecular biology and mathematical modelingApril 17, 2008 9:00 am - 10:00 am
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 blinkersApril 17, 2008 10:30 am - 11:30 am
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.
Lecture 3: Cell cycle regulationApril 17, 2008 3:00 pm - 4:00 pm
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.