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.

Building simple models of cell cycle, circadian rhythm, programmed cell death, glycolysis, Ca²⁺ oscillations, etc.

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

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.

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

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.

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.

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.

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.