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Abstracts and Talk Materials
Network Dynamics and Cell Physiology
April 17-18, 2008


Daniel Forger (University of Michigan)
http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=forger

Lecture 5: Models of circadian rhythms
April 18, 2008

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

Daniel Forger (University of Michigan)
http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=forger

Lecture 6: Synchronization and phase resetting
April 18, 2008

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.

Daniel Forger (University of Michigan)
http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=forger
John J. Tyson (Virginia Polytechnic Institute and State University)
http://mpf.biol.vt.edu/people/tyson/tyson.html

Computer Lab 2: Modeling exercises
April 17, 2008

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

Daniel Forger (University of Michigan)
http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=forger
John J. Tyson (Virginia Polytechnic Institute and State University)
http://mpf.biol.vt.edu/people/tyson/tyson.html

Computer Lab 3: Stochastic Simulation
April 18, 2008

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

Daniel Forger (University of Michigan)
http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=forger
John J. Tyson (Virginia Polytechnic Institute and State University)
http://mpf.biol.vt.edu/people/tyson/tyson.html

Computer Lab 1: Phase planes, vector fields, nullclines, bifurcations
April 17, 2008

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.

Daniel Forger (University of Michigan)
http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=forger

Lecture 4: Stochastic modeling of molecular regulatory networks
April 18, 2008

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.

John J. Tyson (Virginia Polytechnic Institute and State University)
http://mpf.biol.vt.edu/people/tyson/tyson.html

Lecture 2: Network motifs: sniffers, buzzers, toggles and blinkers
April 17, 2008

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.

John J. Tyson (Virginia Polytechnic Institute and State University)
http://mpf.biol.vt.edu/people/tyson/tyson.html

Lecture 3: Cell cycle regulation
April 17, 2008

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.

John J. Tyson (Virginia Polytechnic Institute and State University)
http://mpf.biol.vt.edu/people/tyson/tyson.html

Lecture 1: Cell physiology, molecular biology and mathematical modeling
April 17, 2008

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.

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