Dynamical Models in Biology

SISSA -- PhD Course Announcement, Fall 2010

Dynamical Models in Biology

Lecturer: Claudio Altafini

altafini@sissa.it

~altafini

Format

approx. 10 lectures

Schedule (temptative)

I will begin in the middle of November (first lecture: Monday 22nd at 11:00)

Mondays at 11:00, room 132, SISSA (Santorio MB)
Wednesdays at 11:00, room 132, SISSA (Santorio MB)

Syllabus

The course aims at providing an overview of some of the mathematical tools used in the modeling of biological phenomena. The emphasis is on nonlinear models and system analysis, and the examples are mostly from signaling and metabolic pathways.

Topics:

Qualitative analysis of ODE models
- single and two-species dynamics
- linear and nonlinear systems, equilibria and (multi)stability, monotonicity
- phase plane, oscillations
Examples of specific ``biological mechanisms''
- autoregulatory gene circuits
- epidemic models (HIV dynamics, kinetic of prion replication)
- oscillations (Hodgkin-Huxley and Fitzhugh-Nagumo models)
- adaptation (bacterial chemotaxis)
- autoinduction (quorum sensing)
Whole network dynamical theories:
- Stoichiometric network analysis
- Metabolic control analysis (sensitivity analysis)
- Chemical reaction network theory

Reading material

standard textbooks like
- L. Edelstein-Keshet. "Mathematical Models in Biology", SIAM Classics, 2005.
- J. D. Murray, "Mathematical Biology, Springer-Verlag, 3rd ed. 2001
- E. Sontag, "Lecture Notes in Mathematical Biology", available at the URL: http://www.math.rutgers.edu/~sontag/613.html
- H. Othmer, ``Analysis of complex networks'', Lecture Notes available online at the URL: http://www.math.leidenuniv.nl/~verduyn/Hans.Othmer_course_notes.pdf
M.A. Nowak and R. M. May, "Virus Dynamics", Oxford Univ. Press, 2000.
U. Alon, "An Introduction to Systems Biology", CRC press, 2007.
various sources:
- B. O. Palsson, "Systems Biology", Cambridge Univ. Press, 2006.
- E. Klipp, R. Herwig, A. Kowald, C. Wierling, H. Lerhach, "Systems Biology in Practice", Wiley, 2005.
- M. Feinberg, "Lectures on Chemical Reaction Networks", 1979, available at http://www.che.eng.ohio-state.edu/~FEINBERG/LecturesOnReactionNetworks/