Mathematical Biology and Ecology Seminar
Wednesday, February 3, 2010 - 11:00
1 hour (actually 50 minutes)
Even the simplest biochemical networks often have more degrees of freedoms than one can (or should!) analyze. Can we ever hope to do the physicists' favorite trick of coarse-graining, simplifying the networks to a much smaller set of effective dynamical variables that still capture the relevant aspects of the kinetics? I will argue then that methods of statistical physics provide hints at the existence of rigorous coarse-grained methodologies in modeling biological information processing systems, allowing to identify features of the systems that are relevant to their functions. While a general solution is still far away, I will focus on a specific example illustrating the approach. Namely, for a a general stochastic network exhibiting the kinetic proofreading behavior, I will show that the microscopic parameters of the system are largely important only to the extent that they contribute to a single aggregate parameter, the mean first passage time through the network, and the higher cumulants of the escape time distribution are related to this parameter uniquely. Thus a phenomenological model with a single parameter does a good job explaining all of the observable data generated by this complex system.