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DY: Fachverband Dynamik und Statistische Physik

DY 1: Statistical Physics of Biological Systems I (with BP, talks from DY)

DY 1.9: Vortrag

Montag, 26. März 2012, 11:45–12:00, MA 001

Stochastic description of birth and death processes governed by a mixture of exponential and non-exponential waiting times — •Stephan Eule — Max-Planck-Institut für Dynamik und Selbstorganisation, Göttingen

The dynamics of complex biological systems is significantly influenced by fluctuations originating from intrinsic as well as extrinsic sources. In general, the discrete nature of individual events, such as the birth and death of an individual in a population or the production and degradation of molecules in a chemical reaction, is the main source of intrinsic noise. The occurrence of such events is usually modeled by Poissonian statistics, implying that the probability per unit time for an event to happen is assumed to be constant. Many complex systems however exhibit deviations from elementary Poissonian statistics. Such deviations can arise for example in coarse-grained stochastic models of gene expression, where the waiting time distribution can be more general than the simple exponential distribution.

In this contribution we consider birth and death processes which are governed by both, exponential as well as non-exponential waiting times. We derive the corresponding master equation and present methods to approach this equation analytically. As an example we consider a reaction where the production of molecules is governed by a non-exponential waiting time distribution and the degradation follows regular Poissonian statistics.