Dresden 2014 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 16: Statistical Physics in Biological Systems (joint session DY/ BP)

DY 16.3: Vortrag

Mittwoch, 2. April 2014, 10:00–10:15, ZEU 160

Stochastic Processes with Delays and Their Application to Gene Regulation and Epidemics — •Tobias Brett and Tobias Galla — The University of Manchester, Manchester, United Kingdom

Many of the systems modeled in biology have memory: not all of the effects of interactions can be well approximated as occurring instantaneously. Examples are transcriptional and translational delays in gene regulation, or recovery periods in the context of infectious diseases. We focus on chemical reaction models with delays. For such processes it is not straightforward to formulate Master equations, and it is not clear how to derive systematic Gaussian approximations. We demonstrate that progress can be made using a path-focused view, based on generating functionals. These do not describe the time-evolution of one-time probability distributions, instead they capture the probabilities of entire paths. We derive analytical expressions for Gaussian approximations for a wide class of delay systems, and apply these to two biological problems in which delay is relevant. One is the susceptible-infective-recovered model in epidemiology and the other a model of delayed autoinhibition in gene regulation. This allows us to characterise the phenomena arising from the combination of intrinsic noise and delayed dynamics.

Reference: T. Brett, T. Galla, Phys. Rev. Lett. 110, 250601 (2013)