Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 72: Poster: Stoch. and Nonl. Dy., Modeling, Compl. Sys.

DY 72.3: Poster

Thursday, March 15, 2018, 15:30–18:00, Poster A

The influence of intrinsic noise on the dynamics of small gene regulation modules — •Lara Becker and Barbara Drossel — TU Darmstadt, Germany

We examine how the intrinsic stochasticity associated with small molecule numbers affects the dynamics of simple two-gene modules in gene regulatory networks. To this purpose, we model the module in terms of a set of chemical reactions for the involved mRNA and protein molecules. We compare the dynamics obtained from deterministic rate equations with the stochastic dynamics obtained from the Master equation. For the deterministic version, we use the generalized modelling approach, which is based on a linear stability analysis of fixed points, in order to obtain the stability diagram that shows the saddle-node and Hopf bifurcations of the system. For the stochastic system, we perform stochastic simulations using the Gillespie algorithm. We also perform various analytical studies of the stochastic system. On the one hand, we calculate the power spectral density of the fluctuations based on the Linear Noise Approximation and show that for the two-gene negative feedback loop oscillatory behaviour can occur for the stochastic model while it cannot for the deterministic model. Furthermore, we calculate stochastic phase portraits in order to explore the parameter range that shows bistability in the deterministic model.