Dresden 2009 – wissenschaftliches Programm

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BP: Fachverband Biologische Physik

BP 1: Dynamic Processes and Pattern Formation

BP 1.4: Vortrag

Montag, 23. März 2009, 11:15–11:30, HÜL 186

Generalized analysis of oscillatory systems in cell biology — •Martin Zumsande and Thilo Gross — Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden

We present a generalized approach for the modeling and analysis of oscillatory systems in cell biology. The advantage of this approach is that it does not require detailed knowledge of the functional form of rate laws, which is often not available. Instead, we investigate the system by parameterizing the Jacobian matrices of all steady states that are compatible with a given model structure. We then analyse the bifurcation landscape of the models via statistical sampling methods. This reveals Hopf bifurcations leading to oscillatory dynamics. By computing the first Lyapunov coefficient from a higher order expansion of the dynamics around the steady states we can distinguish between supercritical and subcritical Hopf bifurcations. The latter can lead to a catastrophic loss of stability, while in the former case, the loss of stability is a continuous, and hence reversible, transition. To illustrate our method we show results for small, toy model oscillators and a more complex model of a mammalian circadian oscillator.