Berlin 2012 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 10: Nonlinear Dynamics, Synchronisation and Chaos
DY 10.8: Talk
Tuesday, March 27, 2012, 11:30–11:45, MA 001
Reliable Dynamics in Boolean and continuous networks — •Eva Gehrmann1, Tiago P. Peixoto2, and Barbara Drossel1 — 1Institut für Festkörperphysik, TU Darmstadt — 2Institut für Theoretische Physik, Universität Bremen
We compare continuous and Boolean dynamics of gene regulatory networks that have entirely reliable trajectories, i.e., the sequence of states in the Boolean model does not depend on the order in which nodes are updated. So far, little is known about general conditions under which a Boolean simplification captures correctly the dynamics in gene regulation networks. Previous research suggests that not the topology and size of a network determine the extent of agreement between Boolean and continuous models, but the features of the network. We investigate the dynamical behavior of networks that have entirely reliable trajectories in the Boolean model version, i.e., trajectories with Hamming distance 1 between subsequent states. We translate the Boolean model for gene activity into continuous dynamics for mRNA and protein concentrations using sigmoidal Hill functions and analyze the resulting time-series of hundreds of networks with different sizes and different lengths of the trajectories. For entirely reliable trajectories, we find perfect agreement between the Boolean and the continuous dynamics. In order to assess the importance of having reliable trajectories, we also use models where the average Hamming distance between subsequent states is larger than 1. A careful analysis reveals the reasons why the good agreement between the Boolean and the continuous dynamics is destroyed in many networks with larger Hamming distance.