Institut für Systemtheorie und Regelungstechnik
Dynamical models of biochemical signal transduction pathways are often affected by large uncertainties on the parameter values. Robustness analysis is an efficient tool to quantify the effects of model uncertainty on qualitative properties of the model. This talk addresses in particular the robustness analysis problem for qualitative dynamical behaviour in the pathway, such as sustained oscillations or bistability. The level of parametric uncertainty not affecting the dynamical behaviour is thereby quantified by a suitably defined robustness measure. In the robustness analysis of biochemical networks, there are several challenges which obstruct the direct application of control engineering methods to this problem. These challenges include nonlinearity of the equations, dependence of the steady state on uncertain parameters, and the need to consider a nominally unstable system. This talk presents a novel solution to the robustness analysis problem, overcoming the mentioned challenges within a control engineering point of view. To this end, parameter values yielding a change in the dynamical behaviour are characterised via a feedback loop breaking approach. Based on this approach, two methods are proposed: one to compute robustness certificates, yielding a lower bound on the robustness measure, and one to search for nearby bifurcations, yielding an upper bound. To illustrate the proposed methods, an analysis of the NF-kB pathway is presented. This pathway is a central player in the mammalian immune system and of high biomedical relevance. The uncertainty analysis yields novel biological insights into the oscillatory behaviour of this pathway.
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Steffen Waldherr is a research associate at the Institute for Systems Theory and Automatic Control, University of Stuttgart, and at the Stuttgart Research Center for Simulation Technology. He studied engineering cybernetics at the University of Stuttgart, where he received the diploma degree in 2005, and mathematics at the National Institute of Applied Sciences in Rouen (France). In 2009, he obtained a PhD in engineering from the University of Stuttgart with a thesis about robustness analysis of biochemical networks. His main research interests are the dynamical modelling of biochemical networks and the application of systems theory for the analysis of biological processes.
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