Workshop on Systems Biology, Mon, 05 Nov, 2007
Speaker: Martin Moennigmann
Abstract
Authors: Johannes Gerhard, Martin Moennigmann, Wolfgang Marquardt
Established methods are available for the model-based investigation of nonlinear dynamical systems. Practically all efforts in the field of Nonlinear Dynamics (NLD), however, have focused on methods for system analysis. In contrast, only few efforts have addressed the development of constructive NLD methods so far. By constructive NLD (CNLD) methods we refer to methods that complement analysis methods in that they not only allow creating insight into the behavior of a system, but also permit to design, optimize, or engineer the system for a desired behavior. The transition from NLD analysis methods to CNLD methods is reminiscent of the transition from methods for direct problems to methods for inverse problems.
Recently, a CNLD method has been proposed that is based on normal vectors to critical manifolds. In this approach, the distance between a candidate steady state of operation and the critical manifolds of the system is measured. In a typical case, the set of critical manifolds comprises the stability boundaries of the system, and the distance is a measure of the parametric robustness of stability. By incorporating these distance constraints into steady state system optimization, steady states that are (i) optimal and (ii) have desired nonlinear dynamics characteristics can be determined for nonlinear dynamical systems with parametric uncertainties.
The use of this CNLD method is demonstrated with a model for the biosynthesis of tryptophan. Opportunities for a further application of CNLD in systems biology are pointed out.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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