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Abstract:
Biochemical reaction networks in the form of coupled ODEs provide a powerful modeling tool to understand the dynamics of biochemical processes, including metabolism as well as signal transduction in bacteria or mammalian cells. During the modeling process of biochemical systems from scratch, scientists have to cope with numerous challenges, for instance, limited knowledge about the underlying mechanisms, contradicting experimental results as well as lack of sufficient experimental data. As a result, a large pool of competing nonlinear biochemical reaction networks is generated during the early phase of systems understanding, from which the most plausible set has to be selected. At this point, model-based stimulus experiments can be used to drive model responses of competing models furthest away [1]. However, model-based experiments depend on the prediction power of the models, which is typically very low due to large parameter uncertainties in the initial modeling phase. Ther
efore, alternative criteria have been proposed, which weight the model differences according to their prediction power [1].
In our contribution we present an efficient methodology for designing optimal stimulus experiments for robust model discrimination using the framework of optimal control, taking model uncertainties explicitly into account. The optimal control problem is formulated as a nonlinear program (NLP) in combination with the sigma point method [2] to propagate uncertainties through the dynamic optimization. The advantage of the sigma point method for nonlinear models compared to linearization or Monte Carlo sampling has been illustrated by many authors, including [2,3]. Due to the efficient transformation of model uncertainties, we can apply the non-symmetric Kullback-Leibler divergence as well as the symmetric model-overlap to measure expected model discrepancies [4, 5].
In our presentation we will demonstrate this method considering several competing biochemical reaction networks, which describe the response of NF-kappaB related signaling proteins (cytosol-to-nucleus translocation, posttranslational modifications, e.g., phosphorylation, sumoylation and complexation) in mammalian cells under genotoxic stress, i.e., gamma-irradiation. Being of high practical relevance, this case study illustrates the high potential of the developed methodology.
References
[1] B. H. Chen, S. P. Asprey, Ind. Eng. Chem. Res., 2003, 42, 1379–1390.
[2] S. Julier, J. Uhlmann, H. F. Durrant-Whyte, Automatic Control, 2000, 45, 477-482.
[3] R. Schenkendorf, A. Kremling, M. Mangold, IET Syst. Biol., 2009, 3, 10–23.
[4] S. Kullback, R. A. Leibler, Annals of Mathematical Statistics, 1951, 22, 79–86.
[5] S. Lorenz, E. Diederichs, R. Telgmann, C. Schuette, Journal of Computational Chemistry, 2007, 28, 1384-1399
