Qualitative analysis of nonlinear biochemical networks with piecewise-affine functions
M.W.J.M. Musters, H. de Jong, P.P.J. van den Bosch, N.A.W. van Riel
A. Bemporad, A. Bicchi, G. Buttazzo (eds), Hybrid Systems : Computation and Control, HSCC 2007, Lecture Notes in Computer Science 4416, Springer-Verlag, Berlin, 727-730.
Nonlinearities and the lack of accurate quantitative information considerably hamper modeling and system analysis of biochemical networks. Here we propose a procedure for qualitative mathematical analysis of piecewise-affine (PWA) approximations of these networks. First the biochemical model size was reduced with quasi-steady state approaches by taking a priori information into account. Second, a conversion of a nonlinear model into a PWA approximation and subsequent qualitative analysis of this model was performed. This resulted in different sets of transition graphs that depend on the parameter values, which enables reduction of the parameter search space.