Automatic Complexity Analysis and Model Reduction of Nonlinear Biochemical Systems

• Authors: Dirk Lebiedz;Dominik Skanda;Marc Fein
• Venue: CMSB '08 Proceedings of the 6th International Conference on Computational Methods in Systems Biology
• Year: 2008

Kinetic models for biochemical systems often comprise a large amount of coupled differential equations with species concentrations varying on different time scales. In this paper we present and apply two novel methods aimed at automatic complexity and model reduction by numerical algorithms. The first method combines dynamic sensitivity analysis with singular value decomposition. The aim is to determine the minimal dimension of the kinetic model necessary to describe the active dynamics of the system accurately enough within a user-defined error tolerance for particular species concentrations and to determine each species' contribution to the active dynamics. The second method treats the explicit numerical reduction of the model to a lower dimension according to the results of the first method and allows any species combination to be chosen as a parameterization of the reduced model which may either be tabulated in the form of look-up tables or computed in situ during numerical simulations. A reduced representation of a multiple time scale system is particularly beneficial in the context of spatiotemporal simulations which require high computational efforts. Both the complexity analysis and model reduction method operate in a fully automatic and numerically highly efficient way and have been implemented in a software package. The methods are applied to a biochemical example model describing the ERK signaling pathway. With this example, we demonstrate the value of the methods for various applications in systems biology.