Novel Trajectory Based Concepts for Model and Complexity Reduction in (Bio)Chemical Kinetics

Based on increasing availability of high-accuracy data from high-throughput experimental techniques, detailed kinetic models for complex reaction mechanisms come more and more into applications. They are for instance used in computer simulations aimed at optimization of technical process operation or for virtual experiments in a systems biology approach to cellular biochemistry. Since high-dimensional models from large-scale mechanisms are difficult to handle in both computationally expensive spatiotemporal simulations and interpretation of system functions, sound mathematical methods for model and complexity reduction are important. Here, model reduction aims at reducing the degrees of freedom necessary for a sufficiently accurate description of the system dynamics whereas complexity reduction is supposed to help in providing functional insight into the dynamic structure and functional properties of complex reaction networks which is particularly important in biology. In this article we review recent developments from our group in both areas which rely on trajectory based concepts. First, we review a concept which is related to maximal relaxation of chemical forces under given constraints in terms of least-square minimal entropy production of single reaction steps and present applications for model reduction of chemical reaction mechanisms. Second, we discuss a sensitivity approach to phase flow analysis which can be exploited for complexity reduction in biochemical networks by identifying some aspects of the dynamic coupling structure of system components.