Dynamics of non-linear biochemical systems and the evolutionary significance of time hierarchy

Several non-linear reaction networks are analyzed in order to study the influence of time hierarchy on the dynamics of biochemical systems. The analysis is based on the assumption that the separation of the time constants within metabolic systems is a direct consequence of strong differences of enzyme concentrations. Therefore, as variable system parameters, only the enzyme concentrations are considered. By investigation of the stationary states of various three-component models with feedback-activation bifurcation diagrams within a two-dimensional parameter space, the enzyme simplex, are constructed. The diagrams contain the information about the number of stationary states, their stability properties as well as the type of motion expected at different parameter combinations. The results support the hypothesis that systems with separated time constants generally show a simple dynamic behaviour. Complex motions can be expected mainly for systems without time hierarchy, which are characterized by parameters located within the centre of the enzyme simplex. Quantitative measures for the time hierarchy and the complexity of the dynamics are derived. It is supposed that the separation of time constants is a main feature of the evolution of biochemical systems. The hypothesis is further supported by the consideration of the time hierarchy of the glycolytic pathway.