Model reduction of biochemical reactions networks by tropical analysis methods

Abstract

We discuss a method of approximate model reduction for networks of biochemical reactions. This method can be applied to networks with polynomial or rational reaction rates and whose parameters are given by their orders of magnitude. In order to obtain reduced models we solve the problem of tropical equilibration that is a system of equations in max-plus algebra. In the case of networks with fast nonlinear cycles we have to compute the tropical equilibrations at least twice, once for the initial system and a second time for an extended system obtained by adding to the full system the differential equations satisfied by the conservation laws of the fast subsystem. Our method can be used for formal model reduction in computational systems biology.