Model discrimination and parameter estimation via infeasibility certificates for dynamical biochemical reaction networks

Abstract

Abstract Current approaches to parameter estimation and model invalidation are often inappropriate for biochemical reaction networks. This is because often only noisy measurements and sparse experimental data is available, and since they do not take the special structure of biochemical reaction networks into account. In this work a new method to prove model invalidity and to estimate parameters is introduced. It is based on a certificate of non-existence of feasible parameterizations for a given models. This is done by reformulating the model invalidation task into a set-based feasibility problem. As shown, due to the polynomial structure of many biochemical reaction systems, it is possible to relax the non-convex feasibility problem into a semidefinite program and thus to obtain conclusive results on model invalidity and parameter estimation. Our framework allows us to consider the arising difficulties posed by biochemical reaction networks by taking the specific structure of the dynamics and model outputs into account. It also enables us to discard large parameter regions as infeasible. We also show on a well-known biological example, namely the Michaelis-Menten and the Henri kinetics, how with this method it is possible to discriminate between model hypotheses and how to estimate parameters.