Global Sensitivity Analysis of Biochemical Reaction Networks via Semidefinite Programming

TL;DR

This paper introduces a semidefinite programming approach to compute outer bounds for steady states in biochemical reaction networks, aiding in sensitivity analysis and understanding of system behavior.

Contribution

It develops a novel algorithm based on relaxed feasibility problems and duality to efficiently bound steady state regions in biochemical models.

Findings

Successfully applied to Goldbeter–Koshland cycle

Provides certificates for regions without steady states

Enables sensitivity analysis of biochemical networks

Abstract

We study the problem of computing outer bounds for the region of steady states of biochemical reaction networks modelled by ordinary differential equations, with respect to parameters that are allowed to vary within a predefined region. Using a relaxed version of the corresponding feasibility problem and its Lagrangian dual, we show how to compute certificates for regions in state space not containing any steady states. Based on these results, we develop an algorithm to compute outer bounds for the region of all feasible steady states. We apply our algorithm to the sensitivity analysis of a Goldbeter--Koshland enzymatic cycle, which is a frequent motif in reaction networks for regulation of metabolism and signal transduction.