A measure of concentration robustness in a biochemical reaction network and its application on system identification

Variations in the concentrations of biomolecular species in vivo are inevitable, but regulation systems will act to maintain concentrations of certain species within proper levels. Such a ubiquitous trait in biological systems is the so-called concentration robustness. In this work, we study the concentration robustness of glycerol metabolism system, in which some mechanistic details are not clearly known and the true metabolic system need to be identified from all possible ones. We give a quantitative index to measure the concentration robustness of the considered system, which is characterized as the maximum relative variation in certain entries of steady state caused by the perturbations of operating parameters. Based on the proposed robustness index, a minimax dynamic optimization problem is developed for identifying the kinetic parameters as well as the unknown metabolic mechanisms. A scheme based on Monte-Carlo method is proposed to evaluate the robustness index approximately and convergence result is obtained. An algorithm is constructed to solve the dynamic optimization problem and numerical results are presented to show that the proposed robustness index could measure concentration robustness of the considered system properly.