Evaluation of an S-system root-finding method for estimating parameters in a metabolic reaction model

In a mathematical model, estimation of parameters from time-series data of metabolic concentrations in cells is a challenging task. However, it seems that a promising approach for such estimation has not yet been established. Biochemical Systems Theory (BST) is a powerful methodology to construct a power-law type model for a given metabolic reaction system and to then characterize it efficiently. In this paper, we discuss the use of an S-system root-finding method (S-system method) to estimate parameters from time-series data of metabolite concentrations. We demonstrate that the S-system method is superior to the Newton-Raphson method in terms of the convergence region and iteration number. We also investigate the usefulness of a translocation technique and a complex-step differentiation method toward the practical application of the S-system method. The results indicate that the S-system method is useful to construct mathematical models for a variety of metabolic reaction networks.