Mathematical Model for Small Size Time Series Data of Bacterial Secondary Metabolic Pathways

Measuring the concentrations of metabolites and estimating the reaction rates of each reaction step consisting of metabolic pathways are significant for an improvement in microorganisms used in maximizing the production of materials. Although the reaction pathway must be identified for such an improvement, doing so is not easy. Numerous reaction steps have been reported; however, the actual reaction steps activated vary or change according to the conditions. Furthermore, to build mathematical models for a dynamical analysis, the reaction mechanisms and parameter values must be known; however, to date, sufficient information has yet to be published for many cases. In addition, experimental observations are expensive. A new mathematical approach that is applicable to small sample data, and that requires no detailed reaction information, is strongly needed. S-system is one such model that can use smaller samples than other ordinary differential equation models. We propose a simplified S-system to apply minimal quantities of samples for a dynamic analysis of the metabolic pathways. We applied the model to the phenyl lactate production pathway of Escherichia coli. The model obtained suggests that actually activated reaction steps and feedback are inhibitions within the pathway.