Multi-timescale analysis of a metabolic network in synthetic biology: a kinetic model for 3-hydroxypropionic acid production via beta-alanine

A biosustainable production route for 3-hydroxypropionic acid (3HP), an important platform chemical, would allow 3HP to be produced without using fossil fuels. We are interested in investigating a potential biochemical route to 3HP from pyruvate through [Formula: see text] -alanine and, in this paper, we develop and solve a mathematical model for the reaction kinetics of the metabolites involved in this pathway. We consider two limiting cases, one where the levels of pyruvate are never replenished, the other where the levels of pyruvate are continuously replenished and thus kept constant. We exploit the natural separation of both the time scales and the metabolite concentrations to make significant asymptotic progress in understanding the system without resorting to computationally expensive parameter sweeps. Using our asymptotic results, we are able to predict the most important reactions to maximize the production of 3HP in this system while reducing the maximum amount of the toxic intermediate compound malonic semi-aldehyde present at any one time, and thus we are able to recommend which enzymes experimentalists should focus on manipulating.