An Asymptotic Analysis of the Malonyl-CoA Route to 3-Hydroxypropionic Acid in Genetically Engineered Microbes

There has been recent interest in creating an efficient microbial production route for 3-hydroxypropionic acid, an important platform chemical. We develop and solve a mathematical model for the time-dependent metabolite concentrations in the malonyl-CoA pathway for 3-hydroxypropionic acid production in microbes, using a combination of numerical and asymptotic methods. This allows us to identify the most important targets for enzyme regulation therein under conditions of plentiful and sparse pyruvate, and to quantify their relative importance. In our model, we account for sinks of acetyl-CoA and malonyl-CoA to, for example, the citric acid cycle and fatty acid biosynthesis, respectively. Notably, in the plentiful pyruvate case we determine that there is a bifurcation in the asymptotic structure of the system, the crossing of which corresponds to a significant increase in 3-hydroxypropionic acid production. Moreover, we deduce that the most significant increases to 3-hydroxypropionic acid production can be obtained by up-regulating two specific enzymes in tandem, as the inherent nonlinearity of the system means that a solo up-regulation of either does not result in large increases in production. The types of issue arising here are prevalent in synthetic biology applications, and it is hoped that the system considered provides an instructive exemplar for broader applications.