Abstract
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.
Highlights
3-Hydroxypropionic acid (3HP) is a platform chemical which can be converted into several valuable chemicals, for example acrylic acid and acrylamide (Werpy et al 2004)
We note that there is a bifurcation in the asymptotic structure of the system for the case of continuous pyruvate replenishment, and we investigate this in terms of our goal of maximizing 3HP production
As large-time 3HP production is zero and malonic semialdehyde levels are higher in the subcritical regime, Fig. 3b tells us immediately that the subcritical regime is a bad regime for industrially viable 3HP production, and that the parameter regime k4 > k∗ is much better for our goal
Summary
3-Hydroxypropionic acid (3HP) is a platform chemical which can be converted into several valuable chemicals, for example acrylic acid and acrylamide (Werpy et al 2004). This means that we are able to formulate a mathematical system in terms of ordinary differential equations in time, rather than partial differential equations in time and space These differential equations require initial conditions, and we consider the case where pyruvate is instantaneously introduced to a system containing all of the relevant enzymes, but none of the intermediate metabolites. This assumption facilitates a mathematical analysis by reducing the number of unknown parameters in the system. The latter enhances our physical insight into the underlying system and allows us to derive closed-form expressions for how the
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