Abstract
The mevalonate pathway is normally found in eukaryotes, and allows for the production of isoprenoids, a useful class of organic compounds. This pathway has been successfully introduced to Escherichia coli, enabling a biosynthetic production route for many isoprenoids. In this paper, we develop and solve a mathematical model for the concentration of metabolites in the mevalonate pathway over time, accounting for the loss of acetyl-CoA to other metabolic pathways. Additionally, we successfully test our theoretical predictions experimentally by introducing part of the pathway into Cupriavidus necator. In our model, we exploit the natural separation of time scales as well as of metabolite concentrations to make significant asymptotic progress in understanding the system. We confirm that our asymptotic results agree well with numerical simulations, the former enabling us to predict the most important reactions to increase isopentenyl diphosphate production whilst minimizing the levels of HMG-CoA, which inhibits cell growth. Thus, our mathematical model allows us to recommend the upregulation of certain combinations of enzymes to improve production through the mevalonate pathway.
Highlights
Isoprenoids are a diverse class of naturally occurring organic chemicals found in all organisms
The first pathway is known as the mevalonate pathway, and starts from acetyl coenzyme A, mainly derived from pyruvate, which is converted to isopentenyl diphosphate (IDP) via the key pathway intermediate mevalonate
Recalling that our goal is to maximize IDP whilst minimizing hydroxy-3-methylglutaryl-coenzyme A (HMG-CoA), and noting that the dependence on E1 and E3 is the same for both metabolites of interest, the only way our goal can be achieved by varying enzyme concentration is to significantly increase E4, so that it compensates for any increase in E1 or E3
Summary
Isoprenoids are a diverse class of naturally occurring organic chemicals found in all organisms. We are interested in mathematically modelling this mevalonate pathway, with the goal of understanding how to further modify the pathway by, for example, upregulating genes that control certain enzymes, in order to produce more IDP. We show that the second case shares many similarities with the first until the pyruvate is depleted to a certain critical level, which we determine Understanding these extreme cases allows us to determine the key reactions in this pathway, and to suggest targets for upregulation. Time τ = (S0/k1E1 )t mathematical model using a fully numerical approach, the time taken to investigate the system would be shorter than the purely experimental approach To get around this issue, we supplement and guide our numerical simulations by determining asymptotic approximations (see, for example, Hinch, 1991; Kevorkian and Cole, 2013; O’Malley, Jr., 2012) of the metabolite concentrations.
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