Abstract
Microbes in fragmented environments profit from yield-efficient metabolic strategies, which allow for a maximal number of cells. In contrast, cells in well-mixed, nutrient-rich environments need to grow and divide fast to out-compete others. Paradoxically, a fast growth can entail wasteful, yield-inefficient modes of metabolism and smaller cell numbers. Therefore, general trade-offs between biomass yield and growth rate have been hypothesized. To study the conditions for such rate/yield trade-offs, we considered a kinetic model of E. coli central metabolism and determined flux distributions that provide maximal growth rates or maximal biomass yields. Maximal growth rates or yields are achieved by sparse flux distributions called elementary flux modes (EFMs). By implementing a framework we call Flux-analysis Enzyme Cost Minimization (fECM), we screened all EFMs in the network model and computed the biomass yields and the minimal amount of protein requirements, which we then use to estimate the growth rates. In a scatter plot between the growth rates and yields of all EFMs, a trade-off shows up as a Pareto front. At reference glucose and oxygen levels, we find that the rate/yield trade-off is small. However, in low-oxygen environments, a much clearer trade-off emerges: low-yield fermentation EFMs allow for a growth 2-3 times faster than the maximal-yield EFM. The trade-off is therefore strongly condition-dependent and should be almost unnoticeable at high oxygen and glucose levels, the typical conditions in laboratory experiments. Our public web service www.neos-guide.org/content/enzyme-cost-minimization allows users to run fECM to compute enzyme costs for metabolic models of their choice.
