The Enzyme Cost of Metabolic Pathway Fluxes

Metabolic enzymes comprise many of the most highly expressed genes in all cell types, and altogether occupy roughly 20% to 50% of the proteome. Therefore, pathway efficiency, in terms of enzyme requirement, plays a major role both in evolution and bioengineering. Thanks to the various mechanisms that can regulate gene expression, enzyme levels can evolve much faster than their kinetic parameters. In cases where specific metabolic fluxes are required, the expression of enzymes should thus be optimized to minimize their total cost. To test this hypothesis, we develop a scalable and extensive framework for enzyme cost optimization. We prove that enzymatic metabolite cost minimization (eMCM) -- finding optimal metabolite and enzyme profiles that realize a desired flux at minimal cost -- is a convex optimization problem. This result is facilitated by factoring the enzyme cost function into four terms representing maximal capacity, thermodynamic driving forces, enzyme saturation, and allosteric regulation. We use recently measured metabolite and protein levels in E. coli's central metabolism to validate eMCM. Finally, eMCM provides a direct and physically realistic way to combine considerations of enzyme kinetics and protein abundance with constraint-based metabolic models.