Optimization of metabolic states

This is a chapter from the free textbook "Economic Principles in Cell Biology" Cells in a well-mixed and nutrient-rich environment can be expected to experience selection on their growth rate. Such cells optimize their metabolic state to achieve a high growth rate. Metabolic states that lead to a high growth rate are states that realize a maximal biomass production rate at a minimal enzyme cost. Metabolic states that optimize a specific flux at minimal enzyme cost are called enzyme-efficient metabolic states and in this chapter we refer to them as optimal metabolic states. The calculation of optimal metabolic states is facilitated by the result that, in models without further constraints, the flux distributions in enzyme-efficient states are Elementary Flux Modes (EFMs). This result allows for an algorithm to find enzyme-efficient states by: 1) Enumerating the EFMs, 2) calculating the minimal enzyme cost per EFM, and 3) choosing the one with the lowest enzyme investment. This algorithm finds optimal metabolic states for larger models which cannot be optimized by ’brute force’, but are still small enough to enumerate the EFMs. Finding optimal metabolic states uncovered the effect of changing external nutrient conditions: As growth conditions are changing, the optimal flux profile either changes continuously (and metabolite and enzyme concentrations change continuously as well) when the same EFM remains optimal, or fluxes change discontinuously together with metabolite and enzyme concentrations when a different EFM becomes optimal.