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Enzyme cost plays a major role in the choice of metabolic routes, both in evolution and bioengineering. Given desired fluxes, necessary enzyme levels can be estimated based on known rate laws and on a principle of minimal enzyme cost. With logarithmic metabolite levels as free variables, enzyme cost functions and constraints in optimality and sampling problems can be handled easily. The set of feasible metabolite profiles forms a polytope in log-concentration space, whose points represent all possible steady states of a kinetic model. Enzyme cost is a convex function on this polytope. This makes enzyme cost minimization (ECM) - finding optimal enzyme profiles and corresponding metabolite profiles that realize a desired flux at a minimal cost - a convex optimization problem. By separating the cost contributions from enzyme capacity, energetics, and kinetics, we construct simple enzyme cost functions, applicable even if few or no parameter values are known.
If you use enzyme cost minimization in your work, please cite our article
Noor E., Flamholz A., Bar-Even A., Davidi D., Milo R., Liebermeister W. (2016), The protein cost of metabolic fluxes: prediction from enzymatic rate laws and cost minimization PLoS Comp. Biol. 12 (10): e1005167