  Enzyme costs play 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. We show that enzyme cost is a convex function on this polytope.
This makes enzyme cost minimization - finding optimal enzyme profiles and
corresponding metabolite profiles that realize a desired flux at a minimal cost
- a convex optimization problem.
