Optimal metabolic states in cells

Cells, in order to thrive, make efficient use of metabolites, proteins, energy, membrane space, and time. How, for example, should they allocate the available amount of protein to different metabolic pathways or cell functions? To model metabolic behaviour as an economic problem, some flux analysis model, kinetic models, and cell models apply optimality principles. However, due to their different assumptions these models are hard to compare and combine. Benefits and costs of metabolic pathways - e.g. favouring high production fluxes and low metabolite and enzyme cost - can be derived from general fitness objectives such as fast cell growth. To define pathway objectives, we may assume "optimistically" that, given a pathway state, any cell variables outside the pathway will be chosen for maximal fitness. The resulting fitness defines an effective pathway objective as a function of the pathway variables. Here I propose a unified theory that considers kinetic models, describes the set of feasible states as a state manifold and score each state by cost and benefit functions for fluxes, metabolite concentrations, and enzyme levels. To screen the state manifold and to find optimal states, the problem can be projected into flux, metabolite, or enzyme space, where effective cost and benefit functions are used. We reobtain existing modelling approaches such as enzyme cost minimisation or nonlinear versions of Flux Balance Analysis. Due to their common origin, the different approaches share mathematical optimality conditions of the same form. A general theory of optimal metabolic states, as proposed here, provides a logical link between existing modelling approaches and can help justify, interconvert, and combine metabolic optimality problems.