Combining metabolic pathway analysis with Evolutionary Game Theory: explaining the occurrence of low-yield pathways by an analytic optimization approach.

Elementary-mode analysis is a powerful method for detecting all potential pathways in a metabolic network and computing the associated molar yields. Metabolic pathways can be interpreted as different strategies of organisms. Thus, methods from Evolutionary Game Theory can be employed. In Flux Balance Analysis (FBA), it is usually assumed that molar yields of relevant products (such as biomass or ATP) have been maximized during evolution. This has been questioned on game-theoretical grounds. In particular, in situations that can be characterized as a Prisoner's Dilemma, maximization of flux is not in line with maximization of yield. Under other conditions (that is, for other parameter values of maximal velocities), a Harmony game can result, where the above two maximization criteria give the same result. Here, we analyse the optimal situations under varying conditions. In particular, we consider the case where the cell can allocate a certain amount of protein on several enzymes in a varying distribution and model this by a linear programming problem in which not only the rates but also the maximal velocities are variable. It turns out that in the case of low or moderate synthesis costs for the enzymes of the high-yield pathway, maximizing pathway flux is in line with maximizing molar yield while in the case of high costs, it is not. This may explain the observation that many cells such as striated muscle cells, tumour cells, activated lymphocytes and several yeasts do not reallocate protein away from glycolytic enzymes towards TCA cycle and respiratory chain enzymes, in spite of the higher efficiency of respiration. This provides a straightforward explanation of the Warburg effect in tumour cells.