ATP production optimization in biochemical mass action models with protein turnover

We introduce a simple approach to account for the ATP consumption and production in the case of mass action models of metabolic pathways including protein turnover. Under some simplifying assumptions, the method makes it possible to characterize the optimal rate of enzyme synthesis if the substrate concentrations and other rate constants are known. Furthermore we demonstrate that the proposed approach is capable of the comparison of the efficiency of different feedback laws in dynamic environment, considering time-varying substrate concentration.