Metabolic pathway analysis using a nash equilibrium approach

A novel approach to metabolic network analysis using a Nash Equilibrium (NE) formulation is proposed in which enzymes are considered players in a multi-player game. Each player has its own payoff function with the objective of minimizing the Gibbs free energy associated with the biochemical reaction(s) it catalyzes subject to elemental mass balances while the network objective is to find the best solution to the sum of the player payoff functions. Consequently, any NE solution may not be best solution for all players. Key advantages of the NE approach include the ability to account for (1) aqueous electrolyte behavior, (2) the consumption/production of co-factors, and (3) charge balancing. However, the proposed Nash equilibrium formulation results in a set of nonlinear programming sub-problems that are more demanding to solve than conventional flux balance analysis (FBA) formulations which rely on linear programming. A direct substitution solution methodology for pathways with feedback is described. The Krebs cycle is used to demonstrate the efficacy of the NE approach while comparisons with both FBA and experimental data are used to show that it represents a paradigm shift in metabolic network analysis.