Closing the loop between feasible flux scenario identification for construct evaluation and resolution of realized fluxes via NMR

Abstract

Mixed integer linear programming (MILP) and other methods can provide information on product yield horizons and the optimal “target” values of fluxes to achieve in metabolic networks. These methods can also elucidate the metabolite trafficking possibilities in tissues. While methods that enumerate flux scenarios are useful for the “front-end” analysis of metabolic engineering problems or probing the possibilities in tissue physiology, the evaluation of actual data from a tissue or engineered cells is ultimately needed to verify the veracity of theoretical predictions and mechanistic hypotheses. However, using NMR data to identify fluxes can be problematic because a non-linear optimization problem can result that is highly non-convex due to the bi-linear and tri-linear terms present in the isotopomer balance equations. One consequence is that local versus global solutions can be found. To surmount the problem of obtaining local solutions, we have investigated the utility of using a joint problem formulation. It involves using the results of the “front-end” analysis (MILP solutions) to also provide bounds for the data-to-fluxes problem, where using a deterministic global optimization algorithm of the branch-and-bound type solves the latter. The joint formulation produced the correct solutions for a streamlined example and a more realistic problem. An alternate gradient-based algorithm failed in that it produced an incorrect solution. The utility of different NMR analytes for yielding correct fluxes was also investigated via simulation.