A MILP-Based Flux Alternative Generation and NMR Experimental Design Strategy for Metabolic Engineering

A mixed-integer linear program (MILP) is described that can enumerate all the ways fluxes can distribute in a metabolic network while still satisfying the same constraints and objective function. The multiple solutions can be used to (1) generate alternative flux scenarios that can account for limited experimental observations, (2) forecast the potential responses to mutation (e.g., new reaction pathways may be used), and (3) (as illustrated) design 13C NMR experiments such that different potential flux patterns in a mutant can be distinguished. The experimental design is enabled by using the MILP results as an input to an isotopomer mapping matrices (IMM)-based program, which accounts for the network circulation of 13C from a precursor such as glucose. The IMM-based program can interface to common plotting programs with the result that the user is provided with predicted NMR spectra that are complete with splittings and Lorentzian line-shape features. The example considered is the trafficking of carbon in an Escherichia coli mutant, which has pyruvate kinase activity deleted for the purpose of eliminating acetate production. Similar yields and extracellular measurements would be manifested by the flux alternatives. The MILP–IMM results suggest how NMR experiments can be designed such that the spectra of glutamate for two flux distribution scenarios differ significantly.