| The goal of this research was to develop a structured computational framework for the systematic determination of intracellular fluxes operative in microbial metabolism. Verification of such in silico flux determination through 13C isotopomer labeling experiments is also essential. Hence, we have developed a sequential set of screens for 13C NMR, that may prove useful for evaluating substrate labels and analyte sets for their ability to report on metabolic fluxes. Flux bounds and alternative flux routings are first identified for a particular problem, using our Mixed Integer Linear Programming (MILP)/Depth First Search (DFS) formulation. Analytes are then screened for whether the predicted NMR spectra associated with various analytes can differentiate between different extreme point (or linear combinations of extreme point) flux solutions. The second screen entails determining whether the analytes provide unique flux values or multiple flux solutions. The NMR-to-fluxes inverse problem is highly non-convex. In order to avoid getting trapped in local solutions, we have resorted to a global optimization algorithm that relies on a spatial branch-and-bound search. This algorithm has been modified so that we can obtain all 'global' flux solutions within a prescribed tolerance. Finally, the economics associated with using different analytes is considered in order to further refine the analyte selection process in terms of an overall utility index, where the index summarizes the cost-benefit attributes by quantifying benefit (contrast power) per cost (e.g. NMR instrument time required). We also demonstrate the use of an alternative strategy, the Analytical Hierarchy Process, for ranking analytes based on the individual experimentalist-generated weights assigned for the relative value of flux scenario contrast, unique inversion of NMR data to fluxes, etc. These methodologies are used in the context of a hypothetical abbreviated example and also, the more practical case of an Escherichia coli bacterial system, where the enzyme pyruvate kinase has been deleted to minimize acidic by-product formation. The utility of our design strategy is further discussed in the context of the work of two independent research groups, who have arrived at different metabolic maps of the same E. coli pyk mutant. |
