A framework for direct metabolic flux estimation

We present FluxDirect, a novel computational framework for metabolic flux estimation from incomplete isotopomer data. In FluxDirect isotopomer measurements are first propagated in the metabolic network to obtain new constraints to the isotopomer distributions of metabolites in the network. The efficient propagation is facilitated by a fragment flow analysis of a metabolic network [1]. The method can utilize any measurement information produced by common (tandem) MS- and NMR-techniques [3]. After the propagation step the basic linear stoichiometric equation system bounding the fluxes is augmented with linear measurement constraints derived from the propagated isotopomer information. If the rank of the augmented linear equation system is full, the fluxes can be easily solved. If the rank of an equation system is less than full we can output upper and lower bounds for the fluxes. The general stability of an augmented equation system can be investigated by computing the condition number of the system. Unlike in most existing methods for flux estimation, techniques of nonlinear optimization are not required. Thus FluxDirect escapes the danger of convergence to local optima. Fragment flow analysis techniques introduced for efficient propagation of isotopomer measurement data also facilitate the experimental planning of isotopomer tracer experiments. As the development of measurement techniques for internal metabolites can be tedious, it is worthwhile to look for a small set of metabolites giving adequate flux information. We have shown that such small sets can be found for FluxDirect by applying computational set cover methods [2]. The flux estimation framework is empirically tested with a model of central carbon metabolism of S. cerevisiae.