Symbolic flux analysis for genome-scale metabolic networks

A symbolic Gauss-Jordan elimination routine was developed for analyzing large metabolic networks. This routine was tested by finding the steady state solutions for a number of curated stoichiometric matrices with the largest having about 4000 reactions. The routine was able to find the solution with a computational time similar to the time used by a numerical singular value decomposition routine. As an advantage of symbolic solution, a set of independent fluxes can be suggested by the researcher leading to the formation of a desired flux basis describing the steady state solution of the network. These independent fluxes can be constrained using experimental data. We demonstrate the application of constraints by calculating a flux distribution for the central metabolic and amino acid biosynthesis pathways of yeast.We were able to find symbolic solutions for the steady state flux distribution of large metabolic networks. The ability to choose a flux basis was found to be useful in the constraint process and provides a strong argument for using symbolic Gauss-Jordan elimination in place of singular value decomposition.The explosion of tools available to simulate the systems level properties of biological systems is indicative of the wide scale uptake of integrative biology. The Systems Biology Markup Language (SBML) Web site [1] now lists over 200 packages that make use of their library. This large number of tools reflects both the wide variety and abundance of biological data now available to constrain biological models as well as the large variety of simplifying assumptions made to gain insight from this plethora of data.At the core of many of these analytical tools is the strict requirement of conservation of mass for each biological transformation. Because models of metabolic systems are typically under-determined, a common task when analyzing them is to find all possible steady state regimes when the concentrations of each metabolite do not change appreciably with