Quite generally, constraint-based metabolic flux analysis describes the spaceof viable flux configurations for a metabolic network as a high-dimensionalpolytope defined by the linear constraints that enforce the balancing ofproduction and consumption fluxes for each chemical species in the system. Insome cases, the complexity of the solution space can be reduced by performingan additional optimization, while in other cases, knowing the range ofvariability of fluxes over the polytope provides a sufficient characterizationof the allowed configurations. There are cases, however, in which the thoroughinformation encoded in the individual distributions of viable fluxes over thepolytope is required. Obtaining such distributions is known to be a highlychallenging computational task when the dimensionality of the polytope issufficiently large, and the problem of developing cost-effective {\it ad hoc}algorithms has recently seen a major surge of interest. Here, we propose amethod that allows us to perform the required computation heuristically in atime scaling {\it linearly} with the number of reactions in the network,overcoming some limitations of similar techniques employed in recent years. Asa case study, we apply it to the analysis of the human red blood cell metabolicnetwork, whose solution space can be sampled by different exact techniques,like Hit-and-Run Monte Carlo (scaling roughly like the third power of thesystem size). Remarkably accurate estimates for the true distributions ofviable reaction fluxes are obtained, suggesting that, although furtherimprovements are desirable, our method enhances our ability to analyze thespace of allowed configurations for large biochemical reaction networks.
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