DISCOPOLIS: an algorithm for uniform sampling of metabolic flux distributions via iterative sequences of linear programs

Abstract

Mathematical models of metabolic networks are often underdetermined systems with more unknown fluxes than available equality constraints describing mass balances and external flux measurements. After reduction of the flux space based on the available equality constraints, the admissible reduced fluxes belong to a convex polytope defined by the intersection of half-planes representing the inequality constraints (e.g., upper and lower bounds of the fluxes). Random uniform sampling of this polytope allows building marginal distributions for each flux and computing the mean solution representative of the mean metabolism exhibited by the studied organism. This contribution proposes a new algorithm based on DIscrete Sampling of COnvex POlytopes via Linear program Iterative Sequences (DISCOPOLIS), in which the linear programs are iteratively used to constrain the solutions inside the polytope, taking into account all the previously estimated fluxes. The solutions are weighted to ensure sampling uniformity.