Geometric algorithms for sampling the flux space of metabolic networks
Constraint-based approaches have been widely used for the analysis of such models and led to intriguing geometry-oriented challenges. In this setting, sampling uniformly points from polytopes derived from metabolic models (flux sampling) provides a representation of the solution space of the model under various conditions. However, the polytopes that result from such models are of high dimension (in the order of thousands) and usually considerably skinny. Therefore, to sample uniformly at random from such polytopes shouts for a novel algorithmic and computational framework specially tailored for the properties of metabolic models. We present a Multiphase Monte Carlo Sampling (MMCS) algorithm that unifies rounding and sampling in one pass, yielding both upon termination. It exploits an optimized variant of the Billiard Walk that enjoys faster arithmetic complexity per step than the original. Sampling on the most complicated human metabolic network accessible today, Recon3D, corresponding to a polytope of dimension 5 335, took less than 30 hours.
