  Systems Biology is a fundamental field and paradigm that introduces a new era
in Biology. The crux of its functionality and usefulness relies on metabolic
networks that model the reactions occurring inside an organism and provide the
means to understand the underlying mechanisms that govern biological systems.
Even more, metabolic networks have a broader impact that ranges from resolution
of ecosystems to personalized medicine.The analysis of metabolic networks is a
computational geometry oriented field as one of the main operations they depend
on is sampling uniformly points from polytopes; the latter provides a
representation of the steady states of the metabolic networks. However, the
polytopes that result from biological data are of very high dimension (to the
order of thousands) and in most, if not all, the cases are considerably skinny.
Therefore, to perform uniform random sampling efficiently in this setting, we
need a novel algorithmic and computational framework specially tailored for the
properties of metabolic networks.We present a complete software framework to
handle sampling in metabolic networks. Its backbone is a Multiphase Monte Carlo
Sampling (MMCS) algorithm that unifies rounding and sampling in one pass,
obtaining both upon termination. It exploits an improved variant of the
Billiard Walk that enjoys faster arithmetic complexity per step. We demonstrate
the efficiency of our approach by performing extensive experiments on various
metabolic networks. Notably, sampling on the most complicated human metabolic
network accessible today, Recon3D, corresponding to a polytope of dimension 5
335 took less than 30 hours. To our knowledge, that is out of reach for
existing software.
