Geometric algorithms for sampling the flux space of metabolic networks

TL;DR

This paper introduces a novel geometric sampling algorithm tailored for high-dimensional, skinny polytopes in metabolic networks, enabling efficient uniform sampling of biological steady states, including complex human networks.

Contribution

The authors develop a comprehensive software framework with a Multiphase Monte Carlo Sampling algorithm and an improved Billiard Walk variant for efficient high-dimensional polytope sampling in systems biology.

Findings

Sampling Recon3D took less than 30 hours, demonstrating efficiency.

The framework outperforms existing software on complex metabolic networks.

Efficient uniform sampling of high-dimensional, skinny polytopes is now feasible.

Abstract

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.