Geometric Algorithms for Sampling the Flux Space of Metabolic Networks

Authors Apostolos Chalkis , Vissarion Fisikopoulos , Elias Tsigaridas, Haris Zafeiropoulos

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Author Details

Apostolos Chalkis
  • Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Greece
  • Athena Research Innovation Center, Athens, Greece
Vissarion Fisikopoulos
  • Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Greece
Elias Tsigaridas
  • Inria Paris and IMJ-PRG, Sorbonne Université, France
  • Paris Université, France
Haris Zafeiropoulos
  • Department of Biology, University of Crete, Heraklion, Greece
  • Institute of Marine Biology, Biotechnology and Aquaculture, Hellenic Centre for Marine Research, Anavyssos Attiki, Greece


We would like to thank the anonymous reviewers for their helpful comments and suggestions. We also thank Ioannis Emiris for his useful comments.

Cite AsGet BibTex

Apostolos Chalkis, Vissarion Fisikopoulos, Elias Tsigaridas, and Haris Zafeiropoulos. Geometric Algorithms for Sampling the Flux Space of Metabolic Networks. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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 5335, took less than 30 hours. To our knowledge, that is out of reach for existing software.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Mathematical software
  • Applied computing → Systems biology
  • Computing methodologies → Modeling and simulation
  • Flux analysis
  • metabolic networks
  • convex polytopes
  • random walks
  • sampling


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