Convex Representation of Metabolic Networks with Michaelis–Menten Kinetics

Josh A. Taylor, Alain Rapaport, Denis Dochain

Research output: Contribution to journalArticlepeer-review


Polyhedral models of metabolic networks are computationally tractable and can predict some cellular functions. A longstanding challenge is incorporating metabolites without losing tractability. In this paper, we do so using a new second-order cone representation of the Michaelis–Menten kinetics. The resulting model consists of linear stoichiometric constraints alongside second-order cone constraints that couple the reaction fluxes to metabolite concentrations. We formulate several new problems around this model: conic flux balance analysis, which augments flux balance analysis with metabolite concentrations; dynamic conic flux balance analysis; and finding minimal cut sets of networks with both reactions and metabolites. Solving these problems yields information about both fluxes and metabolite concentrations. They are second-order cone or mixed-integer second-order cone programs, which, while not as tractable as their linear counterparts, can nonetheless be solved at practical scales using existing software.

Original languageEnglish (US)
Article number65
JournalBulletin of Mathematical Biology
Issue number6
StatePublished - Jun 2024

All Science Journal Classification (ASJC) codes

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


  • Flux balance analysis
  • Metabolite concentrations
  • Michaelis–Menten kinetics
  • Minimal cut set
  • Second-order cone


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