Constraining genome-scale models to represent the bow tie structure of metabolism for 13C metabolic flux analysis

Tyler W.H. Backman, David Ando, Jahnavi Singh, Jay D. Keasling, Héctor García Martín*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

151 Downloads (Pure)


Determination of internal metabolic fluxes is crucial for fundamental and applied biology because they map how carbon and electrons flow through metabolism to enable cell function. 13C Metabolic Flux Analysis (13C MFA) and Two-Scale 13C Metabolic Flux Analysis (2S-13C MFA) are two techniques used to determine such fluxes. Both operate on the simplifying approximation that metabolic flux from peripheral metabolism into central “core” carbon metabolism is minimal, and can be omitted when modeling isotopic labeling in core metabolism. The validity of this “two-scale” or “bow tie” approximation is supported both by the ability to accurately model experimental isotopic labeling data, and by experimentally verified metabolic engineering predictions using these methods. However, the boundaries of core metabolism that satisfy this approximation can vary across species, and across cell culture conditions. Here, we present a set of algorithms that (1) systematically calculate flux bounds for any specified “core” of a genome-scale model so as to satisfy the bow tie approximation and (2) automatically identify an updated set of core reactions that can satisfy this approximation more efficiently. First, we leverage linear programming to simultaneously identify the lowest fluxes from peripheral metabolism into core metabolism compatible with the observed growth rate and extracellular metabolite exchange fluxes. Second, we use Simulated Annealing to identify an updated set of core reactions that allow for a minimum of fluxes into core metabolism to satisfy these experimental constraints. Together, these methods accelerate and automate the identification of a biologically reasonable set of core reactions for use with 13C MFA or 2S- 13C MFA, as well as provide for a substantially lower set of flux bounds for fluxes into the core as compared with previous methods. We provide an open source Python implementation of these algorithms at
Original languageEnglish
Article number3
Issue number1
Number of pages17
Publication statusPublished - 2018

Bibliographical note

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (


  • Genome scale models
  • 13C metabolic flux analysis
  • Two-scale 13C metabolic flux analysis
  • Flux balance analysis
  • Linear programming
  • Cellular metabolism
  • Simulated annealing

Cite this