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Constraining Genome-Scale Models to Represent the Bow Tie Structure of Metabolism for ^{13}C Metabolic Flux Analysis

^{1}

Joint BioEnergy Institute, 5885 Hollis Street, Emeryville, CA 94608, USA

^{2}

Agile BioFoundry, 5885 Hollis Street, Emeryville, CA 94608, USA

^{3}

Biological Systems and Engineering Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

^{4}

QB3 Institute, University of California, Berkeley, CA 94720, USA

^{5}

Department of Bioengineering, University of California, Berkeley, CA 94720, USA

^{6}

Department of Computer Science, University of California, Berkeley, CA 94720, USA

^{7}

Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA 94720, USA

^{8}

Novo Nordisk Foundation Center for Biosustainability, Technical University of Denmark, 2970 Horsholm, Denmark

^{*}

Author to whom correspondence should be addressed.

Received: 10 November 2017 / Revised: 23 December 2017 / Accepted: 2 January 2018 / Published: 4 January 2018

(This article belongs to the Special Issue Metabolic Network Models Volume 2)

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. ${}^{13}$ C Metabolic Flux Analysis ( ${}^{13}$ C MFA) and Two-Scale ${}^{13}$ C Metabolic Flux Analysis (2S- ${}^{13}$ C 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 ${}^{13}$ C MFA or 2S- ${}^{13}$ C 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 https://github.com/JBEI/limitfluxtocore .