Mixed-Integer Optimization for Loopless Flux Distributions in Metabolic Networks
Bolusani, Suresh, Besançon, Mathieu, Bestuzheva, Ksenia, Chmiela, Antonia, João Dionísio, Tim Donkiewicz, van Doornmalen, Jasper, Leon Eifler, Mohammed Ghannam, Ambros Gleixner, Graczyk, Christoph, Katrin Halbig, Ivo Hedtke, Hoen, Alexander, Hojny, Christopher, van der Hulst, Rolf, Dominik Kamp, Thorsten Koch, Kofler, Kevin, Lentz, Jurgen · arXiv (Cornell University) · 2024
Constraint-based metabolic models can be used to investigate the intracellular physiology of microorganisms. These models couple genes to reactions, and typically seek to predict metabolite fluxes that optimize some biologically important metric. Classical techniques, like Flux Balance Analysis (FBA), formulate the metabolism of a microbe as an optimization problem where growth rate is maximized. While FBA has found widespread use, it often leads to thermodynamically infeasible solutions that contain internal cycles (loops). To address this shortcoming, Loopless-Flux Balance Analysis (ll-FBA) seeks to predict flux distributions that do not contain these loops. ll-FBA is a disjunctive program, usually reformulated as a mixed-integer program, and is challenging to solve for biological models that often contain thousands of reactions and metabolites. In this paper, we compare various reformulations of ll-FBA and different solution approaches. Overall, the combinatorial Benders' decomposition is the most promising of the tested approaches with which we could solve most instances. However, the model size and numerical instability pose a challenge to the combinatorial Benders' method.