Mixed-Integer Optimization for Loopless Flux Distributions in Metabolic Networks

TL;DR

This paper compares different mixed-integer optimization methods for loopless flux balance analysis in metabolic networks, aiming to improve the prediction of biologically feasible flux distributions without internal cycles.

Contribution

It evaluates various reformulations and solution approaches for ll-FBA, identifying combinatorial Benders' decomposition as the most promising method.

Findings

Most instances solvable with Benders' decomposition

Model size and numerical stability remain challenges

Benders' method outperforms other approaches

Abstract

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.