A Combinatorial Optimisation Approach to Multi-factorial Gap-filling in Genome-scale Metabolic Models (GEMs)

Abstract

Genome-Scale Metabolic Models (GEMs) describe the interactions between genes, proteins, and the biochemical reactions that underpin an organism's metabolism aiming to computationally simulate functions at the cellular level. While many metabolic reactions can be inferred from genome analysis, constructing GEMs often involves incorporating reactions unsupported by genomic data to improve prediction accuracy. This is known as gap-filling, a process that can be performed manually (a time-consuming task) or computationally. Traditional computational gap-filling approaches aim to correct GEM predictions for a single environmental condition (medium) by solving a large Integer Linear Programming problem. Sequential application across multiple media can produce a more robust model, but often introduces unrealistic predictions in other media. They are also slow to run. In this paper, we study multi-factorial gap filling, which aims to gap-fill GEMs across typically 10 or more input media simultaneously, while improving their overall predictive accuracy and minimising unrealistic behaviour. We view the selection of the set of reactions as a combinatorial optimisation problem, and describe a method based on classic metaheuristic approaches which requires the solution of continuous Linear Programming problems only. This paper provides an introduction of this problem to an audience whose speciality lies outside biology, and suggests a practical first-cut solution method. We demonstrate the method gap-filling GEMs for three bacteria strains, selecting 3000 to 4000 reactions from a database of more than 11000 reactions, while attempting to match the empirically measured performance on 9 to 28 separate media conditions. We show that our method outperforms conventional approaches on multiple metrics, including Kendal Tau and RMS Error by an average of 7.3% and 13.3%, respectively.