Complete enumeration of elementary flux modes through scalable demand-based subnetwork definition

Abstract

Elementary flux mode analysis (EFMA) decomposes complex metabolic network models into tractable biochemical pathways, which have been used for rational design and analysis of metabolic and regulatory networks. However, application of EFMA has often been limited to targeted or simplified metabolic network representations due to computational demands of the method. Division of biological networks into subnetworks enables the complete enumeration of elementary flux modes (EFMs) for metabolic models of a broad range of complexities, including genome-scale. Here, subnetworks are defined using serial dichotomous suppression and enforcement of flux through model reactions. Rules for selecting appropriate reactions to generate subnetworks are proposed and tested; three test cases, including both prokaryotic and eukaryotic network models, verify the efficacy of these rules and demonstrate completeness and reproducibility of EFM enumeration. Division of models into subnetworks is demand-based and automated; computationally intractable subnetworks are further divided until the entire solution space is enumerated. To demonstrate the strategy's scalability, the splitting algorithm was implemented using an EFMA software package (EFMTool) and Windows PowerShell on a 50 node Microsoft high performance computing cluster. Enumeration of the EFMs in a genome-scale metabolic model of a diatom, Phaeodactylum tricornutum, identified ∼2 billion EFMs. The output represents an order of magnitude increase in EFMs computed compared with other published algorithms and demonstrates a scalable framework for EFMA of most systems.