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

Abstract

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.

On the feasibility of growth-coupled product synthesis in microbial strains

“…In the Supplements we introduce another approach by transforming the problem of calculating EVs into an equivalent problem for determining EMs allowing one to use existing highperformance algorithms for EM calculations [8,11,30] to compute EVs. The algorithm outputs three groups of EVs: (i) the bounded EVs of the lineality space (which also span the lineality space of P).…”

In SilicoConstraint-Based Strain Optimization Methods: the Quest for Optimal Cell Factories

“…In this work, a maximum of 223 million EFMs were computed for the E. coli core model (74). Another recent effort by Hunt and coworkers tackled the problem by iteratively splitting the network into subnetworks and enumerating their EFMs in powerful computational clusters (75). This approach has allowed the full enumeration of EFMs (ϳ2.2 billion) for a Phaeodactylum tricornutum genome-scale model comprised of 318 reactions and 335 metabolites, the largest to date.…”

Modelling metabolism of the diatomPhaeodactylum tricornutum

“…Although the determination of K is readily achieved for large (genome-scale) metabolic networks, the determination of elementary modes suffers from combinatorial explosion, making it a generally infeasible proposition, requiring large clusters of computers running for weeks or months on a single problem and is therefore not routinely applied to such large networks, although there have been some exceptions to this example [44].…”

“…To date a number metabolic models have been developed for algae, including diatoms [44,49,50]. de Oliveira Dal'Molin et al [50] used FBA techniques to analyse the GSM of Chlamydomonas reinhardtii and predict the fate of glycolate.…”