Discovery of substrate cycles in large scale metabolic networks using hierarchical modularity

A substrate cycle is a set of metabolic reactions, arranged in a loop, which does not result in net consumption or production of the metabolites. The cycle operates by transforming a cofactor, e.g. oxidizing a reducing equivalent. Substrate cycles have been found experimentally in many parts of metabolism; however, their physiological roles remain unclear. As genome-scale metabolic models become increasingly available, there is now the opportunity to comprehensively catalogue substrate cycles, and gain additional insight into this potentially important motif of metabolic networks.

We present a method to identify substrate cycles in the context of metabolic modules, which facilitates functional analysis. This method utilizes elementary flux mode (EFM) analysis to find potential substrate cycles in the form of cyclical EFMs, and combines this analysis with network partition based on retroactive (cyclical) interactions between reactions. In addition to providing functional context, partitioning the network into modules allowed exhaustive EFM calculations on smaller, tractable subnetworks that are enriched in metabolic cycles. Applied to a large-scale model of human liver metabolism (HepatoNet1), our method found not only well-known substrate cycles involving ATP hydrolysis, but also potentially novel substrate cycles involving the transformation of other cofactors. A key characteristic of the substrate cycles identified in this study is that the lengths are relatively short (2-13 reactions), comparable to many experimentally observed substrate cycles.

EFM computation for large scale networks remains computationally intractable for exhaustive substrate cycle enumeration. Our algorithm utilizes a 'divide and conquer' strategy where EFM analysis is performed on systematically identified network modules that are designed to be enriched in cyclical interactions. We find that several substrate cycles uncovered using our approach are not identified when the network is partitioned in a more generic manner based solely on connectivity rather than cycles, demonstrating the value of targeting motif searches to sub-networks replete with a topological feature that resembles the desired motif itself.