A Markov constraint to uniquely identify elementary flux mode weights in unimolecular metabolic networks

Abstract

AbstractMotivationElementary flux modes (EFMs) are minimal, steady state pathways characterizing a flux network. Fundamentally, all steady state fluxes in a network are decomposable into a linear combination of EFMs. While there is typically no unique set of EFM weights that reconstructs these fluxes, several optimization-based methods have been proposed to constrain the solution space by enforcing some notion of parsimony. However, even these approaches may fail to uniquely identify EFM weights and, therefore, return different feasible solutions across objective functions and solvers.ResultsUsing simulated and biological networks, we demonstrate how optimization-based methods may return one of infinitely many EFM weight solutions that reconstruct the network fluxes. For unimolecular flux networks, we propose a natural, Markovian constraint to uniquely identify EFM weights explaining steady state fluxes. We describe an algorithm for computing these weights by reformulating the flux decomposition problem in terms of a certain discrete-time Markov chain. We demonstrate our method with a differential analysis of EFM activity in a lipid metabolic network comparing healthy and Alzheimer’s disease patients.ConclusionOur method is the first to uniquely decompose steady state fluxes into EFM weights for any unimolecular metabolic network.AvailabilityThe Julia software is available through https://www.perkinslab.ca/ or on Github at https://github.com/jchitpin/MarkovWeightedEFMs.jl.Contacttperkins@ohri.ca