Which sets of elementary flux modes form thermodynamically feasible flux distributions?

Abstract

Elementary flux modes (EFMs) are non-decomposable steady-state fluxes through metabolic networks. Every possible flux through a network can be described as a superposition of EFMs. The definition of EFMs is based on the stoichiometry of the network, and it has been shown previously that not all EFMs are thermodynamically feasible. These infeasible EFMs cannot contribute to a biologically meaningful flux distribution. In this work, we show that a set of thermodynamically feasible EFMs need not be thermodynamically consistent. We use first principles of thermodynamics to define the feasibility of a flux distribution and present a method to compute the largest thermodynamically consistent sets (LTCSs) of EFMs. An LTCS contains the maximum number of EFMs that can be combined to form a thermodynamically feasible flux distribution. As a case study we analyze all LTCSs found in Escherichia coli when grown on glucose and show that only one LTCS shows the required phenotypical properties. Using our method, we find that in our E. coli model < 10% of all EFMs are thermodynamically relevant. A steady-state analysis of metabolic networks identifies the so-called metabolic flux cone that contains all feasible steady-state flux distributions. We show that upon integration of the cellular metabolome this cone gets highly fragmented into (possibly) overlapping subcones. The subcones dramatically reduce the available solution space of the network and fully determine all thermodynamically feasible capabilities of an organism. This improves our understanding of the phenotypic properties of an organism.