Conditions for duality between fluxes and concentrationsin biochemical networks

ABSTRACT
Motivation: Mathematical and computational modeling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modeling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner.

Results: We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We also provide a combinatorial
characterisation that is sufficient to ensure flux-concentration duality. That is, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes.

Availability: All numerical experiments may be reproduced with the MATLAB code distributed with The COBRA Toolbox at https://github.com/opencobra/cobratoolbox.