Conditions for duality between fluxes and concentrations in biochemical networks

TL;DR

This paper establishes a necessary and sufficient stoichiometric condition for duality between fluxes and concentrations in biochemical networks, showing that such duality is common and can be characterized combinatorially.

Contribution

It introduces a novel stoichiometric criterion for flux-concentration duality and demonstrates its prevalence through computational experiments and combinatorial analysis.

Findings

Flux-concentration duality is widespread in biochemical networks.

A new stoichiometric condition precisely characterizes duality.

A combinatorial criterion guarantees flux-concentration duality.

Abstract

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling 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. 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.