title: Conditions for duality between fluxes and concentrations in biochemical networks.
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.The condition prescribes that, 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.
authors.affiliation: Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 7 avenue des Hauts-Fourneaux, Esch-sur-Alzette, Luxembourg. Electronic address: ronan.m.t.fleming@gmail.com.
authors.forename: Ronan M T
authors.initials: RMT
authors.lastname: Fleming
authors.affiliation: Adobe Research, 345 Park Ave, San Jose, CA, USA. Electronic address: nikos.vlassis@gmail.com.
authors.forename: Nikos
authors.initials: N
authors.lastname: Vlassis
authors.affiliation: Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 7 avenue des Hauts-Fourneaux, Esch-sur-Alzette, Luxembourg. Electronic address: ines.thiele@gmail.com.
authors.forename: Ines
authors.initials: I
authors.lastname: Thiele
authors.affiliation: Dept of Management Science and Engineering, Stanford University, Stanford, CA, USA. Electronic address: saunders@stanford.edu.
authors.forename: Michael A
authors.initials: MA
authors.lastname: Saunders
mesh_terms: D003198:Computer Simulation; D008954:Models, Biological
keywords: Biochemical network; Concentration; Duality; Flux; Kinetics