Conditions for duality between fluxes and concentrations in biochemical networks. (21st November 2016)

• Record Type: Journal Article
• Authors: Fleming, Ronan M.T.; Vlassis, Nikos; Thiele, Ines; Saunders, Michael A.
• Is Part Of: Journal of theoretical biology. Volume 409(2016)
• Page Start: 1
• Page End: 10
• Publication Date: 2016-11-21
• Subjects: Biochemical network -- Flux -- Concentration -- Duality -- Kinetics; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2016.06.033
• Languages: English
• ISSNs: 0022-5193

Abstract

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. Abstract : Highlights: Flux-concentration duality implies an equivalence between descriptions in terms of concentrations or unidirectional fluxes. A novel stoichiometric condition for duality between unidirectional fluxes and concentrations is proposed. Flux-concentration duality is a pervasive property of biochemical networks.