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Title: Conditions for duality between fluxes and concentrations in biochemical networks

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
 [1] ;  [2] ;  [1] ;  [3]
  1. University of Luxembourg, Esch-sur-Alzette (Luxembourg). Luxembourg Centre for Systems Biomedicine
  2. Adobe Research, San Jose, CA (United States)
  3. Stanford Univ., CA (United States). Dept of Management Science and Engineering
Publication Date:
Grant/Contract Number:
Published Article
Journal Name:
Journal of Theoretical Biology
Additional Journal Information:
Journal Volume: 409; Journal Issue: C; Journal ID: ISSN 0022-5193
Research Org:
University of Luxembourg, Esch-sur-Alzette (Luxembourg)
Sponsoring Org:
USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23)
Country of Publication:
United States
59 BASIC BIOLOGICAL SCIENCES; 97 MATHEMATICS AND COMPUTING; Biochemical network; Concentration; Duality; Flux; Kinetics
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1424910