title: Breaking conceptual locks in modelling root absorption of nutrients: reopening the thermodynamic viewpoint of ion transport across the root.
abstract: BACKGROUND
  The top-down analysis of nitrate influx isotherms through the Enzyme-Substrate interpretation has not withstood recent molecular and histochemical analyses of nitrate transporters. Indeed, at least four families of nitrate transporters operating at both high and/or low external nitrate concentrations, and which are located in series and/or parallel in the different cellular layers of the mature root, are involved in nitrate uptake. Accordingly, the top-down analysis of the root catalytic structure for ion transport from the Enzyme-Substrate interpretation of nitrate influx isotherms is inadequate. Moreover, the use of the Enzyme-Substrate velocity equation as a single reference in agronomic models is not suitable in its formalism to account for variations in N uptake under fluctuating environmental conditions. Therefore, a conceptual paradigm shift is required to improve the mechanistic modelling of N uptake in agronomic models.
  
  
  METHODS
  An alternative formalism, the Flow-Force theory, was proposed in the 1970s to describe ion isotherms based upon biophysical 'flows and forces' relationships of non-equilibrium thermodynamics. This interpretation describes, with macroscopic parameters, the patterns of N uptake provided by a biological system such as roots. In contrast to the Enzyme-Substrate interpretation, this approach does not claim to represent molecular characteristics. Here it is shown that it is possible to combine the Flow-Force formalism with polynomial responses of nitrate influx rate induced by climatic and in planta factors in relation to nitrate availability.
  
  
  CONCLUSIONS
  Application of the Flow-Force formalism allows nitrate uptake to be modelled in a more realistic manner, and allows scaling-up in time and space of the regulation of nitrate uptake across the plant growth cycle.
authors.affiliation: Université de Caen Basse-Normandie, UMR EVA, F-14032 Caen cedex, France INRA, UMR 950, Écophysiologie Végétale & Agronomie Nutritions NCS, F-14032 Caen cedex, France erwan.ledeunff@unicaen.fr.
authors.forename: Erwan
authors.initials: E
authors.lastname: Le Deunff
authors.affiliation: Université Blaise Pascal-INRA, 24, avenue des Landais, BP 80 006, F-63177 Aubière, France INRA, UMR 547 PIAF, Bâtiment Biologie Végétale Recherche, BP 80 006, F-63177 Aubière, France.
authors.forename: Philippe
authors.initials: P
authors.lastname: Malagoli
mesh_terms: D065567:Absorption, Physiological; D017136:Ion Transport; D007700:Kinetics; D008954:Models, Biological; D018517:Plant Roots / Q000378:metabolism*; D013816:Thermodynamics
keywords: Brassica napus; Enzyme-Substrate interpretation; Flow-Force interpretation; Ion uptake isotherms; N uptake efficiency; N uptake modelling; functional–structural plant model; nitrate uptake regulation; root development