title: The Thermodynamic Flow-Force Interpretation of Root Nutrient Uptake Kinetics: A Powerful Formalism for Agronomic and Phytoplanktonic Models.
abstract: The ion influx isotherms obtained by measuring unidirectional influx across root membranes with radioactive or stable tracers are mostly interpreted by enzyme-substrate-like modeling. However, recent analyses from ion transporter mutants clearly demonstrate the inadequacy of the conventional interpretation of ion isotherms. Many genetically distinct carriers are involved in the root catalytic function. Parameters Vmax and Km deduced from this interpretation cannot therefore be regarded as microscopic parameters of a single transporter, but are instead macroscopic parameters (V[Formula: see text] and K[Formula: see text], apparent maximum velocity and affinity constant) that depend on weighted activities of multiple transporters along the root. The flow-force interpretation based on the thermodynamic principle of irreversible processes is an alternative macroscopic modeling approach for ion influx isotherms in which macroscopic parameters Lj (overall conductance of the root system for the substrate j) and πj (thermodynamic parameter when Jj = 0) have a straightforward meaning with respect to the biological sample studied. They characterize the efficiency of the entire root catalytic structure without deducing molecular characteristics. Here we present the basic principles of this theory and how its use can be tested and improved by changing root pre- and post-wash procedures before influx measurements in order to come as close as possible to equilibrium conditions. In addition, the constant values of Vm and Km in the Michaelis-Menten (MM) formalism of enzyme-substrate interpretation do not reflect variations in response to temperature, nutrient status or nutrient regimes. The linear formalism of the flow-force approach, which integrates temperature effect on nutrient uptake, could usefully replace MM formalism in the 1-3-dimension models of plants and phytoplankton. This formalism offers a simplification of parametrization to help find more realistic analytical expressions and numerical solution for root nutrient uptake.
authors.affiliation: Université de Caen Basse-Normandie, UFR des Sciences, UMR EVACaen, France; Institut National de la Recherche Agronomique, UMR 950, Écophysiologie Végétale and Agronomie Nutritions NCSCaen, France.
authors.forename: Erwan
authors.initials: E
authors.lastname: Le Deunff
authors.affiliation: Laboratoire Jacques-Louis Lions, INRIA Paris, EPC Alpines and Université Pierre et Marie Curie Paris 06, UMR 7598 Paris, France.
authors.forename: Pierre-Henri
authors.initials: PH
authors.lastname: Tournier
authors.affiliation: Université Clermont Auvergne, Université Blaise Pascal, UMR 547, PIAFClermont-Ferrand, France; Institut National de la Recherche Agronomique, UMR 547 PIAFClermont-Ferrand, France.
authors.forename: Philippe
authors.initials: P
authors.lastname: Malagoli
keywords: efflux; enzyme-substrate modeling; flow-force modeling; influx; ion transport modeling; nitrate; phytoplankton; potassium