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 and K, 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.
Highlights
The kinetic patterns of ion uptake rates across roots, called ion influx isotherms, were first established in the 1960s by the pioneer work of Emanuel Epstein with 86Rb or 42K radioactive tracers for potassium uptake in barley (Epstein et al, 1963)
Many carriers provided by genetically distinct gene families are involved in the root catalytic function (Touraine et al, 2001; Britto and Kronzucker, 2008; Alemán et al, 2011), and some transporters show double affinity depending on their phosphorylation status, as observed for the NRT1.1 nitrate transporter (Liu and Tsay, 2003; Ho et al, 2009)
Vmax and Km parameters deduced from an enzyme-substrate interpretation cannot be regarded as microscopic parameters of a single transporter, but are instead macroscopic parameters (Vmapp and Kmapp) that reflect the sum of single activities of multiple transporters along the root (Neame and Richards, 1972)
Summary
The kinetic patterns of ion uptake rates across roots, called ion influx isotherms, were first established in the 1960s by the pioneer work of Emanuel Epstein with 86Rb or 42K radioactive tracers for potassium uptake in barley (Epstein et al, 1963). As shown by Kronzucker and co-workers, the pre- and post-wash conditions used in unidirectional influx measurements exhibit minor discrepancies in the HATS range, but large discrepancies in the LATS range of nutrient ion concentrations (Britto et al, 2006; Szczerba et al, 2006) In alternative approaches such as flow-force or compartmental analysis by the tracer efflux method (CATE), the measurements of net influx or efflux rates are more accurate and less chaotic because they are performed in steady-state conditions and are close to equilibrium (Britto et al, 2006). Some of the most serious shortcomings of the enzyme-substrate interpretation to describe nutrient ion uptake have been corrected in the ecological models of phytoplankton in the last three decades (see Section: Changes in the Number and Nature of Transporters Involved in Nutrient Uptake Modify Vmax and Km values and Section: Inducibility of Nutrient Transporters in Relation with Plant Nutrient Status Modifies Apparent Values of Vmax and Km below)
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