Solute Uptake in Plants: A Flow/Force Interpretation

Rates of uptake of silicic acid as a function of its concentration by the roots of various plants have been interpreted by their authors in the framework of a top-down approach based on the theoretical model of Michaelis and Menten. Although a hyperbola was fitted to the set of experimental points, this does not prove that all the simplifying assumptions underlying the Michaelis–Menten approach to transport were warranted. In consequence, the $V_j^m-$ and $K_j^m-$values, which were inferred from these experiments, may not characterize the carrier molecules involved in the uptake process in the way that K _m - and V _m -values characterize classical enzymes ($V_j^m =$ uptake rate when the carriers are saturated by the transported substrate, $1/K_j^m =$ carrier affinity for this substrate). Since the experimental measurements have dealt only with solute uptake by entire biological systems (plant roots in the present case), here we adopt a “top-top” approach. The idea is to find logical parameters that characterize these entire systems rather than look for key molecular constituents (e.g. carriers). By using the fact that the equations relating flows to forces always have a linear approximation when the system is close to equilibrium, we introduce two parameters to describe the uptake features of plant roots in the system of coordinates $\{{\rm ln}c_j^e,J_j(c^e_j)\}:{^\circ}c^e_j=$ the particular value of the concentration $c_j^e$ of the substrate, S _j , in the uptake medium for which the net flow, $J_j(c^e_j)$, of S _j exchange between medium and plant samples is zero and L_j = the overall conductance of the sample for S _j -uptake (= slope of the linear part of the curve $\{{\rm ln}c^e_j,J_j(c^e_j)\})$. We find that (1) the ${^\circ}c^e_j$ values are of the order of magnitude expected in the experimental conditions used and (2) the greater the ability of a plant to accumulate silicon, the greater the L _j -value for the radial absorption of silicon by this plant. The flow/force approach to uptake is applicable to the absorption of any type of substrate by any type of plant. In the flow/force approach, ${^\circ}c^e_j$ must equal the concentration of S _j in the growth solution of the plants prior to the experiments, which can be easily checked. It is possible to complement the interpretation of the uptake kinetics by using (1) a “symmetry criterion” to test whether uptake is active or passive and (2) an Arrhenius plot to check whether a modification of L _j corresponds to a modification of the uptake mechanism that is quantitative (e.g. number of carriers) or qualitative (e.g. post-translational modification of carriers).