Concentration-dependence data (LV Kochian, WJ Lucas Plant Physiol 1982 70: 1723-1731 [1983] 73: 208-215; [1985] [429][430][431][432][433][434][435][436]; LV Kochian, J Xin-zhi, WJ Lucas [1985], 79: 771-776) for potassium uptake by com roots have been claimed to be resolvable into a saturable and a linear component representing two separate uptake mechanisms. A comprehensive analysis shows, however, that the data are not compatible with this concept. They can, in contrast, be precisely represented by multiphasic isotherms, in agreement with many findings for uptake of potassium and other solutes. Solute uptake in plants is proposed to be mediated by multistate entities having camer-like properties at low extemal solute concentrations and channel-like properties at high concentrations.in ice-cold CaSO4 + 1 mm RbCl) periods, thus yielding values which represent plasmalemma influx (6).
AnalysisThe function for the sum of a saturable and a linear component (v = VmaxS/(Km + S) + kS) was fitted to the uptake rates (weighted by l/v2) by a computer program for nonlinear least squares (1). The individual phases in the multiphasic function (v = VmaxjS/(Kmj + S), where j denotes the phase number) was fitted by a program minimizing deviations in log v (cf. Ref. 2). Significance of fit to adjacent phases was determined by an F-test (20).As a measure of goodness of fit, MSD' was used:Despite extensive studies over a quarter of a century, there is still no consensus about the number and nature of uptake mechanisms in plants (13,17,21). Recently, the existence of a 'linear component' has been widely accepted, in part on the basis of work (6-9) purporting to show that uptake of potassium by corn roots can be resolved into a saturable and a linear component. This claim runs counter to numerous findings (12-17, 19, 20 and references therein) for potassium and other solutes that uptake is mediated by a single multiphasic mechanism for each solute or group of related solutes. In the present paper the claim for two separate uptake mechanisms for potassium is examined by analysis of the underlying concentration-dependence data. An abstract of this analysis has appeared (18).
MATERIALS AND METHODSwhere N is the number of points, wi the weight factor 1 /vbs2, v; obs the observed uptake rate (original or estimated data), vi pred the uptake rate predicted from the model, and df the degrees of freedom. Because of the division by df differences in the number of adjustable parameters in kinetic models do not affect their comparison by this measure.MSD was supplemented by the Runs test (3) which gives the cumulative probability with which a number (csn) of'runs' of positive or negative residuals would occur for a given number of such residuals. This test can be used directly to evaluate the fit of a model to a set of data, e.g. the very low probabilities for the 'saturable + linear' interpretation in some experiments are independent of the multiphasic interpretation.