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The use of model-fitting in the interpretation of ‘dual’ uptake isotherms



Abstract. Published data of the concentration dependence of the uptake rate (uptake isotherms) of K+ Na+, Cl, SO24, and L-lysine in barley roots, and glucose and 3-O-methylglucose in potato tuber tissue, were re-examined. In as much as these isotherms yield non-linear, concave upward Eadie-Hofstee plots, they might have been termed ‘dual’ isotherms. In addition, all these isotherms have been considered to display discontinuous transitions in gradient. The following models that yield continuous isotherms were fitted to the isotherms: (1) the sum of a Michaelis-Menten term and a linear term; (2) the sum of two Michaelis-Menten terms; (3) the sum of two Michaelis-Menten terms and a linear one. Goodness of fit was judged from: (i) the weighted mean square of deviates; (ii) the standard errors of the kinetic parameters; (iii) the algebraic significance of the terms; (iv) a Rankits plot of the residuals; (v) a Runs test on the residuals.

For the precise and detailed isotherms of SO2− uptake, only model (3) gave a fit that was satisfactory in all respects. There appeared to be no reason to consider these isotherms as multiphasic. The same conclusion was reached for the L-lysine uptake isotherms. For the other isotherms the results were less conclusive. Thai for K+ and Na+ could, at any rate, be described satisfactorily by a continuous model, the best fit being obtained with model (2). The uptake isotherms of Cl and 3-0-methylglucose could be best described by model (2), and that of glucose by model (3), only the result of the Runs test being unsatisfactory. It is concluded that there is hardly any evidence that the presumed ‘jumps’ or discontinuities or inflections in the gradient of uptake isotherms are not due to experimental error in the data. It is suggested that many uptake isotherms may be described by model (3), although the reason for this is still incompletely understood.

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