Limitations of the Eadie-Hofstee plot to estimate kinetic parameters of intestinal transport in the presence of an unstirred water layer

Summary In the presence of an intestinal unstirred water layer, the relationship between substrate concentration (C₁) and unidirectional flux (J_d) is not described by the equation for a rectangular hyperbole. Accordingly, transformations of the Michaelis-Menten equation may not necessarily be linear and may lead to serious errors in the estimation of the affinity constant (K_m) and maximal transport rate (J_d^m) of carrier-mediated processes. An equation has previously been derived which describedJ_d under conditions of varying effective thickness or surface area of the unstirred water layer, the free diffusion coefficient of the probe molecule, and the distribution of transport sites along the villus. These theoretical curves have been analyzed by using the Eadie-Hofstee transformation (J_d vs. J_d/C₁) of the Michaelis-Menten equation. Use of this plot leads to serious discrepancies between the true and apparent affinity constants and between true and apparent maximal transport rates. These differences are further magnified by failure to correct for the contribution of passive permeation. The Eadie-Hofstee plot is of use, however, to infer certain qualitative characteristics of active transport processes, such as the variation in affinity constants and overlying resistance of the unstirred water layer at different sites along the villus and to predict the adequacy of the correction for the contribution of passive permeation.Abbreviations Used in the Text C₁ Concentration of the probe molecule in the bulk phase - C₂ Concentration of the probe molecule at the aqueous-membrane interface - d Effective thickness of UWL - D Free diffusion coefficient - dⁿ d atn th segment of the villus - f_n Proportion of total carrier transport sites present on each segment of villus - J Unidirectional flux of probe molecule, uncorrected for surface area - J_d Unidirectional flux of probe molecule determined experimentally, corrected for surface area - J_d^m Maximal transport rate, corrected for surface area - J_d^m* Apparent maximal transport rate - J^m Maximal transport rate, uncorrected for surface area - K_m Michaelis constant (true affinity constant) - K_m^* Apparent affinity constant - K_mⁿ K_m atnth segment of the villus - n The perpendicular height of the villus was divided into ten equal segments numberedn₁ ton₁₀ - p Passive permeability coefficient - S_m Functional surface area of the membrane - S_w Effective surface of UWL - S_wⁿ S_w atnth segment of the villus - UWL Intestinal unstirred water layer