Mathematical Analysis of the Dependence of Cell Potential on External Potassium in Corn Roots

Abstract

The K⁺ dependence of normal (ψ) and diffusion (ψ_D) potentials in corn roots [Zea mays L., hybrid (A619 × Oh43) × A632] was determined experimentally and analyzed with respect to the parameter ξ [defined as exp (F ψ/RT)]. In the presence of 10 micromolar carbonyl cyanide p-trifluoromethoxyphenylhydrazone (FCCP), ψ behaved as expected of a diffusion potential. Based upon the assumptions (a) that FCCP did not change any term of the Goldman-Hodgkin-Katz equation, and (b) that total potential was functionally the algebraic sum of ψ_D and ψ_P (the deviation from ψ_D due to an electrogenic system), ψ_P was found to be a complex function of external potassium and to have a minimum value of 0.69 millimolar K ion activity outside the cell. Analysis of ψ allowed us to develop an equation which predicts a complicated K⁺ dependence of ψ such as that found by Mertz and Higinbotham (Membrane Transport in Plants and Plant Organelles. Springer-Verlag 1974).