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

Abstract

The K(+) dependence of normal (psi) and diffusion (psi(D)) potentials in corn roots [Zea mays L., hybrid (A619 x Oh43) x A632] was determined experimentally and analyzed with respect to the parameter xi [defined as exp (F psi/RT)]. In the presence of 10 micromolar carbonyl cyanide p-trifluoromethoxyphenylhydrazone (FCCP), psi 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 psi(D) and psi(P) (the deviation from psi(D) due to an electrogenic system), psi(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 psi allowed us to develop an equation which predicts a complicated K(+) dependence of psi such as that found by Mertz and Higinbotham (Membrane Transport in Plants and Plant Organelles. Springer-Verlag 1974).