Mg++ and K+ distribution in frog muscle and egg: A disproof of the donnan theory of membrane equilibrium applied to the living cells
Authors: Ling Gilbert N. , Walton Cheryl , Ling Mark R. 
Published: February 2005

Abstract
We studied the equilibrium distribution of Mg++ in the form of chloride and sulfate at two temperatures (5° and 25°C) in frog voluntary muscles. External Mg++ concentration was varied between 1.2 and 73.2 mM with the specific purpose of testing the diametrically opposed predictions of the membrane theory and the association‐induction hypothesis.
There was a linear gain of Mg++ over the entire range of external Mg++ concentrations studied at both 5°C and 25°C. In a plot of intracellular Mg++ concentration in μmoles per gram of fresh muscle cells against extracellular Mg++ concentration, the slopes observed were 0.220 at 5°C and 0.0206 at 25°C.
The increase of external Mg++ from 1.2–73.2 mM at constant external K+ concentration (2.5 mM) had no discernible effect on intracellular K+ concentration, which remained constant at its normal levels in the vicinity of 90 μmoles/g/ fresh muscle cells.
We observed a similar rectilinear distribution of Mg++ in frog ovarian eggs. As in muscle tissues, no major alteration of intracellular K+ concentration results from increases of external Mg++ concentration from 1.2–73.2 mM.
With the rectilinear gain of Mg++, there was an entirely parallel gain of chloride in frog muscle cells. Indeed the slope of the Cl− curve and that of the Mg++ curve have essentially the same value. Thus Mg++ has entered the cell accompanied by chloride (and sulfate), rather than by exchange with other intracellular cations.
An increase of external K+ from 2.5 mM to 100 mM at a constant external Mg++ concentration depolarizes the muscle cell resting potential as shown by Ling and Gerard, ('50) and causes an increase of intracellular K+, doubling its normal concentration to 200 μmoles/g fresh muscle cells. Notwithstanding, the intracellular concentration of Mg++ remained totally unchanged from its normal value.
These findings profoundly disagree with the predictions of the Donnan theory of membrane equilibrium, according to which profound alteration of intracellular K+ concentration should follow exposure to high external Mg++ concentration, and vice versa. Furthermore, the postulation of a Mg++ pump is not feasible not only because of its energy requirements, but because it would also be inadequate to explain the lack of effect of varying external Mg++ concentration on the resting potential, the intracellular K+ concentrations, as well as the pattern of Cl− uptake totally different from that predicted by the membrane theory.
On the other hand, Mg++, K+, and Cl− distributions correlated completely with the predictions of the association‐induction hypothesis, according to which Mg++ and K+, in a normal resting cell, are predominantly adsorbed on sites they do not share, hence there is no mutual interference. Saturating all the intracellular sites at an external concentration of 1.2 mM, the concentration of Mg++ in the muscle cells increased further only in the form of free Mg++ (accompanied by its anion) in the cell water.
The q‐value for Mg++ in muscle cells at two different temperatures permits calculation of the thermodynamic parameters of the distribution of Mg++ salt in frog muscle cell water: a moderately favorable ΔH equal to −0.516 Kcal/mole, and an unfavorable entropy of 4.37 cal/degree/mole, showing an entropic cause for the exclusion of Mg++ from cell water.