The interaction of sodium and calcium ions at the cell membrane and the control of contractile strength in frog atrial muscle.

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Abstract
The relationship between [Na]o [extracellular concentration] and the contracture tension, developed by isolated frog trabeculae, has been investigated in the presence of different levels of bathing K and Ca ions and after experimental manoeuvres likely to increase [Na]i [intracellular concentration]. Raising [K]o, [Ca]o or [Na]i increases the strength of the contractures induced by lowering the bathing [Na] except when the [Na]o is close to 0, suggesting that the Ca-Na exchange depends on membrane potential or [K]o. The experimental data was compared to the predictions of 3 relatively simple models of Ca-Na exchange in the membrane, where [Ca]i depends on the [K]o directly or by way of its effect on the membrane potential and tension varies according to a 2nd order relationship with [Ca]i. The scheme to fit all experimental data satisfactorily is one which assumes an exchange of 1 Ca ion for 3 Na ions across the membrane. This scheme requires that the contractile system has an apparent binding constant for Ca2+ similar to that found with skinned cardiac muscle cells or isolated cardiac myofibrils. In intact muscle, when the [Na]i is close to that measured experimentally, the model predicts that tension should vary with the [Ca]o2,1/[Na]o4 and the [Ca]/[Na]o2 ratios.