A model is developed which requires the binding of 4 Na+ to a carrier before a Ca binding site is induced on the opposite side of the membrane. Upon binding Ca, this carrier translocates Na and Ca. The existence of partially Na-loaded but nonmobile forms for the carrier (NaX, Na2X, Na3X) suffices to explain both the activating and the inhibitory effects of Na on the Ca transport reaction. Analytical expressions for Ca efflux and influx in terms of [Na]o, [Na]i, [Ca]o, [Ca]i, and Em are developed for the Na/Ca exchange system at equilibrium; these provide for a quantitative description of Ca fluxes. Under nonequilibrium conditions, appropriate modifications of the flux equations can be developed. These show a dependence of Ca efflux on [Ca]o and of Ca influx on [Ca]i. The large effect of internal ATP on Ca efflux and influx in squid axons, with no change in net Ca flux, can be understood on the single assumption that ATP changes the affinity of the carrier for Na at both faces of the membrane without providing an energy input to the transport reaction.

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