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The potassium:potassium (K-K) exchange through the sodium pump has been measured as the ouabain-sensitive 86Rb uptake by Na-free ghosts resealed to contain various concentrations of ATP, orthophosphate and K. The exchange is activated by increasing either internal or external K+ (Rb+) ion concentration. The activation curves can be described by simple Michaelis kinetics as: exchange = Vmax [K]/(Kapp + [K]). Increasing ATP concentration increases the apparent affinity for external K ions but decreases the apparent affinity for internal K (Ki+). Increasing [ATP] from 1 microM to 1 mM typically increases the Kapp for Ki+ from less than 1 mM to about 30 mM. Increasing ATP first activates the exchange but, after an optimal concentration is reached, further increase of ATP inhibits. The value of ATP concentration which gives the maximum flux depends on the internal and external K+ concentrations. The higher [Ki], the greater the optimal ATP concentration. Increasing external K (Rb) decreases the optimal ATP concentration. Increasing the concentration of orthophosphate (Pi) activates the exchange at high ATP but inhibits at low ATP concentration. A concentration of Pi which stimulates the exchange at high external K (Rb) can inhibit at low external K (Rb). These findings are in agreement with a consecutive or ping-pong model of the K-K exchange. We suggest that previous experiments have not shown the inhibitory effects of ATP and Pi because of the particular range of concentrations investigated.