Final answer:
After hydrolyzing ATP, the Na⁺-K⁺ ATPase pump undergoes allosteric changes that allow it to bind Na⁺ ions, release them into the extracellular fluid, and then bind K⁺ ions and release them into the cytosol.
Step-by-step explanation:
Immediately after the Na⁺-K⁺ ATPase hydrolyzes ATP, allosteric changes occur in the pump proteins. The pump binds three Na⁺ ions, causing a conformational change that releases the Na⁺ ions into the extracellular fluid. This release of Na⁺ ions outside the cell causes another allosteric change, after which two K⁺ ions from the extracellular fluid can bind to the pump protein. K⁺ binding leads to the hydrolysis of the phosphate from the pump protein, returning it to its original conformation and releasing the two K⁺ ions into the cytosol.