If a ligand binds with unequal affinity to two distinct states of a protein, then the equilibrium between the two states becomes a function of the concentration of the ligand. A necessary consequence is that the ligand must also affect the forward and/or reverse rate constants for transition between the two states. For an enzyme or transport protein with such a transition as a slow step in the catalytic cycle, the overall rate also becomes a function of ligand concentration. These conclusions are independent of whether or not the ligand is a direct participant in the reaction. If it is a direct participant, then the kinetic effect arising from the principle of linked functions is distinct from the direct catalytic effect. These principles suffice to account for the biphasic response of the hydrolytic activity of ATP-driven ion pumps to the concentration of ATP, without the need to invoke more than one ATP binding site per catalytic center.