Theory is presented relating to the binding of an effector to two states of a protein acceptor coexisting in equilibrium. The problem is treated in terms of the four possible cases which specify relations between numbers of binding sites and intrinsic binding constants relevant to the acceptor states. It is shown that a distinction between these cases may be possible on the basis of the form of a plot of unbound effector concentration versus the constituent equilibrium coefficient which may be calculated from the sedimentation coefficient of the protein constituent. Particularly noteworthy in this respect is the finding that a turning point may exist in this plot for defined conditions with systems in which binding sites are not conserved (and binding affinities are altered) on polymer formation. The latter type of system is exemplified by studies on methaemoglobin A in 0.25 M sodium acetate, pH 5.4. In the absence of added organic phosphate effectors, a dimer-tetramer equilibrium operates governed by an association constant of 4.15 +/- 0.06 X 10(3) 1/mol, determined from sedimentation equilibrium results. Correlation of sedimentation velocity and equilibrium results shows that addition of adenosine 5'-triphosphate (ATP) results in its binding to one site on each of the dimeric (alpha beta) and tetrameric (alpha beta)2 species with intrinsic binding constants 1.03-10(3)-1.20-10(3) and 1.1-10(4)-2.1-10(4) 1/mol, respectively. It is also shown that 2,3-diphosphoglycerate perturbs the dimer-tetramer equilibrium in a similar way to ATP.