Positive cooperativity, defined as an enhancement of the ligand affinity at one site as a consequence of binding the same type of ligand at another site, is a free energy coupling between binding sites. It can be present both in systems with sites having identical ligand affinities and in systems where the binding sites have different affinities. When the sites have widely different affinities such that they are filled with ligand in a sequential manner, it is often difficult to quantify or even detect the positive cooperativity, if it occurs. This study presents verification and quantitative measurements of the free energy coupling between the two calcium binding sites in a mutant form of calbindin D9k. Wild-type calbindin D9k binds two calcium ions with similar affinities and positive cooperativity--the free energy coupling, delta delta G, is around -8 kJ.mol-1 (Linse S, et al., 1991, Biochemistry 30: 154-162). The mutant, with the substitution Asn 56-->Ala, binds calcium in a sequential manner. In the present work we have taken advantage of the variations among different metal ions in terms of their preferences for the two binding sites in calbindin D9k. Combined studies of the binding of Ca2+, Cd2+, and La3+ have allowed us to conclude that in this mutant delta delta G < -6.4 kJ.mol-1, and that Cd2+ and La3+ also bind to this protein with positive cooperativity. The results justify the use of the (Ca2+)1 state of the Asn 56-->Ala mutant, as well as the (Cd2+)1 state of the wild type, as models for the half-saturated states along the two pathways of cooperative Ca2+ binding in calbindin D9k.