Microcalorimetry, pH potentiometry, and direct binding studies by equilibrium dialysis or gel filtration were performed to determine the thermodynamic functions ΔH°, ΔG°, and ΔS° guiding the interactions of Ca²⁺, Mg²⁺, and H⁺ with bovine brain calmodulin. At pH 7.5, Ca²⁺, and Mg²⁺ binding are both endothermic with enthalpy changes of 19.5 and 72.8 kJ·(mol of calmodulin)^-1, respectively. These enthalpy changes are identical for each of the four ion-binding domains. The affinity constants also are identical with intrinsic values of 10⁵ M^-1 for Ca²⁺ and 140 M^-1 for Mg ²⁺. Ca ²⁺ and Mg ²⁺ do not compete for the same binding sites: at high concentrations of both ions, a calmodulin -Ca₄-Mg₄ species is formed with an enthalpy value of 24.4 kJ·mol^-1 with respect to calmodulin -Ca₄ and -28.8 kJ·mol^-1 with respect to calmodulin-Mg₄. Moreover, in the presence of high concentrations of Ca²⁺, the affinity of each of the four ion-binding domains in calmodulin for Mg²⁺ is decreased by a factor of 4 and vice versa, indicative of negative free-energy coupling between Ca²⁺ and Mg²⁺ binding. Protons antagonize Ca²⁺ and Mg²⁺ binding in a different manner. Ca²⁺-H⁺ antagonism is identical in each of the four Ca²⁺-binding domains in the pH range 7.5-5.2. Our analyses suggest that three chemical geometries, probably carboxyl-carboxylate interactions, are responsible for this antagonism with ionization constants of 10^6.2 M^-1 in the metal-free protein. Mg²⁺-H⁺ antagonism also is identical for each of the Mg²⁺-binding sites but is qualitatively different from Ca²⁺-H⁺ antagonism. The localization of the putative Mg²⁺-binding sites and the structural basis of the Ca²⁺-H⁺ antagonism have been discussed.