In human hemoglobin (Hb) the beta 37 tryptophan residue (beta W37), located at the hinge region of the alpha(1) beta(2) interface, forms many contacts with alpha subunit residues of the opposite dimer, in both the T and R quaternary structures. We have carried out equilibrium O-2 binding studies on a series of recombinant Hbs that have mutations at this residue site: beta W37Y, beta W37A, beta W37G, and beta W37E. Binding isotherms measured at high concentrations of these mutants were found to be shifted toward increased affinity and decreased cooperativity from that of the normal HbA(0) tetramer. Analysis of these binding isotherms indicated that amino acid substitutions at the beta 37 position could both destabilize the tetrameric form of the mutants relative to their constituent dimers and also alter cooperativity of the intact tetrameric species. These alterations from wild-type function are dependent on the particular side chain substituted, with the magnitude of change increasing as Trp is substituted by Tyr, Ala, Gly, and Glu. The dimer to tetramer assembly free energy of deoxy-beta W37E, the most perturbed mutant in the series, were measured using analytical gel chromatography to be 9 kcal/tetramer less favorable than that of deoxy HbA(0). Stabilizing the beta W37E tetramer by addition of IHP, or by cross-linking at the alpha K99 positions, does not restore normal O-2 binding behavior. Thermodynamic parameters of all the mutants were found to correlate with their CO binding rates and with their high-resolution X-ray crystal structures (see accompanying papers: Kwiatkowski et al. (1998) Biochemistry 37, 4325-4335; Peterson & Friedman (1998) Biochemistry 37, 4346-4357; Kavanaugh et al. (1998) Biochemistry 37, 4358-4373].