The mechanism of cooperativity in the human hemoglobin tetramer (a dimer of ␣ dimers) has historically been modeled as a simple two-state system in which a low-affinity structural form (T) switches, on ligation, to a high-affinity form (R), yielding a net loss of hydrogen bonds and salt bridges in the dimer-dimer interface. Modifications that weaken these cross-dimer contacts destabilize the quaternary T tetramer, leading to decreased cooperativity and enhanced ligand affinity, as demonstrated in many studies on symmetric double modifications, i.e., a residue site modified in both ␣-or both -subunits. In this work, hybrid tetramers have been prepared with only one modified residue, yielding molecules composed of a wild-type dimer and a modified dimer. It is observed that the cooperative free energy of ligation to the modified dimer is perturbed to the same extent whether in the hybrid tetramer or in the doubly modified tetramer. The cooperative free energy of ligation to the wild-type dimer is unperturbed, even in the hybrid tetramer, and despite the overall destabilization of the T tetramer by the modification. This asymmetric response by the two dimers within the same tetramer shows that loss of dimer-dimer contacts is not communicated across the dimer-dimer interface, but is transmitted through the dimer that bears the modified residue. These observations are interpreted in terms of a previously proposed dimer-based model of cooperativity with an additional quaternary (T͞R) component.M any tertiary and quaternary conformational events important for catalysis and cooperativity in biological macromolecules are energetically unfavorable, and must be driven by favorable free energy of ligand binding. In the case of human hemoglobin (Hb), initial binding of O 2 to the heme Fe drives intrinsically unfavorable conformation change within the globin. The associated energetic ''penalty'' results in lower binding constants for initial ligation. However, penalties for the additional binding steps are progressively reduced, generating Hb's characteristic sigmoidal binding curve. Contributing to this curve are the partially ligated Hb intermediates, composed of two different subunit types (␣ and ) with four binding sites (␣ 1 ,  1 , ␣ 2 ,  2 ). Up to four labile ligands (O 2 ) are present on each tetramer in multiple configurations of site occupancy within at least two distinct quaternary structures (T and R). The challenge in understanding the mechanism of Hb cooperativity has been to identify and measure the separate energetic penalties for each O 2 binding step, and then to correlate individual penalties with specific structural events.To approach a resolution of this complex problem, energetic components of the system's ligation intermediates were evaluated with no prior assumptions as to their quaternary structures. Analysis of the thermodynamic linkages between dimertetramer assembly and O 2 binding permitted the ligand binding constant of the noncooperative free dimer to be used as the thermodynamic reference s...