Large conformational transitions play an essential role in the function of many proteins, but experiments do not provide the atomic details of the path followed in going from one end structure to the other. For the hemoglobin tetramer, the transition path between the unliganded (T) and tetraoxygenated (R) structures is not known, which limits our understanding of the cooperative mechanism in this classic allosteric system, where both tertiary and quaternary changes are involved. The conjugate peak refinement algorithm is used to compute an unbiased minimum energy path at atomic detail between the two end states. Although the results confirm some of the proposals of Perutz [Perutz MF (1970) Stereochemistry of cooperative effects in haemoglobin. Nature 228:726-734], the subunit motions do not follow the textbook description of a simple rotation of one αβ-dimer relative to the other. Instead, the path consists of two sequential quaternary rotations, each involving different subdomains and axes. The quaternary transitions are preceded and followed by phases of tertiary structural changes. The results explain the recent photodissociation measurements, which suggest that the quaternary transition has a fast (2 μs) as well as a slow (20 μs) component and provide a testable model for single molecule FRET experiments.conformational change | cooperativity | domain motion | protein hinges M any proteins undergo large conformational transitions that are essential for their functions (1-3). The transitions can occur in monomers such as the myosin molecular motor (4-6), in multisubunit complexes such as the chaperone GroEL (7), and in systems such as the flagellar motor of bacteria, which is composed of several hundred proteins (8). Probably the most studied example is the T (tense) to R (relaxed) transition in the vertebrate hemoglobin tetramer (Hb) (9-11), for which the conformational transition increases the efficiency of oxygen transport. Hemoglobin, which is composed of two identical α-and two identical β-subunits, is the paradigm for the development of models of cooperativity and allosteric regulation in proteins (9-13). Phenomenologically, the positive cooperativity involves the increase in the affinity for oxygen of unliganded subunits upon the successive binding of oxygen to other subunits. This is achieved by structural changes within subunits (tertiary changes) and between subunits (quaternary changes). Based on the superposition of the crystallographic structures for the deoxy unliganded T state and the fully liganded R state of the protein, the quaternary T → R transition has been described as involving primarily an approximately 15°rotation of one "dimer" (α 1 β 1 ) relative to the other (α 2 β 2 ) around a virtual axis (Fig. 1A) (9, 14). Together with a small relative translation of the αβ-dimers, this reduces the central cavity between the dimers (a channel along the C2 axis of symmetry), where the heterotropic effector 2,3-bisphosphoglycerate is bound in the T state. An important aspect of these structural ch...