Hemocyanin of the horseshoe crab Limulus polyphemus is composed of 48 oxygen-binding subunits, which are arranged in eight hexameric building blocks. Allosteric interactions in this oligomeric protein have been examined by measurement of high-precision oxygen-equilibrium curves, using an automated Imai cell. Several models were compared in numerical analysis of the data. A number of conclusions can be drawn with confidence. (1) Oxygen binding by Limulus hemocyanin cannot satisfactorily be described by the two-state MWC model [Monod, J., Wyman, J., & Changeux, J.P. (1965) J. Mol. Biol. 12, 88-118] for allosteric transitions with either the hexamer or dodecamer as the allosteric unit. (2) Of the models tested, the data sets can be best described by an extended MWC model that allows for an equilibrium, within the 48-subunit ensemble, between cooperative hexamers and cooperative dodecamers. The model invokes T and R states for both hexamers (T6 and R6) and dodecamers (T12 and R12). Allosteric effectors modulate oxygen affinity and cooperativity by affecting the R to T equilibria within hexamers and dodecamers and by shifting the equilibria between hexamers and dodecamers. (3) The fitted model parameters show that under most conditions the intersubunit contacts within T-state hexamers are more constrained than those within T-state dodecamers. (4) The oxygen affinities of the hexameric and dodecameric R states are the same, but under all conditions examined the conformation of the fully oxygenated molecule is that of the dodecameric R state. (5) Between pH 7.4 and pH 8.5 the dodecameric T state has a higher affinity for oxygen than the hexameric T state, allowing for "T-state cooperativity".(ABSTRACT TRUNCATED AT 250 WORDS)