Trapping quaternary structures of hemoglobin in single crystals or by encapsulation in silica gels has provided a demanding set of data to test statistical mechanical models of allostery. In this work, we compare the results of those experiments with predictions of the four major allosteric models for hemoglobin: the quaternary two-state model of Monod, Wyman, and Changeux; the tertiary two-state model of Henry et al., which is the simplest extension of the Monod-Wyman-Changeux model to include pre-equilibria of tertiary as well as quaternary conformations; the structure-based model of Szabo and Karplus; and the modification of the latter model by Lee and Karplus. We show that only the tertiary two-state model can provide a near quantitative explanation of the single-crystal and gel experimental results.
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