A retrospective on statistical mechanical models for hemoglobin allostery

Understanding allosteric interactions in proteins has become one of the major research areas in protein science. The original aim of the famous theoretical model of Monod, Wyman, and Changeux (MWC) was to explain the regulation of enzymatic activity in biochemical pathways. However, its first successful quantitative application was to explain cooperative oxygen binding by hemoglobin, often called the "hydrogen molecule of biology." The combination of its original application and the enormous amount of research on hemoglobin has made it the paradigm for studies of allostery, especially for multi-subunit proteins, and for the development of statistical mechanical models to describe how structure determines function. This article is a historical account of the development of statistical mechanical models for hemoglobin to explain both the cooperative binding of oxygen (called homotropic effects by MWC) and how oxygen binding is affected by ligands that bind distant from the heme oxygen binding site (called heterotropic allosteric effects by MWC). This account makes clear the many remaining challenges for describing the relationship of structure to function for hemoglobin in terms of a satisfactory statistical mechanical model.