ligand binding site (Y) and the fraction of the proteins in the R state (R): Where is the allosteric constant, that is the ratio of proteins in the T and R states in the absence of ligand, is the ratio of the affinities of R and T states for the ligand, and , the normalized concentration of ligand. It is not immediately obvious that the expression for is a form of the Adair equation, but in fact it is, as one can see by multiplying out the expressions in parentheses and comparing the coefficients of powers of with corresponding coefficients in the Adair equation. This model explains sigmoidal binding properties (i.e. positive cooperativity) as change in concentration of ligand over a small range will lead to a large increase in the proportion of molecules in the R state, and thus will lead to a high association of the ligand to the protein. It cannot explain negative cooperativity. The MWC model proved very popular in enzymology, and pharmacology, although it has been shown inappropriate in a certain number of cases. The best example of a successful application of the model is the regulation of hemoglobin function. Extensions of the model have been proposed for lattices of proteins by various authors. Edelstein argued that the MWC model gave a better account of the data for hemoglobin than the sequential model could do. He and Changeux applied the model to signal transduction. Changeux has discussed the status of the model after 50 years. See also Sequential model References Protein structure