GroEL Allostery Illuminated by a Relationship between the Hill Coefficient and the MWC Model

A fundamental problem that has hindered the use of the classic Monod-Wyman-Changuex (MWC) allosteric model since its introduction is that it has been difficult to determine the values of its parameters in a reliable manner because they are correlated with each other and sensitive to the data-fitting method. Consequently, experimental data are often fitted to the Hill equation, which provides a measure of cooperativity but no insights into its origin. In this work, we derived a general relationship between the value of the Hill coefficient and the parameters of the MWC model. It is shown that this relationship can be used to select the best estimate of the true combination of the MWC parameter values from all the possible ones found to fit the data. Here, this approach was applied to fits to the MWC model of curves of the fraction of GroEL molecules in the high-affinity (R) state for ATP as a function of ATP concentration. Such curves were collected at different temperatures, thereby providing insight into the hydrophobic effect associated with the ATP-promoted allosteric switch of GroEL. More generally, the relationship derived here should facilitate future thermodynamic analysis of other MWC-type allosteric systems.