Partitioning the Hill Coefficient into Contributions from Ligand-promoted Conformational Changes and Subunit Heterogeneity

Heterooligomers that undergo ligand-promoted conformational changes are ubiquitous in nature and involved in many essential processes. Conformational switching often leads to positive cooperativity in ligand binding that is reflected in a Hill coefficient with a value greater than one. The subunits comprising heterooligomers can differ, however, in their affinity for the ligand. Such so-called site heterogeneity results in apparent negative cooperativity that is reflected by a Hill coefficient with a value less than one. Consequently, positive cooperativity due to the ligand-promoted allosteric switch can be masked, in cases of such heterooligomers, by apparent negative cooperativity owing to site heterogeneity. Here, we derived expressions for the Hill coefficient, in the case of a heterodimer, in which the contributions from the ligand-promoted allosteric switch and site heterogeneity are separated. Using these equations and simulations for higher order oligomers, we show under which conditions site heterogeneity can significantly mask the extent of observed positive cooperativity.