Cooperativity: a unified view

Cooperativity, the departure from hyperbolic behaviour of the fractional saturation of a receptor at equilibrium (Y) for different values of ligand concentration (L), is an essential property of many physiological mechanisms and a first clue to the existence of conformational transitions and allosteric interactions. Here we investigate the properties of a simple and sensitive procedure to test and quantify cooperative behaviour. The measure of cooperativity involved is kappa = dK(L)/dL where K(L) = (1- Y) L/Y= [free sites]L/[occupied sites] is called the 'global dissociation quotient' Cooperative behaviour appears when kappa is not equal to 0, i.e., K(L) is a function of L. We have shown, for several equilibrium models of cooperative behaviour (e.g., Monod-Wyman-Changeux and Koshland-Némethy-Filmer), that K(L) can be expressed as the weighted average of the microscopic dissociation constants (K(i)) where the weights are the corresponding fractions of occupied sites (X(i)), K(L)= sigmaK(i)X(i). As a consequence, the change in the global dissociation quotient with ligand concentration for a dimer is kappa = (K1 - K2)dX1/dL. This result shows that the quantitative importance of a cooperative behaviour in a dimer depends on two factors: (i) the difference of the microscopic dissociation constants of the sites and (ii) the change in the fraction of occupied sites with ligand concentration. We analyze the generality of this unified view concluding that it would be fulfilled by every equilibrium model where there is a one-to-one relationship between free and occupied sites.