Conditions for the existence of critical points in scatchard plots of binding results

An equation is presented in Scatchard format which describes the binding of a ligand to a two-state acceptor system (either isomerizing or polymerizing). It is used to formulate a general set of conditions for the existence of critical points in Scatchard plots and this set is explored in detail for particular cases. Explicit relations between the thermodynamic parameters governing the binding are thereby obtained which permit discussion of the boundaries of domains within which critical points may exist. Moreover, several items of evidence are presented which show that there is an exact correspondence between the appearance of critical points in Scatchard plots and points of inflexion in associated binding curves examples are presented where zero, one or more critical points and points of inflexion are observed. Finally, the effects on preferential binding of the variation of the environmental parameters, temperature and pressure (and for acceptor polymerization, the total acceptor concentration) are discussed in terms of the derived conditions of existence of critical points in Scatchard plots and their equivalent domains of sigmoidality of binding curves.