Abstract
Simple systems are considered in which the binding of a ligand at a single site exhibits a doubly sigmoid curve when saturation is plotted against the logarithm of ligand concentration, i.e. where a fraction of the site exhibits one dissociation constant and the rest exhibits another. The condition for this to occur is that the ligand should also combine at another site on the binding molecule with comparable affinity and that the binding at one site should markedly lower affinity at the other. The protonation of simple compounds such as cysteine and 3-hydroxypyridine is taken as an example of this process and the equations derived are also applied to the binding of substrates to enzymes.