J. theor. Biol (1981) 90,365-376 Interactions between Micellar Ligand Systems and Acceptors: Forms of Binding Curves M. J. SCULLEY, L. W. NICHOL Department of Physical Biochemistry, John Curtin School of Medical Research, Australian National University, Canberra, A.C.T. 2601, Australia AND D. J. WINZOR~ School of Science, Griffith University, Nathan, Queensland 4 111, Australia (Received 15 July 1980, and in revised form 10 November 1980) A previously formulated expression describing the competitive binding to an acceptorof two states of a ligand, monomeric and polymeric, coexisting in equilibrium isexamined in termsof the different formsof Scatchard plots which may arise in cases of exclusive and of preferential binding of the ligand states. It is shown by differentiation of the binding equation written in Scatchard format, and by numericalexamples, that exclusivebinding of the monomeric form of ligand leads to Scatchard plots that are either sigmoidal or convex to the abscissa, whereasexclusive binding of the polymeric form results in plots concave to the abscissa and exhibiting a maximum. Particular attention is given to Scatchard plots which possess two critical points, a situation which is shown to be possible when the polymeric form of ligand binds preferentially (but not exclusively) to the acceptor. The two-state ligand concept is especiallypertinent to solutes capableof globular micelle formation and several examples are cited of binding studies which havebeenconductedwith such micellar systems. Of these, the chlorpromazine-brain tubulin system is given detailedconsider- ation in order to illustrate the useof the presenttheory in describing the binding results which exhibit two critical points when plotted in Scatchard format. 1. Introduction Several systems have been studied which involve the reversible binding to acceptors of ligands which themselves are capable of existing in solution as equilibrium mixtures of monomeric and micellar states. Examples are provided by the binding of chlorpromazine to brain tubulin (Hinman & + On study leave from the University of Queensland. 365 0022-5193/81/110365+12 $02.00/O @ 1981 Academic Press Inc. (London) Ltd.