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The general concept of receptor aggregation through the action of a cross-linking ligand is considered, three models being examined in detail. In two, ligand self-interaction leads to the formation of receptor cross-links whereas, in the third, receptor cross-links are formed through a single ligand bridge. Binding equations in closed form are formulated for each case and are shown to predict both concave and convex Scatchard plots in binding studies conducted with such systems. The significant point which emerges is that while each of the systems gives rise to very different types of binding responses, the form of the binding response is always strongly dependent on the total concentration of receptor in the system.

Three models of ligand-induced polymerization are considered, encompassing dimerization of acceptor-ligand complex and cross-linking of monomer units via a ligand bridge to form either dimer or linear chains. For each model a binding equation is developed and examined in terms of limits, form, and intersection within a family of curves, each member constructed with fixed but different total acceptor concentration. The characteristics of the binding curves that emerge are correlated with those found by examining the dependence on ligand concentration of either the weight-average molecular weight of the acceptor constituent or a function of it. In the latter plots, a maximum exists for the cross-linking models at the same ligand concentration that the corresponding binding curves intersect: the existence of the maximum implies that at saturating concentrations of ligand only monomeric acceptor constituent remains. The practical implication of these findings is discussed in terms of experimental systems reported previously in the literature. In addition, particular comment is made on the forms of binding curves for the three models, which assume shapes generally associated with positive and negative cooperativity. Finally, comparison is made with those systems in which a shift toward polymeric constituent is effected by ligand perturbation of a preexisting association equilibrium.

Effects of thermodynamic nonideality are considered in relation to the quantitative characterization of the interaction between a small ligand. S, and a macromolecular acceptor. A, by two types of experimental procedure. The first involves determination of the concentration of ligand in dialysis equilibrium with the acceptor/ligand mixture, and the second, measurement of the concentration of unbound ligand in the reaction mixture by ultrafiltration or the rate of dialysis method. For each situation explicit expressions are formulated for the appropriate binding function with allowance for composition-dependent nonideality effects expressed in terms of molar volume, charge-charge interaction and covolume contributions. The magnitudes of these effects are explored with the aid of experimental studies on the binding of tryptophan and of methyl orange to bovine serum albumin. It is concluded for experiments conducted utilizing either equilibrium dialysis or frontal gel chromatography that, provided a correction is made for any Donnan redistribution of ligand, theoretically predicted acceptor-concentration dependence is likely to be negligible and that use of the conventional binding equation written for an ideal system is appropriate to the analysis of the results. Use of ultrafiltration or the rate of dialysis method requires examination of the assumption that the activity coefficient ratio y(A)y(s)/y(AS) for the reaction mixture approximates unity; but again reassurance is provided that nonideality manifested as a dependence of the binding function on acceptor concentration is unlikely to be significant.

Currently available binding theory is extended to incorporate the concept of indefinite self-association of the ligand. Binding equations are formulated in closed form for the case of the binding to a multivalent acceptor of a ligand capable of isodesmically indefinitely self-associating in a "head-to-tail" mode such that each ligand state bears one site capable of interacting with the acceptor. It is shown both mathematically and by way of numerical example that this system will give rise exclusively to binding curves convex to the r-axis in Scatchard format. Thus, the system provides another example of a binding mechanism capable of generating an apparent negatively co-operative binding response.

Theory is formulated using reacted-site probability functions to relate the concentration of monomer to that of total solute for a multivalent monomer which undergoes indefinite self-association to form an equilibrium array of linear chains and branched networks governed by a single site-binding constant. In turn, this intrinsic constant is related to the stoichiometric equilibrium constants describing successive additions of monomer; and the characterization of the composition of the mixture at different total concentrations is discussed together with the onset of gelation, which occurs when each polymer (excluding the infinite network) attains a maximum concentration. Analogous expressions defining solution composition are presented for indefinitely self-associating systems involving non-identical sites when interactions occur in a head-to-tail fashion between dissimilar sites. Finally, a bivalent monomer is considered with head-to-head and tail-to-tail interactions forming an indefinite array of polymers with alternating bond types. It is shown that the latter description is quantitatively consistent with results obtained previously on the indefinitely self-associating zinc-free insulin system. The postulated self-association pattern involving two site-binding constants of magnitudes 5.75 X 10(4) M-1 and 0.85 X 10(4) M-1 is preferred to earlier suggested models on the basis of information available from X-ray crystallographic studies on insulin.