Ligand binding on ladder lattices

The ligand binding problems on two-dimensional ladders, which model many im portant binding phenomena in molecular biology, are studied in details. The model is represented by four parameters, the interactions between ligands when bound to adjacent sites on opposite legs of the ladder (tau), the inte ractions between bound ligands in the longitudinal direction of the ladder (sigma), the number of binding sites that are covered by a bound ligand (m) , and the intrinsic binding constant (K). The partition functions of ring l adders are approached with the transfer matrix method. A general relation i s derived which connects the partition function of a linear ladder with tha t of a ring ladder. The results obtained apply to the general situation of multivalent binding, in which m > 1. Special attention is paid to the case where the ligand covers one site (m = 1). In this case explicit formulas ar e given for the partition functions of ring and linear ladders. Closed-form expressions are obtained for various properties of the system, including t he degree of binding (theta), the midpoint in the binding isotherm (1/root tau sigma), the initial and end slopes of the Scatchard plots (2 sigma + ta u - 4 and -sigma(2)tau, respectively). From these closed-form formulas, sig ma and tau may be extracted from experimental data. The model reveals certa in features which do not exist in one-dimensional models. Using the general method discussed in [1], the recurrence relation is found for the partitio n functions. The analytical solution found for this model provides test cas es to verify the numerical results for more complex two-dimensional models. (C) 1999 Elsevier Science B.V. All rights reserved.