Kinetics of nucleic acid–large ligand interactions: Multiplet‐closure approximations and matrix‐iteration techniques

Approximate methods are developed and evaluated for treating the rate of binding ligands that cover several contiguous sites to a homogeneous one‐dimensional lattice, which represents a nucleic acid or other linear biopolymer. The model requires as input only the number of lattice sites necessary for binding, the total number (possibly infinite) of lattice sites, and elementary rate constants for the cooperative and noncooperative association and dissociation of the ligand on the lattice. The computational methods employed are an extension of the triplet closure approximation from the helix–coil (single‐site ligand) problem to the large ligand binding problem. It is found that consideration of clusters of n + 2 lattice sites, where each ligand covers n sites, gives a surprisingly accurate description of the kinetics. The approximation is implemented by an extension of the matrix‐iteration approach proposed by Craig and Crothers. The effects of the finite lattice length, as well as the capability to treat ligand motion along the lattice, are incorporated. When all symmetries are taken into consideration, the time required for the matrix iteration calculation rises only linearly with the ligand length n and is considerably less than that of the Monte Carlo method, which is used as a standard for comparison.