Cooperative and Non-cooperative Binding of Large Ligands to a Finite One-dimensional Lattice. A Model for Ligand-oligonucleotide Interactions

A combinatorial approach is employed to calculate exact expressions for the extent of binding to a finite one dimensional lattice of ligands which cover more than one lattice site. The binding may be either cooperative or non-cooperative. It is found that the assumption of an effectively infinite lattice is generally a good one, except with relatively low concentrations of strongly cooperative ligands. An approach to analyzing experimental data is suggested which makes explicit use of the lattice length dependence of binding to extract more information about the binding parameters than can be obtained using the infinite lattice approximation. It is shown that irreversible binding cannot be viewed as a limiting case of reversible binding. The reasons for this difference are discussed, and expressions for the extent of irreversible binding are derived.