Cooperative Multisite Binding to DNA

The method of sequence generating functions is applied to the binding of substrates to a linear array of binding sites such as is encountered in DNA. Cooperativity parameters are introduced for contact between bound ligands and for the extension of interaction over one or two empty binding units. By allowing these parameters to have values less than or greater than one, a large variety of anticooperative and cooperative situations can be developed. These and other parameters are systematically built into the sequence generating function as markers which are useful for statistical averages even in the absence of cooperativity. The resulting equations are applied to a system of highly cooperative binding, resulting in predicted behavior that simulates many features of the binding of T4 gene 32 protein to DNA. A model for the intercalation of dyes in DNA is also proposed which is based on two anticooperativity parameters: one for intercalating dyes in adjacent sites, the other for dyes separated by one empty site. The method of sequence generating functions not only permits the prediction of binding isotherms for systems like those described above, but also provides statistical distributions for any type of binding event to which a statistical weight can be attached. The only limitation is that the chains must be sufficiently long that end effects are negligible.