Random binding of dimers to chains

We develop a probabilistic model for the binding of a small linear polymer to a larger chain. We assume that we can approximate the energy of interaction of the two chains by summing the pairwise interactions between subunits. Because the energy of interaction between a pair of subunits can depend on neighboring subunits, which we assume vary along the chain, we assign the pairwise energies of interactions according to a specified probability distribution. Thus we develop a statistical model for the binding of two molecules. While such models may not be appropriate for studying the interaction of a particular pair of molecules, they can provide insight into questions that deal with populations of molecules, such as why do MHC molecules bind peptides of a certain size? Here we analyze in detail the special case of a heterodimer binding to a polymer.