The Wako-Sait\^o-Mu\~noz-Eaton } (WSME) model  initially introduced in the theory of protein folding can also model some epitaxial phenomena. The advantage of the model is that it admits exact solution in the general inhomogeneous case (Bruscolini and Pelizzola, 2002) which facilitates the modeling of realistic systems. A shortcoming of the model is that it accounts only for interactions within contiguous stretches of native bonds or atomic chains while neglecting interstretch (interchain) interactions. But due to the protein (or atomic chain) flexibility, the residues (atoms) separated by several non-native bonds along the sequence can become very close in the real space which usually causes their strong interaction. Thus, inclusion of non-WSME interactions into the model should make it more realistic and improve its performance. In this paper we augment the WSME model by arbitrary interactions of finite range along the sequence and solve it with the use of a transfer matrix technique. Our method makes it possible to exactly account for the interaction radii along the polypeptide chain which in the proteomics are classified as the medium-range interactions.
The Wako-Sait \^o}-Mu\~noz-Eaton (WSME) model , initially introduced in the theory of protein folding , has also been used in modeling the RNA folding and some epitaxial phenomena. The advantage of this model is that it admits exact solution in the general inhomogeneous case (Bruscolini and Pelizzola, 2002) which facilitates the study of realistic systems. However, a shortcoming of this model is that it accounts only for interactions within contiguous stretches of native bonds or atomic chains while neglecting interstretch (interchain) interactions. But due to the biopolymer ( atomic chain) flexibility, the monomers (atoms) separated by several non-native bonds along the sequence can become closely spaced. This produces their strong interaction. The inclusion of non-WSME interactions into the model makes the model more realistic and improves its performance. In this study we add arbitrary interactions of finite range and solve the new model by means of the transfer matrix technique. We can therefore exactly account for the interactions with the radii along the chain which in the proteomics are classified as medium- and moderately long-range interactions.
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