Transfer matrix solution of the Wako-Sait\^o-Mu\~noz-Eaton model augmented by arbitrary short range interactions

TL;DR

This paper extends the Wako-Saitō-Muñoz-Eaton (WSME) model by incorporating arbitrary short-range interactions and solves it exactly using transfer matrix methods, enhancing its realism for biopolymer folding studies.

Contribution

The study introduces a method to exactly solve the WSME model with added finite-range interactions using transfer matrix techniques.

Findings

Exact solution for the extended model obtained.

Inclusion of medium- and moderately long-range interactions.

Improved modeling of biopolymer folding phenomena.

Abstract

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 the model is that it accounts only for interactions within continuous 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 which in proteomics are classified as medium- and moderately long-range ones.