Transfer matrix solution of the Wako–Saitô–Muñoz–Eaton model augmented by arbitraryshort range interactions

Abstract

The Wako–Saitô–Muñoz–Eaton (WSME) model, initially introduced in the theory of proteinfolding, has also been used in modeling RNA folding and some epitaxial phenomena. Theadvantage of this model is that it admits exact solution in the general inhomogeneouscase (Bruscolini and Pelizzola 2002 Phys. Rev. Lett. 88 258101) which facilitatesthe study of realistic systems. However, a shortcoming of the model is that itaccounts only for interactions within continuous stretches of native bonds oratomic chains while neglecting interstretch (interchain) interactions. But due tothe biopolymer (atomic chain) flexibility, the monomers (atoms) separated byseveral non-native bonds along the sequence can become closely spaced. Thisproduces their strong interaction. The inclusion of non-WSME interactions intothe model makes the model more realistic and improves its performance. In thisstudy we add arbitrary interactions of finite range and solve the new model bymeans of the transfer matrix technique. We can therefore exactly account for theinteractions which in proteomics are classified as medium and moderately long rangeones.