Quinary lattice model of secondary structures of polymers

In the standard approach to lattice proteins models based on nearest neighbor interaction are used. In this kind of model it is difficult to explain the existence of secondary structures—special preferred conformations of protein chains.
In the present paper a new lattice model of proteins is proposed which is based on nonlocal cooperative interactions. In this model the energy of a conformation of a polymer is equal to the sum of energies of conformations of fragments of the polymer chain of length five.
It is shown that this quinary lattice model is able to describe at a qualitative level secondary structures of proteins: for this model all conformations with minimal energy are combinations of lattice models of alpha-helix and beta-strand. Moreover for lattice polymers of length not longer that 38 monomers we can describe all conformations with minimal energy.

Funding Agency	Grant Number
Russian Foundation for Basic Research	11-01-00828-a
Ministry of Education and Science of the Russian Federation	NSh-2928.2012.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
This paper was partially supported by the grant from the Russian Foundation for Basic Research RFBR 11-01-00828-a, by the grant from the President of Russian Federation for the support of scientific schools NSh-2928.2012.1, and by the Program of the Department of Mathematics of the Russian Academy of Science ‘‘Modern problems of theoretical mathematics’’.