Enumeration of all compact conformations of copolymers with random sequence of links

Abstract

Exhaustive enumeration of all compact self-avoiding conformations of a chain of 27 monomers on the 3*3*3 fragment of a simple cubic lattice is given. Total number of conformations unrelated by symmetry is 103 346. This number is relatively small which makes it possible to make a numerically exact calculation of all thermodynamic functions this chain. Heteropolymers with random sequence of links were considered, and the freezing transition at finite temperature was observed. This transition is analogous to folding transition in proteins where unique structure is formed. The numeric results demonstrate the equivalence between random 3-dimensional heteropolymers and the random energy model found previously in analytical investigations. The possible application of these results to some problems of combinational optimization is discussed.