On the level distribution of periodic and non-periodic collagen models

Abstract

The negative factor counting method in its matrix block form is used to calculate the total electronic density of states (DOS) of different collagen models. The computations have been executed for periodic and non-periodic eight-component collagen models consisting of (glycine, proline, hydroxypoline and alanine) together with glutamine, arginine, leucine and aspartic acid. The Fock and overlap matrices of the whole systems (containing 1014 amino acid residues) have been built up from ab initio Hartree-Fock dimer calculations (29 different dimers). In constructing these matrices both for the periodic and non-periodic cases, the well known sequence regularities of collagen have been taken into account. The conformation of the chain has been taken from a collagen-like model triple helix, Némethy and Scheraga having determined the conformation of this triple helix with the aid of empirical potential energy calculations. The DOS histogram of periodic (Gly-X-Y) triplets (similar to the previous six-component case) shows only very narrow peaks in both the valence band and conduction band regions. As a next step the 20 possible different triplets have been arranged in a (composition restricted) random manner (338 triplets). The DOS histogram shows in these cases essentially broader allowed energy regions and a much lower number of very narrow peaks than in the previous six-component case. Therefore we can conclude that if one were able to calculate the DOS of real collagen (with 20 different amino acid residues), the DOS histograms, the Anderson localization and the hopping frequencies would be very similar to those in random polypeptides.