Monte carlo generation of polypeptide random coil conformations; the persistence vector and the chain vector distribution

Polypeptide random coil conformations of various chain lenghts (N = 5, 10, 20, 40, 80 peptide units) are generated by a Monte Carlo procedure. The characteristic ratio obtained for the sets of generated conformations is identical with the exact value calculated with the average transformation matrix procedure, indicating the equivalence of the two treatments. On the basic of the generated sets of conformations the length and direction of the persistence vector (the averaged chain vector expressed in the reference frame of the first two skeletal bonds) are investigated for various chain lengths. The radial distribution function for the chain vector shows the length of the chain vector for small polypeptides (N = 5, 10) not to deviate far from its most probable value. Also for larger chains up to chains of 80 peptide units very significant deviations from a gaussian distribution are observed. The distribution of the length of the vector connecting the remote end of the chain with the end of the persistence vector exhibited behavior much doser to the gaussian approximation, an improvement especially significant for the short chains