Mone Carlo calculations on polypeptide chains. I. A three-state hard-sphere model for randomly coiling poly-L-alanine.

Abstract

A Monte Carlo study of randomly coiling poly-l-alanine was carried out using a model in which the bond lengths and bond angles were held fixed, the peptide bond was fixed in the planar trans configuration, free rotation was assumed about the backbone N–Cα and Cα–C′ single bonds, the individual atoms or groups of atoms interacted pairwise by hard-sphere potentials, and each peptide unit was restricted to three sterically allowed states, the right-handed α-helical state, the left-handed α-helical state, and a third state in the vicinity of the so-called “ribbon structure.” Non-self-intersecting chains of various chain lengths up to 154 amino acid residues were generated using the sample enrichment technique of Wall and Erpenbeck. The attrition parameter λ was found to be an increasing function of chain length and not to have reached its limiting value at N = 154. The data were fitted to an empirical equation of the form λ = λ∞[(N − c) / (N + d)]e. The mean square end-to-end distance was found to approximately obey the usual law 〈r2〉 = aNb and the mean square radius of gyration the usual law 〈s2〉 = a′Nb′ for n ≥ 28. Monte Carlo calculations were also carried out on this model omitting the hard-sphere nonbonded interactions to obtain the unperturbed values of the mean square end-to-end distance 〈r2〉0 and the mean square radius of gyration 〈s2〉0 for comparison with the calculations including the excluded volume effect. A brief discussion is presented for the use of the attrition data to calculate the entropy per residue for both the unperturbed and non-self-intersecting chains and of the interpretation and reliability of the parameters b and b′ and the ratio 〈r2〉 / 〈s2〉 for both of these models.