Monte Carlo Calculations on Polypeptide Chains. II. A Fourhyphen;State Hardhyphen;Sphere Model for Randomly Coiling Polyglycine

摘要

A Monte Carlo study of randomly coiling polyglycine was carried out using the same hardhyphen;sphere model applied previously to polyhyphen;lhyphen;alanine in which the bond lengths and bond angles are held fixed, the peptide bond is fixed in the planartransconfiguration, free rotation is assumed about the backbone Nsngbnd;Cagr;and Cagr;sngbnd;Cprime; single bonds, and the individual atoms or groups of atoms interact pairwise by hardhyphen;sphere potential functions. For polyglycine each peptide unit in the chain is restricted to four sterically allowed conformational states, the righthyphen; and lefthyphen;handedagr;hyphen;helical states and the righthyphen; and lefthyphen;handed ribbon structure states. Nonhyphen;selfhyphen;intersecting chains of various chain lengths up to 150 amino acid residues were generated by the sample enrichment technique of Wall and Erpenbeck and used to calculate the average chain dimensions. Chains were also generated in which the hardhyphen;sphere potentials were neglected and from which the unperturbed average dimensions were calculated. As found previously for polyhyphen;lhyphen;alanine chains, the pointhyphen;byhyphen;point attrition parameterlgr;, defined asNminus;1lnlpar;W0thinsp;sol;thinsp;WNrpar;, was found to be an increasing function of chain length over the entire range included in the calculations, and the data could be fit by an empirical equation of the formlgr;thinsp;equals;thinsp;lgr;infin;lsqb;lpar;Nthinsp;minus;thinsp;crpar;thinsp;sol;thinsp;lpar;Nthinsp;plus;thinsp;drpar;rsqb;e, wherelgr;infin;thinsp;equals;thinsp;0.111070thinsp;plusmn;thinsp;0.000005is the best estimate of the traditional attrition constant for the model. The meanhyphen;square endhyphen;tohyphen;end distance and meanhyphen;square radius of gyration for both nonhyphen;selfhyphen;intersecting and unperturbed chains were found to obey the lawslang;r2rang;thinsp;equals;thinsp;aNbandlang;s2rang;thinsp;equals;thinsp;aprime;Nbprime;for largeNwithbthinsp;equals;thinsp;1.201thinsp;plusmn;thinsp;0.008andbprime;thinsp;equals;thinsp;1.236thinsp;plusmn;thinsp;0.041for nonhyphen;selfhyphen;intersecting chains andbthinsp;equals;thinsp;1.054thinsp;plusmn;thinsp;0.080andbprime;thinsp;equals;thinsp;1.047thinsp;plusmn;thinsp;0.051for unperturbed chains. A reanalysis of the data for polyhyphen;lhyphen;alanine chains yielded similar results except thatbprime;for the nonhyphen;selfhyphen;intersecting chains was found to be 1.31ndash;1.33 rather than 1.21ndash;1.23. It was also found for polyglycine as for polyhyphen;lhyphen;alanine that the ratiolang;r2rang;thinsp;sol;thinsp;lang;s2rang;for both nonhyphen;selfhyphen;intersecting and unperturbed chains when plotted vsNpasses through a maximum atNthinsp;ap;thinsp;10and then, within the statistical reliability of the data, decreases to a value of 6 for the longest generated unperturbed chains and to 6.4ndash;6.6 for the longest generated nonhyphen;selfhyphen;intersecting chains.