Monte Carlo study of cycloamylose: Chain conformation, radius of gyration, and diffusion coefficient

Abstract

Cyclic (1 --> 4)-alpha-D-glucan chains with or without excluded volume have been collected from a huge number (about 10(7)) of linear amylosic chains generated by the Monte Carlo method with a conformational energy map for maltose, and their mean-square radii of gyration <S(2)> and translational diffusion coefficients D (based on the Kirkwood formula) have been computed as functions of x (the number of glucose residues in a range from 7 to 300) and the excluded-volume strength represented by the effective hard-core radius. Both <S(2)>/x and D in the unperturbed state weakly oscillate for x < 30 and the helical nature of amylose appears more pronouncedly in cyclic chains than in linear chains. As x increases, these properties approach the values expected for Gaussian rings. Though excluded-volume effects on them are always larger in cycloamylose than in the corresponding linear amylose, the ratios of <S(2)> and the hydrodynamic radius of the former to the respective properties of the latter in good solvents can be slightly lower than or comparable to the (asymptotic) Gaussian-chain values when x is not sufficiently large. An interpolation expression is constructed for the relation between the gyration-radius expansion factors for linear and cyclic chains from the present Monte Carlo data and the early proposed asymptotic relation with the aid of the first-order perturbation theories.