A Monte Carlo study of the excluded‐volume effect on the amylosic chain conformation

Abstract

SynopsisA Monte Carlo procedure was used to determine the effect of excluded volume on the conformational dimensions of amyloaic chains. The excluded volume was introduced into the model by assuming that hard spheres, which cannot overlap each other, exist at the center of mees of each glucose unit in the chain sequence. Monte Carlo chains, which were generated to be distributed consistent with the potential energy of nonbonded nearest-neighbor interactions, underwent self-intersections, and the attrition rate in the generation of self-avoiding chains was found to obey an exponential decay law with increasing chain length x. Thus, in order to generate effectively a large number of self-avoiding chains with long sequences, we used the Wall- Phys. 30,634-6373. By examinatim of the radial distribution of the end-to-end distance and the chain-length dependence of the quantity ( r 2 ) / d 2 ((r') is the mean square end-to-end distance and I ie the virtual bond length), it was found that unperturbed amylkc chains change in overall conformation from a non-Gaueeian chain having a helical character to Gaussian as x is increased, whereas perturbed chains do not show Gaussian behavior even at x = 500. For the perturbed chains, (r') can be expresaed by the equation ( r 2 ) = atb in the range of 100 5 x < 500, where a and b > 1 are constants From comparisons of the persistence vectors and perspective drawings of representative unperturbed and perturbed chains, we felt the local conformation of the amyloeic chains, i.e., the local helical character, is also afhted by the long-range excluded-volume interaction.

Higher order structure of (1,3)‐β‐D‐glucans and its influence on their biological activities and complexation abilities

“…The character of the energetically preferred chain trajectory of a polymer can be estimated using molecular mechanics 7–11. Since the six‐membered chair form ring is rather rigid, most of the flexibility of a polysaccharide chain arises from rotations about the bonds of the glycosidic linkages 12.…”

Conformation of Amylose and Excluded-Volume Effects on Its Chain Dimensions

“…9 The bond angle for the glucosidic oxygen atom was taken as 118° and the virtual bond length l as 0.44 nm. In computing (S 2 ), each glucose unit was replaced by a hard-core sphere of radius a whose center is located at the center of mass of the glucose unit.…”

“…The Monte Carlo sample for each x contained 5000 chains, but for selfavoiding chains with x > 20, the computation was effected by use of the Wall-Erpenbeck s-p method 13 of chain enrichment, as in the work by Kitamura et al 9 on (R 2 ) (see ref 9 for the details of the procedures). The results all refer to 25°C.…”

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

“…In previous papers,1, 2 we investigated the chain conformation and dimensions of linear amylose with or without excluded volume by the Monte Carlo method, and drew the following conclusions: (1) The polysaccharide molecule in solution is locally helical but flexible, and without excluded‐volume effect, it becomes Gaussian when x (the number of glucose residues) exceeds 500. (2) Monte Carlo data of the mean‐square radius of gyration 〈 S 2 〉 for x > 12 in both unperturbed and perturbed states agree closely with theoretical predictions based on the helical wormlike (HW) chain,3 when the experimentally estimated HW model parameters4 are used.…”

“…The present paper reports a Monte Carlo study undertaken, as an extension of our previous work on linear chains,1, 2 to explore conformational and dimensional characteristics of cycloamylose, i.e., cyclic (1 → 4)‐α‐ D ‐glucan, with or without excluded volume. Translational diffusion coefficients D are also computed for both linear and cyclic chains on the basis of the Kirkwood theory,7 though the theory is not rigorous in that it ignores the fluctuating hydrodynamic interaction 3.…”