The correlation matrix of the position of a polymer chain: Unexpected results for the Gaussian coil model

Abstract

A correlation matrix of the positioning of the elements of a macromolecule is a measure of the diversity of the conformations of these molecules in a considered statistical ensemble. The structure of the correlation matrix of molecules is presented as a relief of the dependence of the correlation coefficients on the relative position of the units of a polymer chain along its contour. This relief is shown to be nonmonotonic; there are significant correlations of the position of far located chain links. When the chain length is more than several tens of units, the relief shape is practically identical in a continuous or discrete space of any dimension, homogeneous or affine-transformed. This invariance may be disrupted by the macrocharacteristic fractioning of the chain system and mixing of the chain set, may be constructed via different algorithms, or may be due to the interaction of the chains. The presence of considerable correlations among the conformations of independently constructed macromolecules should be taken into account during selection of the conformations.