Determinant of the Inertial Tensor and Rotational Entropy of Random Polymers

Abstract

The determinant of the inertial tensor of the freely jointed chains is investigated using statistical simulation. It is found that for the straight chain, equivalent to a Markov chain, the determinant of the inertial tensor follows log-normal distribution at large chain length (N ≥ 20). The ensemble average of this determinant scales with chain length N as N 6.0. For the symmetrically cross-linked chain (two single chains of identical length with a link in between located at identical positions), it is shown that as the link position moves to the center of the chain, the average of the determinant of the inertial tensor decreases. This result is consistent with the previous experimental observation that the stabilizing effect of inerchain disulfide bond on a dimeric α-helical coiled-coil becomes greater as it moves toward the center of the chain. The average of the determinant of the inertial tensor are then used to calculate the reduction in rotational entropy caused by cross-linking two random polymers, using ideal gas statistics. The values obtained are then compared with experimental data on entropy reduction caused by cross-linking unfolded polypeptide chains in aqueous solutions. The results support the conclusion drawn previously from experimental work that ideal gas statistics grossly overestimate the translational and rotational entropy of macromolecules in aqueous solutions.