Diffusion coefficients for segmentally flexible macromolecules: General formalism and application to rotational behavior of a body with two segments

Abstract

We present a formalism to calculate diffusion coefficients for macromolecules with segmental flexibility. Macromolecules composed of several segments of different size and shape can be treated including assemblies with arbitrary types of flexible attachments and multiple branching. The frictional resistance tensor R and the diffusion tensor D are evaluated in generalized coordinates involving all degrees of freedom, and their general properties are established. A simplified approximate expression for R is obtained when hydrodynamic interactions between segments are omitted. We apply this approximate expression to evaluate the rotational behavior of a body composed of two cylindrically symmetric segments flexibly attached at their endpoints by a frictionless universal joint. The effect of size and shape differences of the two segments upon the principal rotational diffusion coefficients of each segment is established. Coefficients governing correlations between rotations of both segments are used to evaluate diffusion coefficients for bending and twisting motions. If the body is completely flexible, the rotational relaxation behavior of each segment reduces to that of some equivalent rigid-body with cylindrical symmetry. Effects of rigid to flexible transitions and enzymatic cleavage of segments are considered. The rotational diffusion coefficient for once-broken rods is up to 2.34 times greater than predicted by Yu and Stockmayer [J. Chem. Phys. 47, 1369 (1967)] and in good agreement with dielectric dispersion measurements by Matsumoto et al. [Macromolecules 7, 824 (1974)].