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)].

Segmental dynamics of the cytoplasmic domain oferythrocyte band 3 determined by time-resolved fluorescence anisotropy:sensitivity to pH and ligand binding.

“…Also, is decreased 1.5-to 2-fold when the labeled segment was cleaved at one node of flexibility (the hinge, Figs. 3 and 4), as theoretically predicted (30). Hence, the C-terminal subdomain of cdb3 is highly flexible because of multiple partially flexible sequences or a single major node offlexibility located within t7 kDa of the hinge.…”

A swivel‐jointed formalism for segmentally flexible macromolecules and its application to the rotational behavior of myosin

“…We have where ai is the distance from P to the segment's center, I is the unit tensor such that I -c = c -I = c holds for any vector c, r f i ) rf) + (3/4)ty), and the dimensionless shape factors t 1; ) and t for translations parallel and perpendicular to the symmetry axis, r f ) for rotations about the symmetry axis, and r y ) for end-over-end rotations about the segment center are given explicitly in Ref. 20 for prolate ellipsoids using Perrin's equations3' and for cylinders using Broersma's equation^.^^,^^ These shape factors only depend on the axial ratio p = ui/bi, where b; is the ellipsoid semiminor axis or the cylinder radius. For cylinders, t y), t I), and r y ) are given only for p > 3.7, and Lamb's infinitely long cylinder e x p r e~s i o n ,~~ r f ) = P -~, is assumed for finite cylinders.…”

“…Certainly S1 is not long and rodlike, although there has been disagreement over its m0rphology.~~J"~8 Rotational diffusion coefficients for various S1 models pivoting about a fixed end point could be obtained from Brenner's relations,l9 as in Ref. 20. However, the joint is not a fixed point, even though its mobility in rod or myosin is diminished, so that these coefficients would be underestimates.…”

“…20 using a generalized coordinate formalism to allow for arbitrary flexible attachments between segments of different size and shape. Of course, the nature of the flexible attachments is usually unknown a priori, and it would be highly desirable to be able to compare experimental results with what would be predicted for a rigid body and for a very flexible body.…”

Electron-nuclear interactions as probes of domain motion in proteins

“…The diffusion of macromolecule with two subunits joined by hinges or swivels has been treated in several places. [45][46][47][48] Moro 47 showed how one can define a macromolecule diffusion tensor as a function of interdomain motion and combine it with the Smoluchowski equation. This route can be incorporated in the formalism presented here.…”