Hydrodynamic modes of arbitrarily shaped flexible macromolecules: Influence on dynamic light scattering

Abstract

SYNOPSISThe diffusional motions of flexible macromolecules are analyzed with a n increasingly realistic Rouse-Zimm model, i.e., by modeling the molecule as an arbitrary set of spheres connected by nearly harmonic springs. New features include ( 1 ) nearly arbitrary arrangements of spheres, ( 2 ) arbitrary arrangements of translational and torsional springs, ( 3 ) significant anharmonic corrections to the elastic potential surface, and ( 4 ) inclusion of torsional damping and various hydrodynamic cross-coupling effects (including two types of translational-rotational coupling) with no additional fitted parameters. contain no adjustable parameters other than temperature, viscosity, and the radii and positions of the spheres. These hydrodynamic interactions allow accurate calculations of rigid body diffusion as well as flexible motions.Given the positions, radii, and spring constant matrix, one can calculate a full set of three-dimensional diffusional modes. Because one uses an off-diagonal hydrodynamic resistance matrix instead of a diagonal mass matrix, the diffusional modes are different in structure from vacuum normal modes, and give rise to different rms motions in the laboratory frame. These hydrodynamic modes include the effects of vibrational-translational crosscoupling (i.e., motion along a vibrational coordinate may give rise to a translational force, and vice versa).The diffusional modes are used to simulate dynamic light scattering (DLS) . I examine various molecules with different shapes, flexibilities, and with different scattering vectors. Radial and angular motions influence DLS decays differently. These effects are dependent upon the molecular shape (straight, bent, or curved) and type of flexibility (stretching or bending). Furthermore, small cubic corrections to the potential surface can be significant for DLS of certain geometries such as straight rods and semicircles. 0 1993 John Wiley & Sons, Inc. 409 410 GOLDSTEIN Schmitz5 and references therein). This technique has the following advantages: HYDRODYNAMIC MODES OF ARBITRARILY-SHAPED MACROMOLECULES 4 1 1 with the rigid body diffusion constants, to compute dynamic light scattering by evaluating the scattered electric field correlation function GI ( k , t ) [expressed as a plane wave expansion in Eq. ( 3 6 ) ] . This evaluation uses the results of the rigid anisotropic rotor [ Eq. ( 2 7 ) ] in terms of the isotropic rotor [ Eq. (53) 1, and includes rotational-translational coupling perturbatively in averages over rigid body angles [ Eq. ( 37 ) 1 , plus some approximation for vibrational averaging and some approximation for the remaining time-ordered expectation value in Eq. ( 3 7 ) , as discussed in the text. At a large scattering vector, however, it is more efficient to evaluate GI (k, t ) from a small angle (or short time) expansion [ Eq. (66) ] rather than the more general plane wave expansion.Probably the easiest way to implement these simulations is to obtain the programs used to compute the examples in this article. ( A copy of the programs...

Brownian motion of a torus

“…Hydrodynamic coupling between different degrees of freedom and its effect on the diffusivity is also important in macromolecules and bio-polymers [15][16][17][18]. The popular Zimm model in polymer dynamics, takes into account, the hydrodynamic interaction between different monomer beads in a macromolecule.…”