Rotational Diffusion Coefficients of Complex Macromolecules
It is necessary to have an accurate theory enabling calculation of the rotational diffusion coefficient Dθθ in terms of molecular structure, if electric birefringence relaxation times are to be interpreted. We have constructed such a theory for rigid macromolecular structures composed of arrays of nonidentical, spherical subunits. Hydrodynamic interaction between the subunits is expressed by a tensor which takes into account the finite size of the subunits. The set of simultaneous interaction equations is solved completely by numerical methods. While substantial improvements over prior theories are obtained, difficulties still remain when a large spherical subunit is located near the center of rotation. The rotation of this subunit about its axis is calculated to contribute less to rotational friction than is in fact the case. We have remedied this by replacing the large central sphere by an array (typically octahedral or cubic) of smaller spheres chosen to have the same Dθθ. Agreement with the Perrin equation for prolate ellipsoids is now good over the entire range of axial ratios. For T-even phage, experimental (20°C) and theoretical values are now in excellent accord: 250–325 sec-1 (exp) and 250–330 sec-1 (theor) for fiber-less or fiber-retracted phage; and 100–120 sec-1 (exp) and 112 sec-1 (theor) for fiber-extended phage. We feel that the theory is now sufficiently refined that adequate calculations of DR for any rigid structure, regardless of shape or symmetry, can be made with a moderate investment of computer time.
KeywordsAxial Ratio Hydrodynamic Interaction Frictional Resistance Small Sphere Large Sphere
Unable to display preview. Download preview PDF.
- 6.Oseen C W, “Hydrodynamik” Akademisches Verlag, Leipzig (1927).Google Scholar
- 7.Burgers J M, “Second Report on Viscosity and Plasticity, Amsterdam Acad. Sci.”, Nordemann, Amsterdam (1938), Ch. 3.Google Scholar
- 10.Wilson R W and Bloomfield V A, submitted for publication.Google Scholar