Measurement of the Rotational Diffusion Coefficient of Lysozyme by Depolarized Light Scattering: Configuration of Lysozyme in Solution

Abstract

We have determined the rotational diffusion coefficient (DR) of lysozyme from the spectrum of the depolarized light scattered by this protein. The sample was illuminated by a single-frequency He–Ne laser and the spectrum of the depolarized scattered light was analyzed using a high-resolution spherical Fabry–Perot interferometer. We have determined D20,wR to be (16.7 ± 0.8) × 106/sec at 15% protein concentration. We have, in addition, measured the translational diffusion coefficient (DT) of lysozyme by employing the now-familiar techniques of optical mixing spectroscopy to observe the spectrum of the polarized light scattered by the protein. We find D20,wT to be (10.6 ± 0.1) × 10−7 cm2/sec, independent of protein concentration between 1% and 15%. Our results for DR and DT, combined with Perrin's expressions for the rotational and translational diffusion coefficients of ellipsoids, indicate that lysozyme in solution is hydrodynamically equivalent to a prolate ellipsoid of revolution with major and minor axes of (55 ± 1) Å and (33 ± 1) Å, respectively. These dimensions are shown to be consistent with an unsolvated molecule of dimensions (48 ± 1) Å by (26 ± 0.8) Å covered with a shell of solvent about 3.5 Å thick. The hydrodynamically equivalent oblate ellipsoid of revolution is shown to be inconsistent with other physical properties of the protein. We have, in addition, determined from our diffusion coefficient results the degree of solvation of lysozyme and find this to be (0.60 ± 0.03) g of solvent per gram of (dry) protein. Finally, we present a novel and unambiguous method for the determination of the depolarization ratio (ρυ) of small molecules and find ρυ = (1.4 ± 0.1) × 10−3 for lysozyme. This value of the depolarization ratio is shown to imply an intrinsic anisotropy in the polarizability of lysozyme.