Protein Chemistry - Part 1 - General Protein Chemistry - Ashmarin, I. P. 1968

Determination of the Size and Shape of Protein Molecules
Light Scattering by Protein Solutions

Colloidal solutions scatter a portion of the incident light, a phenomenon known as opalescence, or the Tyndall effect. While light scattering in solutions of small molecules is minimal, even pure liquids and gases scatter a fraction of incoming light. This scattering occurs because the rapidly fluctuating electric field of the light wave induces molecules to act as oscillating electric dipoles, which then reradiate light in all directions. The larger the molecular size and the greater the dipole moment, the more intense the light scattering.

If the dimensions of a molecule do not exceed 1/20 of the wavelength of light, it scatters light uniformly in all directions. In this case, the intensity of light scattering can be determined by measuring the intensity R_θ of the light scattered at an angle θ relative to the direction of the incident beam. The quantity R_θ is called the Rayleigh ratio and is given by the equation

Class="center"> (26)

where I₀ is the intensity of the incident light, I_θ is the intensity of the scattered light at an angle θ, and r is the distance from the scattering medium to the observer. Typically, measurements are made of light scattered at an angle of 90^°. When the incident light is unpolarized and the solute molecules are small (1/20 λ), the relationship between R_θ and R₉₀ is expressed by the simple ratio

R₀ = R₉₀ ∙ (1 + cos² θ).      (27)

Protein solutions scatter light more intensely than the pure solvent. This difference in scattering intensity is referred to as the turbidity of the solution and is denoted by τ. The relationship between turbidity and the intensity of light scattered at an angle of 90^° is defined by the equation

The turbidity of protein solutions is proportional to the number and size of the protein molecules, as clearly demonstrated by the following formula:

where c is the protein concentration (g/mL) and H is the proportionality constant. By measuring the refractive indices of the pure solvent (n₀) and the protein solution (n), and knowing the wavelength of the incident light (λ), this coefficient can be calculated using the formula

Comparing equations (29) and (30), we can conclude that turbidity depends not only on the size and number of protein molecules, but also on the wavelength of the incident light and the difference in refractive index between the solvent and the protein solution.

The equation above applies strictly to ideal systems devoid of intermolecular interactions. Therefore, to interpret experimental data correctly, an interaction constant B (representing a measure of the "effective volume" of the molecules) must be introduced into the equation:

If the ratio Hc/τ is plotted graphically as a function of c, the slope of the curve yields the value of B, while the intercept on the ordinate axis gives 1/M.

If the turbidity of a protein solution cannot be measured for any reason, the molecular weight can also be determined directly from the intensity of the scattered light (R₉₀) using a similar formula:

where K is a constant that combines all optical parameters (wavelength, refractive index, and refractive index increment). Since all variables in these formulas can be determined experimentally, molecular weight can be established relatively easily and rapidly. However, this method requires that solutions be meticulously clarified to remove dust and suspended particles, as well as traces of strongly scattering contaminants (such as Polysaccharides). It is also essential that protein molecules do not undergo aggregation or Denaturation during the measurement process. The molecular weights of serum albumin and Ovalbumin determined by this method were found to be 74,000 and 45,000, respectively, which are in good agreement with the results obtained by other techniques.

Everything discussed above applies to cases where the dimensions of the scattering molecules are less than 1/20 of the wavelength of light, resulting in isotropic (uniform) scattering. Specifically, the intensity of light scattered at angles of 45° and 135° (R₄₅ and R₁₃₅) will be identical. However, when protein molecules are large enough to be comparable in size to the wavelength of the incident light, light scattered by one part of a molecule may interfere out of phase with light scattered by another part. This internal Interference causes the scattered light to be distributed asymmetrically relative to the direction perpendicular to the incident beam, making R₄₅ and R₁₃₅ unequal. The ratio q = (R₄₅/R₁₃₅) – 1 is termed the dissymmetry coefficient. As dilution increases, q approaches a limiting value known as the intrinsic dissymmetry coefficient. This parameter is a function of the ratio between a certain absolute dimension of the molecule (or more precisely, a molecular model) and the wavelength of light, and it can be utilized to directly determine the dimensions of large particles, such as Viruses.

The intensity of light scattering is typically measured using sensitive photomultiplier tubes mounted on a movable arm that can rotate in a circle around the center of the system. At the center is a semi-octagonal protein solution cuvette equipped with flat optical windows positioned in the path of the incident beam, as well as at angles of 45°, 90°, and 135° (Fig. 35). The scattered light is directed onto the photomultiplier and recorded by a galvanometer. To convert these measurements into absolute values of light scattering intensity, the instrument is pre-calibrated using blocks of polymethyl methacrylate (organic Glass) or Ludox silica Suspensions.

The light scattering technique has successfully determined the molecular weights of numerous globular and Fibrous Proteins as well as viruses, and has also enabled The Study of the Kinetics of Rapid processes such as ovalbumin aggregation, fibrinogen polymerization, the interaction of mercury with mercaptoalbumin, and others.

Fig. 35. Schematic diagram of the apparatus for measuring light scattering intensity (from Stepto, 1963):

1 — light source, 2 — lenses, 3 — filter, 4 — slit, 5 — cuvette, 6 — photomultiplier, 7 — light-tight housing.