Protein Chemistry. Structure, Properties, Research Methods - Shendryk A.N. 2022

Methods for experimental study of protein structure
Methods for determining the molecular weight of proteins
Determination of molecular weight by light scattering

If a beam of light is passed through a protein solution in a darkened room, its path through the vessel becomes visible. This property of colloidal solutions is well-studied and known as opalescence. The phenomenon of opalescence is caused by light scattering, and the effect itself is named the Tyndall effect.

Knowing the wavelength of the incident light, the intensity of the scattered radiation, the refractive indices of the solvent and the solution, as well as the refractive index increment and concentration of the solute, one can calculate its molecular weight.

There are two methodological approaches. The first one is used when the size of the dissolved molecules is 10–20 times smaller than the wavelength of the irradiating light. In this case, the molecule acts as a single radiation-scattering center.

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The second approach is applied when the wavelength of the radiation is comparable to or greater than the size of the molecules. Then, a single molecule may contain several independent oscillators, and it is necessary to take into account the Interference of light rays scattered by different Regions of the same molecule (see fig.).

For the first case, the Rayleigh equation is applicable for the dependence of the intensity of light scattered at an angle 0 on the distance to the scattering particle:

where R₀ is the reduced intensity or the Rayleigh ratio;

I₀,I₀ are the intensities of the incident and scattered light, respectively;

r is the distance from the scattering particle to the light detector.

For ideal dilute solutions, the value R₀ is proportional to the molecular weight (MW) of the solute (M) and its weight concentration (c):

R₀ = KMc

The proportionality coefficient (K) is a function of the form:

where n₀ and n are the refractive indices of the solvent and the solution, respectively; N is Avogadro's number.

The values R_θ, n₀, and dn/dc are determined experimentally, and by substituting them into the equation, the Molecular Weight of the protein is calculated.

For non-ideal solutions, an empirical relation is used:

where B is an empirical constant, and the dependence is plotted in the coordinates:

The intercept on the ordinate axis is equal to the reciprocal of the molecular weight (see equation, figure).

If the sizes of the protein molecules are comparable to X, additional corrections are introduced into the equation:

where R²_G is the so-called radius of gyration.

For various shapes of protein molecules (sphere, cylinder, coil, etc.), special formulas exist for calculating R²_G values. If, upon substituting the R²_G value calculated for a specific molecular shape into the equation, the experimental data fall on a straight line in the coordinates:

then it is considered that the molecular shape, and consequently R²_G, have been chosen correctly.

Light scattering decreases the intensity of radiation passing through a solution. For solutions with particle sizes significantly smaller than the wavelength of the incident light, a relationship analogous to the Lambert–Beer–Bouguer law holds:

where т is the turbidity.

The value of т is measured using nephelometers.