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

Methods for Experimental Investigation of Protein Structure
Methods for Determining Protein Molecular Weight
Determination of Molecular Weight by Sedimentation - Determination of Molecular Weight by Sedimentation Velocity

If the centrifugal force applied to a protein molecule significantly exceeds the counteracting forces of diffusion, the molecule gradually moves in the direction of this force—that is, it sediments from the meniscus toward the bottom of The Cell. Pure solvent is left at the top, separated from the solution by a rather distinct boundary. The movement of this boundary along the centrifuge cell can be observed optically by measuring the refractive index at various distances from the meniscus along the cell.

Let us examine this method in broad terms. In a solution-filled cell rotating in a centrifuge, a particle experiences a centrifugal force:

Class="center">F_ц/б = mω²r

where m is mass, ω is angular velocity, and r is the distance to the center of rotation.

The solvent exerts a buoyant force on the particle, F_выт (or buoyancy factor), directed opposite to the centrifugal force:

F_выт = ω²rmvp

where V is the partial specific volume of the dissolved particles. It is defined as the increase in solution volume (in the presence of a large excess of solvent) upon The addition of 1 g of dry substance (cm³/g). For most Proteins, v≅0.74 cm³/g, and p is the density of the solvent.

Furthermore, as a dissolved particle moves through the solvent, a frictional force arises that opposes this movement:

F_тр = fV

where f is the frictional coefficient and V is the relative velocity.

Under steady-state hydrodynamic conditions, a dissolved particle moves at a constant velocity (without acceleration) because all forces acting upon it are balanced (Newton's law):

F_ц/б = F_выт + F_тр

or:

mω²r - ω2rmvp - fV = 0

From this, the uniform sedimentation velocity of the particle is:

It follows from the final equation that in a gravitational field:

• the velocity of a particle is proportional to its mass;

• denser particles with a smaller specific volume (v) will move faster than less dense ones;

• as the density of the solution (p) increases, the velocity of the suspended particles decreases;

• the velocity is inversely proportional to the frictional coefficient (f).

The sedimentation principles listed above apply to all colloidal particles, regardless of their size.

In cases where the protein sedimentation boundary moves at a constant velocity—that is, when the forces are in equilibrium—the sedimentation rate is expressed in terms of the sedimentation coefficient, s:

s = V/ω²r

Sedimentation coefficients for proteins typically range from 10^-13 to 10^-15 s. Usually, s is expressed in special units called Svedbergs (denoted by the symbol S); 1S = 10^-13 s. As the Molecular Weight of a protein increases, its sedimentation coefficient increases as well, though there is no simple proportionality. However, knowing the value of s and having some additional data, one can calculate the molecular weight of a protein using the Svedberg equation:

M = RTs/D(1-vp)

where D is the diffusion coefficient, R is the universal gas constant, and T is the absolute Temperature.

To obtain more reliable values, s and D are measured in solutions with varying protein concentrations and extrapolated to infinite dilution. The sedimentation coefficients determined in this manner are referred to as sedimentation constants - s⁰.

The Sedimentation Velocity Method yields erroneous results if the particle shape deviates significantly from spherical—especially in the case of long, thin, rod-like molecules. Furthermore, calculating the molecular weight using the Svedberg equation introduces considerable errors due to inaccuracies in determining V. Precise measurement of v on small protein samples is nearly impossible.