Sedimentation

Imaging a solute molecule in a solution that is held in a rapidly spinning rotor. Ignoring the random motion due to the thermal motion, we may say that there are three forces acting on it (centrifugal force F_c, buoyancy force F_b, and frictional force F_d).

	Centrifugal force Fc = w2rm w: angular velocity of the rotor r: distance form the center of the rotor m: mass of the particle
	Buoyancy force Fb = -w2rm0 m0: mass of the solution displaced by the particle
	Frictional force Fd = -fv

When the steady velocity is reached, the system is at equilibrium state, where:

F_c + F_b + F_d = 0

w²rm - w²rm₀ - fv = 0

The mass of the displaced solution, m₀ ,can be expressed as the product of the partial specific volume times the solution density: m₀ = mVr. Thus,

w²rm(1-Vr) - fv = 0

If we express the equation in a molar basis with Avogadro's number N, then, with a little modification, the equation can be written as:

M(1-Vr) / Nf = v/w²r = s

sedimentation coefficient = velocity / field strength

The sedimentation coefficient is proportional to the molecular weight multiplied by theeee buoyancy factor (1-Vr) and inversity proportional to the frictional coefficient. The unit of sedimentation coefficient is defined as 1 Svedberg (1e-13 sec), denoted as S, since the quantity 1e-13 sec is commonly measured.

Note that, the sedimentation coefficient is not a linear additive parameter. For example, the large ribosomal subunit and small ribosomal subunit are 50S and 30S, respectively. Yet, ribosome as a whole is 70S.

Diffusion

A moving boundary sedimentation experiment. There is a solution-free region, a boundary region and a plateau region. The sedimentation coefficient is measured from the midpoint of the boundary. The boundary (indicated by red arrows) broadens with time (green arrow) as a consequence of diffusion.

Diffusion is simply the result of the random thermal motion. The diffusion coefficient D is proportional to RT and inversely proportional to the frictional coefficient.

D = RT / Nf

Combining diffusion coefficient and sedimentation, we can obtain the Svedberg equation:

s / D = M(1-Vr) / RT

Q: A spherical protein of diameter R dimerizes and rearranges to form another spherical shape equal to the sum of the original monomer volumes. What will be the percent increase or decrease in (a) the diffusion coefficient and (b) the sedimentation?

Solution....

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