Ch 24 pages Lecture 10 – Ultracentrifugation/Sedimentation

Ultracentrifugation and Sedimentation Sedimentation is a technique used to separate, purify and analyze all kind of cellular components It can be understood using a simple mechanical analogy. Consider a mass m falling through a fluid. Opposing the gravitational force: is a buoyant force: and a frictional force: m is the mass of the particle, m 0 the mass of the displaced fluid, V 2 the specific volume of the particle,  the density of the fluid, f is the frictional coefficient of the falling body, v the steady-state velocity reached during motion

Ultracentrifugation and Sedimentation At steady state the terminal velocity is obtained from the force balance From which it follows This terms that follows is called buoyancy

Ultracentrifugation and Sedimentation The sedimentation experiment is juxtaposed with the free fall problem in the picture:

Ultracentrifugation and Sedimentation is the centrifugal force, where  is the angular velocity, r is the distance from the solute particle to the axis, and  2 r is the centrifugal acceleration is the buoyant force is the frictional force

Ultracentrifugation and Sedimentation By direct analogy, the steady state velocity of a solute particle being spun in a centrifuge tube can be obtained by balancing all forces once again: Here we have introduced the sedimentation coefficient: Its dimensions are sec, but a more convenient unit of measure for s is the Svedberg: S= s

Standard Sedimentation Coefficient If we remember the definition of frictional coefficient from Stoke’s law, then:  and  are dependent on solvent and temperature, while R brings about again the molecular properties of the molecule undergoing sedimentation

Standard Sedimentation Coefficient Values for s are usually reported in Svedberg and referred to a pure water solvent at 293K=20 o C. It is useful to use these conditions to standardize the measured sedimentation coefficients s. The standard sedimentation coefficient is: A sedimentation coefficient measured under other conditions, i.e. in a buffered aqueous solution b and/or at another temperature T can be related to standard conditions by the equation:

Standard Sedimentation Coefficient This relationship only holds true if changing conditions (temperature or buffer conditions) have not significantly affected the shape or hydration property of the molecule. Conversely, if it is found that the sedimentation coefficient changes, then it can be concluded that one of those properties has changed By measuring the sedimentation coefficient, diffusion coefficient and partial specific volume, we can calculate the molecular mass of any particle under any experimental conditions and follow how it changes (e.g. dimerization).

Standard Sedimentation Coefficient Example: The following data have been gathered for ribosomes obtained from a paramecium We can calculate the molar weight of the ribosome by substituting the diffusion coefficient in place of the frictional coefficient:

Boundary Sedimentation In a first method to measure sedimentation coefficients, a homogeneous solution is spun in a ultracentrifuge. As the macromolecule moves down the centrifugal field, a solution- solvent boundary is generated. We can estimate s by following the movement of the boundary with time. By generating a boundary we also generate a concentration gradient and therefore we would expect the molecule to begin diffusing; however, if the macromolecule is large or the field very large (high spinning speed), then the boundary will be very sharp because transport by sedimentation will be much larger than transport by diffusion. If diffusion is significant, then the boundary broadens as it shifts towards the bottom of the cell with time.

Boundary Sedimentation

If we assume transport by diffusion can be neglected and re- write: Then we can find a solution:

Boundary Sedimentation At zero time, the concentration is uniform throughout the cell; as time increases, a sharp boundary is generated, with solvent to the left and solute to the right; the concentration of solute will be constant on either side of the boundary This equation means that as centrifugation proceeds, the solute concentration boundary, with position r relative to the spinning axis proceeds from an initial position r(t 0 ) to r(t). Rearranging the equation for r(t), we obtain:

Boundary Sedimentation A plot of ln r(t) versus elapsed time t-t 0 is a straight line with slope s  2. The concentration of solute at the right of the boundary is not the same as the starting concentration (uniform) C 0. It can also be shown that:

Boundary Sedimentation

Zone Sedimentation A second way to measure sedimentation is called zone sedimentation. A thin layer of a macromolecular solution is placed at the top of the solvent at the beginning of the centrifugation (left, below). As the centrifugation progresses the macromolecule moves through the solvent as a band or zone (right, below). To prevent mixing of the dense macromolecular band with the solvent, a density gradient is created so that the net density increases in the direction of the centrifugal field. Typically, a linear sucrose concentration gradient is used. Alternatively, one could use a concentrated salt solution (e.g. CsCl), in which case the density gradient will be generated by the sedimentation of the salt itself.

Zone Sedimentation The macromolecule band can become broadened due to diffusion, thus reducing resolution of the macromolecular bands.