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Bios 532
Analytical Ultracentrifugation
Sedimentation of Particles in a
Gravitational Field
The sedimentation coefficient, s:
The s-value is the sedimentation velocity of a
molecule. This may be measured by sucrose gradient
sedimentation or by analytical ultracentrifugation.
The s-value of a molecule is determined both by its
shape and by its mass.
Sedimentation of Particles in a
Gravitational Field
The sedimentation coefficient, s: s = u/2r
where u = velocity of the particle
 = angular velocity of the rotor
r = distance from axis of rotation
s is related to the molar weight (MW) of the solute:
s = MW(1-)/Nf
 = partial specific volume of the solute
 = density of the solvent
N = Avogadro's number
f = frictional coefficient
WARNING: VALUES ARE TEMPERATURE
DEPENDENT
The sedimentation coefficient, s: s = u/2r
10-13 seconds is called a Svedberg, and
given the symbol S
S has implied units of s/radian2, but the
radian2 is generally ignored
 = partial specific volume of the solute (units: cm3/g)
The partial specific volume of a protein is the ratio between it's
volume and molecular weight.
The partial specific volume of a molecule is a measure of
the change in volume (in mL) of the solution per gram of
the molecule in that solution.
Partial specific volume is equal to the inverse of the
density of the particle;  can be measured directly or
estimated.
If the exact sequence of the protein is known, then the partial
specific volume may be calculated from the partial specific
volumes of the constituent amino acids, using the following
equation:
 =(∑ (n(i) M(i) (i) ) )/ (∑ n(i) M(i) )
n (i) = # of residues of type i
M(i) = mass of residue type i
 (i) = psv for residue type i
WARNING:
estimate breaks down if you have detergent
bound, modifications, etc. and
M(i) = M(aa) -18 for all but the last amino acid because water is
released forming the peptide bond!
 = partial specific volume of the solute (units: cm3/g)
One rough estimation of the partial specific volume of a protein,
which may be used if the sequence of the protein is not known, is:
average partial specific volume of proteins = 0.725 cm^3/g
Because the average of experimentally determined partial specific
volumes for soluble, globular proteins is approximately 0.73 cm3/g
(average of experimental values from 13 soluble proteins). This
value varies from protein to protein, but the range is rather narrow,
between 0.70 and 0.75 cm3/g.
 = density of the solvent
units: g/cm^3
The density of many buffers may be approximately equal to the
density of water.
density of water = 0.998 g/cm^3 (at 20 deg. C)
our software (Ultrascan) has a feature for calculating
the density of common buffers with common additives
f = frictional coefficient
f = a (6 π 0)
where a = Stokes radius
approximately, the length of the "long axis" of a
molecule. Stokes radius can be determined by gel
filtration.
and
0 = viscosity of the solvent
Analytical
Ultracentrifugation (AU)
is a spectroscopic
technique.
AU spins a rotor at a
controlled speed and constant
temperature and records the
concentration distribution of
the sample at known times.
The concentration is
determined for solutes obeying
the Beer-Lambert law
(A=*c*l) by measuring the
absorbance of the sample at a
given wavelength at fixed
positions in the cell.
AU Methods:
Sedimentation Equilibrium
Sedimentation Velocity
Sedimentation Velocity
Figure 1.
Cells have a
double-sector
centerpiece.
SAMPLE
REFERENCE
Figure 2. SV absorbance spectrum
Sedimentation Velocity
Movement of the boundary in SV experiments
Sedimentation Equilibrium
The cell contains 6 columns.
One row of 3 columns are for sample,
the other is the reference row.
SAMPLE
REFERENCE
FIGURE 2. SE absorbance profile
Fundamental Applications of
Analytical Ultracentrifugation
1. Examination of Sample Purity
Quantitation of size distributions in polydisperse samples.
2. Molecular Weight Determination
Applicable to MW ranges from 100 to 1,000,000.
3. Analysis of Associating Systems
Determines components of a complex and stoichiometry.
4. Sedimentation and Diffusion Coefficients
Measures macromolecular complex sizes and interactions.
5. Ligand Binding
Distinguish ligands from acceptors of differing absorbance.
Selection of the data for analysis in an SE
experiment - select the area where the
concentration distribution is exponential with the
square of the radial position.
Data Analysis
1. First, fit one individual scan in the single ideal species
model.
2. Next, fit the data from our SE experiment to a model for more
than one species in equilibrium.
3. Goodness of fit - the residual plot.