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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/

2
r


where u = velocity of the particle





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r = distance from axis of rotation

s

is related to the molar weight (MW) of the solute:

s

= MW(1
-

⤯)
f




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f = frictional coefficient

WARNING: VALUES ARE TEMPERATURE
DEPENDENT

The sedimentation coefficient,
s
:
s

= u/

2
r


10
-
13

seconds is called a Svedberg, and
given the symbol
S


S has implied units of s/radian
2
, but the
radian
2
is generally ignored



= partial specific volume of the solute
(units: cm
3
/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: cm
3
/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 cm
3
/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 cm
3
/g.






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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=

⩣⩬)
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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.