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Purification of Proteins Using Displacement Chromatography 81
where the critical displacer partition ration is calculated as
= KV D/ D − P
P
K P/ D − P
D
(12)
By selecting values of C D and substituting them into Eq. 11, the boundary
between displacement and desorption may be mapped onto a plot of salt concentration
versus displacer concentration (solid line, see Fig. 2C).
To draw the boundary between displacement and elution, the following
equations are solved sequentially
[
1 − ( K D
) 1/D
( ) ] 1/P
K P
C D = ( ) 1/P [
( {
K P D −
KD
) 1/D
]} (13)
D + D
C salt =
(
K1D
) 1/D
− D + D C D (14)
By selecting values of the displacer partition ratio, , and substituting into
Eq. 13 and Eq. 14, the boundary between displacement and elution may also
be mapped onto a plot of salt concentration versus displacer concentration. In
Fig. 2C, the boundary between displacement and elution is shown as a dashed
line. To the left of the line, displacement occurs; to the right, elution occurs.
This type of plot is, by definition, specific to a particular protein and a
particular displacer. However, by overlaying several plots for a particular
displacer paired with each of the major components in a feed mixture to be
purified, it is possible to gain significant insight into the effect of displacer
concentration and salt concentration on a given separation.
The next step would be running the displacement experiment under the
conditions established based on the methods described in this section in
order to test and optimize the operating conditions if necessary. Fractions
should be collected for the regions where the feed components elute and the
displacer desorbs. A practical approach would be analyzing displacer containing
fractions via size exclusion chromatography due to the differences between
the molecular weights of proteins and the displacers. There must also be an
analytical technique to differentiate between the feed components. With these
assays in place, purity and yield calculations can be made. It should be noted
that if abbreviated methods have been used due to insufficient time and/or
material, it may take longer to identify optimized operating conditions for the
displacement.