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Purification of Proteins Using Displacement Chromatography 77
The breakthrough volume of the displacer/protein front (with known concentrations
of C d or C p at a salt concentration of C salt ) can be used to calculate the
capacity of the stationary phase for displacer/protein (Q d or Q p )as
Q =
C
(
Vbr
V 0
− 1
)
(5)
where V br is the breakthrough volume for the displacer or the protein. Using
this value along with knowledge of the SMA parameters, K and , the steric
factor () can then be determined from Eq. 1.
2.3. Dynamic Affinity and Affinity Ranking Plots
Once the SMA isotherm parameters are obtained, the next steps will be
predicting the elution order, selecting the right displacer and the operating
conditions for conducting the displacement chromatography. This can be done
one of two ways: via a dynamic affinity plot or an affinity ranking plot as
described below. For non-chromatographic methods of selecting high affinity
displacers, see Note 3.
It has been shown that a stability analysis can be carried out to determine the
elution order of feed components in a displacement train from the following
expression (43):
( ) 1/va ( ) 1/vi Ka Ki
<
(6)
where,
= Q d /C d (7)
where is the partition ratio of the displacer and Q d and C d are the concentrations
of the displacer on the stationary and mobile phases, respectively.
The left-hand side of Eq. 6 can be written as the dynamic affinity () of
component “a”:
( ) K 1/va
a = (8)
which is dependent on the value of that represents the operating conditions
of the displacement experiment, such as the mobile phase salt concentration
and the displacer concentration. Taking the logarithm of both sides of Eq. 8:
log K = log + v log (9)