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326 Heegaard et al.
6.2.1.3. Equations
Data analysis may be conducted in several ways (see Subheading 6.1, e.g.
Eq. 5). Here, two equivalent approaches based on differences in effective
electrophoretic mobility and in peak appearance times are described:
1. Mobility change in experiment with ligand concentration [L] added to the
electrophoresis buffer in comparison with no ligand added:
= max − K d × /L
= effective, corrected electrophoretic mobility. = (lc × ld)/[V × (t − t m )] where
t − t m is the difference between the peak appearance time and the appearance time
of a non-interacting marker. lc is the total capillary length and ld is the length of
the capillary to the detection window. , the mobility shift, i.e. the difference
in between experiments with and without added ligand. max , the maximum
mobility shift (in a fully saturated system).
2. Mobility change and corrected peak appearance time (t) using internal (added to
the sample) reference marker:
= lc/E × 1/t − 1/t r − 1/t 0 − 1/t r0 = lc/E × 1/t
lc is total capillary length, E is field strength, subscript 0 denotes reference experiment
without ligand addition.
1/t = 1/t − 1/t r − 1/t 0 − 1/t r0 i.e. difference in corrected inverse peak
appearance time in experiment with and without added ligand.
3. Mobility change expressed using corrected peak appearance times:
1/t = 1/t max − K d × 1/t/L
4. Plots of as a function of [L] or (1/t) as a function of [L] should show a
definite curvature (saturation).
5. Non-linear curve fitting to the plot using a one binding site–hyperbola function
yields the K d if binding behaves according to a 1:1 molecular association binding
isotherm of the equation: 1/t = 1/t max ×L/K d + L (see Fig. 6B)
6.2.1.4. Mobility Shift ACE Procedure
1. Preconditioning and inter-run washing procedures correspond to those given below
for the pre-eq/FA-CE experiments.
2. Establish reproducible and suitable (e.g. physiological) analysis conditions for
analyte, marker molecule and ligand separately, and ensure that they migrate
differently.
3. Perform electrophoresis in the presence of various known concentrations of ligand
added to the electrophoresis buffer. Depending on the availability, it will be
advantageous to use the most charged molecule as the ligand (the buffer additive).
Mix analyte in a suitable proportion with the marker molecule and perform the
CE analysis. Look for migration shifts not affecting peak shape and size.
4. Perform affinity electrophoresis in the presence of ligand molar concentrations
from 10 to 500 times the expected dissociation constant value while keeping the