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320 Heegaard et al.
where AL is the formed complex, [A], [L] and [AL] the equilibrium
concentrations of the analyte, ligand and complex, respectively, and K the
stability (association) constant. Mobility shift ACE is conducted by performing
a series of CE experiments in which a small volume of the analyte and a noninteracting
marker are introduced into the capillary while the electrophoresis
buffer contains various known concentrations of the ligand. Provided that free
and complexed analyte have different electrophoretic mobilities, the effective
electrophoretic mobility of the analyte, eff , will depend on the concentration
of the ligand added to the electrophoresis buffer according to
A
eff =
A + AL AL
A +
A + AL AL (4)
where A and AL are the electrophoretic mobilities of the free analyte and
the AL complex, respectively. Equation 4 may be combined with Eq. 3 and
rearranged to give
eff = A + AL KL
1 + KL
A plot of eff as a function of the free ligand concentration, [L], will
give the binding isotherm, and the stability constant may be obtained by
non-linear regression analysis using a suitable software package. Given the
use of an internal marker and use of the same buffer, temperature and field
strength conditions in a series of mobility shift ACE experiments, the peak
appearance time t can be used directly in plots to estimate binding constants
(c.f. Subheading 6.2.1., below). The free ligand concentration in Eq. 5 is
assumed to be equal to the total ligand concentration in the electrophoresis
buffer. For this to be approximately true, the analyte concentration in the sample
needs to be more than 10–100 times lower than the ligand concentration (87,88).
Note, however, that in contrast to the ligand concentration, the concentration of
the analyte does not need to be accurately known. If the binding kinetics is not
fast relative to the separation time, it will be evident in the mobility shift experiments
as disappearance, broadening, tailing or splitting of the analyte peak (87).
As a rule, averaged, weighted peaks reflecting the association–dissociation time
distribution will only occur if the dissociation half-time ln 2/k off is equal to or
less than 1% of the peak appearance time (89). If the 1/k off -value is getting
close to the analyte peak appearance time, the complexes are too stable for the
mobility shift approach to be useful (87) (see Fig. 6 see Subheading 6.2.1). The
figure illustrates a mobility shift experiment (of a monoclonal antibody interacting
with its antigen) where the analyte peak is displaced by the anionic ligand
(synthetic oligonucleotide) but otherwise unperturbed. Thus, the experiments
can be used to estimate the binding constant for this interaction. In addition, in
(5)