Dissociation rate constants for nonfluorescent ligands N can be
determined using similar approaches involving competition with a
fluorescent ligand L [14] (see Note 11).
3.2.2 Measuring
the Association Rate
Constant for N Binding to P
The association rate constant for binding of N to P (k +2 in
Scheme C) can be measured using competition with L.
In this case, the experiment involves the following steps:
1. Stopped-flow mix P with a premixed solution of N and L. The
concentration of L ([L tot ]) should be selected as that concentration that gives reasonable saturation of P in the absence of
N. This requires that the K d for formation of PL is known. If
not known from other experimental approaches, it should be
determined as outlined in Subheading 3.1.
2. Repeat the measurement using different [N tot ] at a fixed value
of [L tot ].
3. If the dissociation rate constants (k À1 and k À2 ) are small (Note:
more complex behavior will be observed if the dissociation rate
constants are not small) and both L and N are in large excess
over P, then the observed first-order rate constant will be given
by:
k obs ¼ k 1 L tot
½
þk 2 N tot
½
ð5Þ
A plot of k obs vs. [N tot ] should give a straight line with
slope k 2 and intercept k 1 [L tot ] (Eq. 5). Any value for k 1 determined in this way should be compared with that determined
using approach described in Subheading 3.1.
Figure 4 shows data for the system described in Subheading 3.1
in which Ca 4 –calmodulin (0.1 μM) was reacted with a solution
containing a fixed concentration of fluorescently labelled peptide
NMp ([L tot ] ¼ 2 μM) and varying concentrations of the unlabeled
peptide ([N tot ]). The intercept (¼k 1 [L tot ] ¼ 23.95 Æ 2.3) gives a k 1
value of ~1.2 Â 10
7 M
À1 s
À1 in excellent agreement with the value
determined in Subheading 3.1. The slope corresponds to a k 2 value
of 6.5 Â 10
6 M
À1 s
À1 , indicating that the kinetic properties of the
unlabeled peptide differ somewhat from those of the labeled one.
This was confirmed when direct fluorescence competition titrations
showed that the unlabeled peptide has a K d of 18 Æ 5 nM
(cf. 70 Æ 14 nM for the labeled peptide). The k 2 and K d values
correspond to a dissociation rate constant (k À2 ) of ~0.12 s
À1
(cf. ~0.8 s
À1 for the labelled peptide).
3.3 Ternary Complex
Formation
There are many cases where a protein binds two different ligands to
form a ternary complex. Scheme D is for a protein P interacting
with two ligands (X and Y) to form the ternary complex PXY.
Calmodulin Target Interactions
93
determined using similar approaches involving competition with a
fluorescent ligand L [14] (see Note 11).
3.2.2 Measuring
the Association Rate
Constant for N Binding to P
The association rate constant for binding of N to P (k +2 in
Scheme C) can be measured using competition with L.
In this case, the experiment involves the following steps:
1. Stopped-flow mix P with a premixed solution of N and L. The
concentration of L ([L tot ]) should be selected as that concentration that gives reasonable saturation of P in the absence of
N. This requires that the K d for formation of PL is known. If
not known from other experimental approaches, it should be
determined as outlined in Subheading 3.1.
2. Repeat the measurement using different [N tot ] at a fixed value
of [L tot ].
3. If the dissociation rate constants (k À1 and k À2 ) are small (Note:
more complex behavior will be observed if the dissociation rate
constants are not small) and both L and N are in large excess
over P, then the observed first-order rate constant will be given
by:
k obs ¼ k 1 L tot
½
þk 2 N tot
½
ð5Þ
A plot of k obs vs. [N tot ] should give a straight line with
slope k 2 and intercept k 1 [L tot ] (Eq. 5). Any value for k 1 determined in this way should be compared with that determined
using approach described in Subheading 3.1.
Figure 4 shows data for the system described in Subheading 3.1
in which Ca 4 –calmodulin (0.1 μM) was reacted with a solution
containing a fixed concentration of fluorescently labelled peptide
NMp ([L tot ] ¼ 2 μM) and varying concentrations of the unlabeled
peptide ([N tot ]). The intercept (¼k 1 [L tot ] ¼ 23.95 Æ 2.3) gives a k 1
value of ~1.2 Â 10
7 M
À1 s
À1 in excellent agreement with the value
determined in Subheading 3.1. The slope corresponds to a k 2 value
of 6.5 Â 10
6 M
À1 s
À1 , indicating that the kinetic properties of the
unlabeled peptide differ somewhat from those of the labeled one.
This was confirmed when direct fluorescence competition titrations
showed that the unlabeled peptide has a K d of 18 Æ 5 nM
(cf. 70 Æ 14 nM for the labeled peptide). The k 2 and K d values
correspond to a dissociation rate constant (k À2 ) of ~0.12 s
À1
(cf. ~0.8 s
À1 for the labelled peptide).
3.3 Ternary Complex
Formation
There are many cases where a protein binds two different ligands to
form a ternary complex. Scheme D is for a protein P interacting
with two ligands (X and Y) to form the ternary complex PXY.
Calmodulin Target Interactions
93