Discrimination between Conformational
Selection and Induced Fit Protein-Ligand
Binding using Integrated Global Fit Analysis
Franz-Josef Meyer-Almes*
Department of Chemical Engineering and Biotechnology, University of Applied Sciences,
Darmstadt, Germany
SUPPORTING MATERIALS
Fig. S1: Data simulated according to the CS-mechanism and fitted to the IF-model
Fig. S2: Data simulated according to the IF-mechanism and fitted to the CS-model
Fig. S3: Dependence of IF-Fit to CS-simulated data from a broad range of ligand
concentrations
Fig. S4: Dependence of CS-Fit to IF-simulated data from a broad range of ligand
concentrations
Fig. S5: Experimental binding kinetics of Lu210 ligand to HDAH protein
Fig. S6: Influence of noise on the Global Fit of binding kinetics
Table S1: Rate constants and ligand concentrations used to simulate the data in Fig. S1
according to the CS-mechanism. The rate constants of the Global Fit to the IF-model
are also listed.
Table S2: Rate constants and ligand concentrations used to simulate the data in Fig. S2
according to the IF-mechanism. The rate constants of the Global Fit to the CS-model
are also listed.
Examination of the dependency of kon and koff on the kr/k-r ratio in the IF-model
Fig. S7: Rate constants kon and koff according to the IF-model depending on kr/k-r
Fig. S1: Data sets of binding kinetics simulated according to the CS-model for the
combination of rate constants and indicated ranges of ligand concentration are summarized in
Tab. S1 and subsequently fitted to the IF-model. The ligand range was chosen to cover the
range from 0.4 – 0.8 maximum kobs. The simulation and fit parameters are also summarized in
Tab. S1.
Fig. S2: Data sets of binding kinetics simulated according to the IF-model for the combination
of rate constants and indicated ranges of ligand concentration are summarized in Tab. S2 and
subsequently fitted to the CS-model. The ligand range was chosen to cover the range from 0.4
– 0.8 maximum kobs. The simulation and fit parameters are also summarized in Tab. S2.
Fig. S3: CS-data sets (solid black lines) were simulated for kon=2 x 104 M-1s-1, koff=0.01 s-1,
kr=10 s-1, k-r=10 s-1 and the following ranges of ligand concentrations: A) 0.1-1 µM, B) 1-10
µM, C) 10-100 µM, D) 100-1000 µM, E) 500-2500 µM, F) 1-10 mM, G) 10-100 mM. The
dashed gray lines indicate a Global Fit to the IF-model.
Fig. S4: IF-data sets (solid black lines) were simulated for kon=104 M-1s-1, koff=2 s-1, kr=199 s1
, k-r=1 s-1 and the following ranges of ligand concentrations: A) 1-10 µM, B) 10-100 µM, C)
100-1000 µM, D) 1-10 mM, E) 8-17 mM, F) 10-100 mM. The dashed gray lines indicate a
Global Fit to the CS-model.
Fig. S5: A) Experimental binding kinetics of Lu210 ligand to HDAH protein at 25 0C using a
FRET reporter displacement assay (1). Varying concentrations of Lu210 (8.5 - 50 µM) were
added to an equilibrated mixture of 0.5 µM HDAH and 5 µM of dansyl-probe. Progressing
protein-Lu210 binding is indicated by a decreasing normalized FRET-signal (Exc. 280 nm/
Em. 530 nm).The experimental data are shown as solid black lines, 1-exponential fit curves
are plotted in dark gray and 2-exponential fit curves in light gray, respectively. The deviation
of the data from the fit curves is shown in the upper (1-exponential fit) and in the lower panel
(2-exponential fit) underneath. The observed rate constants for the fast, kfast (B), and the slow
phase, kslow (C), of the binding kinetics are plotted versus the concentration of Lu210. The
observed increase of kslow with ligand concentration is in agreement with both, an IFmechanism and a CS-mechanism, where kr > koff.
Fig. S6: Influence of noise on the Global Fit of binding kinetics time courses. In all diagrams
a set of 5 binding kinetics was simulated according to a CS-model using kon=105 M-1s-1,
koff=0.05 s-1, kr=1 s-1, k-r=1 s-1. The indicated relative noise was superimposed on the
simulated data. Then the data sets were subjected to a Global Fit to the IF-model.
CS-Simulation
IF-Fit Result
#
kon /
M-1s-1
koff /
s-1
kr /
s-1
k-r /
s-1
kon /
M-1s-1
koff /
s-1
kr /
s-1
k-r /
s-1
1
2
3
4
5
6
7
8
9
104
105
2 x 104
2 x 104
1.1 x 104
1.1 x 105
1.1 x 105
1.1 x 104
2 x 105
5 x 10-3
5 x 10-3
0.01
0.01
0.01
0.01
0.01
0.01
0.1
1.0
0.53
10
0.1
10
1
0.1
1
1
1.0
10
10
0.1
1
10
1
0.1
1
1.1 x 104
1.9 x 105
2.0 x 104
1.7 x 104
1.0 x 104
3.7 x 106
5.8 x 104
1.0 x 104
1.8 x 105
9.5
590
87
0.63
1.6
9010
13
0.15
7.0
4.6
6.4
44
0.37
18
11
0.94
1.7
3.9
10-7
10-7
10-7
0.01
0.13
10-7
2.6 x 10-3
0.12
0.09
Tab. S1: Rate constants used to simulate indicated data set according to the CS-mechanism.
The data were fitted to the IF-model as shown in Fig. S1. The resulting rate constants for a fit
to the IF and CS-model are shown in the right part of the table.
IF-Simulation
CS-Fit Result
#
kon /
M-1s-1
koff /
s-1
kr /
s-1
k-r /
s-1
kon /
M-1s-1
koff /
s-1
kr /
s-1
k-r /
s-1
1
2
3
4
5
6
7
8
9
10
104
104
104
104
104
105
105
105
105
105
0.02
0.02
2
2
20
0.2
0.2
0.2
20
20
1
10
199
19.9
200
1
5
10
199
995
1
10
1
0.1
0.1
1
5
10
1
5
2.7 x 105
1.0 x 104
2.5 x 106
1.7 x 105
3.7 x 105
2.9 x 105
4.0 x 105
3.8 x 106
2.1 x 106
1.9 x 106
0.01
0.013
0.041
0.093
0.85
0.10
0.10
0.11
0.99
0.93
1.0 x 104
5.7 x 107
1.6 x 105
2.2 x 106
9.8 x 105
38
2.5 x 106
5000
3.8 x 106
6.5 x 104
2.6 x 105
2.1 x 104
3.9 x 107
3.8 x 107
3.8 x 107
75
7.7 x 106
1.8 x 105
8.1 x 107
1.2 x 106
Tab. S2: Rate constants used to simulate indicated data set according to the IF-mechanism.
The data were fitted to the CS-model as shown in Fig. S2. The resulting rate constants for a fit
to the IF and CS-model are shown in the right part of the table.
Examination of the dependency of kon and koff on the kr/k-r ratio in the IF-model
In the following, the relationship between the experimental apparent dissociation binding
constant, Kd_app, and the apparent dissociation rate constant, koff_app and the microscopic rate
constants kon and koff of the IF-model is examined.
Starting from
IF
k obs

1
k r  k r  k off  k on [L] 0 
2 
k off
2
 k on [L] 0  k r  k r   4k r k off 

(see eq. 2, main paper)
the equation simplifies in the case of pure complex dissociation which means [L]0 = 0:
IF
k obs
 k off_app 
1
k r  k r  k off 
2 
k off
2
 k r  k r   4k r k off 

Some rearrangement leads to:
 k off_app  k  r  k r
k off  k off_app 
 k
off_app  k  r





Three limiting cases can be distinguished:
1) koff_app << k-r
Then koff can be written as

k 
k off  k off_app 1  r 
 k r 
and is only dependent on the kr/k-r ratio.
2) koff_app >> k-r
Then koff simplifies to
k off  k off_app  k r
and depends solely on kr which must be smaller than koff_app.
3) koff_app >> k-r and koff_app >> kr
In this special case with very slow conformational changes and fast dissociation of the
initial compley becomes
k off  k off_app
After some rearrangement of above stated equation (see also scheme 1, main paper) it can be
shown that Kd_app depends only on kr/k-r:
K d_app 
k off

k
k on 1  r
 k r



Kd_app can also be expressed as follows:
K d_app 
k off_app
k on_app
Substituting koff_app by the expression in the first case, where koff_app << k-r, leads to the known
equation for Kd_app of an IF-model demonstrating that kon_app equals the microscopic
kon.Therefore, kon can be directly calculated from the experimentally determined Kd_app and
koff_app values and is independent of the kr/k-r ratio:
k on 
k off_app
K d_app
The dependence of kon and koff on kr/k-r for such a case is shown in Fig. S7. Using a Kd_app of
5.4 µM and a koff_app of 0.0149 s-1, as experimentally determined for the HDAH/dansyl-ligand
system (see description in the main paper), kon is independent of the kr/k-r ratio and, using the
last equation, calculates to 2759 M-1s-1 which is equal to the apparent kon_app directly
calculated from Kd_app and koff_app. On the other hand, koff is also independent on the kr/k-r ratio
and equals the apparent dissociation rate, koff_app, below a value of about 0.1, when the
equilibrium between P*L and PL is largely shifted to the first complex and the second step
does not matter. However, if the portion of PL increases, koff begins to increase significantly.
Fig. S7: Rate constants kon and koff according to the IF-model (case 1) calculated according to
above derived formulas depending on Kd_app, koff_app and the indicated kr/k-r ratio. Kd_app was
determined to be 5.4 µM and koff_app = 0.0149 s-1 from independent experiments using the
HDAH/Dansyl-ligand system as described in more detail in the main paper.
1.
Meyners, C., M. G. Baud, M. J. Fuchter, and F. J. Meyer-Almes. 2014. Kinetic method for the
large-scale analysis of the binding mechanism of histone deacetylase inhibitors. Anal Biochem
460:39-46.