SUPPLEMENTARY MATERIALS
FOR
IMPROVED ACCURACY OF LOW AFFINITY
PROTEIN-LIGAND EQUILIBRIUM DISSOCIATION CONSTANTS
DIRECTLY DETERMINED BY
ELECTROSPRAY IONIZATION MASS SPECTROMETRY
Lucie Jaquillard1, Fabienne Saab2, Françoise Schoentgen2, Martine Cadene1
1. Centre de Biophysique Moléculaire, CNRS UPR 4301, affiliated with INSERM and the University
of Orléans, rue Charles-Sadron, F-45071 Orléans Cedex 2, France.
2. Institut de Minéralogie et de Physique des Milieux Condensés, Université de Paris 6, 75006 Paris,
France.
Table S1. Schemes and equations relating to the “no dissociation” case
SOLUTION PHASE
GAS PHASE
INTERFACE
MGF
KD
P1+L1 ⇌ PL1
equilibrium 1
Kinetic or
equilibrium
constant
KD =
Particular
conditions
Measurement
PF, LF, PLF
PLF →PGPD+LGPD
non-equilibrium
non-equilibrium
[P]1[L]1
[PL]1
[P]0 = [P]1 + [PL]1
Mass
conservation [L] = [L] + [PL]
0
1
1
ANALYZER
PM, PLM
[PL]F (tGPD) = [PL]F . fsat(tGPD)
[P]F tot = [P]F + [PL]F
[P]G tot = [P]G + [PL]G
[P]M tot = [P]M + [PL]M
[L]F tot = [L]F + [PL]F
[L]G tot = [L]G + [PL]G
[L]M tot = [L]M + [PL]M
[P]F = a[P]1
[P]G = [P]GPD + [P]F
[P]M tot = [P]G tot
[L]F = b[L]1
[L]G = [L]GPD + [L]F
[PL]M = [PL]G
[PL]F = a[PL]1
[PL]G =[PL]F (tGPD)
fbound =
[PL]M
[PL]M+[P]M
Mathematical development for the “partial dissociation” case
In the “partial dissociation” case, the complex dissociates after MGF without reaching a new
equilibrium. Between the MGF step and the transfer to the gas phase, the species are
annotated “i” for this intermediary state. In this intermediary state, at every time t, the species
concentrations change.
Table S2. Schemes and equations relating to the “partial dissociation” case
SOLUTION PHASE
GAS PHASE
INTERFACE
LPD
KD MGF
PF, LF, PLF
Pi(t), Li(t), PLi(t)
P1+L1 ⇌ PL1
equilibrium 1 non-equilibrium
Mass
conservation
Measurement
PLLPD →PGPD+LGPD
non-equilibrium
Kinetic or
[P]1[L]1
equilibrium KD =
[PL]1
constant
ANALYZER
PM, PLM
non-equilibrium
[PL]LPD (tGPD)
= [PL]LPD . fsat(tGPD)
[P]0 = [P]1+[PL]1 [P]F tot = [P]F+[PL]F [P]i tot = [P]i(t)+[PL]i(t) [P]G tot = [P]G+[PL]G
[P]M tot = [P]M+[PL]M
[L]0 = [L]1+[PL]1 [L]F tot = [L]F+[PL]F [L]i tot = [L]i(t)+[PL]i(t) [L]G tot = [L]G+[PL]G
[L]M tot = [L]M+[PL]M
Particular
conditions
[P]F = a[P]1
[PL]i (tLPD) = [PL]LPD
[P]G = [P]GPD+[P]LPD
[P]M tot = [P]G tot
[L]F = b[L]1
[P]i (tLPD) = [P]LPD
[L]G = [L]GPD+[L]LPD
[PL]M = [PL]G
[PL]F = a[PL]1
[L]i (tLPD) = [L]LPD
[PL]G = [PL]LPD (tGPD)
fbound =
[PL]M
[PL]M+[P]M
The aim is to express fbound as function of the known parameters a, b, [P]0, [L]0 and of the
unknown factors KD and fsat to be determined by regression.
The equivalent of Equation 10 for the “partial dissociation” case is:
fbound =
[PL]LPD . fsat
𝑎 [P]0
=
[PL]i (tLPD) . fsat
𝑎 [P]0
First [PL]i(t) can be expressed as a function of known parameters and of t.
By definition:
(S1)
𝑑[PL]i(𝑡)
𝑑𝑡
= 𝑘on . [P]i (𝑡). [L]i(𝑡) − 𝑘off. [PL]i(𝑡)
(S2)
At every time t,
[P]i (t) = [P]Ftot − [PL]i(t)
(S3)
[L]i (t) = [L]Ftot − [PL]i(t)
(S4)
Inserting Equations S3 and S4 into Equation S2 gives:
𝑑[PL]i(𝑡)
𝑑𝑡
= 𝑘on . ([P]Ftot − [PL]i (𝑡)). ([L]Ftot − [PL]i (𝑡)) − 𝑘off. [PL]i(𝑡)
(S5)
which can be developed into:
𝑑[PL]i(𝑡)
𝑑𝑡
= 𝑘on ([PL]i (𝑡))2 − [PL]i (𝑡) (𝑘on [L]Ftot + 𝑘on [P]Ftot + 𝑘off) + 𝑘on . [P]Ftot . [L]Ftot
(S6)
Note that Equation S6 can be described as the polynomial expression:
𝑑[PL]i(𝑡)
𝑑𝑡
2
= 𝑎′ ([PL]i (𝑡)) + 𝑏′ [PL]i (𝑡) + 𝑐′
(S7)
with the following constants:
𝑎′ = 𝑘on
𝑏′ = −(𝑘on [L]Ftot + 𝑘on [P]Ftot + 𝑘off)
𝑐′ = 𝑘on . [P]Ftot . [L]Ftot
It can be shown that the discriminant 𝛥 = 𝑏′ 2 − 4𝑎′𝑐′ is always positive.
The integral of Equation S7 is:
𝑡
𝑡
∫0 𝑑𝑡 = ∫0
𝑑[PL]i(𝑡)
(S8)
2
𝑎′ ([PL]i (𝑡)) +𝑏′ [PL]i (𝑡)+𝑐′
which gives:
𝑡=[
1
√𝑏′ 2 −4𝑎′𝑐′
× ln |
which develops as:
2𝑎′[PL]i (𝑡)+𝑏′−√𝑏′ 2 −4𝑎′𝑐′
|]
𝑡
2𝑎′[PL]i (𝑡)+𝑏′+√𝑏′ 2 −4𝑎′𝑐′ 0
(S9)
𝑡=
1
√𝑏′ 2 −4𝑎′𝑐′
2𝑎′ [PL]i (𝑡)+𝑏′−√𝑏′ 2 −4𝑎′𝑐′
2𝑎′ [PL]F+𝑏 ′ −√𝑏′ 2 −4𝑎′𝑐′
2𝑎′ [PL]i (𝑡)+𝑏′+√𝑏′ 2 −4𝑎′𝑐′
2𝑎′ [PL]F+𝑏 ′ +√𝑏′ 2 −4𝑎′𝑐′
× (ln |
| − ln |
|)
(S10)
The expression dependant on [PL]i(t) is isolated and an exponential is applied to both sides of
the equality:
√𝑏′ 2 −4𝑎′𝑐′. 𝑡 + ln|
2
2𝑎′ [PL]F+𝑏′ −√𝑏′ −4𝑎′𝑐′
|
2𝑎′ [PL]F+𝑏′ +√𝑏′ 2 −4𝑎′𝑐′
𝑒
=|
2𝑎′ [PL]i (𝑡)+𝑏′ −√𝑏′ 2 −4𝑎′𝑐′
|
2𝑎′ [PL]i (𝑡)+𝑏′ +√𝑏′ 2 −4𝑎′𝑐′
(S11)
Equation S11 is simplified and both sides of the equality multiplied by (2𝑎′ [PL]i
(𝑡) + 𝑏 ′ + √𝑏′ 2 − 4𝑎′𝑐′):
(2𝑎′ [PL]i (𝑡) + 𝑏 ′ + √𝑏′ 2 − 4𝑎′𝑐′) .
−2𝑎′ [PL]F−𝑏′ +√𝑏′ 2 −4𝑎′𝑐′
2𝑎′ [PL]F+𝑏 ′ +√𝑏′ 2 −4𝑎′𝑐′
.𝑒
√𝑏′ 2 −4𝑎′𝑐′ . 𝑡
= −2𝑎′ [PL]i (𝑡) −
𝑏 ′ + √𝑏′ 2 − 4𝑎′𝑐′
(S12)
Equation S12 is rearranged into:
[PL]i (𝑡) = (−𝑏 ′ + √𝑏′ 2 − 4𝑎′𝑐′ − (𝑏′ + √𝑏′ 2 − 4𝑎′𝑐′ ) ∗
−2𝑎′ [PL]F−𝑏′ +√𝑏′ 2 −4𝑎′𝑐′
2𝑎′ [PL]F+𝑏 ′ +√𝑏′ 2 −4𝑎′𝑐′
2𝑎′
.𝑒
√𝑏′ 2 −4𝑎′𝑐′ . 𝑡
−2𝑎′ [PL]F−𝑏′ +√𝑏′ 2 −4𝑎′𝑐′
2𝑎′ [PL]F+𝑏 ′ +√𝑏′ 2 −4𝑎′𝑐′
.𝑒
) / (2𝑎′ +
√𝑏′ 2 −4𝑎′𝑐′ . 𝑡
)
(S13)
Equations S1 and S13 combine into:
(−𝑏′ +√𝑏′ 2 −4𝑎′𝑐′−(𝑏′+√𝑏′ 2 −4𝑎′𝑐′ )∗
F
fbound =
(2𝑎′ +2𝑎′
(S14)
−2𝑎′ [PL]F−𝑏′ +√𝑏′ 2 −4𝑎′𝑐′ √𝑏′ 2 −4𝑎′𝑐′ . 𝑡
.𝑒
2𝑎′ [PL] +𝑏′ +√𝑏′ 2 −4𝑎′𝑐′
−2𝑎′ [PL]F−𝑏′ +√𝑏′ 2 −4𝑎′𝑐′ √𝑏′ 2 −4𝑎′𝑐′ . 𝑡
.𝑒
)
2𝑎′ [PL]F+𝑏′ +√𝑏′ 2 −4𝑎′𝑐′
𝑎 [P]0
) . fsat
with:
𝑎′ = 𝑘on
𝑏′ = −(𝑘on [L]Ftot + 𝑘on [P]Ftot + 𝑘off)
𝑐′ = 𝑘on . [P]Ftot . [L]Ftot
and
[PL]F = a.
2
[P]0 + [L]0 + KD −√([P]0 +[L]0 +KD) − 4 [P]0 [L]0
[L]Ftot = (a − b)
2
[P]0 + [L]0 + KD −√([P]0 +[L]0 +KD)2 − 4 [P]0 [L]0
2
(from Equations 12 and 15)
+ b [L]0
[P]Ftot = a[P]0
According to Equation S14, fbound depends on four known parameters a, b, [P]0, and [L]0, and
on five unknown parameters KD, kon, koff, t, and fsat, which could be brought back to four
unknown parameters based on the relation between KD, kon, and koff (Equation 6).
However, attempts at fitting this increased number of parameters by non-linear regression
analysis would lead to a greater freedom for the regression to find compatible sets of
parameter solutions, so as to render the result potentially meaningless.
Complement to "Guidelines to determine which model to apply"
We have developed and presented in the main article an explicit model for system behavior in
a new workflow, which offers the opportunity to determine the solution KD for low affinity
systems while addressing both aggregation and gas phase dissociation issues. For a given
system, conscious choices can be made in adjusting the conditions for KD determination to
facilitate the choice and application of the model.
Each binding system can be described in kinetic terms by its equilibrium and kinetic constants
(KD, kon, koff), and its behavior can be predicted as a function of the ligand concentration. The
predicted behavior can be then used to assist in adjusting conditions.
Generating a graph to simulate the association kinetics of the complex (Figure S1)
This section develops an equation to simulate the progress of complex formation given KD,
kon, koff and initial concentrations and shows a simulation graph as an example of application.
We define tx%, the time to reach x % equilibrium, as the time necessary for the complex
concentration to reach x % of the equilibrium concentration (Equilibrium 1 in this work). For
the sake of accuracy, we have developed this equation for a second-order reaction, even
though some ligand concentrations in the experiment may meet pseudo-first order conditions.
When x = 100%,
When x = 0%,
[PL]i (𝑡100 %)
[PL]1
[PL]i (𝑡0 %)
[PL]1
= 1, which gives [PL]i (𝑡100 %) = [PL]1
= 0, which gives [PL]i (𝑡0 %) = 0
(S15)
The time to reach x % equilibrium is the time for which this equality is true:
𝑥%=
[PL]i (𝑡x %)
[PL]1
(S16)
Equation S16 is equivalent to:
[PL]i (𝑡x %) = 𝑥 [PL]1
with:
-
[PL]i (tx%) : the complex concentration at x% of equilibration
(S17)
-
[PL]1 : the complex concentration reached at equilibrium 1
In the above section Mathematical development for the “partial dissociation” case, we found
the relation between tx% and [PL]i (tx%):
𝑡x % = √𝑏′ 2
1
−4𝑎′ 𝑐 ′
× (ln |
2𝑎′ [PL]i (𝑡x %)+𝑏 ′ −√𝑏′ 2 −4𝑎′ 𝑐 ′
2𝑎′ [PL]i (𝑡x %)+𝑏 ′ +√𝑏
′2
−4𝑎′ 𝑐 ′
| − ln |
2𝑎′ [PL]i (𝑡0 %)+𝑏 ′ −√𝑏′ 2 −4𝑎′ 𝑐 ′
2
2𝑎′ [PL]i (𝑡0 %)+𝑏 ′ +√𝑏′ −4𝑎′ 𝑐 ′
|)
(S10)
Equations S15, S17 and S10 combine into:
𝑡x % = √𝑏′ 2
1
−4𝑎′ 𝑐 ′
× (ln |
2𝑎′ 𝑥 [PL]1+𝑏 ′ −√𝑏′ 2 −4𝑎′ 𝑐 ′
2𝑎′ 𝑥 [PL]1+𝑏 ′ +√𝑏
′2
−4𝑎′ 𝑐 ′
| − ln |
𝑏 ′ −√𝑏′ 2 −4𝑎′ 𝑐 ′
2
𝑏 ′ +√𝑏 ′ −4𝑎′ 𝑐 ′
|)
(S18)
with:
𝑎′ = 𝑘on
𝑏′ = −(𝑘on [L]0 + 𝑘on [P]0 + 𝑘off)
𝑐′ = 𝑘on . [P]0. [L]0
and
[PL]1 =
[P]0 + [L]0 + KD −√([P]0 +[L]0 +KD)2 − 4 [P]0 [L]0
2
Equation S18 can be used to calculate the time to reach complete equilibrium.
(12)
kon (M-1.s-1) ; koff (s-1)
1000000
106
1 ; 10-6
1 ; 10-5
100000
105
time to reach 99% equilibrium (s)
1 ; 10-4
10000
104
1 ; 10-3
102 ; 10-3
102 ; 10-4
1000
103
102 ; 10-2
100
102
102 ; 10-1
104 ; 10-1
104 ; 10-2
10 1
10
104 ; 101
1010
0,1-1
10
1E-06
10-6
KD (M)
10-6
10-5
10-4
10-3
104 ; 1
1E-05
10-5
0,0001
10-4
0,001
10-3
ligand (M)
Figure S1. Effect of equilibrium and kinetic constants on association behavior. Theoretical
curves were plotted for time to reach 99% equilibrium as a function of ligand concentration
for different sets of KD, kon and koff values (dotted lines: KD = 10-6 M; dashed lines: KD = 10-5
M; dash-dot lines: KD = 10-4 M; solid lines: KD = 10-3M). This numerical application is based
on [P]0 = 15 µM.
As an example, the theoretical graph in Figure S1 was built by calculating t99%, the time to
reach 99% equilibrium for complexes with low affinity KD values of 10-6, 10-5, 10-4, or
10-3 M, association rate constants kon of 1, 102, or 104 M-1.s-1 and thirty-one ligand
concentrations between 10-6 and 10-3 M. Complexes can be grouped by their KD as shown
with dotted, solid or dashed lines. For kon values of 106 and 108 M-1.s-1, association is even
faster and these curves are not represented on the graph. No assumption regarding the order
of the reaction was made. The bump observed with some of the curves results from secondorder conditions.
Generating of a graph simulating dissociation behavior of a complex after MGF (Figure S2)
This section develops an equation to simulate the transition of a complex to a new equilibrium
after the MGF step, given KD, kon, koff and initial concentrations. Simulation graphs used to
define the “partial dissociation” zone are shown.
The time to reach x % equilibrium after MGF (tx%) is the time necessary for the complex
concentration to undergo x % of the decrease necessary to reach the complex concentration at
the new equilibrium point (corresponding to Equilibrium 2).
When x = 100%, [PL]F − [PL]i (𝑡100 %) = [PL]F − [PL]2
When x = 0%, [PL]F − [PL]i (𝑡0 %) = 0, which gives[PL]F = [PL]i (𝑡0 %)
(S19)
The time to reach x % equilibrium after MGF is the time for which this equality is true:
𝑥%=
[PL]F - [PL]i (𝑡x %)
[PL]F - [PL]2
(S20)
Equation X is equivalent to:
[PL]i (𝑡x %) = (1 − 𝑥)[PL]F + 𝑥 [PL]2
(S21)
with:
-
[PL]F: the complex concentration just after MGF. If a is the yield in protein after
MGF, [PL]F = a[PL]1
-
[PL]i (tx%) : the complex concentration at x% of re-equilibration after MGF
-
[PL]2 : the complex concentration reached at equilibrium 2
Again, we can use Equation S10 relating tx% to [PL]i (tx%):
𝑡x % = √𝑏′ 2
1
−4𝑎′ 𝑐 ′
× (ln |
2𝑎′ [PL]i (𝑡x %)+𝑏 ′ −√𝑏′ 2 −4𝑎′ 𝑐 ′
2𝑎′ [PL]i (𝑡x %)+𝑏 ′ +√𝑏
′2
−4𝑎′ 𝑐 ′
| − ln |
2𝑎′ [PL]i (𝑡0 %)+𝑏′ −√𝑏′ 2 −4𝑎′ 𝑐 ′
2
2𝑎′ [PL]i (𝑡0 %)+𝑏 ′ +√𝑏′ −4𝑎′ 𝑐 ′
|)
(S10)
Equations S19, S21 and S10 combine into:
𝑡x % =
1
√𝑏′ 2 −4𝑎′ 𝑐
× (ln |
′
2𝑎′ ((1−𝑥)[PL]F+𝑥 [PL]2)+𝑏 ′ −√𝑏′ 2 −4𝑎′ 𝑐 ′
2
2𝑎′ ((1−𝑥)[PL]F+𝑥 [PL]2)+𝑏′ +√𝑏′ −4𝑎′ 𝑐 ′
| − ln |
2𝑎′ [PL]F +𝑏′ −√𝑏′ 2 −4𝑎′ 𝑐 ′
2𝑎′ [PL]F+𝑏 ′ +√𝑏′ 2 −4𝑎′ 𝑐 ′
|)
(S22)
with:
𝑎′ = 𝑘on
𝑏′ = −(𝑘on [L]Ftot + 𝑘on [P]Ftot + 𝑘off)
𝑐′ = 𝑘on . [P]Ftot . [L]Ftot
and
[PL]F = a.[PL]1
[PL]1 =
[PL]2 =
[P]0 + [L]0 + KD −√([P]0 +[L]0 +KD)2 − 4 [P]0 [L]0
2
(12)
𝑎[P]0 + 𝑏[L]0 + (𝑎 – 𝑏)[PL]1 + KD −√(𝑎[P]0 – 𝑏[L]0 – (𝑎 – 𝑏)[PL]1 – KD)2 + 4 𝑎[P]0 KD
2
[L]Ftot = (a − b) [PL]1 + b [L]0
[P]Ftot = a[P]0
Equation S22 can be used to calculate t95%. and t5%.
(11)
(a)
(b)
time to reach 95% equilibrium after MGF (s)
1,0E+06
106
1,0E+05
105
; koff
kon (M-1.s-1) ; koff (s-1)
1 ; 10-6
1 ; 10-6
1 ; 10-5
1 ; 10-5
1;
1,0E+04
104
(s-1)
102 ; 10-4
104 ; 10-2
102 ;
10-1
104 ; 10-1
101
1,0E+01
104 ;
102 ; 10-3
Fast
dissociation
104 ; 10-2
1
104 ; 101
1,0E-04
10-4
ligand (M)
1,0E-03
10-3
10-3
1,8.10
1,8E+011
102 ; 10-2
1,8E+000
1,8.10
102 ; 10-1
104 ; 10-1
1,8E-01 -1
1,8.10
104 ; 1
KD (M)
10-6
10-5
10-4
10-3
0
1,0E-05
10-5
1,8E+02
180
1;
Partial
dissociation
10
1,0E+00
10-1
1,0E-01
1,0E-06
10-6
10-4
102 ; 10-4
102 ; 10-2
180
1,0E+02
102
1;
1 ; 10-3
102 ; 10-3
103
1,0E+03
1,8E+033
1,8.10
No
dissociation
10-4
1,8E+044
1,8.10
1,8E-02 -2
1,8.10
104 ;
1,0E-06
10-6
1,0E-05
10-5
1,0E-04
10-4
101
time to reach 5% equilibrium after MGF (s)
kon
(M-1.s-1)
1,8E-03 -3
1,8.10
1,0E-03
10-3
ligand (M)
Figure S2. Effect of equilibrium and kinetic constants on dissociation behavior. Theoretical curves were plotted for (a) time to reach 95%
equilibrium after MGF or (b) time to reach 5% equilibrium after MGF as a function of ligand concentration for different sets of KD, kon and koff
values (dotted lines: KD = 10-6 M; dashed lines: KD = 10-5 M; dash-dot lines: KD = 10-4 M; solid lines: KD = 10-3M). The greyed area (partial
dissociation) corresponds to dissociation between 5 and 95% in the analysis dead-time (in this example, 180 s). The upper and lower areas
correspond to less than 5% and over 95% dissociation, respectively. This numerical application is based on [P]0 = 15 µM, 𝑎 = 0.7 and 𝑏 = 0.15.
The theoretical graphs in Figure S2 were built by calculating the time to reach 95% or 5%
equilibrium after MGF for complexes with low affinity KD values of 10-6, 10-5, 10-4 or 10-3 M,
association rate constants kon of 1, 102, 104, 106 or 108 M-1.s-1 and thirty-one ligand
concentrations between 10-6 and 10-3 M. Complexes can be grouped by their KD as shown
with dotted, solid or dashed lines. For the sake of simplification, the curves corresponding to
kon of 106 and 108 M-1.s-1 are not represented on these graphs. The amount of time required to
reach 95% and 5% are represented on Figure S2a and S2b, respectively. Again, we made no
assumption regarding the order of the reaction and the bump observed with some of the
curves results from second-order conditions.
The dead-time of analysis is the elapsed time between the withdrawal of a reaction aliquot and
the measurement in the instrument. If we consider that a system is fast dissociating when over
95% complex dissociation has occurred in the analysis dead-time (in this case 180 s), then all
systems located in the white area below the grayed area correspond to the "fast dissociation"
model. Conversely, considering that dissociation below 5% within the analysis dead-time is
negligible, the "no dissociation" model applies when the system is described by a point
located in the upper white area. The grayed area corresponds to partial dissociation
conditions.
When koff is sufficiently high (koff  10-1 s-1), the complex re-equilibration occurs within 180 s,
regardless of kon. These systems all fall into the lower white area and match the "fast
dissociation" model. For complexes with slower dissociation kinetics (koff < 10-1 s-1), the
degree of dissociation will depend on the equilibrium dissociation constant and the ligand
concentration.
When kon and KD are sufficiently low (kon  1 M-1.s-1 and KD  10-4 M), the complex will not
dissociate within 180 s. For complexes with 1  kon  102 s-1, the degree of dissociation will
depend on the equilibrium dissociation constant and the ligand concentration.
As explained in Results and Discussion, it is possible to increase the time between the MGF
and MS analysis to bring a partially dissociating system into the “fast dissociation” case.
Alternatively, it is possible to have the whole concentration range fall into the "no
dissociation" or the "fast dissociation" zone by playing on the range of ligand concentrations
used. The flat-looking curves in Figure S2 are the exception, for which one can only play on
time to reach full dissociation.
If the 1:1 protein:ligand stoichiometric point falls into the “no dissociation” case and the
lowest and/or highest ligand concentrations into the “partial dissociation” case, the range of
ligand concentrations can be narrowed and/or displaced so that they all fall into the “no
dissociation” zone. The “no dissociation” model can then be applied to this system.
Similarly, if the 1:1 protein:ligand point falls into the “partial dissociation” case and the
lowest and/or highest ligand concentrations into the “fast dissociation” case, one should
reduce the concentration range around the lowest or the highest ligand concentration,
excluding the 1:1 protein:ligand point, to bring back the system into the “fast dissociation”
zone. The “fast dissociation” model can then be applied to this system.
By applying one of these strategies, i.e. playing on the analysis dead-time or on the ligand
concentration, all the studied systems can fall either into the “fast dissociation” or into the “no
dissociation” case, and thus allowing for the KD determination to be easily performed.
Table S3. Relation between charge state and KD
P-L complex
Experimental
conditions
Charge state
KD (µM)
fsat
R2
1.6 ± 0.24
0.62 ± 0.31
2.1 ± 0.25
0.47 ± 0.07
0.37 ± 0.07
0.51 ± 0.07
0.971
0.891
0.976
Weighted mean
10+
9+ *
8+
11 ± 0.74
1.7 ± 1.6
24 ± 1.0
21 ± 1.8
0.26± 0.02
0.60± 0.16
0.31 ± 0.03
0.14 ± 0.03
0.995
0.818
0.996
0.987
Weighted mean
50 mM NH4OAc,
8+ *
pH 6.6; 37°C
7+
Weighted mean
10 mM ABC,
21+
pH 7.9; 37°C
20+ *
ESI-UHR.Q-TOF 19+ *
18+
Weighted mean
20 mM ABC,
10+
pH 8.4; 37°C
9+ *
8+
20 ± 1.2
19 ± 1.1
38 ± 5.1
4.5 ± 0.54
1.7 ± 0.38
5.2 ± 0.55
9.7 ± 0.85
2.6 ± 0.43
36 ± 0.62
8.7 ± 1.4
26 ± 1.9
36 ± 1.9
1.02 ± 0.08
1.01 ± 0.07
1.03 ± 0.31
0.61± 0.17
0.57 ± 0.14
0.68 ± 0.19
0.73 ± 0.27
0.47 ± 0.12
0.42 ± 0.03
0.41 ± 0.07
0.37 ± 0.07
0.34 ± 0.07
0.993
0.997
0.973
0.964
0.947
0.968
0.965
0.957
0.999
0.969
0.984
0.911
Weighted mean
10+
9+ *
8+
55 ± 5.0
18 ± 4.0
60 ± 5.1
170 ± 7.3
0.40 ± 0.07
0.42 ± 0.08
0.43± 0.08
0.65 ± 0.15
0.970
0.899
0.972
0.989
Weighted mean
10+ *
9+ *
8+
Weighted mean
20 mM ABC, pH 10+
8.4; 37°C + MGF 9+ *
8+
40 ± 1.0
29 ± 0.65
42 ± 0.90
64 ± 1.8
35 ± 3.1
27 ± 3.2
36 ± 5.4
52 ± 12
0.52± 0.05
0.46 ± 0.03
0.55 ± 0.04
0.66 ± 0.10
0.25 ± 0.05
0.41± 0.09
0.24± 0.09
0.16 ± 0.12
0.993
0.995
0.995
0.990
0.967
0.948
0.911
0.795
RNase-CTP
Weighted mean
10 mM NH4OAc,
8+
pH 6.8; 25°C
7+ *
PEBP-P3P
20 mM ABC,
pH 7.4; 25°C
HEWL-NAG3
(CK)2-2ADP
PEBP-GTP
PEBP-GTP
20 mM ABC,
pH 8.4; 37°C
+ MGF
PEBP-GTP
20 mM ABC, pH
8.4; 37°C +
MGF, ESIUHR.Q-TOF
PEBP-FMN
* major peak
KD measurement
with GPD correction
(Equation 3 or 13)