Why IC ’s Are Bad for You And Other Surprises

Transcription

Why IC50’s Are Bad for You
And Other Surprises
Petr Kuzmič, Ph.D.
BioKin, Ltd.
What is enzyme inhibition on the molecular level
COMBINATION OF TWO MOLECULES TO FORM AN ENZYME-INHIBITOR COMPLEX
“Drugs produce their inhibitory action by combining with the enzyme [molecules].”
“One molecule of drug will inhibit the activity of one [molecule] of enzyme.”
Easson, L. H. & Stedman, E. (1936) Proc. Roy. Soc. B 121, 142-151.
E
enzyme
molecule
+
I
E
inhibitor
molecule
IC50's are bad for you
I
molecular
complex
2
1
What is the inhibition constant (Ki)
DISSOCIATION EQUILIBRIUM CONSTANT OF THE ENZYME-INHIBITOR COMPLEX
E+I
E·I
Ki =
[ E ]eq [ I ]eq
[ E ⋅ I ]eq
• low Ki (“dissociation”) means high binding activity
• dimension = concentration (moles/liter, M)
• “good” inhibitors have Ki’s around 10-9 moles/liter or better (nanomolar)
10-3
10-6
10-9
10-12
10-15
10-18
milimicronanopicofemtoatto-
mM
μM
nM
pM
fM
“better” inhibitor
3
A thought experiment: Effect of Ki on “fraction bound”
Assume equal amounts:
E+I
[E]0 = [I]0 =
E·I
1 nM
1.0
[E.I]
/ [E]0
0.8
0.6
0.4
0.2
at nanomolar [E]0 = [I]0
and femtomolar Ki,
there is no free enzyme left
0.0
1e-15 1e-14
10-15
1e-13
1e-12 1e-11
10-12
1e-10
Ki, M
1e-9
10-9
1e-8
1e-7
1e-6
10-6
4
2
A thought experiment: Titrate 1 nM enzyme, Ki = 0.000001 nM
remaining
enzyme
activity
v
V0
recall:
one molecule of
inhibitor inhibits one
molecule of enzyme
0.5 V0
recall:
at [I]0 = [E]0 and
Ki << [E]0, there is
no free enzyme left
0.0
0.5
1.0
[E]0/2
[E]0
1.5
2.0
2.5
[I]0, nM
5
Thought experiment, continued: What is the IC50 ?
CONCENTRATION OF INHIBITOR THAT PRODUCES HALF-MAXIMUM INHIBITORY EFFECT
remaining
enzyme
activity
[E]0 = 1 nM
= 1 fM = 0.000001 nM
Ki
v
V0
IC50 in this case:
IC50 ~ 0.5 nM
IC50 ~ [E]0 / 2
IC50 in every case:
0.5 V0
0.0
0.5
1.0
[E]0/2
[E]0
1.5
IC50 > [E]0 / 2
2.0
2.5
[I]0, nM
6
3
What is the difference between Ki and IC50 ?
IC50 DEPENDS ON ENZYME CONCENTRATION AND IS ALWAYS HIGHER THAN THE Ki
IC50 =
[ E ]0
+ K i( app )
2
K i( app ) = K i (1 + [ S ] / K M )
competitive
K i( app ) = K i (1 + K M /[ S ])
uncompetitive
K i( app ) = K i
noncompetitive
K i( app ) =
[S ] + K M
[S ] / α K i + K M / K i
Cha, S. (1975)
mixed-type
“Tight binding inhibitors. I. Kinetic behavior”
Biochem. Pharmacol. 24, 2177-2185.
7
Implications for drug discovery: “Hitting the IC50 wall”
NO MATTER HOW TIGHTLY THE INHIBITOR BINDS, THE IC50 CAN NEVER GET LOWER THAN [E]0/2
Assume:
Ki(app) = Ki (1 + [S]/KM)
• competitive
• [E]
= 5 nM
• [S]0
= KM
• competitive
• [E]
= 60 nM
= KM
• [S]0
Ki, nM
IC50, nM
Ki, nM
1,000
2,002.5
1,000
100
10
202.5
22.5
100
32
1
0.1
2.6
0.1
0.001
2.502
230
50
4.5
2.52
2,030
10
1
0.01
IC50, nM
0.01
0.001
The IC50 wall.
30.2
30.02
30.002
8
4
What is “tight binding”
THERE IS NO SUCH THING AS A “TIGHT BINDING INHIBITOR”
EXPERIMENTAL CONDITIONS
“Tight binding” kinetics applies when
the enzyme concentration in any given assay
is greater than the inhibition constant.
[E]
[E]
[E]
[E]
/
/
/
/
Ki
Ki
Ki
Ki
~
~
~
~
1
10
100
1000
tight binding is beginning to show up
tight binding is definitely present
highly tight binding
extremely tight binding
9
How prevalent is “tight binding” in a screening campaign?
EXAMPLE: A PROTEASE CAMPAIGN
A typical data set:
Completely inactive:
Tight binding:
~ 10,000 compounds
~ 1,100 ... NOT SHOWN
~ 400
2000
about 4%
of compounds
1500
N
1000
500
0
-12
-9
-6
log K i *
-3
0
Data courtesy of
Celera Genomics
2003-2005
10
5
A word about the Cheng-Prusoff Equation
IT DOES NOT TAKE INTO ACCOUNT “TIGHT-BINDING”!
Cheng, Y.-Ch. and Prusoff, W. H. (1973)
“Relationship between the inhibition constant (Ki) and the concentration
of inhibitor which causes 50 per cent inhibition (IC50) of an enzymatic reaction”
competitive inhibition:
IC50 = Ki (1 + [S]/KM)
Cha, S. (1975)
“Tight binding inhibitor. I. Kinetic behavior”
competitive inhibition:
IC50 = Ki (1 + [S]/KM) + [E]0 / 2
Many J. Med. Chem. papers still use the Cheng-Prusoff equation.
If the conditions are tight binding ([E] > Ki) this produces wrong Ki’s.
11
Misuse of the “fold increase” plot: A case study
unnamed
WT kinase
FGFR2 inhibition mode by IC50 comparison
0.04
0.035
14741087
compound
Cedirinib
known
IC50 (µM)
0.03
“X”
ATP competitor
0.025
0.02
0.015
0.01
0.005
0
0
1000
2000
3000
4000
5000
6000
ATP concentration (µM)
CONCLUSION: Compound “X” is an ATP insensitive inhibitor
not
12
6
A word about the “fold increase in IC50” plot
IT CAN BE VERY MISLEADING – IF “TIGHT BINDING” DOES OCCUR
SIMULATED KINASE EXAMPLE:
• competitive
• KM(ATP) = 100 µM
• Ki
• [E]0
= 0.5 nM
= 66 nM
Very shallow slope, “unexpected”.
[E]0 >> Ki.
13
Another word about the “fold increase in IC50” plot
SOMETIMES IT DOES WORK, BUT ... you don’t know if there is “tight binding” until you get the Ki(app)
SIMULATED KINASE EXAMPLE:
• competitive
• KM(ATP) = 100 µM
• Ki
• [E]0
= 0.5 nM
= 0.25 nM
Steep slope, as “expected”
[E]0 < Ki.
14
7
Compound “X” is an ATP-competitive inhibitor after all
7
6
10-fold increase in IC50
IC50, nM
5
4
3
2
1
0
0
200
400
600
800
1000
1200
[ATP], µM
15
Rules of thumb do not always work
What is the “IC50 Rule of Thumb”:
IC50 for a competitive inhibitor should increase about 10× going from [ATP] = Km to physiological [ATP].
What is “Tight Binding”:
Experimental conditions where the enzyme concentration is comparable with the inhibition constant.
An important fact:
The “Rule of Thumb” does not apply under the conditions of “Tight Binding”.
How do we know this:
Many journal articles on “Tight Binding” : Morrison (1969), Cha (1974), ..., Kuzmic (2000, 2003, 2011)
16
8
Final word about the “fold increase in IC50” plot: Do not use it.
SOMETIMES IT WORKS AND SOMETIMES IT DOESN’T.
NO WAY OF TELLING IN ADVANCE IF IT WILL.
[E]0 = 0.25 nM
[E]0 = 66 nM
SAME INHIBITOR – DIFFERENT ASSAY CONDITIONS
17
Other people still use the “fold increase in IC50” plot
A RECENT PAPER FROM NOVARTIS
What is the main
difference between
Novartis and ArQule?
Chene, P. et al. (2009) BMC Chem. Biol. 9:1, doi:10.1186/1472-6769-9-1
18
9
Review: Measures of inhibitory potency
THE INHIBITION CONSTANT IS AN INTRINSIC MEASURE OF POTENCY:
ΔG = -RT log K i
DEPENDENCE ON
Depends on
Example:
[S]
Competitive inhibitor
[E]
1. Inhibition constant
NO
NO
Ki
2. Apparent K i
YES
NO
K i* = K i (1 + [S]/KM)
3. IC50
YES
YES
IC50 = K i (1 + [S]/KM) + [E]/2
"CLASSICAL" INHIBITORS:
[E] « K i:
IC50 ≈ K i*
"TIGHT BINDING" INHIBITORS:
[E] ≈ K i:
IC50 ≠ K i*
19
Summary: IC50’s are bad for your drug discovery efforts
1.
You can hit the “IC50 Wall”
You could be looking at picomolar Ki inhibitors and yet
they would look “nanomolar” to you, if you are screening at nanomolar [E].
A thousand-fold difference in true vs. “apparent” potency.
2.
You could get very confused about the “mode” of inhibition
A competitive inhibitor can give you almost no “fold increase”
in IC50 if the experiment is done under tight binding conditions.
3.
Muddled communication channels within your enterprise
The question “What is the biochemical IC50 for compound X?”
does not make sense for a competitive inhibitor, without specifying [ATP] level.
Don’t use IC50 as measure of potency in biochemical assays.
IC50’s are perfectly good for cell-based assays.
20
10
What else is there, other than the IC50?
Use intrinsic molecular measures of potency (Ki, ...)
21
Example: Correlation between kinact/Ki and cellular IC50
“Molecular Underpinnings of Covalent EGFR Inhibitor Potency [...]” SUBMITTED
cell-based potency
inhibition of EGFR-L858R/T790M autophosphorylation in H1975 tumor cells
kinact
Ki
22
11
Ki(app) takes into account “tight binding”
IT IS CLOSE TO BEING AN INTRINSIC, MOLECULAR MEASURE OF POTENCY
DEPENDENCE ON
Depends on
Example:
[S]
Competitive inhibitor
[E]
NO
NO
Ki
2. Apparent K i
YES
NO
K i* = K i (1 + [S]/KM)
3. IC50
YES
YES
IC50 = K i (1 + [S]/KM) + [E]/2
What do we need to do to move from IC50 to Ki(app)?
23
The most “obvious” method to get Ki(app) will not work
THIS DOES NOT WORK
IC50 =
[ E ]0
+ K i( app )
2
K i( app ) = IC50 −
[ E ]0
2
• Could we get the IC50 by our usual method, and then just subtract one half of [E]0?
• Not in general:
- This would work very well for non-tight situations, [E]0 << Ki(app)
- In non-tight situation we have IC50 = Ki(app)
- However under tight-binding the Ki(app) could become “negative”
if our enzyme concentration is lower than we think it is.
24
12
Problem: Negative Ki from IC50
FIT TO FOUR-PARAMETER LOGISTIC:
K i* = IC50 - [E] / 2
1.4
1.2
nHill
IC50
1.0
1.4
2.9 nM
rate
0.8
0.6
0.4
[E] = 7.0 nM
0.2
K i* = 2.9 - 7.0 / 2 = - 0.6 nM
0.0
-inf
-11
-10
-9
-8
-7
-6
log [I]
Data courtesy of
Celera Genomics
25
Solution: Do not use four-parameter logistic equation
FIT TO MODIFIED MORRISON EQUATION:
P. Kuzmic et al. (2000) Anal. Biochem. 281, 62-67.
P. Kuzmic et al. (2000) Anal. Biochem. 286, 45-50.
1.4
1.2
1.0
rate
0.8
[E]nominal = 7.0 nM
0.6
[E]fitted = 4.5 nM
0.4
K i* = 0.9 nM
0.2
0.0
-inf
-11
-10
-9
-8
log [I]
-7
-6
Data courtesy of
Celera Genomics
26
13
Surprise #1:
Getting the Ki(app) does not require any additional experiments
We just need to change the way the “IC50 data” are analyzed.
27
The “Morrison Equation” for tight binding inhibition
v = V0
[E] − [I ] − K * +
([ E ] − [ I ] − K )
* 2
+ 4 [E] K *
2[E]
dependent (“Y”) and independent (“X”) variables
v
v
[I]
V0
initial reaction rate (“Y” axis)
inhibitor concentration (“X” axis)
model parameters
[E]
V0
K*
0
0
enzyme concentration
control / uninhibited rate ([I] = 0)
apparent inhibition constant
[I]
[E]
28
14
Caveat: Sometimes we need to fit the same data twice
PROBLEM: WE NEVER QUITE KNOW WHAT THE ENZYME CONCENTRATION REALLY IS
Fit data to the Morrison Equation
while keeping [E]0 constant → Ki(app)
Algorithm:
Ki(app) < [E]0 ?
NO
YES
Fit the same data to the Morrison Equation
while “floating” [E]0 → improved Ki(app), [E]0
Report Ki(app) and optionally also [E]0
Kuzmic, P. et al. (2000) Anal. Biochem. 286, 45-50.
29
Surprise #2:
Ki(app) can be guessed from a single concentration plus control
30
15
The "single-point" method for Ki(app)
AN APPROXIMATE VALUE OF THE INHIBITION CONSTANT FROM A SINGLE DATA POINT
100
V0
Vr = V/V0
Ki = 12 nM
80
enzyme activity, %
Relative rate
"control"
60
Ki = 9 nM
Single-point formula:
Ki = 11 nM
40
Ki = 8 nM
Ki =
V
20
[ I ] − [ E ](Vr − 1)
1 / Vr − 1
[I]
0
0.00
0.02
0.04
0.06
0.08
0.10
[Inhibitor], µM
Kuzmic et al. (2000) Anal. Biochem. 281, 62–67
31
Weighted average to make the initial estimate of Ki(app)
DATA POINTS VERY NEAR “TOP” AND “BOTTOM” ARE LESS TRUSTWORTHY
K* =
[ I ] − [ E ] (1 − v' / Vz )
Vz / v'−1
∂K K *Vz / v'2 −[ E ] / Vz
=
∂v
Vz / v '−1
Error
Propagation
Theory
K * / v'+ v' [ E ] / Vz2
∂K
=−
∂Vz
Vz / v'−1
weighted
average
v' / Vz − 1
∂K
=
∂[ E ] Vz / v'−1
2
2
⎛ ∂K ⎞
⎛ ∂K ⎞
2 ⎛ ∂K ⎞
⎟⎟ + Δ[ E ]2 ⎜⎜
ΔK * = Δv'2 ⎜
⎟⎟
⎟ + ΔVz ⎜⎜
⎝ ∂v ⎠
⎝ ∂[ E ] ⎠
⎝ ∂Vz ⎠
Weight:
2
w = 1 / ΔK *
32
16
Estimate K*: Example
0
1
2
3
4
5
6
7
8
Weighted average.
• [I]max = 50 µM
• 4:1 dilution series
• 8 points + control
33
Surprise #3:
We don’t need “fully developed” IC50 curves
... when using the Morrison Equation for Ki(app)
34
17
It’s OK to have at most 20%-30% inhibition if necessary
HIGHLY PRECISE Ki(app) EVEN WITH LESS THAN 50% INHIBITION AT MAXIMUM [INHIBITOR]
• [I]max = 50 µM
• 4:1 dilution series
• 8 points + control
Ki(app) = (43 ± 2) µM
35
Can we do even better than Ki(app)?
36
18
Getting the “true” Ki from a single dose-response curve
IF POSSIBLE, SCREEN AT [SUBSTRATE] MUCH LOWER THAN THE MICHAELIS CONSTANT
Depends on
DEPENDENCE ON
[S]
[E]
Competitive
Inhibitor
NO
NO
Ki
2. Apparent K i
YES
NO
K i* = K i (1 + [S]/KM)
3. IC50
YES
YES
IC50 = K i (1 + [S]/KM) + [E]/2
At [S] << KM ...
Ki(app) ≈ Ki
37
Getting the “true” Ki from a single dose-response curve
FOR “NONCOMPETITIVE” INHIBITORS Ki(app) = Ki(true) ALWAYS
Depends on
DEPENDENCE ON
[S]
[E]
Noncompetitive
Inhibitor
NO
NO
Ki
2. Apparent K i
NO
NO
K i* = K i
3. IC50
NO
YES
IC50 = K i (1 + [S]/KM) + [E]/2
38
19
Summary and Conclusions
•
Biochemical IC50’s are misleading in multiple ways.
•
They are a relic of previous eras (1950-1980) in pre-clinical research.
•
Even Big Pharma is now gradually moving toward Ki(app) and Ki.
•
Small to medium-size companies should not “follow the Big Guys”.
They should lead.
39
20

Why IC ’s Are Bad for You And Other Surprises

Transcription

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