Why IC 50 s Are Bad for You And Other Surprises Petr Kuzmi , Ph.D. - - PDF document

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Why IC50’s Are Bad for You

And Other Surprises

Petr Kuzmič, Ph.D.

BioKin, Ltd.

IC50's are bad for you 2

What is enzyme inhibition on the molecular level

“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 I + E I

enzyme molecule inhibitor molecule molecular complex COMBINATION OF TWO MOLECULES TO FORM AN ENZYME-INHIBITOR COMPLEX

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What is the inhibition constant (Ki)

DISSOCIATION EQUILIBRIUM CONSTANT OF THE ENZYME-INHIBITOR COMPLEX

E + I E·I

eq eq eq i

I E I E K ] [ ] [ ] [ ⋅ =

• 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 mili- mM 10-6 micro- μM 10-9 nano- nM 10-12 pico- pM 10-15 femto- fM 10-18 atto- “better” inhibitor

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A thought experiment: Effect of Ki on “fraction bound”

E + I E·I

Ki, M

1e-15 1e-14 1e-13 1e-12 1e-11 1e-10 1e-9 1e-8 1e-7 1e-6

[E.I] / [E]0

0.0 0.2 0.4 0.6 0.8 1.0

10-15 10-12 10-9 10-6 Assume equal amounts: [E]0 = [I]0 = 1 nM at nanomolar [E]0 = [I]0 and femtomolar Ki, there is no free enzyme left

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A thought experiment: Titrate 1 nM enzyme, Ki = 0.000001 nM

[I]0, nM remaining enzyme activity 0.5 1.0 1.5 2.0 2.5 0.0 V0 v 0.5 V0 [E]0

recall: at [I]0 = [E]0 and Ki << [E]0, there is no free enzyme left

[E]0/2

recall:

• ne molecule of

inhibitor inhibits one molecule of enzyme IC50's are bad for you 6

Thought experiment, continued: What is the IC50 ?

CONCENTRATION OF INHIBITOR THAT PRODUCES HALF-MAXIMUM INHIBITORY EFFECT

[I]0, nM remaining enzyme activity 0.5 1.0 1.5 2.0 2.5 0.0 V0 v 0.5 V0 [E]0 [E]0/2 IC50 in this case: IC50 ~ 0.5 nM [E]0 = 1 nM Ki = 1 fM = 0.000001 nM IC50 ~ [E]0 / 2 IC50 in every case: IC50 > [E]0 / 2

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What is the difference between Ki and IC50 ?

IC50 DEPENDS ON ENZYME CONCENTRATION AND IS ALWAYS HIGHER THAN THE Ki

) ( 50

2 ] [

app i

K E IC + =

) / ] [ 1 (

) ( M i app i

K S K K + = ]) /[ 1 (

) (

S K K K

M i app i

+ =

i app i

K K =

) ( i M i M app i

K K K S K S K / / ] [ ] [

) (

+ + = α

competitive uncompetitive noncompetitive mixed-type Cha, S. (1975) “Tight binding inhibitors. I. Kinetic behavior”

• Biochem. Pharmacol. 24, 2177-2185.

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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:

• competitive
• [E]

= 5 nM

• [S]0

= KM Ki, nM IC50, nM 1,000 100 10 1 0.1 0.01 0.001 2,002.5 202.5 22.5 4.5 2.6 2.52 2.502 Ki, nM IC50, nM 1,000 100 10 1 0.1 0.01 0.001 2,030 230 50 32 30.2 30.02 30.002

• competitive
• [E]

= 60 nM

• [S]0

= KM

The IC50 wall.

Ki

(app) = Ki (1 + [S]/KM)

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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] / Ki ~ 1 tight binding is beginning to show up [E] / Ki ~ 10 tight binding is definitely present [E] / Ki ~ 100 highly tight binding [E] / Ki ~ 1000 extremely tight binding

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How prevalent is “tight binding” in a screening campaign?

EXAMPLE: A PROTEASE CAMPAIGN

... NOT SHOWN

log K i *

• 12
• 9
• 6
• 3

N 500 1000 1500 2000

A typical data set: Completely inactive: Tight binding: ~ 10,000 compounds ~ 1,100 ~ 400

Data courtesy of Celera Genomics 2003-2005

about 4%

• f compounds

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A word about the Cheng-Prusoff Equation

IT DOES NOT TAKE INTO ACCOUNT “TIGHT-BINDING”!

IC50 = Ki (1 + [S]/KM) competitive inhibition:

Cheng, Y.-Ch. and Prusoff, W. H. (1973) “Relationship between the inhibition constant (Ki) and the concentration

• f inhibitor which causes 50 per cent inhibition (IC50) of an enzymatic reaction”
• Biochem. Pharmacol. 22, 3099-3108.

IC50 = Ki (1 + [S]/KM) + [E]0 / 2 competitive inhibition:

Cha, S. (1975) “Tight binding inhibitor. I. Kinetic behavior”

• Biochem. Pharmacol. 24, 2177-2185.

Many J. Med. Chem. papers still use the Cheng-Prusoff equation. If the conditions are tight binding ([E] > Ki) this produces wrong Ki’s.

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WT FGFR2 inhibition mode by IC50 comparison

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 1000 2000 3000 4000 5000 6000 ATP concentration (µM) IC50 (µM) 14741087 Cedirinib

compound “X”

unnamed kinase

CONCLUSION: Compound “X” is an ATP insensitive inhibitor not

Misuse of the “fold increase” plot: A case study

known ATP competitor

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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

= 0.5 nM

• [E]0

= 66 nM Very shallow slope, “unexpected”. [E]0 >> Ki.

IC50's are bad for you 14

Another word about the “fold increase in IC50” plot

SOMETIMES IT DOES WORK, BUT ...

SIMULATED KINASE EXAMPLE:

• competitive
• KM

(ATP)

= 100 µM

• Ki

= 0.5 nM

• [E]0

= 0.25 nM Steep slope, as “expected” [E]0 < Ki.

you don’t know if there is “tight binding” until you get the Ki

(app)

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[ATP], µM

200 400 600 800 1000 1200

IC50, nM

1 2 3 4 5 6 7

10-fold increase in IC50

Compound “X” is an ATP-competitive inhibitor after all

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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)

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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

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Other people still use the “fold increase in IC50” plot

Chene, P. et al. (2009) BMC Chem. Biol. 9:1, doi:10.1186/1472-6769-9-1

A RECENT PAPER FROM NOVARTIS

What is the main difference between Novartis and ArQule?

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Review: Measures of inhibitory potency

• 1. Inhibition constant
• 2. Apparent K i
• 3. IC50

Depends on [S] [E] NO YES YES NO NO YES K i K i

* = K i (1 + [S]/KM)

IC50 = K i (1 + [S]/KM) + [E]/2 Example: Competitive inhibitor

THE INHIBITION CONSTANT IS AN INTRINSIC MEASURE OF POTENCY: DEPENDENCE ON EXPERIMENTAL CONDITIONS

[E] « K i: IC50 ≈ K i

*

ΔG = -RT log K i [E] ≈ K i: IC50 ≠ K i

* "CLASSICAL" INHIBITORS: "TIGHT BINDING" INHIBITORS: IC50's are bad for you 20

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.

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What else is there, other than the IC50?

Use intrinsic molecular measures of potency (Ki, ...)

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Example: Correlation between kinact/Ki and cellular IC50

“Molecular Underpinnings of Covalent EGFR Inhibitor Potency [...]” SUBMITTED inhibition of EGFR-L858R/T790M autophosphorylation in H1975 tumor cells

cell-based potency kinact Ki

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Ki

(app) takes into account “tight binding”

• 1. Inhibition constant
• 2. Apparent K i
• 3. IC50

Depends on [S] [E] NO YES YES NO NO YES K i K i

* = K i (1 + [S]/KM)

IC50 = K i (1 + [S]/KM) + [E]/2 Example: Competitive inhibitor

IT IS CLOSE TO BEING AN INTRINSIC, MOLECULAR MEASURE OF POTENCY DEPENDENCE ON EXPERIMENTAL CONDITIONS

What do we need to do to move from IC50 to Ki

(app)?

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The most “obvious” method to get Ki

(app) will not work

) ( 50

2 ] [

app i

K E IC + =

THIS DOES NOT WORK

2 ] [

50 ) (

E IC K app

i

− =

• 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.

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Problem: Negative Ki from IC50

log [I]

• 11
• 10
• 9
• 8
• 7
• 6

rate 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

• inf

nHill IC50 1.4 2.9 nM [E] = 7.0 nM K i* = 2.9 - 7.0 / 2 = - 0.6 nM

FIT TO FOUR-PARAMETER LOGISTIC:

K i

* = IC50 - [E] / 2

Data courtesy of Celera Genomics

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Solution: Do not use four-parameter logistic equation

log [I]

• 11
• 10
• 9
• 8
• 7
• 6

rate 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

• inf

[E]nominal = 7.0 nM [E]fitted = 4.5 nM K i* = 0.9 nM

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.

Data courtesy of Celera Genomics

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Surprise #1: Getting the Ki

(app) does not require any additional experiments

We just need to change the way the “IC50 data” are analyzed.

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The “Morrison Equation” for tight binding inhibition

v initial reaction rate (“Y” axis) [I] inhibitor concentration (“X” axis)

[I] v V0 [E]

( )

] [ 2 ] [ 4 ] [ ] [ ] [ ] [

* 2 * *

E K E K I E K I E V v + − − + − − =

dependent (“Y”) and independent (“X”) variables [E] enzyme concentration V0 control / uninhibited rate ([I] = 0) K* apparent inhibition constant model parameters

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Caveat: Sometimes we need to fit the same data twice

PROBLEM: WE NEVER QUITE KNOW WHAT THE ENZYME CONCENTRATION REALLY IS

Kuzmic, P. et al. (2000) Anal. Biochem. 286, 45-50.

Fit data to the Morrison Equation

while keeping [E]0 constant → Ki

(app)

Algorithm: Ki

(app) < [E]0 ?

Fit the same data to the Morrison Equation

while “floating” [E]0 → improved Ki

(app), [E]0

YES NO Report Ki

(app) and optionally also [E]0

IC50's are bad for you 30

Surprise #2: Ki

(app) can be guessed from a single concentration plus control

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The "single-point" method for Ki

(app) AN APPROXIMATE VALUE OF THE INHIBITION CONSTANT FROM A SINGLE DATA POINT

Kuzmic et al. (2000) Anal. Biochem. 281, 62–67 [Inhibitor], µM

0.00 0.02 0.04 0.06 0.08 0.10

enzyme activity, %

20 40 60 80 100

V0 V

"control"

Relative rate Vr = V/V0 [I]

Ki = 12 nM Ki = 9 nM Ki = 11 nM Ki = 8 nM

1 / 1 ) 1 ]( [ ] [ − − − =

r r i

V V E I K

Single-point formula:

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Weighted average to make the initial estimate of Ki

(app) DATA POINTS VERY NEAR “TOP” AND “BOTTOM” ARE LESS TRUSTWORTHY

( )

1 ' / / ' 1 ] [ ] [

*

− − − = v V V v E I K

z z

1 ' / / ] [ ' /

2 *

− − = ∂ ∂ v V V E v V K v K

z z z

1 ' / / ] [ ' ' /

2 *

− + − = ∂ ∂ v V V E v v K V K

z z z

1 ' / 1 / ' ] [ − − = ∂ ∂ v V V v E K

z z 2 2 2 2 2 2 *

] [ ] [ ' ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ Δ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ Δ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ Δ = Δ E K E V K V v K v K

z z *

/ 1 K w Δ =

weighted average

Error Propagation Theory Weight:

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Estimate K*: Example

1 2 3 4 5 6 7 8

• [I]max = 50 µM
• 4:1 dilution series
• 8 points + control

Weighted average.

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Surprise #3: We don’t need “fully developed” IC50 curves

... when using the Morrison Equation for Ki

(app)

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It’s OK to have at most 20%-30% inhibition if necessary

• [I]max = 50 µM
• 4:1 dilution series
• 8 points + control

Ki

(app) = (43 ± 2) µM

HIGHLY PRECISE Ki

(app) EVEN WITH LESS THAN 50% INHIBITION AT MAXIMUM [INHIBITOR]

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Can we do even better than Ki

(app)?

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Getting the “true” Ki from a single dose-response curve

IF POSSIBLE, SCREEN AT [SUBSTRATE] MUCH LOWER THAN THE MICHAELIS CONSTANT

• 1. Inhibition constant
• 2. Apparent K i
• 3. IC50

Depends on [S] [E] NO YES YES NO NO YES K i K i

* = K i (1 + [S]/KM)

IC50 = K i (1 + [S]/KM) + [E]/2

DEPENDENCE ON EXPERIMENTAL CONDITIONS

Competitive Inhibitor

At [S] << KM ... Ki

(app) ≈ Ki

IC50's are bad for you 38

Getting the “true” Ki from a single dose-response curve

FOR “NONCOMPETITIVE” INHIBITORS Ki

(app) = Ki (true) ALWAYS

• 1. Inhibition constant
• 2. Apparent K i
• 3. IC50

Depends on [S] [E] NO NO NO NO NO YES K i K i

* = K i

IC50 = K i (1 + [S]/KM) + [E]/2

DEPENDENCE ON EXPERIMENTAL CONDITIONS

Noncompetitive Inhibitor

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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.