Why IC50’s Are Bad for You And Other Surprises Petr Kuzmič, Ph.D. BioKin, Ltd.

What is inhibition on the molecular level

COMBINATION OF TWO MOLECULES TO FORM AN ENZYME-INHIBITOR COMPLEX

“ produce their inhibitory action by combining with the enzyme [molecules].”

“One molecule of 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

molecular molecule molecule complex

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1 What is the inhibition constant (Ki)

DISSOCIATION EQUILIBRIUM CONSTANT OF THE ENZYME-INHIBITOR COMPLEX

[E] [I] E + I E·I eq eq Ki = [E ⋅ I]eq

• low Ki (“dissociation”) means high binding activity

•dimension = concentration (moles/liter, M)

-9 • “good” inhibitors have Ki’s around 10 moles/liter or better (nanomolar)

10-3 mili- mM 10-6 micro- μM 10-9 nano- nM “better” inhibitor 10-12 pico- pM 10-15 femto- fM 10-18 atto-

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

Assume equal amounts:

E + I E·I [E]0 = [I]0 = 1 nM

1.0

0.8

0 0.6

E.I] / [E] 0.4 [

0.2

at nanomolar [E]0 = [I]0 0.0 and femtomolar K , 1e-15 1e-14 1e-13 1e-12 1e-11 1e-10 1e-9 1e-8 1e-7 1e-6 i 10-15 10-12 10-9 10-6 there is no free enzyme left Ki, M IC50's are bad for you 4

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

remaining enzyme v activity

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 1.5 2.0 2.5

[E]0/2 [E]0 [I]0, nM

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Thought experiment, continued: What is the IC50 ?

CONCENTRATION OF INHIBITOR THAT PRODUCES HALF-MAXIMUM INHIBITORY EFFECT

remaining [E]0 = 1 nM enzyme v K = 1 fM = 0.000001 nM activity i

V0

IC50 in this case: IC50 ~ 0.5 nM

IC50 ~ [E]0 / 2

IC50 in every case: IC50 > [E]0 / 2 0.5 V0

0.0 0.5 1.0 1.5 2.0 2.5

[E]0/2 [E]0 [I]0, nM

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3 What is the difference between Ki and IC50 ?

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

[E] IC = 0 + K (app) 50 2 i

(app) competitive Ki = Ki (1+ [S] / K M )

(app) uncompetitive Ki = Ki (1+ K M /[S])

(app) noncompetitive Ki = Ki

[S] + K (app) M mixed-type Ki = [S]/α Ki + K M / Ki

Cha, S. (1975) “Tight binding inhibitors. I. Kinetic behavior” Biochem. Pharmacol. 24, 2177-2185.

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Implications for : “Hitting the IC50 wall”

NO MATTER HOW TIGHTLY THE INHIBITOR BINDS, THE IC50 CAN NEVER GET LOWER THAN [E]0/2

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

• competitive • competitive • [E] = 5 nM • [E] = 60 nM

• [S]0 = KM • [S]0 = KM

Ki, nM IC50, nM Ki, nM IC50, nM

1,000 2,002.5 1,000 2,030

100 202.5 100 230

10 22.5 10 50

1 4.5 1 32 The IC50 wall.

0.1 2.6 0.1 30.2

0.01 2.52 0.01 30.02

0.001 2.502 0.001 30.002

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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] / 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

A typical data set: ~ 10,000 compounds Completely inactive: ~ 1,100 ... NOT SHOWN Tight binding: ~ 400

2000 about 4% of compounds

1500

N

1000

500

0 -12-9-6-30 Data courtesy of log K i * Celera Genomics 2003-2005 IC50's are bad for you 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”

Biochem. Pharmacol. 22, 3099-3108.

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

Cha, S. (1975)

“Tight binding inhibitor. I. Kinetic behavior”

Biochem. Pharmacol. 24, 2177-2185.

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.

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

unnamedWT kinaseFGFR2 inhibition mode by IC50 comparison

0.04

0.035 14741087compound “X” 0.03 Cedirinibknown ATP competitor 0.025

0.02

IC50 (µM) IC50 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

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6 A word about the “fold increase in IC50”plot

IT CAN BE VERY MISLEADING – IF “TIGHT BINDING” DOES OCCUR

SIMULATED KINASE EXAMPLE:

• competitive (ATP) •KM = 100 µM

• Ki = 0.5 nM

• [E]0 = 66 nM

Very shallow slope, “unexpected”.

[E]0 >> Ki.

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Another word about the “fold increase in IC50”plot

(app) SOMETIMES IT DOES WORK, BUT ... you don’t know if there is “tight binding” until you get the Ki

SIMULATED KINASE EXAMPLE:

• competitive (ATP) •KM = 100 µM

• Ki = 0.5 nM

• [E]0 = 0.25 nM

Steep slope, as “expected”

[E]0 < Ki.

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

7

6 10-fold increase in IC50

5

4 , nM

50 3 IC

2

1

0 0 200 400 600 800 1000 1200 [ATP], µM

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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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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

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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

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9 Review: Measures of inhibitory

THE INHIBITION CONSTANT IS AN INTRINSIC MEASURE OF POTENCY:

ΔG = -RT log K i

Depends on Example: DEPENDENCE ON EXPERIMENTAL CONDITIONS [S] [E] Competitive inhibitor

1. Inhibition constant NO NO K i

* 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] «Ki: IC50 ≈ K i

* "TIGHT BINDING" INHIBITORS: [E] ≈ K i: IC50 ≠ K i

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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 -based assays.

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10 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 potency cell-based

kinact

Ki IC50's are bad for you 22

11 (app) Ki takes into account “tight binding”

IT IS CLOSE TO BEING AN INTRINSIC, MOLECULAR MEASURE OF POTENCY

Depends on Example: DEPENDENCE ON EXPERIMENTAL CONDITIONS [S] [E] Competitive inhibitor

1. Inhibition constant NO NO K i

* 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

(app) What do we need to do to move from IC50 to Ki ?

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(app) The most “obvious” method to get Ki will not work

THIS DOES NOT WORK

[E] [E] IC = 0 + K (app) K (app) = IC − 0 50 2 i i 50 2

• Could we get the IC50 by our usual method, and then just subtract one half of [E]0?

• Not in general:

(app) - 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 could become “negative” if our enzyme concentration is lower than we think it is.

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12 Problem: Negative Ki from IC50

FIT TO FOUR-PARAMETER LOGISTIC: * K i = IC50 - [E] / 2 1.4

1.2

nHill 1.4 1.0 IC50 2.9 nM

0.8

rate 0.6

0.4 [E] = 7.0 nM K * = 2.9 - 7.0 / 2 = - 0.6 nM 0.2 i

0.0

-inf -11 -10 -9 -8 -7 -6

log [I] Data courtesy of Celera Genomics

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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

0.8

[E]nominal = 7.0 nM

rate 0.6 [E] = 4.5 nM 0.4 fitted K * = 0.9 nM 0.2 i

0.0

-inf -11 -10 -9 -8 -7 -6

log [I] Data courtesy of Celera Genomics

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13 Surprise #1:

(app) Getting the Ki 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

2 [E] −[I] − K * + ([E] −[I] − K * ) + 4 [E] K * v = V 0 2[E]

v dependent (“Y”) and independent (“X”) variables v initial reaction rate (“Y” axis) [I] inhibitor concentration (“X” axis) V0 model parameters [E] enzyme concentration

V0 control / uninhibited rate ([I] = 0) K* apparent inhibition constant

0 0 [I] [E]

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14 Caveat: Sometimes we need to fit the same data twice

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

Algorithm: Fit data to the Morrison Equation (app) while keeping [E]0 constant → Ki

K (app) < [E] ? i 0 NO

YES

Fit the same data to the Morrison Equation (app) while “floating” [E]0 → improved Ki , [E]0

(app) Report Ki and optionally also [E]0

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

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Surprise #2:

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

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15 (app) The "single-point" method for Ki

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

100 "control" Relative rate V0 Vr = V/V0 80 Ki = 12 nM

60 Ki = 9 nM Single-point formula: Ki = 11 nM 40 Ki = 8 nM [I]−[E](Vr −1) enzyme activity, % K = V i 1/V −1 20 r

[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 IC50's are bad for you 31

(app) Weighted average to make the initial estimate of Ki

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

[I]−[E](1− v'/V ) K * = z Vz / v'−1

∂K K *V / v'2 −[E]/V = z z ∂v Vz / v'−1 ∂K K * / v'+v'[E]/V 2 = − z weighted ∂V V / v'−1 average Error z z Propagation ∂K v' /Vz −1 Theory = ∂[E] Vz / v'−1

2 2 2 ⎛ ∂K ⎞ ⎛ ∂K ⎞ ⎛ ∂K ⎞ * 2 2 ⎜ ⎟ 2 ΔK = Δv' ⎜ ⎟ + ΔVz ⎜ ⎟ + Δ[E] ⎜ ⎟ ⎝ ∂v ⎠ ⎝ ∂Vz ⎠ ⎝ ∂[E]⎠

Weight: w = 1/ ΔK *

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16 Estimate K*: Example

0 1

2

3

4 5 6 78

Weighted average.

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

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Surprise #3:

We don’t need “fully developed” IC50 curves

(app) ... when using the Morrison Equation for Ki

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

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

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

(app) Ki = (43 ± 2) µM

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(app) Can we do even better than Ki ?

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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 Competitive Inhibitor EXPERIMENTAL CONDITIONS [S] [E]

1. Inhibition constant NO NO K i

* 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

(app) At [S] << KM ... Ki ≈ Ki

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

(app) (true) FOR “NONCOMPETITIVE” INHIBITORS Ki = Ki ALWAYS

Depends on DEPENDENCE ON Noncompetitive Inhibitor EXPERIMENTAL CONDITIONS [S] [E]

1. Inhibition constant NO NO K i

* 2. Apparent K i NO NO K i = K i

3. IC50 NO YES IC50 = K i (1 + [S]/KM) + [E]/2

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19 Summary and Conclusions

•BiochemicalIC50’s are misleading in multiple ways.

• They are a relic of previous eras (1950-1980) in pre-clinical research.

(app) •Even Big Pharma is now gradually moving toward Ki and Ki.

• Small to medium-size companies should not “follow the Big Guys”.

They should lead.

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