Dynamic modeling of cytochrome P450 inhibition in vitro: Impact of inhibitor depletion on IC50 shift

Article abstract of DOI:10.1124/dmd.113.051508

The impact of inhibitor depletion on the determination of shifted IC ₅₀ (IC₅₀ determined after 30 minutes of preincubation with inhibitor) is examined. In addition, IC₅₀-shift data are analyzed using a mechanistic model that incorporates the processes of inhibitor depletion, as well as reversible and time-dependent inhibition. Anomalies such as a smaller-than-expected shift in IC₅₀ and even increases in IC₅₀ with preincubation were explained by the depletion of inhibitor during the preincubation. The IC₅₀-shift assay remains a viable approach to characterizing a wide range of reversible and time-dependent inhibitors. However, as with more traditional time-dependent inactivation methods, it is recommended that IC₅₀-shift experimental data be interpreted with some knowledge of the magnitude of inhibitor depletion. For the most realistic classification of time-dependent inhibitors using IC ₅₀-shift methods, shifted IC₅₀ should be calculated using observed inhibitor concentrations at the end of the incubation rather than nominal inhibitor concentrations. Finally, a mechanistic model that includes key processes, such as competitive inhibition, enzyme inactivation, and inhibitor depletion, can be used to describe accurately the observed IC₅₀ and shifted IC₅₀ curves. For compounds showing an IC₅₀ fold shift >1.5 based on the observed inhibitor concentrations, reanalyzing the IC₅₀-shift data using the mechanistic model appeared to allow for reasonable estimation of Ki, KI, and kinact directly from the IC₅₀ shift experiments.

Full text of DOI:10.1124/dmd.113.051508

Supplemental Material can be found at:
http://dmd.aspetjournals.org/content/suppl/2013/05/06/dmd.113.051508.DC1.html
1521-009X/41/7/1433–1441$25.00
http://dx.doi.org/10.1124/dmd.113.051508
DRUG METABOLISM AND DISPOSITION
Drug Metab Dispos 41:1433–1441, July 2013
Copyright ª 2013 by The American Society for Pharmacology and Experimental Therapeutics
Dynamic Modeling of Cytochrome P450 Inhibition In Vitro: Impact
of Inhibitor Depletion on IC50 Shift s
Loren M. Berry, Zhiyang Zhao, and Min-Hwa Jasmine Lin
Pharmacokinetics and Drug Metabolism, Amgen, Inc., Cambridge, Massachusetts
Received February 8, 2013; accepted May 2, 2013
ABSTRACT
The impact of inhibitor depletion on the determination of shifted
knowledge of the magnitude of inhibitor depletion. For the most
IC50 (IC50 determined after 30 minutes of preincubation with realistic classification of time-dependent inhibitors using IC50-shift
inhibitor) is examined. In addition, IC50-shift data are analyzed methods, shifted IC50 should be calculated using observed inhibitor
using a mechanistic model that incorporates the processes of
inhibitor depletion, as well as reversible and time-dependent in-
concentrations at the end of the incubation rather than nominal
inhibitor concentrations. Finally, a mechanistic model that includes
hibition. Anomalies such as a smaller-than-expected shift in IC50 key processes, such as competitive inhibition, enzyme inactivation,
and even increases in IC50 with preincubation were explained by and inhibitor depletion, can be used to describe accurately the
the depletion of inhibitor during the preincubation. The IC50-shift observed IC50 and shifted IC50 curves. For compounds showing an
assay remains a viable approach to characterizing a wide range of
IC50 fold shift >1.5 based on the observed inhibitor concentrations,
reversible and time-dependent inhibitors. However, as with more reanalyzing the IC50-shift data using the mechanistic model
traditional time-dependent inactivation methods, it is recommen- appeared to allow for reasonable estimation of Ki, KI, and kinact
ded that IC50-shift experimental data be interpreted with some directly from the IC50 shift experiments.
Introduction
preincubation, as occurs with the nicardipine IC50 against CYP2C9
(Berry and Zhao, 2008). Such examples have added some uncertainty
to the interpretation of IC50-shift data in terms of classifying time-
dependent inhibitors. It is often suggested that the main culprit behind
these anomalies is the metabolism of inhibitor during the incubation;
however, the impact of inhibitor depletion on the shifted IC50 has not
been investigated, and that is an aim of the present study.
Previously, we described an IC50 and IC50-shift assay for si-
multaneously determining reversible inhibition potency and classi-
fying reversible and time-dependent inhibitors of CYP3A4, CYP2C9,
and CYP2D6 (Berry and Zhao, 2008). The methods avoided the
secondary dilution step found in most traditional approaches to
identifying time-dependent inhibitors and was able successfully to
characterize noninhibitors, reversible inhibitors, and time-dependent
inhibitors among a wide range of reference and proprietary com-
pounds. Others have also described successful applications of IC50-
shift style assays in various forms (Obach et al., 2007; Grimm et al.,
2009; Perloff et al., 2009; Burt et al., 2010). In addition, both
empirical and mechanistic relationships were explored that examine
the link between enzyme inactivation and IC50 shift and validate the
principle and application of the IC50-shift approach to characterizing
cytochrome P450 (P450) inhibition (Maurer et al., 2000; Berry and
Zhao, 2008; Krippendorff et al., 2009).
Since establishing and implementing such assays, some anomalies
have been observed. In particular, some investigators have noted that
the magnitude of decrease in IC50 after preincubation can at times
appear to underestimate the extent of time-dependent inactivation
observed during traditional KI and kinact experiments. For example,
ritonavir is known to be a highly potent inactivator of CYP3A4
(Kirby et al., 2011), yet it yields relatively little shift in IC50 with
preincubation (Obach et al., 2007; Berry and Zhao, 2008). In addition,
Historically, the best practices to determine enzyme kinetics ac-
curately, including inhibition kinetics, call for keeping the incubations
short such that less than 10% of substrate or inhibitor is depleted.
Experiments to determine time-dependent inhibition, including tradi-
tional dilution methods, as well as IC50-shift experiments, could
potentially violate this guideline. This is because preincubation with
inhibitor often must be carried out for as long as 30 minutes (or
longer depending on the inhibitor) to observe the time dependency
in inhibition (Grimm et al., 2009). Furthermore, mechanism-based
inactivation requires at least partial conversion of the inhibitor to a
bioreactive metabolite or intermediate. Thus, the apparent kinetics of
inactivation relative to nominal inhibitor concentrations could change
over the course of preincubation as inhibitor is depleted. Previously
reported mechanistic relationships that attempt to describe IC50 shift
do not account for inhibitor depletion; therefore, we developed a
dynamic model to describe IC50-shift style data that consider inhibitor
depletion, as well as reversible inhibition and enzyme activation. We
anticipate that the proposed model will be useful for providing more
cases have been observed where the IC50 can appear to increase after robust characterization of P450 inhibitors in vitro.
dx.doi.org/10.1124/dmd.113.051508.
s This article has supplemental material available at dmd.aspetjournals.org.
ABBREVIATIONS: LC-MS/MS, liquid chromatography-tandem mass spectrometry; MPA, mobile phase A; MPB, mobile phase B; m/z, mass-to-
charge ratio; P450, cytochrome P450.
1433

1434
Berry et al.
depletion on the apparent IC50 fold shift, shifted IC50 values were calculated
Materials and Methods
using both nominal inhibitor concentrations and inhibitor concentrations
present at the end of the 30-minute preincubation with inhibitor (observed
inhibitor concentrations). IC50 fold shift is the ratio of IC50 divided by the
All compounds and solvents were obtained from commercial sources as
appropriate. Pooled human liver microsomes (pool of 50 donors) were obtained
from Gibco (Life Technologies Co., Grand Island, NY).
shifted IC50
.
Determination of Metabolite Formation Kinetics. Kinetics for the
formation of 1-hydroxymidazolam, 49-hydroxydiclofenac, and dextrorphan
from the substrates midazolam, diclofenac, and dextromethorphan, respec-
tively, were determined in preliminary experiments. Substrates were incubated
at 37°C for 5 minutes at a concentration range of 0.2–50 mM, in the presence of
0.1 mg of human liver microsomal protein per milliliter, 1 mM NADPH, and
50 mM potassium phosphate buffer, pH 7.4 (300 ml total incubation volume).
At the end of the incubation period, samples were collected into an equal
volume of acetonitrile containing the internal standards (the stable isotopes of
the marker metabolites), and the mixtures were centrifuged and analyzed on an
liquid chromatography-tandem mass spectrometry (LC-MS/MS) system for the
marker metabolites and internal standards. Resulting analyte/internal standard
peak area ratios were converted to concentration by means of comparison with
a calibration curve of marker metabolite and internal standard prepared in the
same matrix as the samples. Metabolite concentrations were converted to
reaction velocity [v = Cform/(incubation time ∙ microsomal protein concentra-
tion)]. Vmax,f and Km,f were estimated from the velocity versus substrate
concentration data using GraphPad Prism version 5 (GraphPad Software Inc.,
San Diego, California) assuming Michaelis-Menten kinetics.
IC50 and IC50-Shift with Inhibitor Depletion. Inhibition of CYP3A4,
CYP2D6, and CYP2C9 was assessed in 96-well format with a TECAN
Freedom Evo automated workstation (TECAN Inc., Durham, NC), optimized
for pipetting accuracy and precision. Test inhibitors were predissolved in 50%
acetonitrile and 50% water (5 mM) and stored at 280°C until use. All
incubation solutions (300 ml) contained 0.1 mg of human microsomal protein
per milliliter and 1 mM NADPH in 50 mM potassium phosphate buffer, pH
7.4. The timeline of the incubation was as follows: In the presence of NADPH,
test inhibitors (0 mM plus seven concentrations, depending on the inhibitor)
were added to the 37°C incubations either at 0 minutes of incubation (for
preincubation with inhibitor, shifted IC50 determinations) or at 30 minutes of
incubation (for IC50 determinations). Each compound was tested in duplicate.
Marker substrate cocktail was added to all incubations at 30 minutes. Addition
of the marker substrate cocktail yielded the final substrate concentrations of
3 mM midazolam, 7 mM diclofenac, and 6 mM dextromethorphan. These
concentrations are near the measured Michaelis-Menten constant (Km) values
for these marker reactions under the incubation conditions used here (Table 1).
The addition of inhibitor or substrate did not significantly dilute the incubation
mixture (i.e., ;5% dilution). After addition of the marker substrate cocktail, the
incubation proceeded for an additional 5 minutes (to 35 minutes of total
incubation time). At the end of the incubation period, samples were collected
into an equal volume of acetonitrile containing the internal standards (the stable
isotopes of the marker metabolites), and the mixtures were centrifuged and
analyzed on an LC-MS/MS system for the marker metabolites, internal
standards, and inhibitor.
Analytical Procedure. Samples were analyzed by multiple reaction mon-
itoring on an LC-MS/MS system consisting of dual Shimadzu LC-10AD high-
performance liquid chromatography pumps and a DGU-14A degasser (Shimadzu,
Columbia, MD), a CTC PAL autoinjector (Leap Technologies, Carrboro, NC), and
an API3000 LC-MS/MS system equipped with an electrospray ion source and
operated by the Analyst software package (Applied Biosystems, Foster City,
CA). Chromatography was conducted on a Sprite Armor C18 (20 ꢀ 2.1 mm,
10 mm) analytical column (Analytical Sales and Services, Pompton Plains, NJ)
with a 0.5-mm PEEK guard filter, using the following mobile phase gradient
program at a flow rate of 0.5 ml/min: mobile phase A (MPA) = H20 with 0.1%
formic acid; mobile phase B (MPB) = acetonitrile with 0.1% formic acid;
0 minutes = 98% MPA, 2% MPB; 0.8 minutes = 2% MPA, 98% MPB; 1.0
minute = 2% MPA, 98% MPB; 1.1 minutes = 98% MPA, 2% MPB; 1.2
minutes = end of run; approximately 1.5 minutes between sample injections.
For the first 0.3 minutes of each sample run, 100% of the LC eluent was
diverted from the ion source to waste, and ;50% was split to waste thereafter;
19-hydroxymidazolam [mass-to-charge ratio (m/z) 342 → 324], 19-hydroxymidazolam
stable isotope (m/z 345 → 327), 49-hydroxydiclofenac (m/z 312 → 230),
49-hydroxydiclofenac stable isotope (m/z 318 → 236), dextrorphan (m/z
258 → 157), and dextrorphan stable isotope (m/z 261 → 157) were detected in
positive ion mode.
Kinetic Modeling of P450 Inhibition. A mechanistic model for P450
inhibition in the IC50-shift assay accounting for the metabolism of inhibitor,
metabolism of substrate, and reversible and time-dependent loss of enzyme
activity was created based on the scheme shown in Fig. 1.
The kinetics of inhibitor metabolism was determined based on the depletion
of inhibitor in the incubation. Briefly, since all IC50 and shifted IC50 samples
were incubated to 35 minutes, the inhibitor depletion rates could be determined
by measuring the loss of inhibitor in the IC50 samples (5 minutes of incubation
with inhibitor) and the shifted IC50 samples (35 minutes of incubation with
inhibitor), relative to samples spiked with inhibitor but not incubated (0 minutes
of incubation). Depletion of the inhibitor at each concentration is described by
eq. 1:
dCinh
Vp
¼ 2 CLint;inh × Cinh
ð1Þ
dt
Inhibition of P450 activity in the presence of varying concentrations of test
compound was calculated as the percent of remaining activity (%activity)
in each sample relative to the control sample (plus NADPH, but without
inhibitor). Values for IC50 and shifted IC50 were calculated from the %activity
data by a four-parameter logistic model model in Galileo v3.2 (Thermo
Electron Corp., Madison, WI). IC50 values were initially calculated using
nominal inhibitor concentrations. To determine the impact of inhibitor
TABLE 1
Michaelis-Menten kinetic parameters for the formation of 1-hydroxymidazolam, 4-
hydroxydiclofenac, and dextrorphan from midazolam, diclofenac, and
dextromethorphan in human liver microsomes
Vmax,f
Km,f
pmol/(min×mg)
mM
1-Hydroxymidazolam
49Hydroxydiclofenac
Dextrorphan
656 6 23
2600 6 40
129 6 4
2.83 6 0.19
7.42 6 0.30
6.34 6 0.46
Fig. 1. Mechanistic model for P450 inhibition, including metabolism of inhibitor,
metabolism of substrate, competitive inhibition, and time-dependent inactivation of
enzyme.

Dynamic Modeling of P450 Inhibition In Vitro
where Cinh is the concentration of inhibitor in the incubation, V is the volume of
1435
Vmax;f × E
CLint;f 9 ¼
ð8Þ
Cinh
the incubation per milligram of microsomal protein, and CLint,inh is the intrinsic
clearance of the inhibitor. When CLint,inh was observed to be concentration
dependent over the concentration range tested, it was as shown in eq. 2:
Km;fð1 þ
Þ þ Csub9
Ki
where Csub9 is the concentration of substrate remaining, Cform9 is the
concentration of metabolite formed, CLint,f9 is the intrinsic formation clearance
in the presence of inhibitor, and Ki is the inhibition constant for the competitive
inhibition. As shown in eq. 9, at each dose of inhibitor, inhibition results are
expressed as the percentage of enzyme activity remaining in the presence of
inhibitor relative that in the absence of inhibitor:
Vmax;inh
CLint;inh
¼
þ CLint;us
ð2Þ
Km;inh þ Cinh
assuming the concentration dependence in inhibitor depletion is reasonably
described by Michaelis-Menten style kinetics with or without an additional
unsaturable component, where Vmax,inh is the apparent maximum reaction
velocity for the depletion of inhibitor, Km,inh is the apparent concentration of
inhibitor required to achieve 50% of Vmax,inh, and CLint,us is the component of
intrinsic clearance that is unsaturable over the concentration range tested (when
applicable). For further discussion purposes, Vmax,inh, Km,inh, and CLint,us were
used to calculate CLint,max, representing the maximum intrinsic clearance
observed for the inhibitor, typically at the lowest concentrations tested. CLint,max
equals CLint,us for those inhibitors with no observed concentration dependence
over the concentration range tested (e.g., troleandomycin). CLint,max equals
Vmax,inh/Km,inh for inhibitors with apparently only a saturable component. CLint,max
equals Vmax,inh/Km,inh + CLint,us for those inhibitors with both saturable and
unsaturable components over the concentration range tested (e.g., delavirdine).
Time-dependent inactivation of P450 enzyme is defined by eq. 3:
C
form9
%Activity ¼ 100 ×
ð9Þ
Cform
Model equations were programmed into Phoenix version 6.3 (Certara L.P.,
St. Louis, MO) as a textual model (see Supplemental Material). To mimic the
conditions used for in vitro IC50 and IC50 shift experiments, doses of inhibitor
were given at 0 minutes (for preincubation with inhibitor, shifted IC50 samples)
or at 30 minutes (for preincubation without inhibitor, IC50 samples). Doses of
substrate were given at 30 minutes. Each dose level and dose time of inhibitor
was treated as a unique subject, for a total of 16 subjects. Model equations were
solved for Vmax,inh, Km,inh, Ki, KI, and kinact in population mode using the
observed values for Cinh and %Activity after 35 minutes of total incubation
time (5 minutes of incubation with substrate).
dE
¼ 2 kobs × E
ð3Þ
dt
Results
where E represents the fraction of active P450 enzyme. At the beginning of the
incubation and in the absence of inhibitor, E equals 1; kobs is the rate of
inactivation of enzyme and is dependent on the concentration of inhibitor such
that, as shown in eq. 4:
IC50 and IC50 Shift. IC50 and shifted IC50 values for a number of
inhibitors are shown in Table 2. Shifted IC50 was initially calculated
using nominal inhibitor concentrations. Using nominal inhibitor
concentrations, a few well known potent inactivators of CYP3A4,
CYP2C9, or CYP2D6 showed a substantial (.10-fold shift) decrease
in IC50 after preincubation, including delavirdine/CYP3A4, mibefradil/
CYP3A4, mifepristone/CYP3A4, paroxetine/CYP2D6, and tienilic
acid/CYP2C9. A number of well-known inactivators also showed more
moderate (1.5-fold to 10-fold shift) decreases in IC50 after preincuba-
tion, including dasatinib/CYP3A4, delavirdine/CYP2D6, erythromycin/
CYP3A4, nicardipine/CYP3A4, and troleandomycin/CYP3A4. Several
inhibitors showed minimal (0.7- to 1.5-fold) shift in IC50, including
delavirdine/CYP2C9, ritonavir/CYP3A4, and saquinavir/CYP3A4.
Finally, several inhibitors tested showed an increase (,0.7-fold shift)
in IC50 after preincubation, including ketoconazole/CYP3A4, nicardipine/
CYP2C9, and nicardipine/CYP2D6.
kinact × Cinh
KI þ Cinh
kobs
¼
ð4Þ
where kinact is the maximum rate of inactivation and KI is the concentration
required to achieve 50% of kinact
.
Since in human liver microsomes midazolam, diclofenac, and dextrome-
thorphan are selective substrates for CYP3A4, CYP2C9, and CYP2D6, re-
spectively, and each only forms one primary metabolite, the rate of metabolite
formation was assumed to equal the rate of substrate depletion. Additionally,
the metabolites formed are assumed not to be subject to further metabolism
under the incubation conditions used. As shown in eqs. 5 and 6, in the
absence of inhibitor, the concentration of metabolite formed from the substrate
is also considered to be driven by Michaelis-Menten kinetics and forms such
that
Since some unusual results were observed, including a lack of IC50
shift with known CYP3A4 inactivators ritonavir and saquinavir and
increases in IC50 after preincubation with ketoconazole and nicardi-
pine, it was hypothesized that depletion of inhibitor (as well as enzyme
inactivation and incubation time) could influence the shifted IC50. To
understand the impact of possible inhibitor depletion on shifted IC50,
the shifted IC50 values were recalculated using the inhibitor concen-
trations observed at the end of the incubation. Based on observed
inhibitor concentrations, several inhibitors yielded substantially re-
duced shifted IC50 levels, including ketoconazole/CYP3A4, mifepristone/
CYP3A4, nefazodone/CYP3A4, nicardipine, ritonavir/CYP3A4,
and saquinavir/CYP3A4. Most dramatically, the CYP3A4 IC50 fold
shift for nicardipine increased from 4.5-fold using nominal con-
centrations to 1750-fold using observed concentrations, CYP3A4
IC50 foldshift for ritonavir increased from 0.9-fold to 45.6-fold,
and CYP3A4 IC50 fold shift for saquinavir increased from 0.5- to
15.2-fold. In addition, the CYP3A4 IC50 fold shift for ketoconazole
increased from 0.6- to 1.3-fold, and the CYP2C9 IC50 fold shift for
nicardipine increased from 0.2- to 1.2-fold. These data indicate that,
in many cases, choice of inhibitor concentrations used to determine
shifted IC50 (nominal versus observed) can influence the interpre-
tation of the data.
dCform
dt
dCsub
dt
V
×
¼ CLint;f × Csub ¼ 2 V
×
ð5Þ
and
Vmax;f
CLint;f
¼
ð6Þ
Km;f þ Csub
where Csub is the concentration of substrate remaining in the absence of
inhibitor; Cform is the concentration of metabolite formed in the absence of
inhibitor; and CLint,f, Vmax,f, and Km,f are the intrinsic clearance, maximal
reaction velocity, and concentration required to reach 50% of Vmax,f for the
formation of metabolite in the absence of inhibitor. Values used in the
equations for Vmax,f and Km,f were determined in preliminary experiments and
are shown in Table 1. As shown in eqs. 7 and 8, in the presence of inhibitor,
metabolite formation is expected to be altered by immediate reversible
(i.e., competitive) inhibition, as well as by time-dependent (i.e., quasi-
irreversible or irreversible) inactivation such that
dCform9
dCsub9
V
×
¼ CLint;f9 × Csub9 ¼ 2 V
×
ð7Þ
dt
dt
and

1436
Berry et al.
TABLE 2
IC50 (mM) based on nominal inhibitor concentrations (Cinh) and shifted IC50 (mM) based on nominal or observed Cinh
Nominal Cinh
Observed Cinh
Compound
P450
IC50
130
9.6
19.3
5.6
51.4
72.8
43.7
Shifted IC50
Fold Shift
Shifted IC50
Fold Shift
Clarithromycin
Dasatinib
Delavirdine
CYP3A4
CYP3A4
CYP3A4
CYP2C9
CYP2D6
CYP3A4
CYP3A4
CYP3A4
CYP2C9
CYP3A4
CYP2D6
CYP3A4
CYP2C9
CYP2D6
CYP3A4
CYP2C9
CYP3A4
CYP2C9
CYP2D6
CYP2D6
CYP3A4
CYP2C9
CYP2D6
CYP3A4
CYP2C9
CYP2D6
CYP2C9
CYP3A4
CYP3A4
41.4
2.6
0.79
6.0
10.7
36.2
18.0
0.021
8.4
0.029
0.51
0.43
2.7
3.1
3.7
24.4
0.9
4.8
2.0
2.4
0.6
1.2
14.5
2.4
11.6
1.8
0.4
9.1
0.7
4.5
0.2
0.2
24.6
0.9
0.9
0.3
0.5
0.9
1.0
12.5
4.3
3.0
41.4
2.2
0.53
5.8
13.1
36.2
18.0
3.1
4.4
36.4
1.0
3.9
2.0
2.4
1.3
1.2
55.3
2.6
41.7
3.8
0.6
636
0.8
1750
1.2
Diltiazem
Erythromycin
Ketoconazole
0.013
0.0099
8.4
9.8
0.42
1.2
5.0
4.9
7.1
2.1
Mibefradil
0.0076
0.46
0.12
1.3
12.5
0.0033
28.0
0.00028
0.30
2.8
0.024
0.00018
2.2
2.9
0.033
Mifepristone
16.3
0.23
32.8
0.11
1.7
Nefazodone
Nicardipine
23.3
0.49
0.35
1.5
0.9
0.0082
2.0
1.0
0.50
29.2
8.4
6.2
0.5
Paroxetine
Ritonavir
0.037
0.0090
2.2
2.9
1.0
33.9
8.5
0.072
1.1
37.9
45.6
0.9
0.3
15.2
0.9
Saquinavir
31.2
3.5
0.018
0.19
6.5
2.4
Tienilic acid
Troleandomycin
Verapamil
0.90
4.7
21.7
50.0
24.7
3.3
7.2
Dynamic Modeling of P450 Inhibition. Since shifted IC50 appears inhibitor CLint,max values, which represent the rates of depletion at
to depend on the depletion of inhibitor as well as enzyme inactivation the lowest concentrations tested. Depletion of many inhibitors was
and incubation time, it was hypothesized that a more mechanistic remarkably rapid, particularly at low concentrations, whereas the
approach to modeling IC50 and shifted IC50 curves could further values for apparent Km were often very low (;1 mM or lower).
explain the anomalies and provide more robust and meaningful Therefore, saturation of metabolism was observed at the higher
information about P450 inhibition. The model developed incorporated concentrations tested, typically preventing or minimizing depletion of
metabolism kinetics of both inhibitor and substrate, as well as the inhibitor at the higher concentrations tested. This finding suggests that
contribution of both competitive inhibition- and time-dependent the calculation of shifted IC50 would be influenced mostly by the
inactivation; and the timelines of dosing of inhibitor and substrate in depletion of inhibitor at low, unsaturating concentrations and confirms
the model were matched to that in the in vitro experiments. The best- that accurate characterization of P450 inhibition kinetic parameters
fit values for the apparent Vmax and Km of the model parameters for for many of the inhibitors tested requires consideration of inhibitor
depletion of the inhibitor are given in Table 3. Also calculated are the depletion kinetics.
TABLE 3
Apparent Vmax and Michaelis-Menten dissociation constant (Km) for the depletion of various P450 inhibitors
Vmax
Km
CLint,us
CLint,max
Concentration Range
pmol/(min/mg)
mM
ml/(min/mg)
ml/(min/mg)
mM
Clarithromycin
Dasatinib
Delavirdine
Diltiazem
Erythromycin
Ketoconazole
Mibefradil
Mifepristone
Nefazodone
Nicardipine
Paroxetine
Ritonavir
Saquinavir
Tienilic acid
Troleandomycin
Verapamil
21.7 6 8.1
194 6 23
189 6 20
0.509 6 0.248
0.844 6 0.116
0.651 6 0.083
77.3 6 17.1
42.6
230
307
66.3
28.9
402
0.069–50
0.069–50
0.069–50
0.069–50
0.069–50
0.0014–1.0
0.0027–2.0
0.069–50
0.014–10
0.0027–2.0
0.0069–5.0
0.0014–1.0
0.069–50
0.0069–5.0
0.014–10
0.069–50
17.0 6 7.9
5122 6 1056
28.9 6 11.4
12.3 6 5.1
25.6 6 5.4
828 6 218
1658 6 122
552 6 56
13.4 6 5.71
18.9 6 5.2
935 6 28
0.0306 6 0.0151
0.0387 6 0.0095
1.59 6 0.497
687
521
1.16 6 0.094
1429
2022
250
1500
1676
720
0.273 6 0.031
0.0535 6 0.0297
0.0126 6 0.0019
0.558 6 0.024
0.0589 6 0.016
42.4 6 8.3
611 6 96
611
212
494 6 77
2.33 6 0.423

Dynamic Modeling of P450 Inhibition In Vitro
1437
TABLE 4
Dynamic model fit parameters Ki, KI, and kinact from IC50-shift experimental design considering kinetics of inhibitor depletion, compared with KI and kinact values determined
from traditional experimental design and parameter fitting
Values are 6 S.E. or a range of values as appropriate.
IC50 Shift by Substrate Addition (Fit with Dynamic Model)
Traditional Dilution Method (Range of Reference Values)a
Compound
P450
Ki
KI
kinact
KI
kinact
mM
mM
min-1
mM
min-1
Clarithromycin
Dasatinib
Delavirdine
CYP3A4
CYP3A4
CYP3A4
CYP2D6
CYP3A4
CYP3A4
CYP3A4
CYP2D6
CYP3A4
CYP2C9
CYP3A4
CYP3A4
CYP2D6
CYP3A4
CYP3A4
CYP2D6
CYP2C9
CYP3A4
CYP3A4
62.6 6 8.5
5.25 6 0.71
14.5 6 2.1
15.9 6 1.5
23.2 6 5.2
25.6 6 12.2
1.17 6 0.39
1.45 6 0.85
3.34 6 0.97
1.76 6 0.85
0.0204 6 0.0059
0.0245 6 0.0044
0.0716 6 0.0079
0.0265 6 0.0030
0.00779 6 0.00227
0.0148 6 0.0034
0.0539 6 0.0045
0.0164 6 0.0031
0.0541 6 0.0040
0.0307 6 0.0096
0.205 6 0.072
0.0864 6 0.0175
0.0790 6 0.0087
0.439 6 0.180
0.0416 6 0.0091
0.0388 6 0.0322
0.0840 6 0.0161
0.0404 6 0.0025
0.0260 6 0.0017
13.2–41.4
2.6–6.3
3.8–15.9
3.89 6 1.07
0.48–18.1
1.7–17
0.13–2.3
1.09 6 0.31
0.61–1.6
0.0192–0.063
0.024–0.034
0.056–0.29
0.0215 6 0.0030
0.005–0.019
0.017–0.081
0.042–0.7
Diltiazem
Erythromycin
Mibefradil
20.7 6 2.3
5.27 6 2.19
0.297 6 0.038
0.410 6 0.040
3.59 6 0.67
1.83 6 0.31
2.82 6 0.95
0.338 6 0.043
0.721 6 0.068
0.00456 6 0.00038
0.251 6 0.027
3.41 6 0.82
0.690 6 0.093
2.42 6 0.14
13.0 6 2.06
0.0200 6 0.0033
0.161 6 0.054
0.308 6 0.041
1.86 6 0.88
0.414 6 0.190
0.0424 6 0.0141
0.0789 6 0.0141
0.0527 6 0.0239
0.484 6 0.167
2.99 6 3.24
0.0220 6 0.0021
0.061–0.091
Mifepristone
None reported
Nefazodone
Nicardipine
Paroxetine
Ritonavir
1.0–1.6
0.72–1.3
0.81–4.85
0.0106–0.5
1.54–5.9
0.09–0.094
0.047–0.06
0.074–0.17
0.05 - 0.45
0.026–0.0379
Saquinavir
None reported
Tienilic acid
Troleandomycin
Verapamil
0.0969 6 0.0605
0.271 6 0.047
0.201 6 0.058
1.0–4.5
0.19–2.4
0.74–3.5
0.066–0.46
0.032–0.171
0.023–0.07
a Reference values compiled from the following sources: Mayhew et al., 2000; Bertelsen et al., 2003; Ito et al., 2003; Zhao et al., 2005, 2007; Obach et al., 2007; Watanabe et al., 2007; Berry and
Zhao, 2008; Perloff et al., 2009; Li et al., 2009; Mori et al., 2009; Xu et al., 2009; Kirby et al., 2011; Albaugh et al., 2012; Kenny et al., 2012; Amgen in-house data; University of Washington Drug
Interaction Database (www.druginteractioninfo.org).
For compounds with an IC50 fold shift .1.5 based on observed CYP3A4 (Fig. 2B). After the fitting of Ki, KI, and kinact, omitting
inhibitor concentrations, best-fit values for Ki, KI, and kinact from the inhibitor depletion by setting inhibitor Vmax to zero in a subsequent
dynamic model are given in Table 4 and compared with available KI simulation can help illustrate what the shifted IC50 curve might look
and kinact values gathered from various sources for reference. Several like had inhibitor concentrations remained constant throughout the
simulations are illustrated in more detail representing various effects course of the incubation. In the case of erythromycin, omitting
of inhibitor depletion on the magnitude of IC50 shift. Erythromycin inhibitor depletion yielded minimal change in the simulated shifted
was not rapidly depleted during the incubation, with an average CLint IC50 curve (Fig. 2B) since depletion of inhibitor was initially slow.
of 28.9 ml/(min/mg) and showed moderate potency in the inactivation
Depletion of nicardipine was rapid and concentration dependent
of CYP3A4 (Fig. 2A). The simulated and observed shifted IC50 curves (Fig. 3A), whereas CYP3A4 inactivation was estimated to be rapid
were shifted to the left (more potent) relative to the simulated and and nonlinear over the course of the incubation (Fig. 3B). The
observed IC50 curves, indicating time-dependent inactivation of simulated and observed shifted IC50 curves were shifted to left (more
Fig. 2. Dynamic modeling of erythromycin IC50 shift. (A) Simulated time-dependent loss of CYP3A4 activity after preincubation with erythromycin. (B) Simulated (lines)
and observed values (points) for CYP3A4 %Activity after preincubation with (shifted IC50) or without (IC50) erythromycin. Solid lines are simulations considering depletion
of erythromycin. Dashed line is a simulated shifted IC50 curve without considering erythromycin depletion and using the fitted values for KI and kinact. (C) Model predicted
versus observed values for %Activity. Depletion of erythromycin during the preincubation was minimal. E, represent the fraction of active P450 enzyme as defined by eq. 3.

1438
Berry et al.
Fig. 3. Dynamic modeling of nicardipine IC50 shift. (A) Simulated (lines) and observed (points) depletion of nicardipine. (B) Simulated time-dependent loss of CYP3A4
activity after preincubation with nicardipine. (C) Simulated (lines) and observed values (points) for CYP3A4 %Activity after preincubation with (shifted IC50) or without
(IC50) nicardipine. Solid lines are simulations considering depletion of nicardipine. Dashed line is a simulated shifted IC50 curve without considering nicardipine depletion
and using the fitted values for KI and kinact. (D) Model predicted versus observed values for %Activity. E, represent the fraction of active P450 enzyme as defined by eq. 3.
potent) relative to the simulated and observed IC50 curves, indicating
Comparison of the KI and kinact values derived from the dynamic
time-dependent inactivation of CYP3A4. However, omitting inhibitor model versus the reference values is given in Table 4. Looking across
depletion from the simulation yielded a more dramatic leftward shift in a set of inhibitors with a wide range of potencies, kinact values, derived
the shifted IC50 curve. In this case, it appears that depletion of inhibitor from the dynamic model fit of the IC50 and shifted IC50 curves,
(and resulting loss of reversible and time-dependent inhibition) re- appeared to fall within the range of available reference values or
duced the magnitude of the observed IC50 shift.
within 2-fold of the reference value when only one reference value
Depletion of saquinavir was also rapid and concentration dependent was available. On the other hand, KI values derived from the dynamic
(Fig. 4A). However, despite relatively potent apparent CYP3A4 in- model tended to be more potent than the reference values. Since the
activation (Fig. 4B), the simulated and observed shifted IC50 curves traditional experimental methods used to determine the reference
were actually shifted to the right (less potent) relative to the simulated values often used higher microsomal protein concentrations than the
and observed IC50 curves (Fig. 4C). Omitting inhibitor depletion from dynamic IC50 shift method, we considered that some of the discrepancy
the simulations resulted in a leftward shifted IC50 curve, as would in KI values could be due to nonspecific microsomal binding. Therefore,
be expected, given the CYP3A4 inactivation. It can be considered KI values were further corrected for microsomal binding at the protein
that depletion of inhibitor during the incubation (and loss of revers- concentrations used in the experiments. Correcting KI values for
ible inhibition) more than compensated for the CYP3A4 inactiva- microsomal binding by calculating unbound KI (KI,u) appeared to
tion occurring during the incubation, particularly at the lowest improve the correspondence between the dynamic model and the
concentrations.
reference values (Fig. 5).

Dynamic Modeling of P450 Inhibition In Vitro
1439
Fig. 4. Dynamic modeling of saquinavir IC50 shift. (A) Simulated (lines) and observed (points) depletion of saquinavir. (B) Simulated time-dependent loss of CYP3A4
activity. (C) Simulated (lines) and observed values (points) for CYP3A4 %Activity after preincubation with (shifted IC50) or without (IC50) saquinavir. Solid lines are
simulations considering depletion of saquinavir. Dashed line is a simulated shifted IC50 curve without considering saquinavir depletion and using the fitted values for KI and
kinact. (D) Model predicted versus observed values for %Activity. E, represent the fraction of active P450 enzyme as defined by eq. 3.
Discussion
Discrepancy in shifted IC50 was also dependent on the saturation
kinetics of inhibitor depletion. For some shifted IC50 values, the
discrepancy was not as large as expected given the CLint,max for the
inhibitor. This was mainly the case for shifted IC50 values greater than
In the present study, depletion of inhibitor was found to influence
the apparent shifted IC50 for many compounds. Although the widely
used IC50 and IC50-shift–type assays can distinguish between re-
versible and time-dependent inhibitors in most cases, rapid depletion
of inhibitor could cause a reduction in observed IC50 fold shift or even
an increase in IC50 with preincubation time, potentially interfering
with the classification of time-dependent inhibitors. A strong re-
lationship exists between potential discrepancy in shifted IC50 and
CLint,max for the inhibitors tested (Fig. 6). Inhibitor depletion of 50%
over the 30-minute preincubation with 0.1 mg of microsomal protein
per milliliter equates to a CLint of 230 ml/(min×mg) and will result in
a 2-fold increase in shifted IC50. As CLint,max increases, the potential
for discrepancy in shifted IC50 increases exponentially. Therefore, the
IC50-shift assay is best interpreted with knowledge of inhibitor
the apparent Km for the depletion of inhibitor. If the shifted IC50
.
Km, depletion of inhibitor at these concentrations and, therefore,
discrepancy in shifted IC50 is expected to be limited. However, if the
IC50 is near or below the apparent Km, the discrepancy in shifted IC50
could be pronounced. An example of this phenomenon is ritonavir.
For ritonavir, shifted IC50 values against CYP2C9 and CYP2D6 were
similar whether calculated using nominal or observed concentrations,
whereas the shifted IC50 against CYP3A4 was substantially lower
using observed concentrations. Since the phenomenon also appears to
be dependent on the saturation kinetics of inhibitor depletion, it is
important to evaluate inhibitor depletion over a range of concen-
turnover, either from preliminary stability studies with human liver trations to assess fully the impact of inhibitor depletion on shifted IC50.
microsomes or by monitoring inhibitor depletion during the IC50-shift
Although compared with IC50 the shifted IC50 is useful for the rapid
experiment itself. Using observed inhibitor concentrations at the end classification of time-dependent inhibitor in vitro, we considered that
of the 30-minute preincubation is likely to yield the most accurate it might not be the best measure of time-dependent inactivation
assessment of IC50 fold shift and the most realistic classification of potency. This is because the shifted IC50 is dependent on the choice of
time-dependent inhibitors, particularly for inhibitors with CLint,max inhibitor concentration used for its calculation (nominal versus ob-
.230 ml/(min×mg).
served), in addition to the extent of reversible inhibition and incubation

1440
Berry et al.
Fig. 6. Relationship between potential discrepancy in shifted IC50 versus inhibitor
CLint,max. Shifted IC50 ratio is a measure of the discrepancy and equals shifted IC50
determined using nominal inhibitor concentrations divided by shifted IC50
determined using observed inhibitor concentrations. Solid horizontal lines are line
of unity and a ratio of 2, respectively. Dashed vertical line represents a CLint,inh,max
of 230 ml/(min/mg). Curved line represents the maximum potential error in shifted
IC50 for a given CLint,max
.
available reference values, as was the case for nicardipine, saquinavir,
and tienillic acid. The discrepancies could be due to interlaboratory
variations, which have been quite large on occasion. They might also
be explained by a “bias” in the KI values determined by traditional
experimental and parameter fitting methods, particularly when inhi-
bitor depletion is rapid (Yang et al., 2005). Rapid inhibitor depletion
causes nonlinearities in the enzyme inactivation profile over the course
of the preincubation. An example from the present data set can be
visualized in the inactivation of CYP3A4 by nicardipine (Fig. 3B). As
nicardipine is depleted, the inactivation rate slows, particularly at
low inhibitor concentrations, as it depends on the saturation kinetics
of inhibitor depletion. In traditional approaches to fit inactivation
Fig. 5. Comparison of the KI,u (A) and kinact (B) values determined from different
methods. Bars represent the range of the available reference values, and points
indicate values derived from the dynamic modeling. Values are for CYP3A4
inactivation unless otherwise noted. Note: Microsomal binding could not be
determined for troleandomycin because of instability in microsomes; free fraction in
microsomes is assumed to be 1 for troleandomycin.
time. Inhibition parameters KI and kinact have been more important in parameters KI and kinact, depletion of inhibitor is typically assumed to
this regard, particularly in the application of extrapolation to in vivo be minimal. Even so, best practices have called for using only the
drug-drug interactions. Therefore, a more complete mechanistic model initial observed rate of inactivation (kobs) at each inhibitor concentra-
was established to explain more fully the processes occurring in the tion in the subsequent fitting of KI and kinact. Choosing which time
IC50-shift assay based on the scheme shown in Fig. 1 and applied to points to consider becomes a judgment made by each individual
those inhibitors showing an IC50 fold shift .1.5 based on observed scientist. In practice, it might be difficult to resolve the initial brief
inhibitor concentrations. The model did a reasonable job of describing inactivation from the subsequent nonlinearity because of the lack of
IC50-shift data for all inhibitors, including those displaying anomalies intensity of sampling or error resulting from sample dilution or
in shifted IC50 discussed previously herein, such as nicardipine and analysis. Therefore, the kobs may often be underestimated at low
saquinavir. It was also used to demonstrate the likely effect of concentrations. The ultimate effect is a bias that overestimates the KI
inhibitor depletion on the shifted IC50 curves for erythromycin, value when inhibitor depletion is rapid. Mechanistic approaches to
nicardipine, and saquinavir. Inhibitor depletion caused a rightward fitting KI and kinact in inactivation experiments have been proposed to
shift in the shifted IC50 curves that opposes the leftward shift caused help reduce such bias and provide more accurate characterization of
by enzyme inactivation. Combining the processes of inhibitor depletion these parameters (Yang et al., 2007). Hence, application of a mechanistic
and enzyme inactivation, the model was able to fit the fundamental approach that incorporates inhibitor depletion should also provide more
parameters used in characterizing P450 inhibitors, Vmax,inh, Km,inh, Ki, KI robust characterization of inhibitors using IC50-shift methods.
and kinact, thereby definitively linking these process to observed shifts
in the IC50 curves.
The processes occurring in in vitro experiments to characterize
P450 inhibition are clearly complex. In practice, assumptions are made
The model did a reasonable job of estimating KI,u and kinact values to simplify the interpretation of P450 inhibition results. However, the
for a wide range of inhibitors compared with reference values (Fig. 5). present data set further demonstrates that the assumption regarding
In a few cases, the KI,u determined by the dynamic modeling of IC50 minimal inhibitor depletion is often not realistic and can dramatically
and shifted IC50 curves appeared to be lower (more potent) than the impact interpretation of the data. Therefore, one can and should take

Dynamic Modeling of P450 Inhibition In Vitro
Acknowledgments
1441
reasonable steps to account for depletion of inhibitor during time-
dependent inactivation experiments, including IC50-shift assays.
Additional processes may be of some importance in both IC50-shift
and traditional dilution methods. First, in the present model, we have
assumed that inhibitor depletion kinetics can be reasonably estimated
using Michaelis-Menten kinetics. In reality, the contribution of
substrate or product-dependent inhibition, as well as time-dependent
autoinactivation, cannot be ruled out. Despite the limitation, the
current model does a reasonable job of describing inhibitor con-
centrations over the course of the incubations, given the current data
set (see Figs. 2–4 for examples). The current model, which incor-
porates inhibitor depletion kinetics (even in a simplified form), can be
used to explain mechanistically the anomalies (reduced IC50 shift or
increased IC50 with preincubation) described already. We therefore
consider that the present model represents an improvement over
previously reported models that neglect inhibitor depletion. Second,
the ability of metabolites formed from the depletion of inhibitor to
inhibit P450 is not typically considered and was not applied in the
present model. In fact, a number of inhibitors are thought to be
converted to metabolites that meaningfully inhibit P450, such as
verapamil and diltiazem. The impact of these processes on the esti-
mation of shifted IC50, and KI and kinact, has not been widely eval-
uated. Whereas further accuracy in inhibition parameters might be
gained by modifying the model equations to account for them, a vastly
larger data set is required to demonstrate applicability. For example,
atypical inhibitor metabolism kinetics may be best characterized using
metabolite formation experiments, which would require identification
and quantification of all major metabolites of the inhibitor rather than
inhibitor depletion as done currently. The impact of autoinhibition and
autoinactivation on inhibitor-depletion kinetics requires knowledge of
the fraction the inhibitor is metabolized by specific P450 in vitro.
Finally, the impact of metabolite formation on the observed combined
P450 inhibition requires proper characterization of each metabolite
separately, which could themselves cause a combination of compet-
itive or time-dependent inhibition. With this in mind, some assumptions
must still be made, and a proper balance must be established between
the desire for reasonably accurate inhibitor classification and parameter
estimation and simplicity in experimental design.
In summary, the IC50 shift assay remains a viable approach to
characterizing a wide range of reversible and time-dependent inhibitors.
The value of the approach lies in the ability to evaluate both competitive
and time-dependent inhibition in a single experiment. Further effi-
ciencies are gained by omitting the dilution step found in traditional
experimental designs and by using a substrate cocktail approach, which
allows the evaluation of several P450s simultaneously. Anomalies, such
as smaller-than-expected shift in IC50 and increases in IC50 with
preincubation, were explained by depletion of inhibitor during the
preincubation. As with traditional time-dependent inactivation methods,
it is recommended that IC50-shift experimental data be interpreted with
knowledge of the extent of inhibitor depletion. For the most realistic
classification of time-dependent inhibitors using IC50-shift methods,
shifted IC50 should be calculated using observed inhibitor concen-
trations at the end of the incubation rather than nominal inhibitor
concentrations. Finally, a mechanistic model that includes key processes
such as competitive inhibition, enzyme inactivation, and inhibitor
depletion can be used to describe accurately observed IC50 and shifted
IC50 curves. For compounds showing an IC50 fold shift .1.5 based on
observed inhibitor concentrations, reanalyzing the IC50-shift data using
the mechanistic model appeared to allow for reasonable estimation of
Ki, KI, and kinact directly from the IC50 shift experiments.
The authors thank Gary Skiles and Magang Shou for early discussions on
the application and implementation of the IC50/IC50 shift assay.
Authorship Contributions
Participated in research design: Berry, Zhao, Lin.
Conducted experiments: Berry.
Performed data analysis: Berry.
Wrote or contributed to the writing of the manuscript: Berry, Zhao, Lin.
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Address correspondence to: Loren M. Berry, Amgen, Inc., 360 Binney St.,
Cambridge, MA, 02142. E-mail: loren.berry@amgen.com