Download Enzyme Kinetics for Clinically Relevant CYP Inhibition

Current Drug Metabolism, 2005, 6, 241-257
241
Enzyme Kinetics for Clinically Relevant CYP Inhibition
Zhi-Yi Zhang* and Y. Nancy Wong
Drug Disposition, Eisai Research Institute, Andover, MA 01810, USA
Abstract: In vitro cytochrome P450 (CYP)-associated metabolic studies have been considered cost-effective for
predicting the potential clinical drug-drug interactions (DDIs), one of the major attritions in drug development. The
breakthroughs during the past decade in understanding the biochemistry of CYP-mediated biotransformation and
molecular biology of CYP gene regulation in humans have provided the scientific bases for such endeavors in early drug
development.
In this review, the enzyme kinetics of CYP inhibitions is described, with the primary focus on the ones proven with
clinical relevance, namely the competitive inhibition and mechanism-based inactivation (MBI). Competitive CYP
inhibition, the most often detected reversible inhibition, is well understood and has been studied extensively both in vitro
and in clinical setting. Recently, MBI has received increasing attention. It has been recognized that MBI could occur more
often than anticipated, due in part to the redox cycling-allied enzymatic action of CYPs. As commonly as an irreversible
inhibition, MBI would inactivate the target proteins, and thus would be generally considered of high potential for causing
clinical DDI. Moreover, the reversible inhibitions other than the competitive, namely noncompetitive, uncompetitive and
mixed, were also documented for the important drug-metabolizing CYP members, particularly CYP1A2 and CYP2C9.
Finally, the unusual kinetic interactions, which did not follow the Michaelis-Menten (M-M) kinetics, were detected in
vitro for the majority of drug-metabolizing CYP members, and manifested for CYP3A4. However, the clinical relevance
of the interactions involving the unusual CYP kinetics has not yet been fully understood. Nonetheless, the reversibility
and inhibitory potency should be considered as the major determinants of the clinical relevance, particularly in
combination with the therapeutic exposure levels. With rapid expansion of knowledge and technology, the evaluation of
the clinically relevant CYP-associated DDIs in vitro is not only desirable but also achievable.
Key Words: Cytochrome P450, drug-drug interaction, enzyme inhibition, mechanism-based inactivation, atypical kinetics, in
vitro-in vivo correlation, pharmacokinetics and clinic.
INTRODUCTION
The inhibition of metabolic enzymes, particularly cytochromes P450 (CYPs), has been recognized as the pivotal
cause of the drug-drug interactions (DDIs) in clinic [1, 2].
With the increasing number of new therapeutic agents on the
market and the therapeutic trend in drug combination, the
DDI becomes one of the focal points for the drug development and clinical application [3, 4]. Fortunately, the breakthrough in understanding the mechanism of action for human
drug-metabolizing enzymes, CYPs in particular, during the
past decade, has shed some light on examining DDI in vitro
to predict the DDI in clinic [5]. The methods for in vitro
CYP-associated DDI studies have been well established, and
the human enzyme preparations, from recombinant individual metabolic enzymes to freshly isolated primary hepatocytes, are commercially available. Thus the in vitro DDI
studies, recently enforced by the US Food and Drug Administration (FDA) [6-8], are routinely performed during drug
development in pharmaceutical companies.
However, in vitro-in vivo correlation for DDI, though
occasionally successful [9, 10], has not always been satisfactory, due in part to the intrinsic differences between the
simplified non-physiological in vitro models and the
*Address correspondence to this author at the Eisai Research Institute, Drug
Disposition, 100 Research Drive, Wilmington, MA 01887; Tel: 978-6617242; Fax: 978-657-7715; E-mail: [email protected]
1389-2002/05 $50.00+.00
dynamic physiological human bodies, besides the ambiguity
of in vivo CYP kinetic behaviors. Therefore, the reliability of
in vitro DDI study is uncertain. On the other hand, some of
the potential biases for the in vitro-in vivo correlations, as
suggested by the recent studies [11, 12], are amendable,
providing opportunities for further refinement of the predictive kinetic models. Although challenging, the improvement
of the predictability of in vitro results by integrating the key
in vivo factors such as pharmacokinetics (PK) characteristics,
should be anticipated and encouraged. Therefore, we would
like to, both from theoretic and practical prospective, provide
our thoughts on the kinetic mechanisms of CYP inhibitionassociated DDI, which will hopefully enhance the predictability of the findings in DDI studies in vitro.
The present paper is divided into two sections: the kinetics of CYP inhibitions in DDI and some practical concerns
for the prediction of clinical DDI using in vitro data.
A. Enzyme Kinetics in CYP-Mediated Biotransformation
and CYP Inhibition
Both Michaelis-Menten (M-M) kinetics and nonMichaelis-Menten kinetics (or atypical kinetics) have been
detected for CYP-mediated drug metabolism and its inhibition. Though not yet convincingly proven, the mechanisms
underlying these distinct kinetic behaviors are, at least
empirically, believed to be due to the existence of divergent
interactions between the drug molecules and the active
© 2005 Bentham Science Publishers Ltd.
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Zhang and Wong
site(s) of the enzymes. Thus, M-M kinetics would be simply
elucidated using the model of single binding site, whereas
atypical kinetics might be interpreted using the model of two
or possibly more binding regions within the enzyme active
site(s).
1. One-Binding Site
(1) Substrate Alone
One-binding site, or M-M hyperbolic kinetic model (Eq.
1), the most simple, however, the basis of the majority of the
derived complex kinetic models later described, is historically applied to CYP-mediated metabolism.
V = Vmax*S/(S + Km) = Vmax/(1 + Km/S)
1
Where V is reaction rate, and Vmax is the maximal, and Km
is the substrate concentration at which the reaction rate is
half of its maximum. S is substrate concentration. Interestingly, in contrast to the unequivocal definition, the calculation of Vmax may not always be consistent in literature [1316]. To avoid such a potential inconsistency, the classic
enzyme kinetic concept is depicted here.
E+S
k1
k2
ES
k3
E+P
where E, S, ES and P are the concentrations of the enzymes,
substrates, substrate-bound enzymes and enzyme products
(metabolites), respectively. k1 is the association rate constant,
and k2 and k3 are the dissociation rate constants from ES to E
and S, and E and P, respectively.
As shown in Scheme 1,
2
In steady state,
k1*E*S = k2*ES + k3*ES,
thus, ES = E*S*k1/(k2 + k3)
3
Michaelis constant (Km) is defined as
Km = (k2 + k3)/k1
4
Eq. 3 becomes ES = E*S/Km, and Eq. 2 is converted to
V = (k3/Km)*E*S
As typical enzyme catalysis per se, ET is usually
unchanged during the catalytic process, particularly in the
reconstituted in vitro system (in the absence of mechanismbased inactivation). Therefore, differentiating the potential
difference in defining Vmax may not be crucial, and both the
connotations might be used interchangeably. However, for
the prediction of metabolic enzyme-associated DDI in clinic
in which the enzyme quantities may vary, the later
connotation should be more applicable, as demonstrated by
intrinsic clearance (CLint). CLint, the key parameter bridging
enzyme kinetics and PK, is defined as Vmax/Km.
In a well-stirred model with the assumptions of complete
intestinal absorption and exclusive hepatic elimination, the
intrinsic clearance can be directly associated to the area
under the plasma-concentration-time curve of an orally
administered drug (AUCpo), as shown in Eq. A (Equations
for enzyme kinetics are listed in numerical order, while those
for PK in alphabetic order.) [17].
Dosepo/AUCpo = fu*CLint or
Scheme 1. The Classic Enzyme Catalytic Process.
V = k3*ES
thought to be the maximal conversion rate from substrate to
product [16], then it should be regarded as kcat*ET (derived
from Eq. 2, and the concentration of total active enzymes ET
= ES + E. ET is approximately equal to ES when enzymes
are saturated with substrates.). In that case, Vmax is no longer
a constant, but the function of ET.
5
Therefore, the reaction rate (V) depends on the concentrations of both unbound enzyme (or the available active
sites of enzymes) and substrate in steady state. Eq. 5 could
be further converted to Eq. 1.
When the enzymes are saturated by the substrates, the
enzyme catalytic rate reaches the maximum (Vmax) and
becomes substrate concentration-independent. The dissociation rate constant k3 would be viewed simply as kcat, the
maximal catalytic rate constant. Therefore, if Vmax is
considered the capacity of the enzyme catalysis, it could be
interpreted as a parameter in a unit of enzymes, however, it
might not be suitable in a unit of unpurified proteins, i.e., mg
of proteins, as sometimes used in the literature. Thus, Vmax is,
in this case, identical to kcat. On the other hand, if Vmax is
AUCpo = Dosepo/(fu*CLint)
A
Where fu is the unbound drug fraction in the blood, and
AUCpo is applicable for both that of time zero to infinity in a
single dose and over a dosing interval in steady state in
multiple doses.
ET in vivo is controlled by protein synthesis and degradation. In steady state or equilibrium of these inverse processes, ET could be denoted as Ess, the concentration of total
enzymes available for the metabolism in steady state. Thus,
Vmax = kcat*Ess. However, such equilibrium or the level of Ess
would be potentially modulated by a series of factors,
particularly the exogenous effectors including enzyme
inducers or inactivators. Therefore, in contrast to likely
quasi-constant Vmax in vitro, Vmax and CLint in vivo (CLint =
(kcat/Km)*Ess, and kcat/Km is defined as catalytic efficiency.)
are subject to variation, which potentially affects AUCpo of
drug substances in clinic (Eq. B).
AUCpo = Km/kcat*(Dosepo/(fu*Ess))
B
Therefore, the concept of Vmax as kcat*ET is used
throughout the paper.
CLint, or Vmax/Km, can be determined in vitro by applying
the traditional biochemical plots, including M-M plot
constructed by non-linear regression analyses, and those
transformed from M-M plot such as Lineweaver-Burke or
Eadie-Hofstee plot (Fig. 1) [18, 19], in the assays using
different enzyme sources including recombinant human
CYPs, human liver microsomal preparations (HLM) or even
hepatocyte suspensions [20, 21]. Each of these enzyme
sources has the intrinsic pros and cons, as discussed
previously [22]. Thus, the selection of in vitro systems
should facilitate the experimental goals, since different in
vitro systems would provide, though still some overlapping,
differential kinetic information.
Enzyme Kinetics for Clinically Relevant CYP Inhibition
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243
Fig. (1). Biochemical plots for the determination of kinetic parameters of CYP-mediated reactions. A, Lineweaver-Burk or double-reciprocal
plot; B, Eadie-Hofstee plot.
Double-reciprocal plot, though frequently used, may not be ideal, particularly compared to Eadie-Hofstee plot. The data points in doublereciprocal plot tend to be unevenly distributed thus potentially lead to the unreliable reciprocals of lower metabolic rates (1/V), which
however dictate the linear regression curves therefore the apparent values of Km and Vmax. In contrast, the data points in Eadie-Hofstee plot
are usually homogeneously distributed, and thus tend to be more accurate. Moreover, Eadie-Hofstee plot appears diagnostic of recognizing
deviations from Michaelis-Menten kinetics, such as homotropic cooperation.
(2) Substrate and Inhibitor
In the presence of two different compounds interacting
with the same enzymes, either compound would interfere
with the binding, or more generally with the interactions of
the other with the enzymes. In regard to metabolism, the
resulting outcome is typically an enzyme, particularly CYP
inhibition, i.e the essence of this review. The enzyme
inhibitions in the arena of M-M kinetics are usually
categorized into four different modes as shown in Scheme 2,
namely competitive, uncompetitive, noncompetitive and
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Zhang and Wong
mixed inhibition, with competitive inhibition being the
prevalent and the uncompetitive, the rare [4].
E+S
I
1 Ki
EI
Ks
S
Ks'
3
ES
E+P
I
Ki'
2
ESI
Finally, the mixed inhibition would be considered as the
upshot of the inhibitor-enzyme binding with simultaneous
two or more above mechanisms, particularly the combination
of the competitive with the noncompetitive. To demonstrate
the potential utilities of differentiating these M-M inhibition
patterns for DDI studies, IC 50, the inhibitor concentration at
which the reaction rates are suppressed by 50%, is further
described here. The values of IC50 in different models could
be calculated using Eqs. 10-13, as directly derived from Eqs.
1 & 6-9.
Competitive:
Scheme 2. Reversible Enzyme Inhibitions Follows MichaelisMenten Kinetics.
Competitive inhibition, inhibitor binds only unbound
enzyme (Pathway 1).
Uncompetitive inhibition, inhibitor binds only substratebound enzyme (Pathway 2).
Noncompetitive inhibition, inhibitor binds both unbound
and substrate-bound enzyme at the site(s) different from the
substrate-binding site (Pathways 1 and 2).
Mixed inhibition , inhibitor binds, in a similar manner as
the noncompetitive, but possibly at the site(s) overlapped
with substrate-binding site, the unbound and the substratebound enzyme with potentially different affinities (Pathways
1, 2 and 3).
The equations of reaction rate derived from these models are
as follows:
V = Vmax/(1+Km/S/(1+I/Ki))
6
V = Vmax/(1+I/Ki+Km/S)
7
V = Vmax/(1+Ks/S)/(1+I/Ki)
8
V = Vmax/((1+I/Ki’)+(1+Ks/S)*(1+I/Ki))
9
Eq. 6 is for the competitive, Eq. 7 for the uncompetitive,
Eq. 8 for the noncompetitive, and Eq. 9 for the mixed
inhibition model. I is the inhibitor concentration. Ki is the
inhibition constant, while Ki' is the noncompetitive inhibition
constant for the binding of inhibitor with the substrate-bound
form of enzyme (ES) in the mixed inhibition model. K i and
Ki' may simply be viewed as the indicators of the binding
affinities between inhibitor and enzyme, similar to Km as that
of the binding affinity between substrate and enzyme. Ks, the
dissociation constant of the enzyme-substrate complex, is
approximately equal to Km (k3 << k2).
In competitive inhibition, the inhibitor usually binds to
the enzyme at the same site as the substrate, or possibly
different site(s), and subsequently blocks the substrate
binding. In contrast to clearly defined competitive inhibition,
uncompetitive and noncompetitive inhibitions appear
occasionally ambiguous [23]. The uncompetitive inhibition
might be viewed as that the inhibitor binds effectively to the
enzyme only in the substrate-bound form; while in the
noncompetitive manner, the inhibitor binds to the enzyme in
both unbound and substrate-bound forms with the same
binding affinity (Ki), or in other words, without apparent
preference. The enzyme inhibition by the polyclonal antibodies could be often in a noncompetitive manner [24].
IC50 = Ki*(1 + S/Km)
10
Uncompetitive: IC50 = Ki*(1 + Km/S)
11
Noncompetitive: IC50 = Ki
12
Mixed: IC50 = Ki*(1 + S/Km)/ (1 + (Ki/Ki')*(S/Km))
13
IC50 usually depends on the substrate concentrations,
with the exception in the noncompetitive model, and likely
higher than Ki as shown by Eqs. 10 & 11. When competitive
inhibition occurs, IC50 rises. In other words, the degree of
inhibition reduces if the inhibitor concentration is fixed,
along with the increase of substrate concentration. However,
such a scenario would be a reverse for uncompetitive
inhibition, in that, the higher the substrate concentration, the
lower the IC50 value, since the inhibitor effectively binds
only to the substrate-bound form of the enzyme (ES). In
contrast, IC50 in noncompetitive inhibition is a constant and
equal to Ki (Eq. 12), because the inhibitor binds only to the
enzyme at the sites different from the substrate-binding site.
In other words, the enzyme-inhibitor binding is independent
of the enzyme-substrate binding. Moreover, if substrate
concentration is low (or S/Km << 1), as often occurred in
vivo, IC50 values would be similar, when calculated using
different inhibition models excluding the uncompetitive
(Eqs.10, 12 & 13). The competitive model thus might be
chosen for IC50 determination if the mechanism of a
reversible inhibition is unclarified in vivo. However, the
inhibition would be potentially more pronounced in a
noncompetitive than that in a competitive manner, if the
substrate concentration available to the enzymes is indeed
substantial and comparable to Km, as likely the case when the
substrate is actively extracted by the metabolic tissues [25].
Therefore, the clinical CYP-associated DDI could be
potentially underestimated if noncompetitive inhibition is
misconceived as competitive inhibition. On the other hand,
uncompetitive inhibition, besides the rare occurrence, tends
to be less significant since the inhibitor would exhibit
diminished inhibitory effects because of much higher than Ki
IC50 values at low substrate concentration (or Km/S >> 1)
(Eq. 11). Therefore, noncompetitive inhibition, though
unlikely common, might be possibly relevant in DDI in
clinic.
Interestingly, the mechanisms of reversible inhibitions by
a given inhibitor may also elicit substrate dependence even if
the substrates and inhibitor presumably bind to the same
enzyme active site (but possibly at different regions and/or
with different binding orientations within the active site).
One such example is the differential inhibitions of CYP1A2mediated O-deethylation of 7-ethoxyresorufin (EROD) and
7-ethoxycoumarin (EOC) by α-naphthoflavone (αNF) [26].
The inhibitions of EROD and EOC by αNF are very potent
Enzyme Kinetics for Clinically Relevant CYP Inhibition
due to the tight-binding between CYP1A2 and αNF, with the
apparent Ki values of 1.4 and 55 nM in reconstituted system
containing the purified recombinant CYP1A2, respectively.
However, EROD inhibition by αNF was delineated as the
competitive, whereas EOC inhibition by αNF, the noncompetitive, as proposed by Cho et al. [26].
The equation for IC50 determination in the mixed model
(Eq. 13) appears complex. It could be easily converted to the
other IC50 equations following M-M kinetics (Eq. 10-12).
For instance, if the competitive is the predominant
component of a mixed inhibition, or Ki << Ki', (1 +
(Ki/Ki')*(S/Km)) in Eq. 13 is approximately equal to 1, Eq. 13
becomes Eq. 10. If the noncompetitive is the predominant
component of a mixed inhibition, or Ki = Ki', (1 +
(Ki/Ki')*(S/Km)) is equal to (1 + S/Km), Eq. 13 becomes Eq.
12. Finally if the uncompetitive is the predominant
mechanism, or Ki >> Ki', Eq. 13, to be better illustrated,
should be first converted to IC50 = Ki'*(1 + S/Km)/(Ki'/Ki +
S/Km), after both the numerator and denominator of the
equation are multiplied by Ki'/Ki. Thus, the denominator or
(Ki'/Ki + S/Km) in the transformed Eq. 13 is approximately
equal to S/Km, and Eq. 13 becomes IC50 = Ki'*(1 + Km/S), or
Eq. 11. Ki' here is the same as Ki in Eq. 11, since inhibitor in
this case effectively binds only the substrate-bound enzyme
[4].
Although numerous plot methods are available [15], it
may not be straightforward to classify the enzyme kinetics of
reversible inhibitions. Therefore, the computational simulation methods, such as simultaneous nonlinear regression
(SNLR), should be considered as the alternative, and they
Current Drug Metabolism, 2005, Vol. 6, No. 3
245
are being increasingly appreciated and applied [28, 29]. As
demonstrated by Fig. 2, the experimental data could be fitted
using SNLR with all possible kinetic models, thus the
potential inhibitory mechanism assigned would be unlikely
biased. Meanwhile, the traditional plots, such as the Dixon
plot, are still often required for visually inspecting the inhibitory mechanism, particularly when more than one kinetic
models are suggested using SNLR [29].
2. Two-Binding Sites
Non-M-M kinetics or atypical CYP kinetics, a topic in
academia for quite sometime, has recently received some
attention in pharmaceutical industry [30-34]. The mechanisms of such reversible kinetics, or so-called 'allosterism',
have been substantially studied and generally associated with
the assumed existence of two or more substrate binding
regions in enzyme active site [32, 35-37]. Atypical kinetics
for CYPs in vitro appeared more common than expected in
the past when our knowledge in CYP actions was limited,
thus the classic reversible kinetics, e.g. M-M kinetics, in
most cases was assumed. CYP3A4, among the major drugmetabolizing CYP forms, is most known for its atypical
kinetic behavior [38, 39]. However, besides some of the
minor CYP members [40, 41], CYP2C9 and CYP1A2 were
also proven to exhibit potential atypical kinetics [32, 42-44].
As drug metabolism per se, the three major CYP forms
would likely be responsible for the metabolism of more than
half of the therapeutics currently on the market [5]. The
bodies of evidence for the potential two (or multiple) substrate-binding sites were mostly derived from the numerous
enzyme kinetic studies, especially for CYP3A4 and CYP2C9
Fig. (2). 3D plots of simultaneous nonlinear regression (SNLR). A, by fitting the real data; B, by fitting the data applying a presumed
competitive model.
Apparently, the competitive model was quite appropriate in this case (p < 0.01). However, if two or more kinetic models appear applicable
using SNLR, the standard biochemical plots such as Dixon plot should be considered since SNLR analysis provides little or limited
information for the mechanism of enzyme inhibition.
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Zhang and Wong
[32, 39, 42, 43]. Atypical CYP kinetics has recently been
extensively reviewed [4, 45, 46]. Therefore, a brief description with the focus on clinical DDI is provided.
(1) Substrate Alone
Atypical CYP kinetics associated with substrates only
could be simplified as biphasic kinetics owing to the
assumption of two (or possibly more) substrate-binding sites,
as suggested by an elegant work from Korzekwa et al. [37].
These types of kinetics, exhibiting characteristic concentration dependence, are most known for substrate inhibition and
autoactivation.
The substrate inhibition is not uncommon in vitro [47].
The mechanism for such phenomenon is, though still not
clear, generally attributed again to two or more binding
regions in CYP activity sites [47]. Between two binding
regions, one site is presumed 'productive', and the other
'unproductive'. The binding at the unproductive site is
thought to suppress the productivity of the enzyme, but
unnecessarily due to the repression of the substrate binding
at the productive site. The substrate could thus behave as an
inhibitor upon the regions it binds. Consequently, the
interactions among the molecules of substrates within the
enzyme active site would be somewhat similar to the
competitive or possibly uncompetitive inhibition following
M-M kinetics (Eq. 14). However, such interactions would
not likely resemble the noncompetitive one due to the
presumed involvement of enzyme active sites.
V = Vmax/(1+S/Ki+Km/S)
14
Several points are worth noting. (i) Ki is usually much
greater than Km, as the substrate preferably binds to the
productive region than the unproductive region. At low
substrate concentrations (S <<Ki), the inhibitory effect is
likely unobservable, thus the enzyme reaction is rather
'typical'. However, the inhibitory effect begins to elicit along
with the rise of substrate concentration, and becomes
apparent when the concentration approaches the level at
which the activities start to be saturated if in a typical
hyperbolic kinetics. (ii) The concentrations of substrate and
'inhibitor' are the same within the enzyme active sites. (iii)
The largely different affinities for the binding of substrate to
two different regions within the enzyme active site and the
identical concentrations of substrate and 'inhibitor' would
differentiate substrate inhibition from typical competitive
inhibition following M-M kinetics. In competitive inhibition,
inhibitor concentration is totally independent to substrate,
thus even a weak inhibitor (Ki > Km) may markedly suppress
the substrate-enzyme binding if the inhibitor concentration is
sufficiently high. Therefore, the substrate inhibition would
most likely resemble the uncompetitive in M-M kinetics, as
shown by Eq. 14 (or Eq. 7).
Misconception of substrate inhibition would potentially
lead to underestimate the true values of Vmax and Km.
However, the resulting biases for CLint (Vmax/Km), attenuated
by the reductions of both Vmax and Km, may not be necessarily significant [47, 48]. Moreover, substrate inhibition would
be unexpected in clinic, as the near enzyme-saturating levels
of drug concentrations in patients are unfeasible.
Autoactivation is somewhat opposite to substrate inhibition, which is often detected by a sigmoidal concentrationactivity plot (Fig. 3). Autoactivation is usually referred to the
homotropic cooperation, in differentiating from the heterotropic cooperation that involves two (or more) different
Fig. (3). Homotropic activation in standard biochemical plots. A, Michaelis-Menten plots; B, Eadie-Hofstee plots.
Both plots would elicit the potential cooperation. However, homotropic cooperation would be more evidently shown by Eadie-Hofstee plots,
which therefore should be selected for the detection of atypical kinetics, particularly for autoactivation.
Enzyme Kinetics for Clinically Relevant CYP Inhibition
Current Drug Metabolism, 2005, Vol. 6, No. 3
247
ligands. Again, the phenomenon could be simply interpreted
by applying the model with two different substrate-binding
sites, as demonstrated in Eq. 15 [37].
prediction of clinical DDI, the goal of this review. Therefore,
atypical CYP kinetics beyond the aforementioned will not be
discussed further.
V = (Vmax2/(Km1*Km2) + Vmax1/(Km1*S))/(1/(Km1*Km2) +
1/(Km1*S) + 1/S2)
15
The bodies of evidence on atypical CYP kinetics, in
general, are substantial in vitro, however, very limited in
vivo, and if so, almost exclusively from experimental
animals [53, 54]. Atypical kinetics is often concentration
dependent, requiring a large concentration range, particularly
high concentrations of substrates and/or modulators to be
detected [33]. In this regard, although the heterotropic
cooperation between CYP3A4 substrates and endogenous
steroids is well acknowledged [55, 56], the extrapolation of
such in vitro findings to that in human bodies should be
cautious in that the concentrations and ranges of the drugs
and particularly the modulators such as the endogenous
steroids are much lower and narrower in vivo, compared to
those studied in vitro, respectively [55, 57]. Therefore, even
with the supporting ex vivo results [58, 59], atypical CYP
kinetics and the potential relevance to DDI in clinic, though
suggested by the recent study [42], are largely uncertain,
which should be further investigated.
The subscripts '1' and '2' of the parameters (Vmax and Km)
are denoted to the individual binding sites (or singly- or
doubly-ligated binding state).
It should be worthwhile to show the relationship between
Eq. 15 and Eq. 14, since both are derived from the same
model, one substrate with two binding sites. After being
carefully examined, Eq. 14 appears to be a special form of
Eq. 15 in which Vmax2 = 0 and Km2 = Ki. Therefore, Eq. 15
could be written as V = (Vmax/(Km*S))/(1/(Km*Ki) + 1/(Km*S)
+ 1/S2), thus readily converted to V = Vmax/(S/Ki+ 1 + Km/S)
or Eq. 14.
Eq. 15, though considered as a simplified version of
those for the two-site model, is still complex. Thus, if the
individual kinetic parameters of the models are determined,
the computational methods, such as SNLR, have to be
employed [37, 48]. Nevertheless, like the majority of atypical kinetics, sigmoidal kinetics may be common in vitro,
however uncertain in vivo [49].
(2) Substrate and Effector (Modulator)
Heterotropic cooperation, often detected for CYP3A4mediated reactions in vitro [50], involves two different
ligands, substrate S and activator B. The rate of biotransformation of the substrate is enhanced by the existence of
activator [46]. Though more than one potential mechanism
might be speculated, the putative two-binding site model
appears prevailing [37, 51]. The mathematical expressions
for heterotropic cooperation in two-binding site kinetic
models are usually complex, as exemplified by Eq. 16.
V = Vmax*(α*KB + β*B)/[(α*KB + B) + α*(KB + B)*(Km/S)]
16
Eq. 16 is directly converted from the previously reported
equation as follows [43].
V = Vmax*S/{Km*(1 + B/KB)/[1 + (β*B)/(α*KB)] + S*[1 +
B/(α*KB)]/[1 + (β*B)/(α*KB)]}
3. Irreversible CYP Inhibition or Mechanism-Based
Inactivation (MBI)
Three types of mechanism-based inactivation of CYP
were reported: (i) inhibitor covalently binds to enzyme
apoprotein, (ii) covalently binds to prosthetic heme, or (iii)
chelates to the heme or tightly binds to the apoprotein. The
third type of inhibition is, strictly speaking, still noncovalent
and pseudo-irreversible [60]. A CYP inhibition has to meet a
number of criteria to be classified as MBI [61], and some of
the important ones are briefly described: (i) Time-dependent
inactivation occurs at the condition supporting the enzyme
reactions, e.g., in the presence of NADPH for CYP-mediated
reactions. This is the key characteristic of MBI. (ii) Inactivation of CYP is practically irreversible, thus the removal of
inhibitor by dialysis or filtration would not recover the
enzyme activities. (iii) A conversion from inactivator to a
reactive intermediate during the enzyme catalyses should
take place, and thus be proposed. (iv) The rate of inactivation
typically follows the hyperbolic kinetic pattern, similar to MM kinetics in enzyme catalyses.
In Eq. 16, B is activator concentration, and KB the
binding constant for the activator. α is the relative alteration
of Km, and β the relative alteration of Vmax resulting from the
activator binding, while α < 1 and β > 1 would be expected
in heterotropic activation.
CYP mechanism-based inactivators (MBI, which is used
both for mechanism-based inactivation and the inactivator),
though not yet been fully delineated structurally, often
confer terminal unsaturated carbon atom, alkylamino, furan
or furano-pyridinyl group, or sulphur-containing aromatic
systems such as thiophene [60, 62-65].
The mathematical expressions would indeed become
more sophisticated for some of the heterotropic interactions
other than the activation, i.e. so-called differential kinetics
among substrate, effector and enzyme [45, 51]. Nonetheless,
despite the successes in interpreting the unusual CYP kinetic
behaviors, the existing two-binding site models for atypical
kinetics including heterotropic interactions and associated
mathematical expressions tend to be elusive and static, with
little or no concern of other possible origins, i.e., protein
conformation or motion, CYP catalytic mechanism, and thus
are still subject to further refinement [50, 52]. Moreover, due
to the empirical nature, these models tend to be retrospective
rather than prospective, thus with limited value for the
In contrast to atypical reversible CYP inhibitions, MBI
appears to occur both in vitro and in clinic [65-68]. All
human hepatic drug-metabolizing CYP members, including
the abundant forms such as CYP3A4, CYP2C9 and CYP1A2
[64, 69, 70], the important polymorphic forms, i.e., CYP2C19
and CYP2D6, and the minor members, i.e., CYP2A6,
CYP2B6 and CYP2E1, are subject to MBI [62, 65, 71-73].
However, MBI, if not intentionally sought, could be easily
overlooked, even in vitro. Reconstituted in vitro systems
may not always be apt for detecting time-dependent events
including MBI, due in part to the limited thermal stability of
CYP activities particularly during an extended assay period.
Moreover, MBI is the substrate, thus the competitive
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Zhang and Wong
inhibitor for the other substrates of the target enzyme. The
component of competitive inhibition may, if potent, obscure
the component of MBI. Fortunately, in accordance with the
explicit concept as described and schematically shown
(Scheme 3), the methods for detecting MBI are readily
available.
E+I
k1
k2
EI
k3
k4
[EI]
E-I
zero-order, while the degradation is considered to be of the
first-order, resulting in steady state,
-dE(t)/dt = R – Kdeg*Ess = 0, or R = Kdeg*Ess
Where R is rate of protein synthesis, Ess the concentration
of active enzyme in steady state, and Kdeg the overall rate
constant of protein degradation due to both the endogenous
(kE) and exogenous forces such as MBI (kI). kI could be
practically substituted with kobs determined in vitro, and the
equation could be revised to
R = (kE + kI)*Ess-I, or Ess-I = R/(kE + kI)
k5
In the absence of MBI (kI = 0),
Ess-0 = R/kE, thus
E+P
Ess-I/Ess-0 = [R/(kE + kI)]/(R/kE) = kE/(kE + kI)
Scheme 3. Mechanism-based Inactivation.
Where EI is the inactivator and enzyme at the initial noncovalent interaction stage. [EI] is metabolic intermediate
complex (MIC). E-I is the inactivated enzyme covalently
bound with the inactivator.
The rate of enzyme inactivation by MBI (-dE(t)/dt) could
be depicted as
-dE(t)/dt = kobs*E(t) = kinact*I*E(t)/(I + KI)
where kobs is the observed first order inactivation rate
constant. kinact is the maximal inactivation rate constant,
while KI irreversible inhibition constant that might be viewed
as the inactivator concentration at which the inactivation rate
is the half of the maximum. I is inactivator concentration. E(t)
is the concentration of active enzymes at some time t.
The relationship among k obs, KI, and kinact is illustrated in
Eq. 17 [74].
kobs = kinact*I/(I + KI)
17
kobs ≈ (kinact/KI)*I, if I << KI, as often expected in the clinical
setting.
KI and kinact, according to the kinetic model in Scheme 3,
could be described as
KI = (k2 + k3)*(k4 + k5)/[k1*(k3 + k4 + k5)]
KI ≈ (k2 + k3)/k1, if k4 + k5 >> k3
18
kinact = k3*k4/(k3 + k4 + k5)
kinact ≈ k3, if k4 >> k3 + k5
19
As KI and kinact, shown in Eqs. 18 & 19, resemble Km (Eq.
4) and kcat in M-M enzyme kinetics, respectively, it would be
reasonable to consider that MBI of CYP is the 'unproductive'
version of CYP catalysis. Therefore, k inact/KI, the potency of
MBI, might be simply viewed as the unproductive counterpart of kcat/Km, the catalytic efficiency in M-M kinetics. The
important MBI constants (kobs, KI, and kinact) could be estimated applying the plotting methods shown in Fig. (4) [62, 64].
In contrast to continuous decreases of active enzyme
quantities during MBI in vitro, the degradation of enzymes
comprising that caused by MBI in vivo, is compensated by
the protein synthesis, thus the equilibrium or steady state
between enzyme degradation and production could be
reached. Protein synthesis is usually considered to be of
where Ess-I and Ess-0 are the steady sate concentrations of
active enzymes in the presence and absence of MBI.
Obviously, the declined level of active enzymes due to
MBI in steady state would result in reduced overall metabolic capacity, thus altering the associated PK characteristics, as demonstrated by the elevation of the area under the
plasma-time-concentration curve (AUC) in a well-stirred
model with the assumptions of complete intestinal absorption and exclusive hepatic elimination (Eq. C).
CLint = (kcat/Km)*Ess, and AUCpo = Dosepo/(fu*CLint), thus
AUCpo = Dosepo*Km/(fu*kcat*Ess)
AUCpo-I/AUCpo-0 = [Dosepo*Km/( fu*kcat*Ess-I)]/[Dosepo*Km/(
fu*kcat*Ess-0)], or
AUCpo-I/AUCpo-0 = Ess-0/Ess-I = (kE + kI)/kE, or
AUCpo-I/AUCpo-0 = 1 + kI/kE
C
where AUCpo-I and AUCpo-0 are the AUCs of orally administered drugs in the presence and absence of MBI. As
demonstrated by Eq. C, the increase of AUC due to MBI
would largely depend on the ratio of MBI rate constant (kI)
to endogenous protein degradation rate constant (kE). Both kI
and kE would be possibly estimated. kE in humans has been
suggested for a few CYP members including CYP3A4 [7579]. A kE of approximately 0.693/day (or 0.00048/min),
corresponding to a half-life ( t1/2) of 1 day (averaged from 0.5
to 2 days), might be projected for CYP3A4 degradation. [7578]. In addition, the concentration of human hepatic
CYP3A4 (Ess) was suggested to be about 5 nmol/g liver [79].
However, such data associated with CYP degradation in
humans were somewhat indirect, and the rate of protein
degradation is apparently conditional, i.e., increase during
MBI. Therefore, the existing literature information of CYP
degradation should be cautiously applied.
Nevertheless, MBI might be one of the major causes for
the clinical DDIs [80-82], which has been potentially
overlooked in the past [12].
B. In vitro-In vivo Correlation: A Practical Consideration
The applicability of the prediction of CYP-associated
DDI in clinic using in vitro approaches has been demonstrated to be appreciable in some cases, but challenging for
the others [3, 21, 83-85]. This is indeed not surprising since
Enzyme Kinetics for Clinically Relevant CYP Inhibition
Current Drug Metabolism, 2005, Vol. 6, No. 3
249
Fig. (4). Plots for kinetic characterization of CYP mechanism-based inactivation (MBI). A, for the estimation of kobs; B, for the determination
of kinact and KI.
It should be worth noting that enzyme inactivation is kinetically assumed in a standard hyperbolic manner. Therefore, the similarities
between MBI and M-M kinetics are apparent, as kobs, kinact, and KI in MBI appears the counterparts of V/E (V per unit of enzyme), kcat, and Km
in M-M kinetics, respectively.
CYP inhibition in vivo is governed by multiple factors, some
of which would not be easily envisioned or accurately
evaluated in vitro, i.e. CYP induction following the inhibition, or simultaneous and/or sequential metabolism in
different metabolic tissues. With the concerns of the in
vivo variables, a variety of empirical and physiologybased models for the prediction of PK alterations due to
CYP inhibition using in vitro data are emerging [12, 86, 87].
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Therefore, only a few crucial in vivo variables directly
affecting the predictability of in vitro data and the equations
associated with these variables are presented. In addition,
some factors, though potentially important, may also be
excluded in the following context, as either too intricate to
be rationalized and often evaluated on a case-by-case basis,
or deviated from the scope of this review, e.g. CYP
inhibitions by multiple inhibitory species including the
metabolites [88-90] or involvements of metabolism-associated proteins other than CYPs such as active transporters
[91, 92].
DDIs in clinic have been simply categorized into six
common patterns, based mainly on the types of CYP
interactions and the sequences of drug co-administration
[93]. Moreover, as have recently summarized by Levy and
his colleagues [2], both reversible and irreversible CYP
inhibitions occur in an inhibitor dose (concentration)-dependent manner, in the clinical setting. Therefore, to quantitatively predict the clinical DDIs using in vitro approaches,
though highly challenging, should be considered practically
achievable.
1. Multiple Enzymes In vivo
hyperbolic kinetic model with a fraction being competitively
inhibited by the concomitant. Thus, it does not appear
practically straightforward to ascertain the actual value of fm,
particularly in vivo, apparently limiting the applicability of
Rowland and Matin equation (Eq. D). Nevertheless, this
equation has been, though rather infrequently, applied for in
vitro-in vivo correlation of CYP inhibition, and proven of
value, especially for competitive inhibition in a retrospective
manner, as demonstrated by the clinical study of the effect of
sulphaphenazole on tolbutamide metabolism [94, 95].
If the metabolic enzymes responsible for the drug
biotransformation would be both hepatic and extrahepatic,
the situation would become more complex. The extrahepatic
tissues particularly intestine, kidney and lung are known to
express quantifiable metabolic enzymes, including the ones
tissue-specifically expressed [96-98]. However, other than
the concerns for the intestinal CYP metabolism and/or
inhibition as part of the first-pass effect [99, 100], DDI, CYP
inhibition in particular, involving both hepatic and extrahepatic enzymes, has not been generally addressed due in
part to the complexity of the processes and the lack of
appropriate in vitro model systems.
Where fm is the fraction of the dose eliminated by the
enzyme being inhibited in the absence of inhibitor. I is the
inhibitor concentration, while Ki inhibition constant.
It is often desirable for the therapeutic agents to be
converted by several enzymes in humans. Such a multiple
enzymes-mediated metabolism tends to attenuate the ramification of enzyme inhibition, particularly in a competitive
manner, in clinic [101, 102]. On the other hand, metabolism,
in fact metabolic inhibition in the small intestines, could be
substantial for orally administered drugs, particularly the
substrates of the enzymes highly expressed in the enterocytes, i.e., CYP3A4 [103]. Oral co-administration with a
CYP3A4 inhibitor may consequently enhance oral bioavailability and the potential of DDI for the drugs primarily
metabolized by CYP3A4. Therefore, the enzyme suppression
in gut provides the common ground for both risks and
benefits, demonstrated by the severe elevation of DDI
potential due to the co-administration of mibefradil in clinic
[104] and the possible promise for the development of orally
available paclitaxel [105].
Eq. D could be transformed to
2. CYP Inactivation In vivo
AUCpo-i/AUCpo-0 = (1 + I/Ki)/(1 + I/Ki - fm*I/Ki)
As mentioned earlier, the inhibitory effect in vivo would
likely manifest if MBI is the major component of overall
enzyme inhibition [106, 107]. This could be illustrated by
the equation for the alteration of AUC (Eq. E) proposed by
Hall and his colleagues [12, 108]. In the model that Eq. E
was derived from, one of the responsible enzymes in the
liver, was affected by MBI.
The drugs, particularly those undergone both phase 1 and
2 enzymes-mediated, or even just CYPs-mediated conversions, are likely metabolized by several enzymes either
simultaneously or sequentially in vivo. Meanwhile, the
enzyme inhibition in vivo may involve one or a few of these
responsible enzymes. Therefore, the impact on the overall
metabolism in vivo due to CYP inhibition should be
weighted, as described by Rowland and Matin (Eq. D) [94],
with the assumptions of oral administration, linear (or firstorder) PK, complete absorption (or fa ≈ 1; fa, the fraction
absorbed from gut to the portal vein), and prevailing hepatic
metabolism with negligible non-hepatic clearance.
AUCpo-i/AUCpo-0 = 1/[fm/(1 + I/Ki) + 1 – fm]
D
Apparently, the AUC alteration by the enzyme inhibition,
as shown by the ratio, is largely controlled by the fraction of
the metabolism being inhibited (fm), the inhibitor concentration (I), and the inhibition potency (Ki). The determining
variable in Eq. D appears to be the inhibitor concentration I,
since fm might be viewed as a pseudo-constant under certain
circumstances, i.e., an oral drug with a fixed dose metabolized by a limited number of abundant CYP members.
However, it is important to mention that fm often varies along
with the drug concentrations (or drug doses) due to
potentially different kinetic characteristics, such as substrateenzyme binding affinities (Km) or catalytic efficiencies
(Kcat/Km), among the responsible enzymes, besides the
interindividual variations in enzyme activities and quantities.
Furthermore, due to the potential existence of atypical
kinetics, particularly for the CYP3A4-mediated [56], the
effect on drug metabolism by a concomitant would not
always be appropriately estimated using an assumed
AUCpo-I/AUCpo-0 = 1/{[fm/(1 + kI/kE)] + 1 – fm}
E
If both reversible inhibition and MBI occur
simultaneously, the ramification could be additive. The
changes of AUC due to reversible (usually the competitive)
and MBI might be postulated using Eq. F derived from Eqs.
D & E.
AUCpo-iI/AUCpo-0 = 1/{[fm-i/(1 + I/Ki)] + [fm-I/(1 + kI/kE)] + 1 –
fm-i – fm-I} or
AUCpo-iI/AUCpo-0 = 1/{[fm-i/(1 + I/Ki)] + [fm-I/(1 + kinact*I/((I +
KI)*kE)] + 1 – fm-i – fm-I}
Enzyme Kinetics for Clinically Relevant CYP Inhibition
If I << KI (and often I << Ki), as usually occurred in the
clinical setting,
AUCpo-iI/AUCpo-0 = 1/{[fm-i/(1 + I/Ki)] + [fm-I/(1 +
(kinact/kE)*I/KI)] + 1 – fm-i – fm-I}
F
AUCpo-iI is the AUCpo, in the presence of both the components of reversible and irreversible inhibition. fm-i is the
fraction of the dose being eliminated by the enzymes
inhibited by the competitive inhibitor, and fm-I is the fraction
of the dose being eliminated by the enzymes inactivated by
MBI, in the absence of inhibitors. The terms other than fm-i
and f m-I in Eq. F were previously described. However, Eq. F,
though might be theoretically sound, clearly needs to be
validated in the real case studies. When the competitive
inhibition and MBI occur for the same enzyme, fm-i and fm-I
should be identical. kE is again the rate of CYP degradation
(kdeg) under normal physiological conditions. The values of
kE, as mentioned earlier, are expected to be 0.5-2/day, or
0.00035-0.0014/min, for hepatic CYP3A4 in humans, and
possibly some of the other CYP members [77, 109]. kE thus
appears much smaller than kinact, as the latter, in the case of
MBI of CYP3A4, are usually in the range of 0.05-1/min
[12]. Therefore, in contrast to likely comparable Ki and KI,
often in the order of micromolar concentrations, the values
of kinact and kE tend to be markedly disparate, resulting in the
ratio of kinact/kE around or often higher than 100, thus the
much greater (kinact/kE)*I/KI than I/Ki in Eq. F. Therefore,
though competitive inhibition and MBI should, in principle,
take place simultaneously [110, 111], the change of AUCpo
due to both the inhibitory mechanisms would be primarily
attributed to MBI, the usual cases in the clinical setting. For
example, CYP3A4 inhibition by erythromycin was earlier
considered competitive, however, mechanism-based recently,
since the PK alteration associated with the enzyme inhibition
would not be reasonably explicated unless MBI is the
predominant, if not the sole, mechanism [106, 107]. MBI
appeared to occur more frequently than expected in the past,
particularly for the drugs that form reactive intermediates in
vitro such as tamoxifen, diltiazem and erythromycin [108,
111-114]. One of the potential indications for MBI, besides
the nonlinear PK, would be the prolonged effect after the
concurrent discontinuation or removal from the body.
3. Inhibitor Concentration In vivo
The concentration of an inhibitor within the active site of
enzyme, where DDI takes place, dictates the inhibitory
effect, regardless of the inhibitory mechanism. However,
such a concentration has been often assumed as the one in
the systemic circulation. Besides the apparently higher
exposure level of the cells in the gut wall during the oral
administration of drugs, the intracellular drug concentration
in the metabolic tissues could be quite different from the
blood concentration, particularly if active cellular uptake or
secretion is involved [115, 116]. The difference between the
drug concentration in the tissues and that in the blood could
be depicted by tissue-to-plasma (or tissue-to-blood) concentration ratio (Kp). For instance, high Kp values for azithromycin, a macrolide antibiotic, were suggested in humans,
while determined in rats to be in the range from 40 to 80 in
several tissues, including liver [117]. There are many
controlling factors for Kp, mostly associated with the
physiochemical properties of the drugs and the interactions
Current Drug Metabolism, 2005, Vol. 6, No. 3
251
between the drugs and the host cells [25, 118]. Apparently,
Kp of human tissues is usually unavailable and unlikely
generalized for structurally diversified therapeutic agents.
Therefore, in the absence of direct implication, i.e. the
involvement of active cellular uptake or efflux in metabolic
tissues, the concentration available to the liver metabolic
enzymes might have to be simply assumed as the one in the
circulation.
However, the concentrations in the circulation and that in
the metabolic organs, even without the involvement of active
cellular processes, are unlikely identical, which could be in
part elucidated by the model proposed by Ito and his
colleagues. (Eq. G) [119].
Iin = I + ka*Dose*fa/Qh
G
Where Iin is the inhibitor concentration at the inlet of
liver (or the hepatic artery), while I is the inhibitor plasma
concentration after an oral administration. ka is the
absorption rate constant, and fa, the fraction absorbed from
gut to the portal vein. Qh is the hepatic blood flow. If the
unbound fraction of inhibitor in the blood (fu) is known, the
equation could be expressed as
Iin, u = (I + ka*Dose*fa/Qh)*fu
H
Where Iin, u is the unbound fraction of Iin. ka, fa, and Qh are
assumed to be 0.1 min-1, 1 (completely absorbed), and 1610
ml/min, respectively. In this model, the blood-to-plasma
concentration ratio (RB) is assumed to be 1, and the inhibitor
concentration available to the enzyme is presumed to be the
one in the blood entering the liver (Iin or Iin, u). One of the
utilities of the model is the prediction of clinical CYP
inhibition-associated DDI, as Iin, u/Ki (or Iin/Ki), higher than
I/Ki, the widely accepted term for DDI prediction [6, 119],
would be relatively conservative, hence leads to a minimal
false-negative prediction.
The concentration available to the metabolic enzymes is
very difficult to determine and unlikely generalized because
the physiochemical properties of therapeutics are diverse,
and so are the interactions of these chemicals with the hosts
at the cellular and molecular level. Therefore, it may not be
fully appropriate to employ the intracellular concentration in
metabolic tissues, even if determined, as the drug
concentration available to the metabolic enzymes due to the
potential influences of cell physiology and functions such as
organelle sequestration and/or transportation. For example,
the metabolic enzymes are either cytosolic or intracellular
membrane-associated, while the majority of monooxidases
including CYPs and some of the conjugative enzymes such
as UDP-glucuronosyltransferases (UGTs) are endoplasmic
reticulum (ER)-bound. Moreover, the locations of the ERassociated metabolic enzymes (or their catalytic domains)
could be distinctive, i.e., the cytosolic CYP versus the
lumenal UGT active domains [120]. It has been suggested
that the ER lumenal catalytic domains would be less
accessible for their substrates/co-substrates/inhibitors, as
supported by the well-known activity latency of UGTs [121].
Therefore, enzymes at different intracellular locations, such
as CYPs and UGTs, may interact with drugs at different
effective concentrations in vivo.
It would be worthwhile to mention that the drug
concentration in the in vitro metabolic systems, particularly
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Zhang and Wong
that reconstituted without cellular matrices and functions,
might not represent the enzyme systems in vivo.
4. Non-Specific Binding
As one of many determinants for the drug effective
concentration, the non-specific binding to proteins and lipids
has been known for over 40 years [122], and often viewed as
the variable to be taken into account for the prediction of
DDI [123-125]. Interestingly, the effectiveness of considering non-specific binding in enzyme assays has been
suggested depending on the drug physiochemical properties,
thus the considerations of protein binding appeared helpful
for the acidic, while fortuitous for the basic agents for the in
vitro-in vivo correlation [126]. Moreover, the effect of nonspecific binding is thought to be concentration-dependent
[124, 127], principally in a hyperbolic saturation manner
(Eq. I) [124]:
fu = Kd/(B + Kd)
I
where fu is the unbound fraction; Kd, dissociation constant;
and B, the concentration of binding component such as CYP
substrate or inhibitor. The effective concentration of the
substrates or inhibitors available for CYPs is generally
viewed as the unbound portion thus the fu*B being in steady
state. The non-specific bindings would thus exert impacts on
both biotransformation and enzyme inhibition [125, 127].
The apparent kinetic parameters determined in vitro are
clearly affected by the non-specific bindings and could be
rectified applying the fraction of free drugs (fu) if desired
[128, 129]. One such example is the estimation of Km or Ki
using the apparent value detected in vitro (Eqs. J & K).
Km = Kmapp *fu
Ki =
Kiapp *fu
J
K
where Km is Michaelis-Menten constant, and Kmapp the
apparent Km detected in vitro. Similarly, Ki is inhibition
constant, and Kiapp the apparent Ki detected in vitro.
It would thus be beneficial to understand the non-specific
bindings in vivo, particularly for the prediction of clinical
DDIs using in vitro data. The potential divergences among
the non-specific bindings of the concomitants may affect
DDI outcomes. For instance, the potential of CYP inhibition
because of the co-administration of a substrate of highly
non-specific binding with an inhibitor of the low binding
would be likely greater than the prediction using in vitro
inhibitory results, in which the non-specific binding is not
taken into account. Nevertheless, the relevance of nonspecific binding to the clinical DDI is also governed by other
determinants, particularly pharmacokinetics.
likely be limitedly affected by the hepatic flow for the orally
administered drugs, particularly those with substantial firstpass effect, while significantly for the intravenously (i.v.)
administered as illustrated by the following equations (Eqs.
L & M):
Clpo = Clint intestinal + Clint hepatic*fu
L
Cliv = Qh*Clint hepatic*fu/(Qh + Clint hepatic*fu)
M
Clpo is hepatic clearance of orally administered drugs,
during the process of first-pass in particular. Cliv is hepatic
clearance of i.v. administered drugs, which should also be
applicable for the orally administered drugs with negligible
presystemic elimination or already in systemic circulation. fu
is the unbound fraction of drug and Qh is hepatic blood flow
rate. Clint hepatic and Clint intestinal are the hepatic and intestinal
intrinsic clearance that could be estimated in vitro. These
intrinsic clearances should be viewed as the sums of the
intrinsic clearances of individual responsible enzymes in the
tissues.
Therefore, for an orally administered drug, the clearance
(Clpo) is likely governed both by intestinal and hepatic metabolism (Eq. L), thus the inhibition of the metabolic enzymes,
particularly the ones highly expressed, e.g. CYP3A4, in one
or both of these tissues, would directly suppress the clearance. Similarly, the likely reduction of clearance should also
be expected if the metabolism is mediated by multiple CYP
members, and the dose fraction metabolized by the enzymes
being inhibited in the absence of inhibitor is known. In
contrast, it may not be so straightforward to estimate the
impact on the clearance (Cliv) from the enzyme inhibition by
an i.v. concomitant, which is therefore elaborated as follows.
Eq. M could be expressed as
Cliv = Qh*Eh and Eh = 1/[1 + Qh/(Clint*fu)]
N
where Eh is hepatic extraction; Clint, intrinsic clearance by the
hepatic enzymes (or Clint hepatic).
If Cliv or Eh is high (e.g., Eh ≥ 0.8), Clint*fu >> Qh, thus Eq. N
becomes
Eh ≈ 1, and Eq. M becomes
Cliv ≈ Qh
O
Thus, hepatic clearance (Cliv) appears blood flow (Qh)dependent, however, metabolism (Clint)- and non-specific
binding (fu)-independent for the drugs with high hepatic
extraction (Eh).
If Cliv or Eh is low (e.g., Eh ≤ 0.2), Clint*fu << Qh, Eq. N
becomes
5. Pharmacokinetics
Eh ≈ Clint*fu/Qh, and Eq. M becomes
Largely because of the apparent disparities between close
and defined in vitro model systems and open and dynamic
human bodies, pharmacokinetics (PK)-related variables,
such as the methods of drug co-administration, would be
difficult to assess in vitro, thus create hurdles for clinical
DDI prediction. However, a few of PK variables may still be
incorporated into the scheme for in vitro-in vivo correlation.
Thus, hepatic clearance (Cliv) appears metabolism (Clint)and non-specific binding (fu)-dependent, however blood flow
(Qh)-independent for the drugs with low hepatic extraction
(Eh). Apparently, hepatic clearance would be controlled by
both metabolism and blood flow if the extraction is moderate
(0.3 ≤ Eh ≤ 0.7).
The routes of drug administration may influence the in
vivo outcome of the potential CYP inhibition, due in part to
the first-pass metabolism. The hepatic clearance (Clh) would
Cliv ≈ Clint*fu
P
Therefore, the potential scenarios of i.v. co-administration with the inhibitory concomitant might be expected as
follows with the assumption of constant hepatic blood flow:
Enzyme Kinetics for Clinically Relevant CYP Inhibition
(i) If the drug is mainly metabolized by single enzyme,
regardless of the catalytic efficiency of the enzyme, the
clearance (Cliv) would likely be minimally affected if the
drug is highly hepatic extracted, while markedly reduced if
the drug is weakly hepatic extracted in the presence of the
inhibitor. (ii) If the drug is metabolized by several enzymes
of high catalytic efficiency and the suppression of one of
these enzymes, particularly the meagerly expressed, would
not largely affect the overall hepatic extraction, the alteration
of hepatic clearance due to the enzyme inhibition by the
concurrent would unlikely be markedly elicited (Eq. O). (iii)
If the drug is metabolized by the enzymes of both high and
low catalytic efficiencies, the effect of the concurrent would
largely depend on the enzyme being inhibited. Apparently, if
the enzyme(s) of low efficiency is involved thus overall high
hepatic extraction unaffected, the reduction of clearance due
to enzyme inhibition is expected to be, if any, unsubstantial.
(iv) This may however not be the case if the enzyme(s)
of high catalytic efficiency, particularly the abundantly
expressed, is indeed suppressed. The inhibition of enzyme(s)
of high efficiency may lead to the overall hepatic extraction
from high to low, thus potentially switch the controlling
factor of hepatic clearance from blood flow to liver
metabolism. (v) Finally, if the drug would be metabolized by
several enzymes with low catalytic efficiency, hepatic
clearance, governed mainly by the intrinsic clearance of
responsible enzymes (Eq. P), would be likely affected by
enzyme inhibition if the dose fraction metabolized by the
enzyme being inhibited is substantial. These aforementioned
potential scenarios would also be projected for the clearance
of orally administered drugs already in systemic circulation.
The PK-related variables are numerous. Dosing sequence,
frequency and duration of co-administration, and drug
formulations including the racemic co-formulation, are just a
few examples [130-133]. DDI from a PK standard point is
generally beyond the scale of this paper, and should be
thoroughly presented elsewhere. Regardless, the amalgamation of PK-related factors serves as one of many determinants for the final outcome of CYP inhibition in clinic.
6. Others
(1) CYP up-regulation by the inhibitors or so-called autoinduction, sometimes regarded as the feedback of the
enzyme suppression, occurs in clinic, and is frequently
reported for the inducible drug-metabolizing CYP members,
such as CYP1A2 and CYP3A4 [93, 134, 135]. Apparently,
the clinical output of the combination of CYP inhibition and
induction is intricate, depending largely on the net upshot of
the inverse effects [135, 136]. Due to the transcriptional
activation of genes, CYP induction tends to be gradual.
Therefore, the temporal difference between the instantaneous
inhibition and the delay-responded induction, besides the
inducibility of the enzymes involved, would serve as one of
the important indications for detecting auto-induction in
clinic. In vitro, CYP induction at the protein level should be
assessed in the intact cells, preferably the primary culture of
human hepatocytes, for at least 2 days of exposure [137], in
contrast to CYP inhibition in the reconstituted system
containing one of possibly a variety of enzyme preparations
for at the most 2 hours of incubation. CYP inhibition and
induction, therefore, should be separately studied in vitro.
Current Drug Metabolism, 2005, Vol. 6, No. 3
253
Clinical DDI due to enzyme induction (or possibly the
combination of both induction and inhibition) might be
demonstrated by the concurrence of tamoxifen and Letrozole. Letrozole, a non-steroidal aromatase inhibitor, is
metabolized by CYP3A4 and CYP2A6 in humans [138].
While tamoxifen, an estrogen receptor antagonist widely
used for the treatment of hormone-dependent breast cancer,
is known to effectively inhibit CYP3A4 in vitro both in
reversible (Ki ~ 6-22 µM) and irreversible manner (KI ~ 0.2
µM and kinact ~ 0.04/min) [110]. The steady state plasma
concentrations of tamoxifen after conventional clinical doses
(20-40 mg/day) in patients were usually in the range from
0.25 to 1.1 µM, though could be as high as 3.6 µM [139].
Therefore, these in vitro and in vivo data in combination
suggested that tamoxifen might, particularly after an extended period of continuous dosing, reduce the hepatic clearance of other concurrent drugs that are mainly metabolized
by CYP3A4. Surprisingly, it was not the case for the
combination therapy of tamoxifen and Letrozole, as AUC of
Letrozole was indeed reduced by 38% as compared to that
detected in the mono-therapy of Letrozole, indicating the
induction of one or both of CYP3A4 and CYP2A6 by
tamoxifen [140].
(2) Interindividual variations in CYP-associated DDI are
drastic due to the divergences of genetic predisposition and
living environment [141]. Clearly, genetic makeup, exposure
background, health condition, and other factors such as race,
gender, age, body size and shape, etc. would potentially
influence the response to CYP inhibition for a given individual or possibly a sub-population [142]. Genetic polymorphism, the pivotal CYP genetic variation associated with drug
metabolism, was recognized as a risk factor for clinical DDI
and studied extensively [143-145]. Virtually all of the important drug-metabolizing CYP members are phenotypically
heterogeneous in population [146-148], the majority of
which could be attributed to the corresponding genetic bases
[149]. Among the polymorphic CYP forms, CYP2D6 and
CYP2C19 are particularly noticeable because of the clear
genetic origins, broad substrate spectra, and drastic phenotypic imprints resulting in poor (PM) and extensive metabolizers (EM) in the population [150-152]. The outcomes of
CYP inhibition involving the polymorphic members in clinic
are complex and highly variable for different individuals.
The risk of DDI would be difficult to predict for a given
individual without knowing CYP genetic makeup. Therefore,
it would not be desired, in principle, to pursue a new
chemical entity that is an inhibitor, particularly a MBI of the
polymorphic CYP2C19 or CYP2D6. CYP polymorphismassociated interindividual variability is crucial for clinical
DDI, and should be and has been solely discussed [141,
153].
(3) Some of diseases, particularly the chronic ones such
as chronic inflammation and a certain type of diabetes, have
been recently shown to modulate the expression of CYPs, to
potentially act as a variable for the clinical DDI via the
alteration of enzyme quantities or activities in the metabolic
tissues [154, 155]. CYP modulation by the diseases appears
bi-directional. Type II diabetes might be associated with the
up-regulation of hepatic CYP2E1 [155], while chronic
inflammation is speculated to down regulate the expression
of several CYP members via the LPS-activated signaling
254
Current Drug Metabolism, 2005, Vol. 6, No. 3
Zhang and Wong
pathways [156, 157]. However, the significance of diseases
on CYP regulation and CYP-associated DDI should be
further investigated, particularly in clinic.
clinical DDI. Besides the common competitive CYP inhibition, the mechanism-based inactivation may occur more
frequently than anticipated in the past, and is potentially one
of the key underlying mechanisms for DDIs in clinic. On the
other hand, atypical enzyme kinetics is still elusive with no
concrete support by structural details [172-174]. Thus, the
significance of atypical CYP kinetics and the value of
proposed associated kinetic models should be investigated in
clinic. In contrast to the rapid advance in CYP enzymology,
the prediction of CYP inhibition in clinic, though being
improved continuously, has not yet been generally appreciated, due in part to the uncertainty of CYP kinetic behaviors
including atypical kinetics in vivo, which potentially depend
on the substrates/inhibitors/effectors and their concentrations. The suitable kinetic model may therefore need to be
established based on which drug and drug combination is
being applied. Moreover, with the knowledge of CYP inhibition as the predominant DDI determinant, DDI associated
with other metabolism- and toxicity-related proteins, such as
UDP-glucuronosyltransferases (UGTs), P-glycoprotein (Pgp), and human ether-a-go-go related gene (hERG) potassium channel [175-180], should not be overlooked. UGT
and P-gp inhibition could be the potential causes, while the
inhibition of hERG channel is likely the severe consequence
of clinical DDI. Similar to CYPs, UGTs, P-gp and hERG are
membrane-bound, and promiscuous for the substrates/
inhibitors/ligands. Therefore, it is challenging to delineate
the interactions between these proteins and therapeutic
(4) Finally, assay condition is practically deemed the
most important prerequisite for all in vitro, including DDI
studies. The possible variations in the in vitro reaction
systems are present but are not limited to buffers/matrices,
co-factors/co-substrates, probe substrates, the concentration
(or concentration ranges) of the substrates and inhibitors (or
effectors), enzyme and protein quantities, vehicle or organic
solvent selection and quantities, and assay procedures. The
assay conditions, though being largely standardized, will be
continuously refined with the expansion of our knowledge,
and should be adjusted in accordance with the aims of the
studies. Nevertheless, the current consensuses on performing
CYP inhibition assays appear to be appropriate [6]. The
substrate concentration-dependent CYP form-specific
activities, one of the pivotal variables in DDI study in vitro,
is highlighted in Table 1. The appropriate experimental
condition and the criteria for the selection of probe substrates
in detail should be referred to the consensus papers with a
regulatory perspective and the review articles published
previously [4, 6-8].
SUMMARY AND OUTLOOK
In the article, we presented the enzyme kinetics for the
study of CYP inhibition with a focus on the relevance to
Table 1.
Substrate Concentration-Dependent CYP Form-Specific Activities
Human Drug-Metabolizing CYP
Substrate Probea,b
Phenacetin
S-Warfarin
O-DeEt
7-OH
Conc. (µM)
50
500
1A2
2C9
+
+
+
+
+
+
+
50
500
2C19
S-Mephenytoin
4'-OH
50
500
+
+
Bufuralol
1'-OH
5
50
500
+
+
Dextromethorphan
Chlorzoxazone
TST/MDZ
a
Reactionc
O-DeMe
6-OH
6β-OH/1'-OH
5
50
500
5
50
500
50
500
+
+
+
+
+
+
2D6
2E1
3A4/5
+
+
+
+
+
+
+
+
+
+
+
Recommended by FDA; TST, testosterone; MDZ, midazolam.
References: Phenacetin, [158, 159]; S-Warfarin, [160]; S-Mephenytoin, [161]; Bufuralol, [162, 163]; Dextromethorphan, [164, 165]; Chlorzoxazone, [166, 167]; Testosterone, [168,
169]; Midazolam, [170, 171].
c
O-DeEt, O-deethylation; O-DeMe, O-demethylation; OH, hydroxylation.
+, responsible enzyme.
b
Enzyme Kinetics for Clinically Relevant CYP Inhibition
agents at the molecular level, which will warrant future
endeavors to thoroughly understand thus reliably predict
clinical DDIs including both the CYP-associated and the
CYP-unrelated.
Current Drug Metabolism, 2005, Vol. 6, No. 3
[30]
[31]
[32]
ACKNOWLEDGEMENTS
We gratefully acknowledge Dr. E. Liang and Mr. R.
Pelletier for the helpful discussions.
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