Atypical Cytochrome P450 Kinetics

Drugs R D 2006; 7 (6): 349-363REVIEW ARTICLE 1174-5886/06/0006-0349/$39.95/0

© 2006 Adis Data Information BV. All rights reserved.

Atypical Cytochrome P450 KineticsImplications for Drug Discovery

Timothy S. Tracy

Department of Experimental and Clinical Pharmacology, College of Pharmacy, University ofMinnesota, Minneapolis, Minnesota, USA

ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3491. Michaelis-Menten Kinetics and Intrinsic Clearance Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3502. Atypical Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3513. Homotropic Cooperativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

3.1 Sigmoidal (Auto-Activation) Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3523.2 Biphasic Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3543.3 Substrate Inhibition Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

4. Heterotropic Cooperativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3564.1 Activation Kinetics (Positive Cooperativity) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

5. Substrate-Dependent Inhibition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3586. Potential Artefactual Causes of Atypical Kinetic Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3597. In Vivo Examples of Atypical Enzyme Kinetics and Implications for Disease Therapy . . . . . . . . . . . . . 3608. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

The Michaelis-Menten model is commonly used to estimate a drug’s potentialAbstractin vivo hepatic clearance based on in vitro data obtained during drug discoveryand development. This paradigm assumes that the drug obeys ‘typical’ enzymekinetics and thus can be described by this model. However, it is increasingly beingrecognised that a number of drugs metabolised not only by the cytochrome P450enzymes but also by other enzymes and transporters can exhibit atypical kineticprofiles, and thus are not accurately modeled with the Michaelis-Menten model.Application of an incorrect model can then lead to mis-estimation of in vitrointrinsic clearance and thus affect the prediction of in vivo clearance. Thisreview discusses several types of atypical kinetic profiles that may be observed,including examples of homotropic cooperativity (i.e. sigmoidal kinetics, biphasickinetics and substrate inhibition kinetics) as well as heterotropic cooperativity (i.e.activation). Application of the incorrect kinetic model may profoundly affectestimations of intrinsic clearance. For example, incorrectly applying the Michael-is-Menten model to a kinetic profile exhibiting substrate inhibition kinetics willresult in an underestimation of Km (Michaelis-Menten constant) and Vmax(maximal velocity), whereas application of the Michaelis-Menten model to sig-moidal kinetic data typically results in an overestimation of Km and Vmax at thelower substrate concentrations that are typically therapeutically relevant. Onemust also be careful of potential artefactual causes of atypical kinetic profiles,such as enzyme activation by solvents, buffer dependent kinetic profiles, or

350 Tracy

altered kinetic parameter estimates due to nonspecific binding of the substrate toproteins. Despite a plethora of data on the effects of atypical kinetic profiles invitro, only modest effects have been noted in vivo (with the exception of substratedependent inhibition). Thus, the clinical relevance of these phenomena remainsinconclusive.

Clearance of drugs from the body occurs either amounts and the contribution of various routes ofby elimination of unchanged drug (usually via the metabolism, blood flow, in vivo plasma proteinkidneys or bile) or by metabolism, generally by the binding, etc. These calculations then factor into pre-gut and/or liver. Metabolism is carried out primarily dictions about the human pharmacokinetics of theby oxidative and/or conjugative enzymes such as the drug of interest.cytochrome P450 (CYP450) enzymes or the uridine Traditionally, estimation of CLint has been per-diphosphate-glucuronosyl transferases (UGT). In formed by applying the principles of Michaelis-the drug discovery process, significant effort is ex- Menten kinetics.[3,4] The rate of metabolism of apended in assessing the degree of metabolism of a drug is related to the substrate concentration by thenew chemical entity by the various enzymes and to parameter of CLint, where rate of metabolism =assess its propensity for exhibiting drug-drug inter- CLint • [S]. In this case, [S] is the substrate concen-actions. Through various in vitro methods, scientists tration and CLint is the intrinsic (unbound) clear-seek to estimate the rate at which a new chemical ance. If the drug’s metabolism can be described byentity will be metabolised by the enzymes and extra- Michaelis-Menten kinetics (figure 1), as is observedpolate the findings to predictions of expected in vivo with the 4’-hydroxylation of (S)-flurbiprofen,[5] thenpharmacokinetics. These in vitro-in vivo correla- the rate of metabolism can be estimated by thetions are critical to the drug discovery process in Michaelis-Menten equation (equation 1):that they are used as a critical measure of the ‘dru-gability’ of a compound with respect to its in vivopharmacokinetics; furthermore, they are also used to

Vmax • [S]Km + [S]

Rate of metabolism (v) =

formulate estimations of doses to be used in humans. (Eq. 1)This review discusses the parameter (intrinsic clear- where Vmax represents the maximal velocity ofance [CLint]) used as the basis for in vitro-in vivo the reaction and Km represents the concentration ofcorrelation estimates and how application of inaccu- substrate that produces half-maximal velocity.rate enzyme kinetic models can result in mis-estima-

Under conditions in which [S] is much lower thantion of CLint and the potential ramifications of suchKm, equation 1 reduces to produce equation 2:inaccuracies.

1. Michaelis-Menten Kinetics andVmax • [S]

KmCLint =

Intrinsic Clearance Calculations (Eq. 2)where CLint is the intrinsic (unbound) clearance.A fundamental tenet of in vitro-in vivo correla-Equation 2 is then related to determination of thetions is that the in vitro CLint is fundamentally

rate of metabolism (rearranged to CLint = rate ofequivalent to the in vivo CLint, presuming that themetabolism/[S]), such that equation 2 can be furtherrequisite assumptions are fulfilled. Using modelsreduced to equation 3:such as the ‘well-stirred’ model[1] or the ‘parallel

tube’ model,[2] one can then begin to scale the resultsCLint = Vmax/Kmobtained from in vitro data to predict in vivo hepatic

clearance by applying estimates of in vivo enzyme (Eq. 3)

© 2006 Adis Data Information BV. All rights reserved. Drugs R D 2006; 7 (6)

Atypical Cytochrome P450 Kinetics 351

proposed, based on kinetic observations, that manyof the phenomena of atypical kinetic profiles (bothhomotropic and heterotropic cooperativity; see be-low) might be the result of simultaneous substratemolecule binding within the active site: either twomolecules of the same substrate (homotropic) or asubstrate and an effector molecule (heterotropic).[6]

It should be noted that homotropic and heterotropiccooperativity have also been reported with the UGTenzymes and transporters.[14-23]

Recent experimental evidence has lent furthersupport to the dual molecule binding hypothesis.Hummel et al., using relaxation time T1 nuclearmagnetic resonance experiments that measure pro-

(S)-Flurbiprofen (μmol/L)

0 100 200 300 400

4'-H

ydro

xyflu

rbip

rofe

n fo

rmat

ion

(pm

ol/m

in/p

mol

P45

0)

10

8

6

4

2

0

Km = 19.4 μmol/LVmax = 9.6 min−1

CLint = 0.5 μL/min/pmol P450

Fig. 1. Example kinetic profile of a drug metabolism process exhib-iting classical Michaelis-Menten kinetics.[5] Data were fit to theMichaelis-Menten model (equation 1). The ratio of Vmax (maximalvelocity) to Km (Michaelis-Menten constant) [Vmax/Km] can be usedto estimate the intrinsic clearance (CLint) for this process (seeequation 3). ton to haem-iron distances of substrate molecules

within the CYP450 active site, were recently able toThrough these rearrangements and equalities, demonstrate that in CYP2C9 the presence of dap-

one can then use the commonly estimated Michae- sone altered the distance of flurbiprofen protons tolis-Menten parameters (Vmax and Km) to estimate in the haem-iron.[24] These investigators were able tovitro CLint. monitor concurrently the distances of dapsone pro-

Again, through use of these relationships, one tons from this same haem-iron, suggesting simulta-can then use in vitro data to estimate the in vivo neous binding of both substrate (flurbiprofen) andCLint and potentially the elimination rate of a new effector (dapsone). Employing deuterated substratechemical entity. Because of the extrapolations in- and measuring subsequent isotope effects, Rock andvolved, it becomes imperative that Km and Vmax be colleagues observed a change in the regioselectivityestimated accurately as any errors will be propagat- of CYP450BM3-mediated palmitate metabolismed during the scale-up procedure. Thus, assurance when co-incubated with laurate, together with athat the kinetics of this enzymatic process follows kinetic isotope effect that could only be explainedthe Michaelis-Menten model is crucial. In the subse- by simultaneous binding of both molecules withinquent sections, cases in which the Michaelis-Menten the active site.[25] Dabrowski and colleagues ob-model is not appropriate are discussed, along with served via fluorescence spectroscopy the formationdiagnostic plots for assessing model type and appli- of pyrene excimers when bound within the CYP3A4cations of these models. active site, a finding consistent with the simultane-

ous presence of multiple pyrene molecules in the2. Atypical Kinetics

active site.[26] However, it should be realised thatbinding of multiple substrate molecules may be sim-Examples of atypical kinetic profiles have beenply one mechanism in enzyme cooperativity. Koleyreported for quite some time, but it was not until theet al.[27-29] and Atkins et al.[30] have suggested thatlast decade that the phenomenon began to be moremultiple enzyme conformers may exist, and thuswidely reported and kinetic models and equations tomay also play a role in atypical kinetics (and subse-describe the findings were published.[6-12] Shou et al.quent multiplicity of apparent Km and Vmax valuesproposed in 1994 that the phenomenon of CYP450estimated from the cooperativity models). Further-activation (heterotropic cooperativity; see below)more, allosterism caused by binding of substrate ormay be due to simultaneous binding of two mole-effector at remote sites may also play a role incules (one substrate molecule and one effector mole-cooperativity. For example, a crystal structure ofcule) within the active site.[13] It was subsequently


352 Tracy

CYP3A4 has been reported that contains progester- characterised by a low Km and a low Vmax. Anotherone bound to a peripheral site[31] and, similarly, a molecule of the same substrate is then presumed toreported crystal structure of CYP2C8 has demon- bind at another region within the enzyme active sitestrated binding of palmitic acid to a peripheral and undergo metabolism; thus, its kinetics aresite.[32] The implication in both cases is that binding characterised by a high Km and high Vmax (relativeto this peripheral site could influence catalytic activ- to that exhibited at the other binding region). In theity and kinetics. Thus, although it has become gener- other scenario, the binding of this second substrateally accepted that the observance of atypical kinetic molecule does not result in metabolism via thisprofiles (at least in the CYP450 enzymes) is at least second site, but through cooperativity influences thein part related to the presence of multiple molecules kinetics of metabolism of the first binding substrate(homotropic or heterotropic) within the enzyme ac- molecule. Sigmoidal kinetics can be ‘fit’ with thetive site simultaneously, multiple factors may be Hill equation[33] (equation 4) but this provides limit-involved. Work is ongoing to ascertain the precise ed information about the kinetic parameter estimatesmechanism(s) by which this phenomenon alters sub- at both binding sites and provides no informationstrate metabolism. regarding the mechanism of the interaction at the

binding sites.3. Homotropic Cooperativity

Homotropic cooperativity can be both positiveVmax • [S]n

K' + [S]nv =

and negative in nature, with each resulting in differ-(Eq. 4)ent kinetic profiles. It has been hypothesised that

where ‘n’ is the Hill coefficient and can be usedpositive homotropic cooperativity occurs when theas an index of cooperativity where ‘n’ values >1 arepresence of a second substrate molecule within theassociated with positive cooperativity and values <1enzyme active site alters substrate affinity and/orwith negative cooperativity (values of ‘0’ imply nocatalytic efficiency of substrate turnover in a posi-cooperativity). Through the Hill equation, one ob-tive way. Examples of positive homotropic coopera-tains an estimate of Vmax as well as an estimate oftivity include sigmoidal (auto-activation) kineticsK’ (the dissociation constant). However, K’ is notand biphasic kinetics (see section 3.2). Negativeequivalent to Km (unless n = 1) since it is comprisedhomotropic cooperativity results in a decrease inof both Km and the interaction factors.[7] To obtain areaction velocity at certain substrate concentrationsmore complete picture of the kinetics at each of the(i.e. a convex velocity versus substrate plot) andbinding sites, a more sophisticated model and equa-results in substrate inhibition kinetics (see sectiontion is required. The use of equation 5[7] allows3.3).estimation of Km and Vmax for substrate binding atboth sites and thus is more informative.3.1 Sigmoidal (Auto-Activation) Kinetics

Observation of sigmoidal kinetic profiles has be-come more common in recent years as a result of theadvent of sensitive and precise analytical methodsthat allow identification of the non-linear portion of

Vmax (2) • [S]2

Km (1) • Km (2)

Vmax (1) • [S]

Km (1)[S]2

Km (1) • Km (2)[S]

Km (1)

+

+1 +v =

the velocity versus substrate curve at very low sub-(Eq. 5)strate concentrations. As stated above, this results

from either an increase in binding affinity or an Use of equation 5 allows for estimation of Km (1)increase in the overall rate of reaction. This type of and Vmax (1) and Km (2) and Vmax (2). As impliedkinetic profile may arise from at least two possible above, it is unclear whether Vmax (1) and Vmax (2)scenarios. In one case, a substrate molecule is pre- relate to substrate molecules binding at unique sitessumed to bind at one region within the active site within the enzyme active site or result from differ-



Dapsone (μmol/L)

0 100 200 300 400 500 600

N-H

ydro

daps

one

form

atio

n(p

mol

/min

/pm

ol P

450)

0.5

0.4

0.3

0.2

0.1

0.0

Sigmoidal modelKm (1) = 10 μmol/L, Vmax (1) = 0.02 min−1 Km (2) = 110 μmol/L, Vmax (2) = 0.58 min−1

CLint (1) = 0.002 μL/min/pmol P450CLint (2) = 0.005 μL/min/pmol P450

Michaelis-Menten modelKm = 163 μmol/L, Vmax = 0.63 min−1


Velocity/S

Vel

ocity

Fig. 2. Kinetic profile of a drug metabolism process exhibiting sigmoidal kinetics (homotropic cooperativity or autoactivation).[6] Data were fitto both a sigmoidal kinetics model (equation 5) and the Michaelis-Menten model (equation 1). Note the mis-estimation of Km (Michaelis-Menten constant) and Vmax (maximal velocity) when the Michaelis-Menten model is incorrectly applied to this profile. Inset depicts theEadie-Hofstee plot for these data, demonstrating the classic ‘hook’ behaviour indicative of sigmoidal kinetics. CLint (1) and CLint (2) refer tothe ratios of Vmax (1)/Km (1) and Vmax (2)/Km (2) determined by fitting to equation 5, and thus reflect the efficiency of the reaction in thosephases. Since the curve is not linear at any point, the actual intrinsic clearance (CLint) changes continuously with substrate concentration.

ences in metabolism at the primary site following Eadie-Hofstee plot. The inset of figure 2 depicts thecharacteristic ‘hooked’ Eadie-Hofstee plot obtainedcooperativity induced by binding of a second sub-when plotting data that is sigmoidal in nature. Thesestrate molecule that is not metabolised. In eitherdiagnostic plots can be invaluable for confirmingcase, the more data-points collected, the better thethat the appropriate kinetic equation has been ap-kinetic parameter estimates that will be obtained,plied in the non-linear regression fitting, particularlyand thus one should ensure collection of sufficientwhen the sigmoidicity may be subtle.data-points to adequately characterise the kinetic

In relation to calculating CLint in situations ofprofile and make accurate parameter estimations.sigmoidal kinetic profiles, underprediction of the inFigure 2 depicts a velocity versus [S] plot of the N-vivo situation is common. To address this issue,hydroxylation of dapsone[6] that is representative ofHouston and Kenworthy have proposed the concepta substrate-enzyme interaction that exhibits sigmoi-of a maximum clearance (CLmax), which providesdal kinetics; the data have been fit to both thean estimate of the highest clearance attained asMichaelis-Menten model (equation 1) and to thesubstrate concentration increases before any satura-more appropriate sigmoidal kinetics model (equa-tion of the enzyme active site occurs.[34] The equa-tion 5). It is clear from this example that applicationtion derived to estimate CLmax is listed below (equa-of the incorrect model results in mis-estimation oftion 6):CLint that can subsequently affect in vitro-in vivo

predictions. Visually, it may be difficult to correctlyidentify the appropriate kinetic model and thus non-linear regression fitting to multiple models may be

CLmax = where H = 1n

=Vmax • H

S50

(n−1)

n(n−1)

v[S]

(Eq. 6)tried. To assist in identification of the appropriatemodel for parameter estimation, it is frequently with n = Hill coefficient and S50 is the substratehelpful to employ diagnostic plots, such as the concentration producing half-maximal velocity.


354 Tracy

(S)-Naproxen (μmol/L)

0 500 1000 1500 2000

Des

met

hyln

apro

xen

form

atio

n(p

mol

/min

/pm

ol P

450)

12

10

8

6

4

2

0

Michaelis-Menten fitKm = 795 μmol/L, Vmax = 15.5 min−1


Biphasic fitKm = 125 μmol/L, Vmax (1) = 5.0 min−1 CLint (2) = 0.004 μL/min/pmol P450Vmax /Km = CLint = 0.04 μL/min/pmol P450

Velocity/S

Vel

ocity

Fig. 3. Kinetic profile of a drug metabolism process exhibiting a biphasic kinetic profile.[5] Data were fit to both the biphasic kinetics model(equation 7) and the Michaelis-Menten model (equation 1). Note the differences in estimation of Vmax (maximal velocity) and Km (Michaelis-Menten constant) depending on the model employed. Inset depicts the Eadie-Hofstee plot for these data, demonstrating that two processesare occurring simultaneously. CLint = intrinsic clearance.

Use of CLmax may be particularly useful in high tem. Obviously, biphasic profiles may occur in mul-throughput screening procedures where only a sin- ti-enzyme systems in which two enzymes producegle substrate concentration is employed and the con- the same metabolite, but at different rates and withcentration of substrate is substantially below KS (the different Km values. In the past, this type of phe-binding constant).[35] nomenon has also been attributed to ‘not reaching

high enough substrate concentrations to be saturat-ing’. Although this is true to some extent, the real3.2 Biphasic Kineticscause is the inability to reach saturating concentra-tions for the second phase of the process. SaturationBiphasic kinetic processes occur when a givenof the first phase is confounded by the increasingreaction, in this case metabolite formation, occurscontribution of the second phase.when cooperativity results in two ‘apparent’ phases

occurring at continuously differing net rates of total In the case of biphasic kinetics, it is hypothesisedmetabolism depending on the substrate concentra- that one substrate molecule binds to a region of thetion. In this type of profile, which is observed during enzyme that is a high-affinity–low-capacity site (i.e.the demethylation of (S)-naproxen,[5] at lower sub- low Km – low Vmax) and a second substrate mole-strate concentrations the reaction shows characteris- cule binds to a region that is a low-affinity but high-tics of exhibiting a hyperbolic profile (‘apparent’ capacity site (i.e. high Km – high Vmax). Clearly,first phase). However, since saturation never occurs, graphical representation of the data in an Eadie-the contribution of this first phase becomes a minor Hofstee plot (inset of figure 2) demonstrates thepart of the overall metabolism rate and the profile biphasic nature of the process. The more disparateeventually becomes linear (second ‘apparent’ phase) the Km and Vmax values, the greater the resulting[figure 3] as a result of the continuously changing biphasic profile will diverge from a typical hyper-rate of metabolism with [S]. For the purposes of this bolic plot. The low Km – low Vmax process isdiscussion, descriptions of biphasic kinetic profiles operational for the initial pseudo-hyperbolic portionare limited to those involving a single enzyme sys- of the kinetic profile and, conversely, the high Km –



high Vmax process then produces the linear portion of the profile) as well as the CLint (2) associated withof the profile. Thus, biphasic profiles actually exhib- the linear portion at high substrate concentrations.it two CLint values, one representing the linear phase Indirectly, these kinetic parameter estimates provideof the initial pseudo-hyperbolic portion of the pro- some information regarding the degree of coopera-file (i.e. CLint (1)) and a second (i.e. CLint (2)) repre- tivity because the greater the value for CLint (latersenting the linear portion of the profile exhibited at linear portion), the more cooperativity is occurringhigh substrate concentrations. At the non-linear por- and the more the values of apparent Km and appar-tions of the curve, CL is constantly changing with

ent Vmax will differ from the true values (in thesubstrate concentration. Regardless of whether one

absence of cooperativity). However, these parame-is able to saturate the second process (CLint (2)),ters provide little insight into the mechanism(s) ofsince it is probable that plasma (and likely liver)the cooperativity (i.e. whether metabolism is occur-concentrations of the drug will most likely approxi-ring from both binding sites). As can be seen in themate those seen at the initial portion of the profile, itresults of figure 3, application of the incorrect modelis imperative that the correct kinetic model be ap-in this case results in a 2-fold error in estimation ofplied to accurately estimate the apparent Km and

apparent Vmax for the initial pseudo-hyperbolic por- CLint (1) representing the initial portion of the pro-tion of the profile and the CLint for the second linear file, when compared with the results obtained usingphase. A kinetic equation has been derived[6] to equation 7. Again, an Eadie-Hofstee plot (figure 3describe this kind of biphasic kinetics and allows inset) can be quite informative as to whether moreestimation of the apparent Km, apparent Vmax and than one process appears to be operational. OneCLint (2); this is presented as equation 7. must use enough substrate concentrations to proper-

(Vmax (1) • [S] + (CLint (2)) • [S]2

(Km (1) + [S]) v =

(Eq. 7)

As can be seen in figure 3, application of differ-ent kinetic models can result in disparate estimationsof Vmax and Km. Use of the Michaelis-Mentenmodel (an inappropriate model for this dataset)tends to underestimate the data in the initial portionsof the profile, overestimate data from the middle ofthe kinetic profile and again underestimate points atthe high end of the profile. This mis-estimation ofthe predicted data-points through use of the Michae-lis-Menten equation results in an incorrect estima-tion of an apparent CLint (Vmax/Km) that is derivedfrom the apparent Km and apparent Vmax and asso-ciated with the initial pseudo-hyperbolic portion ofthe profile (not to be confused with the CLint (2)associated with the second linear portion of theprofile that is estimated with equation 7). Applica-tion of the biphasic kinetic equation (equation 7)results in an acceptable fit of the data and estimatesof the apparent Km and apparent Vmax (from whichan apparent CLint can be estimated for this portion

Piroxicam (μmol/L)

0 200 400 600 800 1000

5' H

ydro

xypi

roic

am fo

rmat

ion

(pm

ol/m

in/p

mol

P45

0)

0.16

0.10

0.12

0.14

0.08

0.06

0.04

0.02

0.00

Substrate inhibition fitKm = 30.5 μmol/L, Vmax = 0.18 min−1 Ki = 1277 μmol/LCLint = 0.006 mL/min/pmol P450

Michaelis-Menten fitKm = 14.5 μmol/L, Vmax = 0.14 min−1

CLint = 0.01 mL/min/pmol P450

Fig. 4. Kinetic profile of a drug metabolism process exhibiting asubstrate inhibition profile.[5] Data were fit to both a substrate inhibi-tion model (equation 8) and the Michaelis-Menten model (equation1). Note that the Km (Michaelis-Menten constant) and Vmax (maxi-mal velocity) of this process are both underestimated when theMichaelis-Menten model is incorrectly applied to this process.CLint = intrinsic clearance; Ki = the inhibition constant for the bind-ing of the second substrate molecule.


356 Tracy

ly characterise both phases of the profile and obtain these types of data, one can also use a more complexreliable estimates of all kinetic parameters. equation (equation 9).[36]

3.3 Substrate Inhibition Kinetics

A third type of kinetic profile encountered peri-odically when studying drug metabolism is that of

1S

v =

⎛⎜⎝

⎞⎟⎠

+ + +

+

1Ks

1Ks

β • [S]αKi Ks

[S]αKs Ki

1Ki

substrate inhibition kinetics. In this case, product (Eq. 9)formation continues until it reaches a maximum and where Ks ≈ Km, Ki is the dissociation constant ofthen with further increasing substrate concentrations substrate binding to the inhibitory site, α is thethe velocity of the reaction begins to decline (figure factor by which the dissociation (KS and Ki) of4), as is observed with hydroxylation of the NSAID substrate at both sites changes when a second sub-piroxicam.[5] As with the previous two types of strate is bound, and β is the factor by which Vmaxatypical kinetic profiles, substrate inhibition kinetics changes when a second substrate is bound. Becauseis believed to be due to simultaneous binding of two of the number of parameters being estimated insubstrate molecules in the enzyme active site. How- equation 9, modeling with this equation requires aever, in this case the binding of the second substrate substantial number of data-points to achieve reliablemolecule has an ‘inhibitory’ effect on substrate me- estimates.tabolism. It is still unclear whether binding of the Again, as one can see from figure 4, applicationadditional substrate molecule results in steric hin- of the wrong kinetic model can result in mis-estima-drance of substrate molecules reaching the primary tion of kinetic parameters, and thus CLint. In thebinding site or whether binding of this second mole- past, many investigators have applied the Michaelis-cule causes a conformational change in the enzyme Menten equation to these types of data in theiractive site such that binding at (and turnover from) entirety or have truncated the data at the greatestthe primary site is reduced. In either case the net velocity and ignored all descending points thereaf-result is a decrease in the overall rate of substrate ter. As seen in figure 4, when applying the standardmetabolism as substrate concentration is increased. Michaelis-Menten equation to all the data, one sys-

Observation of substrate inhibition kinetics is not tematically underestimates data at the apex anduncommon, but is frequently dismissed as assay overestimates data in the descending portion of theerror or improper modeling of the data. Kinetic profile. In the current example this results in anequations of varying complexity have been devel- underestimation of Vmax, underestimation of Kmoped for the modeling of substrate inhibition kinet- and an overestimation of CLint as evidenced by theics data. The simplest equation for evaluating these almost 2-fold difference in CLint value estimates. Intypes of data is that presented as equation 8.[6]

cases where the degree of inhibition and thus de-scent of the curve is greater, these errors in estima-tion of CLint will be even larger.

Vmax

Km[S]

v =

1 + + [S]Ki 4. Heterotropic Cooperativity

(Eq. 8)where Vmax and Km represent the usual Michae-

4.1 Activation Kineticslis-Menten parameters and Ki is the inhibition con-

(Positive Cooperativity)stant for the binding of the second substrate mole-cule. Again, one must be sure to collect enough data- New chemical entities are evaluated not only inpoints to accurately characterise the kinetic profile terms of their kinetic profiles and parameters butand provide reliable parameter estimates. In an at- also for their propensity to interact with other drugs.tempt to derive even more kinetic information from Thus, compounds undergoing drug discovery and



development are subjected to screening for interac- Because one must consider the kinetics of boththe probe substrate and the effector molecule, thetion against model probe substrates for various en-kinetic equations used to model heterotropic posi-zymes (e.g. the CYP450 isoforms). Typically, thistive cooperativity can be quite complex. Korzekwatype of screening evaluates the potential for a newand colleagues have proposed a model and equationchemical entity to inhibit metabolism by a specificfor heterotropic positive cooperativity that, albeitenzyme. However, it sometimes occurs that the me-still complex, makes reasonable assumptions (e.g.tabolism of the target drug (probe substrate) is actu-rapid equilibrium, product release is fast, only sub-ally increased when it is co-incubated with the effec-strate is metabolised) that minimise the number oftor drug. This phenomenon has been referred to asparameters estimated, and thus the number of data-heterotropic positive cooperativity (or activation)points required (equation 10).[6]

since it involves two different drugs (i.e. hetero-tropic) and the process results in greater metabolism(positive cooperativity) than when the probe is incu-bated alone with the enzyme.

The mechanism(s) resulting in positive hetero-tropic (and homotropic) cooperativity have not been

v = ⎛⎜⎝

⎞⎟⎠

1 + [B]αKB

Vmax • [S] ⎛⎜⎝

⎞⎟⎠

1 + [B]KB

⎛⎜⎝

⎞⎟⎠

1 +β[B]αKB

⎛⎜⎝

⎞⎟⎠

1 +

+ [S]Km β[B]αKB

fully elucidated and may be multifactorial. Again, (Eq. 10)the simultaneous presence of two drug molecules in From this equation, Vmax and Km can be estimat-the enzyme active site is thought to be operational. ed even though effector is present. Additionally,However, there are numerous possible explanations interaction factors including α, which is the effectfor why the ‘effector’ molecule alters the metabo- on Km due to the presence of effector (α < 1 islism of the probe or target substrate in a positive indicative of a decrease in Km and α > 1 is indica-manner. An increase in coupling and decrease inuncoupling of the CYP450 reaction cycle by theeffector molecule has been implicated as one poten-tial causative factor.[37] Binding of the effector mole-cule may also alter the conformation of the enzymeactive site such that the affinity of the target sub-strate is increased or the target substrate becomesoriented in a position more favourable for metabo-lism.[24] It may also be that binding of the effectormolecule increases the conversion of the CYP450 tothe high spin state or affects the putative protontransfer of water from binding as the sixth ligand ofthe haem to a threonine molecule located adjacent inthe active site. In theory, any combination or all ofthese potential mechanisms could be involved inpositive cooperativity depending on the enzyme, thetarget substrate and the effector molecule. For clari-fication, it should be noted that this phenomenon ofheterotropic positive cooperativity is different fromenzyme induction, which is related to an increase inenzyme expression that subsequently results in in-creased substrate turnover.

Km = 26.5 μmol/LVmax = 12.2 min−1 KB = 17.6 μmol/Lα = 0.3β = 1.7

25

20

10

15

5

0

10080

6040

20 0

50100

150

250300

200

4' H

ydro

xyflu

rbip

rofe

n fo

rmat

ion

(pm

ol/m

in/p

mol

P45

0)

Dapsone (μmol/L)

(S)-F

lurb

ipro

fen

(μm

ol/L

)

Fig. 5. Three-dimensional kinetic profile of a drug metabolism pro-cess exhibiting heteroactivation (heterotropic cooperativity) whentwo drugs are co-incubated.[38] Data were fit to a model for twobinding sites on an enzyme and the interaction of two differentsubstrates (equation 10). KB = binding constant of the effector. Km= Michaelis-Menten constant; Vmax = maximal velocity.


358 Tracy

tive of an increase in Km) and β, which is the effect The abovementioned model assumes that onlytwo substrate molecules are bound to the enzymeon Vmax due to the presence of effector (β < 1 isactive site simultaneously. However, it has beenindicative of a decrease in Vmax and β > 1 is indica-proposed that in some cases up to three differenttive of an increase in Vmax) are estimated with thedrug molecules can be bound in the enzyme activenet result being either inhibition or activation bysite simultaneously, most often involvingeffector, depending on the relative changes in theCYP3A4.[11,39] In the least kinetically complex situ-two parameters. Finally, estimates of the bindingation involving three molecules in the enzyme activeconstant (KB) for the effector drug (denoted as [B]site simultaneously, two molecules of the probein the model) are obtained. Figure 5 depicts ansubstrate bind in the enzyme active site simultane-example of heterotropic positive cooperativity in aously along with one molecule of the effector drug.

3-dimensional surface plot as occurs when dapsoneThis type of kinetic model can be described by

is co-incubated with (S)-flurbiprofen.[38] Figure 5 equation 11.[11]

shows that as the concentration of effector drugincreases, the production of metabolite also in-creases at a given substrate concentration. The fig-ure also shows that, with use of equation 10, oneobtains estimates of the Km and Vmax in the absence

vVmax

=

+ + +[S]

Ks

1 + + +2[S]

Ks

[S]2

αKs

[S][A]

αKs Ka

[S]2

αKs2

2 + +2[S][A]

αKs Ka

[S]2[A]

α Ks Ka

[S]2[A]

α Ks Ka2 2

2 2

[A]

Ka

of effector, a KB estimate for the effector molecule, (Eq. 11)an α value of 0.3 (suggesting that the highest con- In this case, S is the substrate, A is the effector,centration of effector [i.e. greatest effect measured] Ks is the binding affinity, α is the change in bindingreduces Km to 30% of control), and a β value of 1.7 affinity and Ka is the equilibrium dissociation con-(suggesting that the effector increased the Vmax by stant for the effector. Obviously, to obtain reasona-70% over control). From this information one can bly accurate estimates of these parameter values,then calculate the CLint in both the presence and one will need a well behaved and extensive dataset.absence of effector, obtaining an estimate of theoverall change caused by the presence of the effec- 5. Substrate-Dependent Inhibitiontor molecule. Multiplication of the Km and Vmax by

The aforementioned cases of atypical kineticsα and β, respectively, will allow determination ofhave dealt with two situations that impact upon thethe maximum and minimum Km and Vmax valuesdrug discovery process. In the first case, applicationfrom which the CLint (Vmax/Km) can be calculatedof the incorrect model to atypical kinetic data resultsat these extremes of effector concentration. Whenin a mis-estimation of CLint and thus can adversely

coupled with the expected in vivo concentrations ofaffect the accuracy of in vitro-in vivo correlations. In

substrate and effector, one can then assess the mini- the second case, upon drug-drug interaction screen-mum and maximum degrees to which the CLint ing, heteroactivation is noted with an unclear rela-would change because of effector. Since the results tionship to the in vivo situation (see section 7).are obtained at multiple effector concentrations, one However, a third case of atypical kinetics can pro-can also choose an individual effector concentration foundly affect the quality of predictions of potentialthat might be expected in vivo and the respective drug-drug interactions. In this case, the inhibitionvelocities of substrate metabolism observed from noted by a particular compound is different depend-the in vitro studies to estimate the apparent Km and ing on the target substrate studied. The principles ofVmax. These parameter estimates can then be used to competitive inhibition (the most common type ofcalculate the CLint at that specific effector concen- inhibition observed in drug-drug interactiontration and again compare with CLint in the absence screens) are based on the idea that the degree ofof effector. inhibition noted with a competitive inhibitor is inde-



pendent of the target substrate. However, several concentration available to interact with the enzyme)examples of substrate-dependent inhibition have re- is substantially lower than believed, resulting incently been noted. Kumar and colleagues recently overestimates of kinetic parameters such as Km, Ki,studied the inhibition of five different CYP2C9 etc. Specifically with respect to atypical kinetics,probe substrates in the presence of 28 different binding to microsomal protein has been shown toinhibitors. As much as a 100-fold difference in Ki result in an increase in the apparent S50 for a com-values was noted across the five substrates for a pound with no change in the Vmax or Hill coeffi-given inhibitor.[40] Similar differences in Ki values cients.[44] Nonspecific binding can be minimised byfor a given inhibitor with multiple substrates has using as low a protein concentration in the incuba-been noted for CYP3A4 as well.[41,42] This topic has tions as possible. It has been suggested that thisrecently been extensively reviewed by Wienkers, should be as low as 0.1–0.2 mg/mL of microsomaland its impact on drug discovery extensively dis- protein,[45] although even then substantial bindingcussed.[43] may occur, depending on the compound.

Although less of an issue in today’s environment6. Potential Artefactual Causes of of widespread liquid chromatography/mass spec-Atypical Kinetic Profiles trometry/mass spectrometry availability, insuffi-

cient analytical sensitivity to accurately andDuring the conduct of in vitro drug metabolism

reproducibly quantitate metabolite production at theexperiments, it is prudent to be alert for the possible

extreme low end of the substrate concentration-occurrence of atypical kinetics. However, the re-

velocity curve may result in erroneous assignmentsearcher must also be aware that there are alsoof the kinetic profile. This is most problematic in theseveral potential artefactual causes of atypical kinet-case of sigmoidal kinetics, where inadequate sensi-ic profiles that may lead to a misinterpretation of thetivity hinders determination of the less steep slopedata. Thus, extreme care must be taken to assure theduring the initial portion of the curve. One must alsovalidity of the results. The comments below willbe cautious when using multi-enzyme systems (e.g.address several of these potential sources of errorhuman liver microsomes) for kinetic characterisa-and how to minimise their impact on the kinetiction since multiple enzymes are present. This isprofiles observed.particularly problematic with respect to observa-One of the fundamental assumptions when con-tions of biphasic kinetics, since more than one en-ducting enzyme kinetic experiments is that the sub-zyme may be producing the metabolite. In this case,strate (and effector concentration if drug-drug inter-the kinetic phenomena observed are actually a hy-actions are being studied) remains constant through-brid of the concerted effects of multiple enzymesout the experiment (i.e. assumption of steady-stateand result in apparent kinetic constants.conditions). For substrates and effectors that exhibit

Finally, the kinetic profile observed may be af-substantial turnover, one must worry about sub-fected by incubation conditions and preparation.strate/effector depletion. This will result in constant-The choice of buffer salt to be used in the incubationly changing substrate/effector concentrationscan result in differing kinetic profiles[46] and thethroughout the experiment and invalidate the as-presence of certain organic solvents (particularly atsumption of steady state. Related to constantlyconcentrations >2%) have also been shown to acti-changing (and decreasing) drug concentrations arevate enzyme kinetic processes.[47,48] Thus, organicpotential sources of error when the actual substrate/solvent concentrations should be kept as low aseffector concentration is lower than believed. Thispossible and it may be prudent to examine the reac-can occur if either compound undergoes substantialtion in the presence of different buffer salts. Thenonspecific binding to the incubation matrix (i.e.inclusion (or exclusion) of cytochrome b5 can alsoprotein) or when the drug has very low solubility. In

these cases, the free drug concentration (i.e. the result in different kinetic profiles being observed.[49]


360 Tracy

Thus, one must pay particular attention to controls (Tracy et al., unpublished data), and finally to theand conditions when making the assignment of atyp- human in vivo situation (see below). Yet, someical kinetic phenomena. modest examples of atypical CYP450 kinetics have

been observed. Tang et al. demonstrated that co-administration of quinidine and diclofenac to7. In Vivo Examples of Atypicalmonkeys resulted in heteroactivation of diclofenacEnzyme Kinetics and Implications formetabolism such that steady-state plasma concentra-Disease Therapytions of diclofenac were reduced approximately

Atypical kinetic phenomena, such as homotropic 50%.[50] In the same study, the researchers alsoor heterotropic activation, substrate inhibition or conducted corollary in vitro experiments with mon-sigmoidal kinetics could in theory result in non- key liver microsomes and demonstrated that thelinear in vivo kinetics. For example, heteroactivation increased diclofenac metabolism was most likelycould result in increased clearance of the target drug due to activation of 5-hydroxydiclofenac formationand potential subtherapeutic effect. Substrate inhibi- by CYP3A enzymes. In a study of heterotropiction at higher substrate concentrations could result activation in humans, Hutzler and colleagues as-in unexpectedly high plasma concentrations with sessed the ability of dapsone to stimulatedosage increases due to non-linearity of the dose- flurbiprofen metabolism.[51] A minimal (~10%) in-concentration relationship. However, the observa- crease in flurbiprofen clearance was noted intion and identification of atypical kinetic phenome- humans following co-administration of these twona in vivo is somewhat inconclusive, perhaps be- drugs. Lastly, Egnell et al. conducted a meta-analy-cause of numerous confounding factors (e.g. in- sis of human clinical studies involving the co-ad-volvement of other enzymes or routes of ministration of carbamazepine and felbamate in anmetabolism, protein binding, etc.) that may limit the attempt to determine whether heteroactivation couldability to discern their occurrence. For example, use occur in vivo.[52] Their analysis suggested that felba-of single enzyme systems (or even microsomal sys- mate activated carbamazepine epoxidation resultingtems in which only CYP450 metabolism is studied) in increased carbamazepine clearance (~30%) asmay exhibit atypical kinetic profiles, but when this

well as increased production of the carbamazepinephenomenon is evaluated in vivo, competing path-

epoxide metabolite. In vitro experiments by theseways for either substrate or effector metabolism,

authors verified that co-incubation with felbamatesuch as glucuronidation, may reduce the concentra-

resulted in increased epoxidation of carbamazepinetion of effector or substrate to a range where atypical

while inhibiting the subsequent metabolism of thiskinetics or heteroactivation are not observed. Inmetabolite. Thus, observations of heterotropic acti-addition, these competing pathways may contributevation in vivo to date have been modest but suggestso much more greatly to the overall clearance of thethat these phenomena can be observed in humans.drug that changes in clearance due to atypical kinet-

Related to the issue of atypical kinetics and mul-ics comprise a small portion of the overall clearancetiple substrate binding, substrate-dependent drug-and thus are not readily discernible. In the case ofdrug interactions have also been noted in vivo. Inprotein binding, extensive binding to plasma pro-this case, two compounds that are substrates for theteins may again reduce effector (or substrate) con-same enzyme may interact but a third substrate maycentrations to levels that do not result in atypicalnot interact with one or both of the other two. Ankinetics or heteroactivation.example of this has been noted in vivo. IsradipineIn unpublished data from our laboratory, thehas been shown to have a pronounced effect onheteroactivation of flurbiprofen 4′-hydroxylation bythe pharmacokinetics of midazolam, but produceddapsone is progressively less pronounced as oneno effect on triazolam pharmacokinetics evenmoves from an expressed, single enzyme system tothough all three compounds are almost exclusivelyhuman liver microsomes, then to human hepatocytes



metabolised by CYP3A4.[53] Interestingly, 8. Conclusionmibefradil, another calcium channel antagonist, like

The occurrence of atypical kinetic profiles inisradipine, and also metabolised by CYP3A4, mark-

drug metabolism experiments can confound estima-edly affects triazolam pharmacokinetics, whereas tions of kinetic parameters and CLint that are usedisradipine does not. Although the exact mechanism for decision making with respect to drug discoveryfor these disparate results is unclear, one can imag- and drug development. Characterisation of the ap-ine a model such as that described above for simulta- propriate kinetic model and use of the associatedneous binding of multiple substrates within the kinetic equation can help in proper kinetic parameterCYP3A4 active site wherein two drugs that bind in estimation. Furthermore, when two compounds arethe same region of the active site will interact and evaluated for potential drug-drug interactions, oneresult in a drug interaction but no interaction will must be cognisant of the potential for positive heter-

otropic cooperativity or substrate-dependent inhibi-occur if their binding regions differ.[43]

tion that can make predictions of drug interactionIn an attempt to address the issue of homotropicpotential more difficult. Houston and Kenworthyand heterotropic cooperativity and their effects onhave also shown that one must also take into account

prediction of drug-drug interactions, an equationthe shape of the velocity curve when designing

based on rapid equilibrium/steady-state assumptionsinhibition screens and obtain a sufficient number of

has been derived (equation 12) using in vitro data to data-points at several concentrations of substrate.[34]

predict in vivo interactions: Furthermore, these same investigators have pro-posed using a fractional inhibition-inhibitor concen-tration plot that may provide evidence of multisiteeffects on inhibition of substrate metabolism. In vivoobservations of atypical kinetics have been modest,

AUCi

AUC=

⎛⎜⎝

⎞⎟⎠

1 +2[l]

Ki

1 +γ[l]δKi possibly suggesting that the primary effects of atypi-

cal kinetics occur during the drug discovery process(Eq. 12)and with in vitro-in vivo correlations.where AUCi is the area under the curve in the

presence of inhibitor, I is the in vivo inhibitor con- Acknowledgementscentration, γ represents the change in catalytic activ-

Supported in part by Public Health Service grantity, δ represents the change in binding affinity in the#GM 063215 from the National Institutes of Health.

presence of the inhibitor and Ki is derived from a The author has no conflicts of interest that are directlygeneric two-site model.[35] These authors suggest relevant to the content of this review.

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362 Tracy

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anion on cytochrome P450 2D6-mediated metabolism in vitro:Minneapolis, MN 55455, USA.the potential role of multiple oxygenating species. Arch Bio-

chem Biophys 2003; 417 (2): 165-75 E-mail: [email protected]


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Atypical Cytochrome P450 Kinetics