Multiple Sequential Steps Involved in the Binding of Inhibitors to Cytochrome P450 3A4*

Cytochrome P450 (P450) 3A4 is an extensively studied human enzyme involved in the metabolism of >50% of drugs. The mechanism of the observed homotropic and heterotropic cooperativity in P450 3A4-catalyzed oxidations is not well understood, and together with the cooperative behavior, a detailed understanding of interaction of drug inhibitors with P450 3A4 is important in predicting clinical drug-drug interactions. The interactions of P450 3A4 with several structurally diverse inhibitors were investigated using both kinetic and thermodynamic approaches to resolve the steps involved in binding of these ligands. The results of pre-steady-state absorbance and fluorescence experiments demonstrate that inhibitor binding is clearly a multistep process, even more complex than the binding of substrates. Based on spectrophotometric equilibrium binding titrations as well as isothermal titration calorimetry experiments, the stoichiometry of binding appears to be 1:1 in the concentration ranges studied. Using a sequential-mixing stopped-flow approach, we were also able to show that the observed multiphasic binding kinetics is the result of sequential events as opposed to the existence of multiple enzyme populations in dynamic equilibrium that interact with ligands at different rates. We propose a three-step minimal model for inhibitor binding, developed with kinetic simulations, consistent with our previously reported model for the binding of substrates, although it is possible that even more steps are involved.

Cytochrome P450 (P450) 3A4 is an extensively studied human enzyme involved in the metabolism of >50% of drugs. The mechanism of the observed homotropic and heterotropic cooperativity in P450 3A4-catalyzed oxidations is not well understood, and together with the cooperative behavior, a detailed understanding of interaction of drug inhibitors with P450 3A4 is important in predicting clinical drug-drug interactions. The interactions of P450 3A4 with several structurally diverse inhibitors were investigated using both kinetic and thermodynamic approaches to resolve the steps involved in binding of these ligands. The results of pre-steady-state absorbance and fluorescence experiments demonstrate that inhibitor binding is clearly a multistep process, even more complex than the binding of substrates. Based on spectrophotometric equilibrium binding titrations as well as isothermal titration calorimetry experiments, the stoichiometry of binding appears to be 1:1 in the concentration ranges studied. Using a sequential-mixing stopped-flow approach, we were also able to show that the observed multiphasic binding kinetics is the result of sequential events as opposed to the existence of multiple enzyme populations in dynamic equilibrium that interact with ligands at different rates. We propose a three-step minimal model for inhibitor binding, developed with kinetic simulations, consistent with our previously reported model for the binding of substrates, although it is possible that even more steps are involved.
Cytochrome P450 (P450) 2 3A4 is one of the 57 human P450 enzymes (2) that catalyze mixed-function oxidation reactions (3). P450 3A4 is expressed mainly in the intestine (4) and liver (5), where it is the major P450 and is involved in the metabolism of Ͼ50% of marketed drugs (6,7). The capability of P450 3A4 to accommodate and oxidize a large number of structurally diverse drug molecules as well as endogenous substrates has made it an extensively studied enzyme (2, 8 -11).
Most of the studies on P450 3A4 aimed at understanding its mechanism are based on steady-state kinetic methods (2,12). These studies indicate that P450 3A4 displays homotropic and heterotropic cooperative behavior in a number of substrate oxidations (13)(14)(15)(16), providing a basis for some earlier observations made in microsomal systems (17,18). The unusual kinetic behavior is not unique to P450 3A4; P450 2C9 (19 -21), P450 1A2 (22,23), and P450 2B6 (24) also show such phenomena. Several models have been proposed to explain the cooperative behavior (12,25,26). Occupancy of the active site with multiple ligands has been discussed frequently (14,(27)(28)(29), although direct evidence is very limited (30). Another proposal is the presence of an effector site distinct from the active site (16), which may have some support from two recent crystal structures (9,31). Although the models may provide insight into mechanisms of P450-catalyzed oxidations, these are based mainly on steady-state kinetic experiments and do not directly provide information on the individual steps of the catalytic cycle. Our own focus has been on substrate binding by P450 3A4, the first step in the catalytic cycle (29), and several other laboratories have also examined certain aspects of substrate binding (32)(33)(34)(35)(36). The recent availability of x-ray crystal structures provides further information on the binding of ligands by P450 3A4 (9 -11, 31), although the multiplicity of observed sites raises additional questions (37,38).
Recently we utilized transient-state kinetic methods as well as equilibrium binding studies to study the steps involved in substrate binding by P450 3A4 and demonstrated that binding is a complex process involving multiple-sequential steps for five substrates, testosterone, midazolam, bromocriptine, flavone, and ␣-naphthoflavone (39). This complexity is in contrast with the simple single-step enzyme-ligand binding interactions commonly observed for other P450s (40,41). In the present work we extended our studies to the binding of inhibitors to P450 3A4 using the structurally diverse drug molecules ketoconazole, itraconazole, clotrimazole, and indinavir plus the synthetic peptide morphiceptin (YPFP-NH 2 ) ( Fig. 1) (29). Our transient kinetic experiments show that inhibitor binding by P450 3A4 is even more complex than substrate binding. Kinetic modeling yielded a minimal binding model consistent with our previous three-step model for substrate binding (39). Stoppedflow fluorescence studies using morphiceptin yielded evidence for this "silent" step, providing further confirmation for our previous observations with bromocriptine and ␣-naphthoflavone. Sequential-mixing stopped-flow experiments were used to eliminate an alternate multiple enzyme populations model (42)(43)(44)(45) in favor of sequential-step binding, and thus, we demonstrate the general applicability of our model (39) for binding of ligands by P450 3A4.

EXPERIMENTAL PROCEDURES
Chemicals-Indinavir was kindly provided by J. H. Lin (Merck). Itraconazole, clotrimazole, ketoconazole, and morphiceptin (the peptide YPFP-NH 2 ) were purchased from Sigma. Itraconazole and ketoconazole were used as racemates. Testosterone was obtained from Steraloids (Newport, RI). All other reagents and solvents were obtained from general commercial suppliers. All chemicals were used without further purification.
Enzymes-Recombinant P450 3A4 with a C-terminal His 5 tag (46) was expressed in Escherichia coli and purified as described previously (29).
Spectroscopy-An Aminco DW2a/OLIS or a Cary 14/OLIS spectrophotometer (On-Line Instrument Systems, Bogart, GA) was used to collect steady-state absorbance spectra. Most stopped-flow experiments were done with an OLIS RSM-1000 instrument using a 4 ϫ 20-mm cell for absorbance measurements and a 4 ϫ 4-mm cell for fluorescence measurements. Sequential mixing stopped-flow experiments were conducted using an SX-18MV stopped-flow instrument (Applied Photophysics, Leatherhead, UK) equipped with a 20-l observation cell (10-mm path length). For all sequential mixing experiments, a non-return valve was fitted before the inlet port on the stop valve, and the pressure-held option was selected during the data collection to minimize pressure artifacts.
Spectral Binding Titrations-Spectrophotometric equilibrium binding experiments were carried out by titrating P450 3A4 (1 M) with the ligand (at 23°C) in a total volume of 1.0 ml of 100 mM potassium phosphate buffer (pH 7.4). Final CH 3 OH concentrations were Յ2% (v/v). The reference cuvette, containing an equal concentration of enzyme in buffer, was titrated with an equal volume of the vehicle solvent. UV-visible spectra (350 -500 nm) were recorded after each addition, and the absorbance differences (at the wavelength maximum and minimum) were plotted against the added ligand concentrations. Spectral dissociation constants (K s , indicates a spectrally estimated dissociation constant) were estimated as described previously (39) using GraphPad Prism software (GraphPad software, San Diego, CA) or DynaFit (47) simulation software (Biokin, Pullman, WA). Because of the high affinities of the ligands (K s within 5-fold of the P450 concentration), a nonlinear regression analysis using a quadratic equation was applied to determine the K s for all the ligands reported in this study: [L]} 1/2 }, where A is the absorbance difference, B max is the maximum absorbance difference extrapolated to infinite ligand concentration, L is the ligand concentration, and E is the total enzyme concentration (A 0 is a coefficient in each analysis and not relevant here). In all cases reported in this study, the quadratic equation proved to result in more satisfactory fits compared with the hyperbolic equation (⌬A ϭ B max [L]/(K s ϩ [L])). With ketoconazole, the best fit was obtained with the Hill where n is a measure of cooperativity.
Single-mixing Stopped-flow Experiments-Binding kinetics of ligands to P450 3A4 was monitored at 23°C using the OLIS RSM-1000 stopped-flow instrument by observing the changes in heme Soret spectra as a function of time (in the absorbance mode) or the fluorescence quenching of ligands (in the fluorescence mode). One of the drive syringes contained purified P450 3A4, diluted to 2-6 M in 100 mM potassium phosphate buffer (pH 7.4). The second drive syringe contained the ligand solution (indinavir, dissolved in H 2 O, was diluted in buffer to the desired concentration, and the stock solutions of all other ligands, dissolved in CH 3 OH, were diluted in buffer to Յ2% (v/v) final CH 3 OH concentration). Immediately after mixing equal amounts (150 l) of reagent from both syringes, UVvisible spectra (350 -500 nm) were collected in the rapid-scanning mode with a 16 ϫ 1-mm scan disk, which is a component of the instrument and is used to acquire spectra rapidly. Depending on the data collection time, between 10 and 1000 scans s Ϫ1 were acquired. Time-resolved spectra were collected with at least five ligand concentrations for each ligand. Kinetic traces were extracted from the acquired spectra utilizing either ⌬A 390 or ⌬A 390 -A 418 (or ⌬A 390 -A 420 ) measurements and were analyzed using the manufacturer's software (OLIS), GraphPad Prism, or DynaFit.
In the fluorescence experiments, after mixing the contents of the drive syringes, emission spectra were collected as a function of time with a mid-plane photomultiplier accessory and using the 16 ϫ 1-mm scan disk. The excitation wavelength was 280 nm for morphiceptin. In general, an excitation monochromator slit of 1.24 mm was used, corresponding to an 8-nm bandpass. A 0.6-mm slit was used before the chamber housing the scan disk and mid-plane photomultiplier for the time-resolved scans. Time-resolved scans were analyzed and deconvoluted using the OLIS SVD global fitting software (48 -54). Alternatively, data were collected using a Ͼ285-nm long-pass filter in the single-wavelength mode. Generally, averages of the results of four to eight individual experiments were used in the subsequent data analyses, and S.E. indicate the goodness of the fit to the average of the multiple experiments.
Sequential-mixing Stopped-flow Experiments-In the sequential mixing experiments (done in the Applied Photophysics SX-18MV instrument), P450 3A4 (8 M, 110 l) was mixed with an equal volume of the first ligand, and the mixture was "aged" in the delay loop. After a predetermined amount of time, the contents of the delay loop were pushed into the mixing chamber using 90 l of 100 mM potassium phosphate buffer (pH 7.4) and combined with the second ligand (90 l).
The changes in the Soret spectrum were monitored as ⌬A 390 in the single-wavelength mode.
ITC-ITC titrations were carried out at 25°C using a VP-ITC instrument (MicroCal, Northampton, MA) as described previously (39). In a typical experiment, before the titration, P450 3A4 was dialyzed twice against 100 volumes of 100 mM potassium phosphate buffer (pH 7.4) at 4°C for 4 h. The clotrimazole solution (5 M in dialysis buffer) in the ITC cell was titrated with P450 3A4 (32 M) loaded into the ITC syringe. The first injection (2 l, omitted from analysis) was followed by 4 injections of 5 l and 23 injections of 10 l with 8-min intervals between injections. The cell contents were stirred at 450 rpm to provide immediate mixing. The thermal power (heat per unit time) required to keep the cell temperature constant was monitored with time. The peaks observed in the power versus time plots (thermograms, not shown) were integrated using the ORIGIN software (MicroCal). The heats of dilution were obtained from the saturating part of the thermograms and subtracted from each integrated peak. The total heat change was plotted versus the concentration of P450 added to give a titration curve (binding isotherm), expressed in units of kJ mol Ϫ1 .
Kinetic Modeling of Data-Kinetic binding data were fit to various proposed models using DynaFit software (47). Rate constants were estimated by globally fitting the raw kinetic data obtained at five different ligand concentrations to the proposed models. The initial ligand concentrations were allowed to float within 10% of the starting value in the system, and in most cases the concentration adjustment was Ͻ5%. Sample scripts and some of the pertinent results are included in the supplemental.

RESULTS
Spectral Equilibrium Binding Titrations-Spectrophotometric titrations were first carried out to estimate the binding affinities of various ligands to P450 3A4, and spectral dissociation constants (K s ) were obtained from the titration curves as described under "Experimental Procedures." The P450 3A4 inhibitors indinavir, clotrimazole, itraconazole, ketoconazole, and morphiceptin (the peptide YPFP-NH 2 ) all showed a "type II" shift in the heme Soret spectra ( Fig. 2A), typical of a ligand (nitrogen atom) coordinating to the heme iron (1, 3, 55, 56). Estimated K s values are summarized in Table 1. The amplitudes of the changes varied due to the specific interactions of the various inhibitors with the heme iron (Fig. 2).
All of the inhibitors except morphiceptin showed tight binding to P450 3A4 (Table 1), clotrimazole being the highest affinity ligand with an estimated K s of 30 nM. The results obtained for the azole inhibitors are consistent with the previously obtained inhibition potencies for these compounds (57,58). The titration plot obtained for ketoconazole binding displayed some sigmoidicity, and a fit to the Hill equation was more satisfactory compared with a hyperbolic (results not shown) or quadratic equation (which did not consider cooperative behavior) (Fig. 2B).
Binding Kinetic Experiments-The kinetics of binding of type II ligands to P450 3A4 were studied using stopped-flow absorbance by monitoring the changes in the heme Soret spectra over time. Spectra collected over time showed a decrease in absorbance at ϳ390 nm and an increase in absorbance at ϳ420 nm for all the ligands, consistent with coordination to the heme iron (Fig. 3A). Kinetic traces extracted at these wavelengths were used to describe the kinetics of ligand binding (Fig. 3B). In all cases, a single-exponential fit (results not shown) applied to the kinetic data (⌬A 390 -A 420 ) was not adequate to describe the binding kinetics, suggesting a complex multi-step binding event. Therefore, bi-exponential fitting was used in an attempt to describe the binding kinetics of these ligands with P450 3A4 (Fig. 4, A, C, E, and G). Although reasonable fits were obtained, visual inspection of the residuals plots (Fig. 4, A, C, E, and G, top panels) suggests that the binding events are probably even more complex than can be defined by a classical bi-exponential binding fit. This deviation from a bi-exponential fit became more apparent at increasing ligand concentrations. The data were also fit to a tri-exponential equation (Fig. 4, B, D, F, and H), resulting in more evenly distributed residuals plots (Fig. 4, B, D, F, and H, top panels).
The observed rates of binding in the two phases (k a and k b ), resulting from bi-exponential fits, showed that molecules we studied bind to P450 3A4 at apparently significantly different rates (Table 1). Two structurally similar azoles, itraconazole and ketoconazole, displayed the most rapid binding kinetics; clotrimazole, indinavir, and morphiceptin showed slower apparent binding rates. It is important to note that the observed kinetic behavior of binding was not directly correlated with the binding affinities estimated in the spectrophotometric equilibrium titration experiments (Table 1).
Fluorescence Quenching-Our previous work with type I ligands had demonstrated the existence of a rapid initial silent step in the binding mechanism, which does not alter the heme spectra but could be detected by monitoring ligand fluorescence quenching (39). In light of this earlier observation, we investigated the fluorescence quenching of type II ligands upon interaction with P450 3A4. Among the ligands, morphiceptin proved to be the most suitable ligand for kinetic fluorescence quenching experiments. The tyrosine moiety of morphiceptin was excited at 280 nm, and the changes in fluorescence intensity were monitored upon mixing with P450 3A4 in the stopped-flow apparatus (OLIS RSM-1000). No change was observed in the fluorescence emission intensity of morphiceptin after mixing with P450 3A4 when monitored using a stand-  ard Ͼ285-nm (long-pass) filter. Therefore, emission spectra were collected over time using a mid-plane photomultiplier tube accessory, and the emission spectra attributed to two fluorescent species were deconvoluted by analysis of acquired spectra with the global fitting option using SVD methods of the OLIS software (Fig. 5, A and B). In the best-fitting model, the emission intensity of one of the two species decreased at a firstorder rate of 46 s Ϫ1 , and the emission intensity of the second species increased at a first-order rate of 35 s Ϫ1 , essentially identical (Fig. 5C). The emission spectrum ( max 332 nm) of the decaying species suggests a tyrosine residue (attributed to morphiceptin), and the emission spectrum ( max 357 nm) of the growing species is typical of tryptophan (from P450 3A4). The residuals analysis (Fig. 5C, lower panel) was devoid of systematic error for the two-component fit, although we cannot rule out a more complex model. 3 Determination of Binding Stoichiometry-Based on our previous proposed model (39), the initial interaction between a ligand and P450 3A4 may occur at a peripheral site. After this initial interaction, either a second ligand molecule may bind close to the heme, resulting in the observed changes in the absorbance spectrum, or the same ligand molecule may dissociate from the peripheral site and move toward the heme. We have shown previously, at least in the case of bromocriptine, that the latter case is likely to be operative, as judged by the 1:1 binding stoichiometry observed in the studied concentration range using ITC (39). In this study the data from the P450 3A4 titrations with clotrimazole and itraconazole (Fig. 2, C and D) can be plotted to show a nearly 1:1 ligand:P450 stoichiometry, at least for the events observed by absorbance. We have used a similar approach to study the possibility of multiple ligand binding to P450 3A4 using ITC. Clotrimazole, the ligand with the smallest molecular volume (supplemental Fig. S1), was chosen for these studies. Details of the ITC experiment were as described previously (39) and in the "Experimental Procedures" of this article. A solution of clotrimazole (5 M) in the ITC cell was titrated to saturation with a high concentration (32 M) of P450 3A4, resulting in an exothermic heat change as frequently observed for ligand-enzyme interactions (1, 55, 59 -61). The total change in heat was shown to reach a plateau when the P450 concentration in the cell reached a concentration of ϳ5 M (Fig. 6). Although it is not possible to exclude binding of multiple ligands at significantly higher concentrations, this outcome suggests a 1:1 binding stoichiometry between clotrimazole and P450 3A4, at least in the concentration range studied.
Sequential-mixing Stopped-flow Experiments-One possible model proposed for ligand binding to P450 3A4 involves the existence of multiple enzyme populations in dynamic equilibrium (Scheme 1B) (1,(42)(43)(44)(45)62). In principle, multi-phasic kinetics could be the result of different rates of binding of a ligand to individual enzyme species. In our previous study we were able to eliminate this possibility in favor of sequential binding events (Scheme 1A) by demonstrating that all the steps of substrate binding must be completed for the P450 reduction to be stimulated at least in the case of bromocriptine. In the presence of the type II ligands, reduction experiments had to be carried out in the absence of CO because these nitrogenous ligands interact with the heme iron in a manner identical to CO binding, i.e. direct iron coordination. Therefore, CO binding to ferrous P450 can occur only after the displacement of the type II ligand from the heme iron, altering the observed reduction kinetics (i.e. the rate of formation of the Fe 2ϩ -CO complex is dominated by the rate of dissociation of the Fe 2ϩ -ligand complex). In the absence of CO, however, the absorbance changes due to P450 reduction overlapped with the concurrent absorbance changes due to the reduction of flavin from NADPH-P450 reductase (or heme from cytochrome b 5 ), making the monitoring of reduction kinetics via absorbance infeasible. 4 We also attempted to monitor the reduction kinetics in the presence of type II ligands via fluorescence or circular dichroism, but in both cases the signal changes were marginal, and it was not sufficient to monitor the reduction via stopped-flow kinetic methods.
These experimental issues led us to utilize sequential-mixing stopped-flow kinetics as an alternate approach to distinguish between a multiple enzyme populations model (Scheme 1B) versus a (3-step) sequential binding model (Scheme 1A). If the slow phase of binding observed in the stopped-flow absorbance experiments is due to the existence of a slow binding population of P450 3A4, then this population should be unoccupied and available for binding during the fast phase observed in the binding kinetics experiments. To test this hypothesis, we incubated P450 3A4 with indinavir for a given amount of time in the stopped-flow apparatus before mixing with testosterone, a significantly faster binding ligand also displaying biphasic binding kinetics (39). The times of (pre)mixing were selected to cover the fast and part of the slow phase of indinavir binding to detect any effects of occupancy on the binding of testosterone.
In the absence of indinavir, testosterone showed binding kinetics identical to that observed in the normal (2-syringe), single-mixing mode (see Fig. 9). When indinavir was introduced before mixing the enzyme with testosterone, the amplitude of the signal change upon testosterone binding decreased, as expected. However, the attenuation in absorbance change was already obvious after 10 ms of preincubation of P450 3A4 with indinavir and did not show any appreciable time dependence (Fig. 7). If a slow-binding population of P450 3A4, exists it should be available for testosterone binding, which is significantly faster than indinavir binding and should decrease over time as indinavir molecules start to occupy this slow binding population during the "aging" period. Therefore, these results are in agreement with a model having sequential binding events rather than multiple enzyme populations. Furthermore, the decrease in signal change observed even after 10 ms provides additional evidence for a rapid silent binding event because, by 10 ms, spectrally detectable binding of a significant amount of indinavir to P450 3A4 is not observed (Fig. 4E).

DISCUSSION
Although cooperative behavior observed in P450 3A4-catalyzed oxidations has been extensively investigated (26,29,33,35,36) only a few studies have focused on the interactions of inhibitor molecules with P450 3A4 (65), which have significant practical importance in understanding drug-drug interactions.
In this work the interaction of inhibitors with P450 3A4 was investigated primarily with transient-state kinetic approaches. Absorbance stopped-flow experiments revealed that the interaction of inhibitors with P450 3A4 is a complex multistep process, as demonstrated by the requirement of tri-exponential fits to describe the kinetics of binding for all studied ligands (Fig. 4, B,  D, F, and H). The deviation from biexponential fits was more apparent at higher inhibitor concentrations (results not shown). For all of the inhibitors examined, the apparent rates (Table 1, Fig. 4) were too slow to be consistent with diffusion-limited enzyme interactions. The multiple steps observed in inhibitor binding may be explained with several possible models, which are considered here. The binding kinetic experiments, based on fluorescence and absorbance changes, suggest the involvement of at least three steps. In our analyses, we have focused on the minimal models (Scheme 1), although the actual situation may be even more complex.
One possibility is the three-step sequential binding model (Scheme 1A), in which the initial step does not cause a change in the heme Soret spectrum and is, hence, silent. Previously we provided evidence for a rapid, silent interaction for bromocriptine as well as ␣-naphthoflavone binding to P450 3A4 (silent in absorbance but detectable with fluorescence), possibly as a result of binding to a peripheral site of the enzyme (39). A similar "absorbance-silent" interaction has been reported previously in the steady-state binding of testosterone to P450 3A4 using EPR (33), time-resolved 2-p-toluidynlnaphthalene-6-sulfonate fluorescence studies (35) and steady-state absorbance measurements with monomeric P450 3A4 Nanodisc preparations (32). It is also important to note that recently published x-ray crystal structures of P450 3A4-ligand complexes (with progesterone and testosterone) provide further evidence for the existence of a possible peripheral site (9,31). We used fluorescence stopped-flow methods to probe for the presence of a possible absorbance-silent step in inhibitor binding to P450 3A4. For these studies we took advantage of the tyrosine moiety of the synthetic peptide morphiceptin and monitored the fluorescence quenching of tyrosine emission upon binding. SVD analysis of the emission spectra collected over time revealed the presence of two spectrally distinguishable species (Fig. 5, A and    MARCH 2, 2007 • VOLUME 282 • NUMBER 9 B). The emission intensity of the peak, attributed to the tyrosine, rapidly decreased with a rate of 46 s Ϫ1 accompanied by an increase in the emission intensity at ϳ350 nm with a comparable rate (35 s Ϫ1 ) (Fig. 5C), which is attributed to one or more of the four tryptophan residues of P450 3A4. 3 The rates obtained from the stopped-flow fluorescence experiments are significantly faster (2 orders of magnitude) than the (apparent) rate of the first phase observed for morphiceptin binding in the absorbance mode (Table 1, Fig. 4G), demonstrating that the initial step is indeed absorbance-silent and does not cause a change in the Soret spectrum of heme. This outcome was consistent with the three-step sequential binding model (Scheme 1A), and the global fitting of the ketoconazole and clotrimazole kinetic data to this model using DynaFit indicates the plausibility of the three-step sequential binding model (Figs. 8A and 9A).

P450 3A4 Binding Kinetics
When the initial silent step was omitted, reasonable fits can still be obtained (supplemental Fig. S3) based on the two-step model (Scheme 1E). The rate constant obtained for the first step of ketoconazole binding (k 1 ϭ 1.8 ϫ 10 6 M Ϫ1 s Ϫ1 ) in this model (Scheme 1E) is somewhat slower than what might be expected from a diffusion-controlled enzyme-ligand encounter in the absence of an ionic interaction (66) but is consistent with rate constants for substrate binding (ϳ10 6 M Ϫ1 s Ϫ1 ) we reported for P450 3A4 and other mammalian P450s (39,41,67). The rate constants of ϳ10 4 M Ϫ1 s Ϫ1 for binding of itraconazole and ketoconazole published recently by Pearson et al. (65) are too slow to be attributable to primary encounters, as clearly shown by the comparisons with the initial phase of the absorbance changes shown here for both of these inhibitors (Figs. 4, C and D, supplemental Fig. S2, and Table 1), which is not even considered the first kinetic event. The rates estimated by surface plasmon resonance measurements are ϳ10 2 -fold lower because of the immobilized nature of the protein and probably the response time of the instrument. Exactly what P450 transitions are reported in the plasmon resonance experiments is unknown, but they may be events associated with some of the latter steps (Scheme 1A, Fig. 4).
Another possible model to consider is the existence of multiple enzyme populations in dynamic equilibrium (Scheme 1B). Evidence in favor of this model for substrate binding has been presented previously by several laboratories (42)(43)(44)(45). DynaFit modeling of the binding kinetic data obtained for ketoconazole and clotrimazole using the multiple enzyme populations model (Scheme 1B) also resulted in satisfactory fits, at least for ketoconazole (Fig. 8B), which led us to further examine this model. In our previous work describing substrate binding to P450 3A4 (39), we were able to eliminate the possibility of the multiplepopulations model in favor of a sequential binding model using anaerobic reduction kinetics experiments. In the possibility that the steps involved in substrate binding are due to different enzyme populations interacting with the substrate at different rates, reduction of the (iron of the) substrate-bound population should be stimulated, because the reduction had already been shown to be stimulated by prior binding of the particular substrate. On the contrary, our results had indicated that all the steps of substrate binding have to be completed before the stimulation of the reduction (39).
A similar approach was attempted here in the case of inhibitors to distinguish between these two models (Schemes 1, A and B) but failed due to the overlapping absorbance signals (as described in detail under "Results"). 4 Therefore, we used sequential-mixing stopped-flow experiments as an alternate approach involving a type II inhibitor with apparent slow binding kinetics and a type I substrate with rapid binding kinetics (as judged by absorbance measurements). Thus, events involved in the binding of these two ligands are expected to be separated in time, facilitating the kinetic analysis. In the absence of indinavir, binding of testosterone displayed kinetic behavior identical to the previously reported results (39). However, when P450 3A4 was mixed with indinavir and aged for a finite amount of time before mixing with testosterone, there was a decrease in the amplitude of ⌬A 390 even after 10 ms of preincubation (Fig.  7). There was no significant further decrease in the amplitude of the absorbance change between 10 ms of aging time and the subsequent aging times. In the multiple-populations model, the slow binding enzyme population would be expected to be still available for testosterone binding after short aging times and then expected to decrease gradually as the aging time is increased. Therefore, the lack of change in the amplitude of ⌬A 390 after 10 ms of aging time is clearly in agreement with a sequential model and not the multiple-populations model. Furthermore, the significant decrease in ⌬A 390 even after 10 ms provides further evidence for the existence of a silent rapid interaction, because at this time point virtually all of P450 3A4 enzyme should be available for testosterone binding based on the kinetics of indinavir binding to P450 3A4 determined by absorbance stopped-flow experiments (Fig. 4, E and F).
Despite a paucity of direct evidence, e.g. Ref. 30, binding of multiple ligands to P450 3A4 has been discussed extensively as a possible explanation for the cooperative behavior observed for oxidation of various substrates (16,27,28,36,68,69). Recently, the report of a crystal structure of P450 3A4 with two ketoconazole molecules bound in the active site highlights the possibility of multiple inhibitor binding as well (11). Our spectrophotometric equilibrium titrations with indinavir (29), clotrimazole, itraconazole, and ketoconazole were consistent with tight binding of a single inhibitor molecule per P450 3A4 (Fig. 2, B, 2C, 2D) except for cooperativity observed in ketoconazole FIGURE 8. DynaFit modeling of ketoconazole binding kinetic data. A, fit to a three-step model. ⌬A 433 -A 405 data for ketoconazole binding (at 0.2, 0.4, 0.6, 0.8, and 1 M) were fit globally to a 3-step sequential binding model (Scheme 1A) using the simulation software DynaFit with the rate constants k 1 ϭ 1 ϫ 10 7 M Ϫ1 s Ϫ1 (kept constant during the fitting procedure. This rate constant was based on that estimated for bromocriptine-P450 3A4 interaction (4 ϫ 10 6 M Ϫ1 s Ϫ1 (39)), with the assumption that initial interaction should be at least as fast). Also, k Ϫ1 ϭ 36 s Ϫ1 , k 2 ϭ 14.7 s Ϫ1 , k Ϫ2 ϭ 3.5 s Ϫ1 , k 3 ϭ 2.2 s Ϫ1 , k Ϫ3 ϭ 0.1 s Ϫ1 . The extinction coefficients for the species LE and LE* were assumed to be equal. B, fit to the multiple enzyme populations model shown in Scheme 1B.
⌬A 433 -A 405 data for ketoconazole binding (as in A) were fit globally to a multiple enzyme populations model (Scheme 1B), and the rate constants k 1 ϭ 2.9 s Ϫ1 , k Ϫ1 ϭ 0.6 s Ϫ1 , k 2 ϭ 2.0 ϫ 10 6 M Ϫ1 s Ϫ1 , k Ϫ2 ϭ 0.03 s Ϫ1 , k 3 ϭ 6.4 ϫ 10 6 M Ϫ1 s Ϫ1 , and k Ϫ3 ϭ 0.001 s Ϫ1 were derived from the fitting. C, fit to a two-ligand simple binding model (Scheme 1C). ⌬A 433 -A 405 data for ketoconazole binding (as in A) were fit globally to a 2-step binding model (Scheme 1C) with the rate constants k 1 ϭ 1.5 ϫ 10 6 binding, which may be an indication of multiple ligand binding (Fig. 2B). However, these experiments are based on the changes in the heme Soret spectra and do not exclude the possibility of an inhibitor molecule bound to a peripheral site without disturbing the heme spectra. Therefore, we determined the stoichiometry of inhibitor binding with ITC experiments using clotrimazole, i.e. not depending on spectral changes to monitor inhibitor binding. The heat change observed upon ligand binding reached a plateau at approximately a 1:1 ligand-enzyme ratio, suggesting a binding stoichiometry of unity (Fig. 6). Modeling of kinetic data based on the three-step two-ligand sequential binding model (Scheme 1D) using DynaFit did not result in satisfactory fits (results not shown). The two-step sequential binding model (Scheme 1C), the other multiple ligand binding model we have considered, did not give satisfactory fits for clotrimazole (Fig. 9C). For ketoconazole the fits were reasonable (Fig. 8C), but the rate constant for the first step was slower than the second step, which is probably not plausible. Although it is not entirely possible to exclude multiple-ligand binding at concentrations comparable with the ones used in the crystallization experiments, 5 our transient-state kinetic as well as equilibrium binding studies are consistent with the presence of a single inhibitor molecule bound to P450 3A4 in the concentration ranges under investigation.
In summary, based on our absorbance and fluorescence stopped-flow experiments, we propose a three-step sequential binding model for inhibitor binding to P450 3A4 (Scheme 1A) that is consistent with our previous proposed model for substrate binding (39). Although inhibitor binding seems to be even more complex than substrate binding to P450 3A4, this model is shown to provide a sufficient and globally applicable minimal model to describe the interaction of ligands with P450 3A4. We employed (for the first time) sequential-mixing stopped-flow experiments, which proved to be a powerful tool for investigating inhibitor binding by P450 3A4. Our results provide further evidence in favor of a sequential step model (Scheme 1A) rather than the existence of multiple enzyme populations. Despite the crystallographic evidence for multiple inhibitor binding by P450 3A4 (11), we did not observe any direct evidence for presence of multiple inhibitors, except possibly with the cooperative binding behavior observed with ketoconazole (Fig. 2). It is likely that this difference is a consequence of the different concentration ranges used in our experiments and the crystallization experiments. 5 Finally, it is also interesting to note that different inhibitors interact with P450 3A4 with significantly different kinetic parameters (i.e. rate constants for steps following the initial encounter), although inhibition potency and equilibrium binding affinities of these inhibitors are comparable. These observations may contribute to a better understanding and prediction of some of the observed drugdrug interactions. In addition similar kinetic studies may be employed to understand ligand binding by other enzymes including P-glycoprotein, which has been shown to interact FIGURE 9. DynaFit modeling of clotrimazole binding kinetic data. A, fit to a three-step model. ⌬A 427 -A 391 data for clotrimazole binding at (0.5, 1, and 2.5 M) were fit globally to a 3-step sequential binding model (Scheme 1A) using the simulation software DynaFit with the rate constants k 1 ϭ 1 ϫ 10 7 M Ϫ1 s Ϫ1 (kept constant during the fitting procedure), k Ϫ1 ϭ 6 s Ϫ1 , k 2 ϭ 0.4 s Ϫ1 , k Ϫ2 ϭ 0.3 s Ϫ1 , k 3 ϭ 0.1 s Ϫ1 , k Ϫ3 ϭ 0.01 s Ϫ1 . The extinction coefficients for the species LE and LE* were assumed to be equal. B, fit to the multiple enzyme populations model shown in Scheme 1B. ⌬A 427 -A 391 data for clotrimazole binding (as in A) were fit globally to a multiple enzyme populations model (Scheme 1B), and the rate constants k 1 ϭ 4.6 s Ϫ1 , k Ϫ1 ϭ 1.1 s Ϫ1 , k 2 ϭ 3.6 ϫ 10 5 M Ϫ1 s Ϫ1 , k Ϫ2 ϭ 0.3 s Ϫ1 , k 3 ϭ 6.9 ϫ 10 4 M Ϫ1 s Ϫ1 , k Ϫ3 ϭ 0.003 s Ϫ1 were derived from the fitting. C, fit to a two-ligand simple binding model (Scheme 1C). ⌬A 427 -A 391 data for clotrimazole binding (as in A) were fit globally to a 2-step binding model (Scheme 1C) with the rate constants k 1 ϭ 8.1 ϫ 10 4 M Ϫ1 s Ϫ1 , k Ϫ1 ϭ 0.03 s Ϫ1 , k 2 ϭ 6.4 ϫ 10 3 M Ϫ1 s Ϫ1 , k Ϫ2 ϭ 0.001 s Ϫ1 .
with a diverse range of substrates most likely via a complex induced-fit mechanism (70 -74).