Allosteric Behavior in Cytochrome P450-Dependent in Vitro Drug

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Perspective Allosteric Behavior in Cytochrome P450-Dependent in Vitro Drug-Drug Interactions: A Prospective Based on Conformational Dynamics William M. Atkins,*,† Regina W. Wang,‡ and Anthony Y. H. Lu§ Department of Medicinal Chemistry, University of Washington, Seattle, Washington 98195, Department of Drug Metabolism, Merck Research Laboratories, Rahway, New Jersey 07065, and Laboratory for Cancer Research, College of Pharmacy, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854 Received October 5, 2000

The cytochrome P450s (P450s), collectively, contribute to the metabolism of nearly every drug to which we are exposed. As a result, these enzymes are studied intensely by an enormous number of academic and industrial labs (see refs 1-4 for reviews). However, our ability to quantitatively predict metabolism-based drug-drug interactions in P450 active sites is limited. A relevant characteristic of cytochrome P450-dependent metabolism that recently has received increased attention is the apparent “allosteric” behavior of some P450 isozyme/ substrate/effector combinations, where the term allosteric is used to refer to cases where nonhyperbolic substrate concentration versus velocity curves are obtained, or when kinetic parameters for a given substrate are altered by addition of a second ligand (5, 6). In fact, with increased awareness of the possibility of such behavior, it is reasonable to expect additional examples of allosterism in P450-dependent metabolism to be discovered. Therefore, it is critically important to establish at an early stage in this potential “trend” useful models for conceptualizing these processes, and to identify experimental parameters that will aid in quantitation. Homology models have been proposed for several liver microsomal cytochrome P450s based on the structural homology between the mammalian P450s and one or several crystallized bacterial P450s (7, 8). These models, along with site-directed mutagenesis studies, have proved to be useful tools for the investigation of structurefunction relationship of various P450s and the interactions between substrates and enzymes. For example, Harlow and Halpert (6) reported that the L211F/D214E double mutant of P450 3A4 displays an increased rate of testosterone and progesterone 6β-hydroxylation at low substrate concentrations (i.e., absence of homotropic cooperativity) and a decreased level of heterotropic stimulation elicited by R-naphthoflavone. These results indicate that Leu-211 and Asp-214 in P450 3A4 play an important role in eliciting both homotropic and heterotropic cooperativity in steroid hydroxylation catalyzed by * To whom correspondence should be addressed. Phone: (206) 6850379. Fax: (206) 685-3252. E-mail: [email protected]. † University of Washington. ‡ Merck Research Laboratories. § Rutgers, The State University of New Jersey.

this enzyme. Also, the recently reported X-ray structure of a chimeric mammalian P450 (9) provides optimism for the eventual determination of additional structures which yield directly insight into P450 allosterism. Still, experimentally based structural models for many mammalian cytochrome P450 isoforms are not likely to be available soon, and several fundamental questions concerning the properties of these enzymes remain unanswered. The goals of this overview are to evaluate several models already proposed for P450-dependent allosterism in the context of quantitative views of allosterism, and to suggest a general model that accommodates the greatest range of experimental observations. To achieve these goals, it is useful to consider the characteristics of more traditional allosteric systems, and to identify similarities or differences between the well-studied allosteric enzymes and the limited allosteric behavior documented so far for the P450s. The vast majority of allosteric proteins have been oligomeric, with distinct ligand binding sites on noncontiguous peptide subunits. In contrast, P450s are monomeric enzymes, and this feature alone should prompt both skepticism and excitement about the putative allosteric behavior of the P450s.

Well-Documented Allosteric Models The two limiting models of allosterism that traditionally are used to analyze experimental kinetic data are the Monod-Wyman-Changeux (MWC) model (10), or the “symmetry model”, and the Adair-Koshland-Nemethy-Filmer model (11), also known as the “sequential model”. It is not our intent to review these models; this has been done elegantly and exhaustively by many others (12-14). It is however useful to highlight the essential features of each. In the symmetry model (Figure 1), an allosteric enzyme contains multiple substrate binding sites on each of two or more conformers of the enzyme. Each of the sites on one conformer is identical to the other binding sites, due to a symmetry constraint that is an inherent assumption of the model. Each of the sites on the second conformer of the enzyme is also identical with the other sites on that conformer. Thus, for the case of two interconverting enzyme conformers,

10.1021/tx0002132 CCC: $20.00 © 2001 American Chemical Society Published on Web 03/08/2001

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exist for simple ligand binding in this model. However, negative homotropic interactions can occur at the level of Vmax effects, wherein binding of a substrate drives an enzyme to a form that has a Vmax lower than that of an alternative conformer favored at low substrate concentrations. This gives rise to substrate inhibition. The symmetry model is summarized schematically in Figure 1. The initial rate of product formation, ν, for a homotropic system that behaves as an MWC enzyme is shown in eq 1:

ν)

Figure 1. Traditional models of allosteric proteins. At the top left, the symmetry model (Monod-Wyman-Changeux) includes two protein conformers in equilibrium, the R state (E1) and the T state (E2). The binding sites on each conformer are identical to the other sites on that conformer. As a result of this symmetry constraint, the number of different KM values or Vmax values that describe the system is identical to the number of conformers. The “degree of cooperativity” is determined by the KM ratio for the R and T states, the Vmax ratio for the R and T states, the number of binding sites on each conformer, n, and the equilibrium constant that determines the relative populations of each conformer, L. At the top right, the sequential model (AdairKoshland-Nemethy-Filmer) allows each of the binding sites to exist in multiple conformers. The distribution of conformers is linked to the presence or absence of ligand. The number of different KM values or Vmax values required to describe the system is equal to the number of different conformers which cannot exceed the number of ligand binding sites. At the bottom is shown a nested allosteric system with two macrostates in equilibrium. Each macrostate can populate multiple conformers with addition of ligands, and the ligands determine the relative population of the different macrostates via differential affinity for them.

there are only two classes of binding sites for each ligand, corresponding to enzyme forms E1 and E2. Traditionally, the conformers are designated as “R” and “T” states. The basis for allosterism resides in the ability of substrates to bind with greater affinity to either the R state or the T state, thus favoring an increase in the relative concentration of this conformer and the fraction of the protein displaying the higher-affinity binding sites. The degree of cooperativity observed in substrate binding or turnover depends on the magnitude of the difference in binding parameters or turnover parameters for the two conformers [KM(R)/KM(T) and Vmax(R)/Vmax(T)], the number of binding sites (n), and the relative population of the two conformers in the absence of substrate, defined by the equilibrium constant L. Although the symmetry model provides an extremely useful context for conceptualizing many systems, and for predicting behavior of some allosteric enzymes, it is hampered by the fact that it cannot account for negative homotropic binding interactions. Ligand binding can never be used to drive a protein to a form with lower affinity for additional ligands of the same type, so negative homotropic effects cannot

VRn(1 + R)n-1 + VTLcRn(1 + cR)n-1 (1 + R)n-1 + L(1 + cR)n

(1)

where VT and VR are the Vmax values for the T and R states, respectively, KT and KR are the binding dissociation constants for the T and R states, respectively, R ) [S]/KR, n is the number of binding sites for each state, and c ) KR/KT. In the sequential allosteric model, a single conformer state is populated in the absence of ligand, but binding of each ligand molecule results in a conformational change concomitant with a change in the binding or kinetic parameters for the next ligand or substrate. The sequential model is more general, inasmuch as the symmetry constraint imposed in the Monod-WymanChangeux model is relaxed, and not all binding sites on an individual conformer are required to behave identically. This model, which incorporates the notion of “induced fit”, can easily account for negative homotropic effects, even for nonenzymatic ligand binding reactions. In the sequential model, conformer abundance is explicitly linked to ligand binding so that some conformers are not present in the absence of ligand and some are present only in the absence of ligand. Moreover, each binding site may have different properties in the presence of the substrate or ligand, as a result of each sequential addition generating a “new” conformer (K1 * K2 * Ki; Vmax1 * Vmax2 * Vmaxi). In the sequential model of allosterism, the observed kinetics depend on the differences in binding or turnover parameters for the different conformers. The sequential model also is depicted schematically in Figure 1. The most general and complex description of allosteric proteins systems would include all conformer states in all ligand states, and would be represented by a composite of the sequential and symmetry models shown, with each square in the 4 × 4 matrix occupied by an “allowed” state. The rate of product formation for a sequential system is shown in eq 2: n

ν)

∑ i)1

nVSiK1K2‚‚‚Ki[S]i

1 + Ki[S] + ‚‚‚ + (K1K2‚‚‚Kn[S]n)

(2)

where VSi is the Vmax value for the E‚Si species, K1, K2, and Ki are the dissociation constants for the first, second, and ith bound ligand, respectively, and n is the number of total binding sites. Obviously, the rate expressions for both the symmetry and sequential models are very complex. Of interest here, in light of the proposals we make below, is the concept of “nested allosterism”. In nested allosteric systems, there is a hierarchy of conformational changes, for example, the pH-dependent changes in both the R and T states of hemoglobin (15), which allows each

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of these states to exist as “subconformers”, and the oxygen-dependent change in the tertiary structure of subunits prior to the global quaternary R f T “switch” (16). In essence, nested allosterism occurs when cooperativity exists within a subset of binding sites within the entire ensemble. A nested system is depicted in Figure 1, with two manifolds in equilibrium, where each manifold behaves like the sequential model. There is no requirement for the number of binding sites within each manifold to be the same, as shown in Figure 1. Nested allosteric proteins are usually complex oligomeric structures, but nested allosteric behavior has also been observed for cooperative binding of ligands in inorganic complexes and nonprotein receptors in host-guest systems (17, 18), and the concept may be useful in considering the complex kinetics of P450s. The nested allosteric system incorporates fundamental properties of both the symmetry model and the sequential model. There may be more than one enzyme conformation with any specific number of ligands bound, as in the symmetry model (e.g., 1 E2‚S2 and 2E2‚S2). In addition, however, each macrocomplex may exist in different microconformations induced by each successive ligand as in the sequential model.

Conformational Change and Allosterism This brief summary of well-established allosteric models reveals that a common element of each is the central role of protein conformational changes in allosteric interactions between ligands, either heterotropic or homotropic. In fact, protein conformational changes are required to allow free energy coupling between ligand binding events or ligand binding and catalysis. We propose that this characteristic of allosteric systems should be considered while establishing early allosteric models for P450. The role of conformational dynamics in P450 allosterism is viable particularly in light of experimental data that indicate the existence of multiple conformations in the absence of drugs or substrates (19, 20). These studies have exploited flash photolysis methods for monitoring the kinetics of rebinding of CO to the heme cofactor of several P450 isozymes in the presence and absence of various substrates. For example, this approach has led to the suggestion that P450 1A2 and P450 3A4 exist in multiple conformations in the absence of substrate, and addition of a drug such as nifedipine or testosterone causes a change in the distribution of these conformations to alter the apparent kinetics of CO binding. Confirmation of the existence of equilibrium ensembles of P450 conformers by other methods is required, but even in the absence of additional data, the flash photolysis experiments provide a strong indication of the conformational diversity of individual P450 active sites and the presence of multiple persistent states in the absence of ligands. A recent study further supports the notion that protein conformational changes contribute to allosteric kinetics observed with P450s. Schrag and Wienkers (21) reported that the degree of allosterism observed kinetically and the regioselectivity of porphyrin adducts obtained with phenyldiazene were altered simply by the addition of Mg2+. It is unlikely that a divalent cation has significant binding affinity for a P450 active site, and the observed effects provide a compelling argument for conformation-dependent active site topology, linked to Mg2+ binding.

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Figure 2. Static two-substrate binding site model for the homotropic and heterotropic allosteric kinetics of P450s. In this example, S1 is a substrate that affords product P1, and may demonstrate homotropic cooperativity due to multiple binding events. S2 binds to the same active site as S1, and yields the product P2. The curved arrows indicate the enzyme species remaining after formation of P1 from S1 or P2 from S2.

Static Kinetic Models of P450 Unusual steady-state kinetics led Johnson et al. to consider the possibility that an allosteric site existed on P450 3A6 (22). Subsequently, Shou et al. (5) proposed allosteric interactions between phenanthrene and 7,8benzoflavone based on kinetic arguments, wherein each of the substrates altered the kinetic properties or regioselectivity of turnover for the second substrate without alteration of KM values. As pointed out by these authors, this observation requires that either (1) two ligands occupy the active site at the same time, both having access to the iron-oxo species responsible for substrate oxidation, or (2) the substrate and two “effectors” are bound simultaneously. The observation that binding of multiple substrates to a single conformation of an enzyme can produce allosteric effects is well-documented. Wang et al. (23) and Ueng et al. (24) documented homotropic and heterotropic interactions for P450 3A4-dependent metabolism of various combinations of substrates and effectors. Both groups acknowledged the scenario in which two ligands, either two substrates or a substrate and an effector, occupied the active site simultaneously. Each of these groups converged on a kinetic model that can account for the observed allosteric behavior of P450s, in which a single enzyme conformer bound two substrates or a substrate and an effector simultaneously at a single active site, wherein both molecules may have access to the oxygenating species, as depicted schematically in Figure 2, and as proposed by Shou et al. (5). A potential enigma perceived with this model was the observation that for some combinations of substrates, there was a lack of reciprocity in the effects of one substrate on the other. For example, it was observed that R-naphthoflavone metabolism was completely unaffected by aflatoxin, whereas aflatoxin efficiently inhibited the metabolism of R-naphthaflavone (24). Similarly, testosterone was found to have no affect on the metabolism of nifedipine, although the latter inhibits testosterone metabolism in a concentration-dependent manner (23). In fact, these observations are accommodated by the model in Figure 2, as long as Vmax for one of the substrates is allowed to remain unchanged regardless of the presence or absence of the second substrate. As discussed by these authors and others, the velocity of product formation in a system described by Figure 2 is given by eq 3:

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ν ) Vmax[S1]/{KM[(1 + [S2]/KS2)/(1 + β[S2]/RKS2)] + [S1][(1 + [S2]/RKS2)/(1 + [S2]/RKS2)]} (3) where S1 is the substrate and S2 is the effector, KS2 is the “KM” for the effector, and R and β are proportionality constants that scale the KM and Vmax, respectively, when the effector binds. R and β may be less than, greater than, or equal to 1. The essential point is that R and β can be used to “scale” the steady-state kinetic parameters relative to one another, but it is difficult to assign a physical or mechanistic basis to changes in R or β. A particularly thoughtful analysis of kinetic characteristics of P450s in the context of the “two-site binding model” described by Figure 2 and eq 3 was provided by Korzekwa et al. (25). These authors used a combination of simulated kinetic data obtained by varying parameters in the model of Figure 2, and fitting experimental data to the equation to obtain possible, although not unique, parameters that afford the observed kinetics. In this work, it was nicely demonstrated that a scheme such as Figure 2 can account for all of the possible homotropic interactions and heterotropic interactions, including nonreciprocity of effects, sigmoidal substrate kinetics, and nonhyperbolic nonsigmoidal kinetics, as observed for various P450-ligand combinations. Korzekwa et al. described a physically reasonable model in which a large, but static, active site can accommodate two molecules simultaneously. The presence of a second molecule, either the same type or a chemically distinct effector, alters the conformational space accessible to the substrate, and the substrate dynamics within the active site depend on whether a second molecule is present. The active site is sufficiently large to allow access of both molecules to the iron-oxo complex. Interestingly, these authors refer to the flash photolysis experiments described above (19, 20), but suggest that inclusion of ligand-induced conformational changes at the level of the protein active site in Figure 2 would make it hopelessly complex. This model has been used and extended by Shou et al. (26) to describe the metabolism of diazepam, with an emphasis on the notion that for a two-substrate binding site, the singly ligated species (E‚S and S‚E) may have properties different from each other’s and different from those of the doubly ligated species (E‚S‚S). Notably, there is no direct experimental evidence for simultaneous binding of two ligands at a single mammalian P450 active site, although Hosea et al. (27) have provided a compelling argument based on inhibition studies. Specifically, they found a peptide that clearly bound to the active site, as evidenced by formation of a low-spin complex, and which inhibited binding and turnover of several substrates that yield high-spin complexes. The spectrally measured KI values measured for this peptide varied with the substrate, providing additional support for the presence of an inhibitor and substrates at distinct subsites within a single “active site”. A striking feature of the discussions already presented in the literature is the apparent assumption that the multiple-substrate binding site model and the conformationally based model are mutually exclusive. In fact, a marriage of these models is likely to be the most physically reasonable situation, albeit a more complex case than either model individually.

Figure 3. Nested allosteric model for homotropic and heterotropic interactions. Two enzyme conformers (E1 and E2) are in equilibrium, defined by the equilibrium constant L ()[E2]/[E1]). For homotropic interactions, each conformer can bind two substrates at a single active site. The singly ligated and doubly ligated states have different kinetic properties, KM or Vmax. For heterotropic interactions, each active site can bind an effector, S2. In the most general case, S2 is also a substrate that can exhibit homotropic interactions. Thus, each conformer, E1 or E2, may bind one or two S1 molecules, one or two S2 molecules, or one of each. The scheme for homotropic interactions is a subset of the model for heterotropic interactions. Simulations based on these models yield kinetics consistent with all possible in vitro drug-drug interactions. This model may be envisioned as the joining of two of the schemes in Figure 2, where E1 and E2 each behave as a two-substrate binding site.

A Model Involving Nested Enzyme States At this point, we propose that it would be valuable to link the biophysical data concerning conformational relaxation kinetics and the biochemical kinetics obtained from turnover studies. We agree with Korzekwa et al. (25) that inclusion of multiple protein conformations will increase the complexity of the simplest working model (Figure 2), but in light of the flash photolysis data and the effect of divalent cations, the wealth of examples in which conformational changes are critical to allosteric behavior in other proteins, and the universally dynamic nature of proteins, we propose that the simplest model for conceptualizing P450-dependent allosteric kinetics must include more than one active site or protein conformation. From this starting point, and beginning with homotropic interactions followed by heterotropic interactions, we present kinetic simulations that include equilibrating conformers of P450s as proposed by Friedman et al., and explore the kinetic patterns that result when these conformational states are differently populated. If it is assumed that two P450 conformers are in equilibrium, and that each can bind two substrate molecules, the resulting scheme is depicted in Figure 3. In essence, this scheme consists of two conformers which can each behave according to the two-binding site model described by others (23-25), and which can account for the positive and negative homotropic and heterotropic interactions. Note that as L approaches 0 or ∞ the model collapses to the two-binding site model described by eq 3. The scheme is drawn in a manner to facilitate comparison to welldocumented allosteric models of Figure 1, and to the scheme that follows for heterotropic interactions. A critical point is the fact that substrate activation, manifested by sigmoidal substrate concentration versus veloc-

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Figure 4. Homotropic cooperativity resulting from multiplesubstrate binding and varying L. The homotropic model summarized in Figure 3 was used to simulate the rate of product formation for variable L values. Multiple conformers alone, in the absence of multiple-substrate binding, cannot result in homotropic cooperativity. With respect to Figure 3, capital K’s are equilibrium constants and italicized lower case k’s are rate constants: K1 ) 10 µM, K3 ) 1 µM, K5 ) 100 µM, K7 ) 100 µM, k1 ) 1 s-1, k3 ) 20 s-1, k5 ) 1 s-1, and k7 ) 1 s-1. L varied as indicated in the figure ()[E2]/[E1]).

ity curves, requires multiple binding sites even in the presence of multiple conformers, unless the rapid equilibrium binding constraint is removed, as described by Hosea et al. (27). Here, we employ the rapid equilibrium binding assumption. That is, multiple conformations alone are not sufficient to account for sigmoidal velocity versus substrate concentration curves. However, in cases where multiple-substrate binding occurs, an appropriate value of L may unmask allosteric properties that would not be readily observed with a single conformer. This is demonstrated with kinetic simulations in Figure 4 (Figure 4, L ) 10 vs L ) 0.1). In short, L contributes to the extent of observable cooperativity, as with “traditional” models. More interesting cases arise with heterotropic interactions. To link the biophysical experiments suggesting the presence of interconverting conformers with the simple two-site binding models previously utilized, and to limit the model to the smallest number of discrete states, we introduce the model shown in Figure 3. Comparison of Figures 3 and 1 reveals that the former is an example of nested allosterism in which distinct ligand-bound species with variable kinetic parameters are nested within two “manifolds” of equilibrating P450 conformers. Within each manifold, the kinetic parameters of the individual states may not necessarily result from conformation changes in active site structure, but may be due to differences in the conformational space sampled by substrates and/or ligands within an active site, as proposed by Korzekwa et al. (25). We have simulated several situations, including positive and negative heterotropic interactions, and cases where complex nonhyperbolic substrate saturation curves are obtained, wherein an effector may either activate turnover or inhibit turnover of a substrate, depending on their relative concentrations. We have chosen to summarize the simulations in plots of percent inhibition or activation versus effector concentration for several concentrations of substrate to facilitate comparison to results we have previously published (28), and to present a useful distinction between models. The same conclusions are obtained if plots of velocity versus substrate concentration are used with variable inhibitor concentrations. Most importantly, the equilibrium constant L is shown to be an additional

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source of modulation of the kinetic character of the system. The first example simulates the case observed for P450 3A4-dependent nifedipine-testosterone interactions or aflatoxin-7,8-benzoflavone interactions. One member of each of these pairs of ligands is a potent inhibitor of P450 3A4-dependent metabolism of the other, but no reciprocity is observed. For example, testosterone has no effect on the metabolism of nifedipine, but the latter is a potent inhibitor of testosterone hydroxylation. Here we use kinetic simulations that model this behavior to demonstrate that the equilibrium population of two P450 conformers may be, in principle, one of the parameters that controls the concentration dependence of these drug-drug interactions. In this example, S1 represents testosterone and S2 is nifedipine. Nifedipine has equal affinity for E1, E2, and E1‚S1, and this affinity is greater than the affinity of testosterone for E1. The E1‚S1 complex turns over 10 times faster than the E‚S1‚S2 complex; that is, nifedipine slows testosterone hydroxylation by E1. The values for the percent inhibition of turnover for each of two substrates are compared for multiple concentrations of each in Figure 5. Equilibrium and kinetic parameters, and concentration ranges, were chosen to approximate the experimentally observed results (28). The simulations were identical except for the value of L. For the results shown in the top panels of Figure 5, L was 1.0, whereas in the bottom panels, it was 0.1. For either case, there is no inhibition of nifedipine metabolism at any concentration of testosterone (left panels). For inhibition of testosterone hydroxylation, the percent inhibition is nearly identical when L ) 0.1 and 1.0 at very low or very high concentrations of testosterone. However, when the concentration of testosterone is intermediate (50 µM), the percent inhibition is modestly sensitive to changes in L. For the case when the equilibrium of conformers lies toward the manifold that includes E1 (L ) 0.1), the concentration dependence of testosterone has a steeper threshold of total inhibition. For example, at saturating concentrations of nifedipine, the extent of inhibition of testosterone turnover is nearly identical for testosterone concentrations of 50 and 100 µM, but significantly lower at 20 µM. When L ) 1.0, there is a more gradual change in percent inhibition in the testosterone concentration range of 20-100 µM. In short, the extent of inhibition by nifedipine depends on the relative contribution of the two manifolds (E1 vs E2) which in turn is more sensitive to testosterone concentration when L deviates from 1. An essential point is that the only parameter that varied for these simulations was L, which has a modest effect on the concentration dependence of these drug interactions. Notably, the effect of changing L is observed only at the higher concentrations of testosterone. The concentrations of ligand at which a change in L will lead to changes in inhibition depend on each of the other equilibrium constants. An equally important point is that the effect is modest, rather than dramatic, even for a 10-fold change in L. With 13 adjustable parameters and eight enzyme species which contribute to the observed substrate turnover rate during the steady state, it is not surprising that adjustment of a single parameter may have only a modest effect under some conditions. Additional heterotropic effects that have been experimentally observed highlight the complexity of these interactions, and a detailed comparison of the physical

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Figure 5. Heterotropic effects with a nested allosteric model. The simulations mimic the interactions between testosterone and nifedipine, wherein testosterone has no effect on nifedipine metabolism, but nifedipine is an inhibitor of testosterone hydroxylation (20). S1 is testosterone; S2 is nifedipine. The testosterone concentration dependence of the inhibition by nifedipine depends on the value of L. With respect to Figure 3, the parameters used for these simulations were as follows: K1 ) 20 µM, K2 ) 0.5 µM, K3 ) 0.5 µM, K4 ) 1 µM, K5 ) 0 (i.e., S1 does not bind to E2), K6 ) 0.5 µM, K7 not applicable, K8 ) 0 (i.e., S1 does not bind to the E2‚S2 complex), k1 ) 10 s-1, k2 ) k3 ) k4 ) k6 ) k8 ) 1 s-1, k5 ) k7 ) 0. L varies as indicated. A modest effect on the concentration dependence of the nifedipine-dependent inhibition is observed with varying L, as observed experimentally.

bases for similar kinetic results obtained with different models is instructive. A case explicitly considered by Korzekwa et al. (25) involves the concentration-dependent effects caused by effectors. For example, a fixed concentration of effector may activate substrate turnover at low substrate concentrations and inhibit substrate turnover at high substrate concentrations (not saturating). This behavior is readily accommodated by the static two-binding site model (Figure 2), and the magnitude of the effect depends on the relative turnover rates for E‚S1, E‚S1‚S2, and E‚S1‚S1, where S1 is the substrate and S2 is the effector. Notably, this behavior is also accommodated by the allosteric models described above that include conformational changes, so this situation does not appear to provide any experimentally addressable distinction between the models. In contrast, complex heterotropic effects observed upon changing the effector concentration at a fixed substrate concentration may provide some insight. At specific substrate concentrations, an effector may activate or inhibit turnover depending on the effector concentration. For example, it has been observed that for some concentrations of terfenadine, low concentrations of testosterone or midazolam activate P450 3A4-dependent terfenadine metabolism, but higher concentrations of testosterone or midazolam inhibit terfenadine oxidation (28). This situation can be explained by the static

two-binding site model. In Figure 2, at a fixed concentration of S1 (substrate), addition of low concentrations of S2 (effector) will lead to formation of E‚S2 and E‚S1‚S2. If E‚S1‚S2 oxidizes S1 more rapidly than E‚S1, and as long as the affinity of S2 for E is not too much greater than for E‚S1, then S2 will be an activator. As the concentration of S2 is increased, E‚S2‚S2 becomes the predominant species and inhibition is observed. A qualitative plot of this situation is depicted schematically in Figure 6. This behavior is also readily explained by the traditional allosteric models, including even the simple symmetry model. In fact, a classic example of this type of behavior is seen with effects of malate and N-(phosphonacetyl)-L-aspartate (PALA) on aspartate transcarbamoylase-dependent turnover (29, 30). Thus, an effectorinduced shift in the relative population of conformers (shift in L) can result in this behavior. However, the analogous situation, wherein an effector acts as an inhibitor at low concentrations and activator at high concentrations, is not allowed with the static twosite model. Using Figure 2 again, at low effector concentrations (S2) and a fixed S1 (substrate) concentration, the enzyme will be inhibited if E‚S2 predominates or if E‚S1‚S2 is less reactive than E‚S1. As the concentration of S2 increases, the level of E‚S2 or E‚S2‚S2 will increase at the expense of E‚S1, and the extent of inhibition will be greater, not less. Thus, in the static model with a

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Atkins et al.

Figure 6. Simulation of heterotropic interactions that afford minima in plots of relative enzyme activity vs effector concentration: (top left) L ) 0.5, (bottom left) L ) 2.0, (top right) steady-state concentration of E1‚S1‚S2 and E2‚S1‚S2 at variable effector concentrations of S2 for L ) 0.2, and (bottom right) steady-state concentration of E2‚S1‚S2 at variable concentrations of S2 for L ) 2.0. To simplify the simulation, the E1‚S1‚S1, E1‚S2‚S2, E2‚S1‚S1, and E2‚S2‚S2 states were omitted. In this model, P1 is derived only from E1‚S1 and E2‚S1‚S2, and the latter produces P1 at a faster rate. At low concentrations of S2, the combination of L < 1 and the higher affinity of S2 for E1‚S1 compared to E2 leads to increasing steady-state concentrations of the inhibitory complex E1‚S1‚ S2 as S2 the concentration increases. However, at higher concentrations of S2, the E2 manifold becomes increasingly populated, the steady-state concentration of the E1‚S1‚S2 species begins to decrease, and the E2‚S1‚S2 species becomes favored. The parameters were as follows: K1 ) 1 µM, K2 ) 100 µM, K3 ) 10 µM, K4 ) 10 µM, K5 ) 50 µM, K6 ) 50 µM, K7 ) 1 µM, K8 ) 1 µM, k1 ) 1 s-1, k2 ) 1 s-1, k3 ) 0, k4 ) 1 s-1, k5 ) 0, k6 ) 0, k7 ) 3 s-1, k8 ) 1 s-1, and L ) 0.5 or 2.0.

single E‚S1‚S2 state, an effector cannot be an inhibitor at low concentrations and an activator at high concentrations without allowing for states that bind more than two ligands, such as E‚S1‚S2‚S2. In other words, it is possible for allosteric sites on multiple enzyme forms (E1‚S1‚S2 and E2‚S1‚S2) to yield a minimum in the plot of relative enzyme activity versus effector concentration [S2]. A model with only a single E‚S1‚S2 state cannot have a minimum in such a plot because E‚S1‚S2 will be populated at lower concentrations of S2 than the E‚S2‚S2 will be populated. If E‚S1‚S2 is inhibited in its ability to produce the product of S1, compared to E‚S1 or E‚S1‚S1, then the additional S2 cannot drive the system to a more reactive state. In contrast, the nested allosteric model shown in Figure 3 does allow for such plots because it allows for two states with S1 and S2 bound, E1‚S1‚S2 and E2‚S1‚S2, with different kinetic characteristics. One of these states may be preferentially populated at low S2 (effector) concentrations and the other state preferred at high S2 concentrations, depending on the value of L. To demonstrate this behavior, we have used the nested allosteric model in Figure 3 to simulate the reaction velocity with variable S1 and S2 concentrations. For simplicity, we have not included the E1‚S1‚S1 and

E2‚S2‚S2 states, but their inclusion will not eliminate the possibility of the observed effect. The results of typical simulations are shown in Figure 6. The equilibrium constants and kinetic constants were chosen for convenience of simulation, and are not intended to accurately reflect the relevant parameters for any specific P450‚ ligand complexes. Rather, they are intended to demonstrate the behavior discussed above. As shown, plots of relative velocity versus S2 concentration that have welldefined “minima” are readily obtained. In addition to the rate of product formation, the steady-state concentrations of the enzyme-bound states (E1‚S1‚S2 and E2‚S1‚S2) were monitored and plotted versus the effector (S2) concentration. These results demonstrate that the relative concentrations of E1‚S1‚S2 versus E2‚S1‚S2 determine the concentration of S2 at which the minima occur in plots of relative activity versus S2 concentration. In the model we have constructed, in which the E2‚S1‚S2 species is more reactive, the minima in reaction velocity occur at the S2 concentration that affords the maximum steady-state concentration of E1‚S1‚S2. In principle, experimental data that indicate a change from inhibition to activation as the effector concentration is raised, at a fixed substrate concentration, may provide a kinetic basis

Perspective


for invoking multiple conformational states. Moreover, the simulations run with different L values demonstrate the role that the equilibrium between states plays in allowing the lower-affinity E1‚S1‚S2 state to predominate at low S2 concentrations, prior to S2 “shifting” the equilibrium toward the E2‚S1‚S2 state (Figure 6). Such minima in plots of relative activity versus effector concentration are not required by the nested allosteric model; however, they are possible, and if observed within experimental data, they should not be dismissed as an artifact. In principle, this behavior may occur also with spectrally monitored binding cooperativity. If the E1‚S1‚S2 and E2‚S1‚S2 states have different high-spin and low-spin fractions, then an effector may appear to inhibit ligand binding at low effector concentrations and promote ligand binding at high effector concentrations. Interestingly, the results of Hosea et al. (27), in which the binding isotherms for testosterone are presented at several inhibitory peptide concentrations, hint at such an effect, albeit a very modest one, at high testosterone concentrations. To the extent that indinavir mimics the inhibitory peptide described by Hosea et al. (27), their experimental data suggest that the E‚S2‚S2 complex (where S2 is the inhibitory peptide) is not populated, thus increasing the likelihood of observing a minimum in such plots of fraction protein bound, or relative reaction rate versus effector concentration. Also, we acknowledge that the behavior we describe here for heterotropic effects could be observed if two or more effectors can bind simultaneously with a substrate. It has been suggested that three ligands may bind simultaneously to P450 3A4 (6, 27). None of the simulations shown here are intended to accurately model any specific P450-dependent drug interactions or to predict specific kinetic parameters. In fact, we have not explicitly defined an exact solution for the rate equations relating the rate of product formation to the relevant parameters. The simulations are intended to demonstrate that traditional models of allosterism afford complex kinetics that mimic the experimentally observed interactions in P450-dependent processes. As pointed out for the static two-site model (25), fitting experimental data to any equation describing our model is likely to yield multiple solutions of equal statistical “goodness of fit”, and several combinations of parameters will appear to reproduce the observed experimental data, as for the more simple two-binding site model. As a result, simulations of the type presented above cannot be used to predict kinetic parameters for P450-dependent processes. Similarly, our model will not improve the accessibility of individual kinetic parameters via curve fitting based on results from steadystate kinetic experiments. However, the more complex model appears to be necessary to accommodate all of the effectors that modulate catalytic parameters of P450 3A4.

Multiple Products Many P450s generate multiple products from a single substrate, and allosteric kinetics may be observed only for one product (25-28). This additional complexity has not been explicitly addressed by any of the models, including ours. However, each of the models accommodates this possibility. For example, the static multiple binding site allows for an effector or second substrate, S2, that alters the partitioning to different products from

S1, just as kcat or KM for S1 may change. The product partitioning, or the absolute rate constants for their production, are just kinetic parameters that change on going from the E‚S1 to E‚S1‚S2 state. Similarly, the nested allosteric model L could contribute if the effector preferentially binds to one conformation that has an altered kcat for one product but not the other. The case of multiple products from a single substrate and with multiple enzyme conformers will require even more complex models, but each of the models can result in allosteric effects on one of multiple products arising from a single substrate.

How Cooperative Should P450s Be? Although a quantitative model for P450 allosterism is not yet available (including the intuitive model presented here), several of the parameters that determine the extent of cooperativity may be estimated roughly on the basis of information that is already available. For example, an approximation of L is already available from the data reported by Friedman et al. (19, 20). To the extent that the pre-exponential terms recovered in fitting the CO binding kinetics reflect relative contributions of different conformations, and if it is assumed that these conformations have identical heme absorbance properties, these parameters provide a crude preliminary estimate of L. For kinetics of reassociation of CO with P450 3A4, the majority of the experiments yield preexponential terms (a1 and a1′) with ratios (a1 and a1′) very close to 1 (0.2 < a1 and a1′ > 5). Thus, it may be expected that the conformations responsible for differential binding exist in roughly equivalent concentrations in the absence of ligands. This is informative, as demonstrated by the simulations presented above. For specific values of parameters in each of the available ligand states, the greatest degree of cooperativity is expected when L is very large (>10) or very small (

Allosteric Behavior in Cytochrome P450-Dependent in Vitro Drug

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