J. Phys. Chem. B 2006, 110, 10139-10143
10139
Investigations into the Analysis and Modeling of the Cytochrome P450 Cycle Yonghua Wang,† Yan Li,‡ Yanhong Li,† Xiaohua Ma,† Shengli Yang,† and Ling Yang*,† Lab of Pharmaceutical Resource DiscoVery, Dalian Institute of Chemical Physics, Graduate School of the Chinese Academy of Sciences, 457 Zhongshan Road, Dalian 116023, China, and School of Chemical Engineering, Dalian UniVersity of Technology, 158 Zhongshan Road, Dalian 116012, China ReceiVed: February 21, 2006; In Final Form: March 21, 2006
The main focus of our research is to explore the fundamental dynamics of the mechanism of the cytochrome P450 (CYP450) cycle. For this purpose we propose a system-theoretical approach, a time-dependent metabolic control analysis (tdMCA), to the analysis and quantitative modeling of the CYP450 catalytic pathway. This provides theoretical enlightenment for us to assess the transient response of the system to perturbations. In addition, the robustness of the cycle has also been observed, where perturbations elicit very weak responses and the system quickly recovers to the steady state (in an average of 10-5 s). The tdMCA also shows that the two electron transfers to the cycle have different impacts on the system, and the cycle is more sensitive to the first electron than to the second one. Knowing the dynamics of transient fluctuations, the robustness of the cycle, and the effects from the key interim steps, one has a deeper understanding of the catalytic mechanism of cytochrome P450.
I. Introduction Cytochrome P450 (P450 or CYP), belonging to a superfamily of heme-containing mono-oxygenases, found in virtually all forms of life, plays an important role in the metabolism and biosynthesis of a wide range of exogenous and endogenous compounds and has attracted the interest of chemists and biochemists for many years.1,2 Experimental and computational approaches are being applied to examine the interactions of P450s with substrates, inhibitors, membrane lipids, and microsomal proteins. Since these interactions modulate P450 activity, elucidation of their molecular mechanism will aid in (i) clarifying the mechanism of P450-mediated drug and carcinogen metabolism and (ii) developing specific P450 inhibitors. Oxidation of organic molecules by P450s is quite complex,3,4 probably involving 10 steps independent of protein conformational changes (Figure 1). The first step is substrate binding. The binding of a substrate to P450 causes a lowering of the redox potential by approximately 100 mV, 5 bringing about a conformational change of the enzyme that triggers an interaction with the redox component.6 The second is the reduction of the Fe3+ ion by an electron transferred from NAD(P)H via an electron-transfer chain. Subsequently, an oxygen molecule binds rapidly to the complex of Fe2+-RH, which becomes a more stable complex of Fe3+-O2- after undergoing a slow conversion. Then the second reduction occurs by the introduction of another electron to the system.7 The following steps include O-O cleavage, formation of a hydroxylated form of the substrate, and the product release.2 After all of these steps, the enzyme returns to its initial state. A general scheme for P450 catalytic cycle is shown in Figure 1.5 Here, for clarity in the following sections, all 10 of the molecules or intermediate complexes are represented by M1, M2, ..., or M10 according to their positions in the cycle (Figure 1). * Author to whom correspondence should be addressed. Fax: +86-41184676961. E-mail:
[email protected]. † Graduate School of the Chinese Academy of Sciences. ‡ Dalian University of Technology.
Figure 1. Catalytic cycle of cytochrome P450. Each intermediate molecule or complex in the cycle is represented by Mx, where x is their serial number enclosed in a circle, and each step of reaction is indicated by its serial number in this paper. This scheme is developed later in the MCA simulations.
Research into the use of different methods to probe the P450 catalytic cycle is being actively pursued.8-13 Guengerich and co-workers have defined the rate-limiting steps of the P450 cycle using the pre-steady-state kinetics and kinetic deuterium isotope effects.3,4 In most cases, chemists tend to focus on the ratelimiting steps and exclude all other steps in the enzyme catalytic cycle. However, in this work, we will show how all of these steps are closely related to one another and which step contributes most to the sensitivity of the cycle. This property for certain enzyme catalytic cycles has also been paid attention to by Shaik and co-workers.14 Using a combined kineticquantum mechanical model, they discussed which states contribute most to the reaction rate. However, up to now few of the methods and techniques, including the combined quantum mechanical/molecular mechanical calculations, were found capable of dealing with the whole P450 catalytic cycle.
10.1021/jp061119i CCC: $33.50 © 2006 American Chemical Society Published on Web 05/04/2006
10140 J. Phys. Chem. B, Vol. 110, No. 20, 2006
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An enzyme catalytic cycle is susceptible to a perturbation, which probably arises from the fluctuations in reaction conditions, such as in the substrate concentration or system temperature and structure, with no exceptions to the cytochrome P450 enzyme. A perturbation in the cycle may result in a transient increase or decrease of the flux of an intermediate molecule, causing unexpected impacts on the system performance. The control coefficients give a first approximation of which proteins or steps may exert more control on the system properties to be modified. In the present work, when the P450 system is perturbed, the robustness of the cycle has been first observed. Meanwhile, the impacts of some key steps such as the electron transfers, in light of time-dependent metabolic control theory on the mammalian cytochrome P450 catalytic cycle, are also discussed. II. Theoretical and Computational Methods Metabolic control analysis (MCA) is a powerful quantitative framework for understanding the relationship between the steady-state properties of a (bio)chemical reaction network as a whole and the properties of its component reactions.15-18 MCA provides a focused approach in the research to identify and characterize the influential metabolic reactions in cell behavior, which can be used as targets for effective therapeutic interventions against those diseases whose processes are still poorly understood.19 To assess the degree to which a parameter can change the reaction velocity it is convenient to use the elasticity coefficient. MCA has had great success in describing the control and regulation of systems at steady state but is not able to evaluate the sensitivity of a system along nonsteady trajectories. However, in the analysis of an increasing domain of applications it becomes necessary to consider the transient or oscillatory behavior along nonsteady trajectories.20 Therefore, a timedependent version of MCA (tdMCA) that can follow the sensitivity of a system to the perturbation throughout the time evolution is required. The following is a brief introduction to this method. First, let us consider a biochemical network consisting of n molecules involved in m reactions. The concentrations of each species (s) are defined in the model. The vector p contains any external parameters that have a direct effect on the reaction rates (e.g., kinetic constants of enzymes and external effectors). Therefore, the kinetic model for any (metabolic) network of coupled chemical reactions can be written as a set of nonlinear differential equations. For all t g0
ds(t) ) NV(s(t),p,t) dt
(1)
where V is an n-dimensional column vector of reaction rates by the functional relationship of V ) V(s,p,t). The topological structure of the reaction network is embodied in the stoichiometric matrix N. The equation equals 0 when the system is in steady state. As s is a function of t and s0, thus s ) s(t,s0,p) where s0 is the initial concentration of the species. The timedependent sensitivity coefficients Rt are then defined by a firstorder linear ordinary differential equation that follows from taking the derivative of eq 1 with respect to parameter p20
Rt )
(
)
∂V(t) ∂s(t) ∂V(t) d ∂s(t,p) )N + dt ∂p ∂s ∂p ∂p
for all t g 0 (2)
TABLE 1: Rate Constants for Phenacetin Oxidation by P450 1A2a rate constants k1 ) 6000 k2 ) 700 k3 ) 6000 k4 ) 700 k5 ) 110
k-1 ) 120000 k-3 ) 6
rate constants k6) 30 k7) 660 k8 ) 50 k9 ) 50
k-7 ) 6000
a Rate constants for k1, k3, and k-7 are in min-1 µM-1, and the rest are in min-1.
In the present work, the tdMCA was applied on cytochrome P450 1A2 for phenacetin, a prototypical substrate of the enzyme.21,22 Due to tdMCA having been fully presented by Ingalls,20 here we only briefly describe what we have implemented from the approach as follows: 1. Consider the pathway shown in Figure 1, a 10 × 9 stoichiometric matrix N was obtained, as there are 10 species taking part in 9 reactions. 2. The reaction steps 1, 3, and 7 are defined as reversible. After that, we assume mass-action kinetics for each of the reactions. 3. The parameter values used in this modeling are shown in Table 1. According to the experimental conditions or references,3,4 the kinetic parameters for phenacetin were obtained, with the substrate s0 ) 0.4 µM and the initial concentration of enzyme s1 ) 45 µM. In metabolic control analysis, M8 (H2O2) and M9 (H2O) were considered as external metabolites. 4. We computed the sensitivity coefficients Rt numerically by our internally developed C-language program, with the fourth- and fifth-order Runge-Kutta method 23 and Gear’s backward differentiation method for stiff differential equations.23,24 III. Results and Discussion In enzyme catalytic processes, the enzyme-to-enzyme channeling of metabolic intermediates is not an uncommon process. The term “channeling” refers to mechanisms in which the product of one enzyme is transferred directly to another enzyme that uses it as a substrate without necessarily passing through the free solution. Metabolic control theory is incapable of analyzing situations with channeling reactions. However, in the P450 cycle, the direct transfer of products from one enzyme to another does not occur; instead, different dynamic intermediate species or complexes are transiently generated in the series of interim catalytic reactions.4 This allows metabolic control analysis to be conducted on this process. Figures 2-8 show our main results obtained from the tdMCA of the P450 cycle. To make the pictures as clear as possible, only the representative part (from 0 to 0.05 min in Figure 8 or even much shorter time in other figures) of the whole trajectories (0.8 min) results are shown. This part, i.e., the beginning of the trajectories, is “representative” because it is just this part where the marked effects the perturbation has caused, one being of our most interest, is described. It should be noted that as time tends to infinity each trajectory (all curves in Figures 2-8) will converge to its steady state, and so the response coefficient will converge to the steady-state response of MCA. In this work, most of the interpretations were made on M7 not only because of its importance, the direct reactant for product ROH, but also of its analysis convenience, a final species in the circle (Figure 1). As for the first reaction step (the substrate binding), the sensitivity of time evolution to a perturbation in k1 is shown in
Modeling of the Cytochrome P450 Cycle
Figure 2. Perturbation in k1. The legend represents the 10 molecules according to the series number in Figure 1.
J. Phys. Chem. B, Vol. 110, No. 20, 2006 10141
Figure 4. Perturbation in s0.
Figure 5. Perturbation in k2. Figure 3. Perturbation in k-1.
Figure 2. It can be seen that a small increase in k1 produces a transient increase in M2, which then fades gradually as M1 and M10 reach their steady states, and M7 decreases to accommodate the perturbed parameter (here, M1 and M10 decrease in a similar way). The strongest response for M2 appears at about t ) 0.05 × 10-4 min (which is extremely fast). M1 and M10 change also in a very fast way (Figure 2). By the way, the situation for perturbation in k-1 is similar in k1 but reversed (Figure 3), which is fairly consistent with our intuitions on the reversible reaction. An unexpected finding is that M7 also decreases in Figure 2, which reduces its valley at 0.18 × 10-4 min (also very quick) and then restores its steady state slowly. One possible reason for this is that the two steps 1 and 7 are reversible and coupled; thus to drive the reaction forward would decrease the concentration of M7 in the cycle. Therefore, a conclusion can be made that a perturbation of the substrate binding to the enzyme could possibly have impacts on the two reactions simultaneously, no matter at its upstream or downstream positions. Figure 4 shows the effects of a perturbation in the substrate molecule M1 on the pathway. The results are just as what we have expected, which will not be described fully here. On the basis of the low concentration of NADPH-P450 reductase in microsomes and the slow rates of ferric P450
reduction observed in the absence of substrate,25,26 most of investigators believe that the introductions of the first (k2) and the second electrons (k4) into the cycle are the rate-limiting steps.27 However, metabolic control analysis begins by recognizing that flux control is not a unique property of one ratelimiting enzyme or step in a pathway but is a distributed property shared among all of the enzymes or steps. The coefficient distribution between the various enzymatic steps in the pathway gives us the initial assessment of where to intervene within the cycle. In this part, by giving a small perturbation (increase) in k2, we attempt to analyze how the effect on each species changes over time. Some findings can be inferred from Figure 5, where all intermediate molecules have been heavily influenced, except the two external metabolites M8 and M9 that do not participate in the cycle again as reactants. This shows that the first electron transfer plays a very important role in affecting the stability and dynamics of the system. Interestingly, the same phenomenon as k2 has caused does not occur for other perturbation analysis in this work, where few intermediate species can be influenced or influenced slightly (see other figures). This also in this regard justifies the significance of the first electron transfer to the P450 cycle. For other species, M4 and M5 increase very slowly until the steady state of zero value, along with a slow decrease of M7. The change of M3 is felt the strongest at about t ) 0.5 × 10-4 min (quick recovery).
10142 J. Phys. Chem. B, Vol. 110, No. 20, 2006
Figure 6. Perturbation in s2.
Wang et al.
Figure 8. Perturbation in k6.
Figure 7. Perturbation in k4.
And there are transient and relatively weak effects on M1, M2, and M10 that wash through the pathway. For comparison with k2, M2 (the enzyme-substrate complex) was perturbed (Figure 6). Two interesting findings emerged from these comparisons. M7 (Fe3+ROH) responds positively for M2 but negatively for the k2 perturbations. This is an interesting finding because our intuition suggests that perturbations in k2 and M2 should cause similar responses. The intuition may be ka
true for a one-step reaction, such as A 98 B, where perturbations in A and ka may cause a similar response of B, but it is not definite for a coupled multistep reaction like the P450 case. In a complex system, any perturbation in a species or the relevant reaction may present totally different impacts on the whole cycle. Another interesting finding from the comparisons may be of more biological importance. The response strength of M7 differs sharply in the two perturbations, about 100% (very strong) for M2 but only about 0.001% for k2. This finding enables us to believe that the formation of the final product is more sensitive to the fluctuations in the enzyme-substrate complex (M2) than the relevant reaction rate, which is worthy of concern for research in experiments. When a perturbation occurs in k4 as shown in Figure 7, there is an initial increase of M5, M6, and M7 and a decrease of M4. A novel finding is that the perturbation in k4 produces different
dynamic effects on the whole pathway from what the perturbation in k2 has caused. This is particularly evident in the influences on M7, where there exists a transient increase for k4 but a decrease for k2 perturbations, although the change extent and recovery time are almost of the same amount. Thus we conclude that the fluctuations in the rate of the two successive electrons transfers lead to totally reverse effects on M7. Seemingly, the two reactions are both rate-limiting, and even their rates are equal in values in this work, but the situation is more complicated than what we have observed as above. In the cytochrome P450 system, the two electrons donated by NADPH are transferred to P450 via two electron-transfer proteins, adrenodoxin reductase, which is an FAD-containing flavoenzyme, and adrenodoxin, which is a [2Fe-2S] ferredoxintype iron-sulfur protein.28 Both the electron-transfer proteins are not specific to individual P450 and serve as electron donors for different cytochrome P450s in different tissues.28 Obviously, kinetic mechanisms for different acceptors may vary. In the MCA presented here, the direct transfers of the two electrons also show different responses in the system. A recent report showed that the internal electron transfer is limited by conformational change and regulated by coenzyme binding.29 The nonsteady-state kinetic approaches have demonstrated that the kinetic mechanism of cytochrome P450 reductase (P450R) is sequential random bi-bi rather than ping-pong.30 However, due to the existence of a number of enzyme isoforms (containing different reduction states of the flavins) that are kinetically indistinguishable, the detailed kinetic scheme for P450R may include a number of steps that branch out and merge again, which is most probably more complicated than the classic random bi-bi mechanism.30 The complexity may explain why the two electrons show different impacts on the dynamics of the whole system. Many authors also believe that the sixth step of the reaction (k6), the production of Fe3+ROH (M7), is a rate-limiting step, as it is the slowest reaction in the chain.3,4,26 MCA can be used to identify where particular metabolic enzymes with high substrate flux-control coefficients reside along the network of enzyme pathways as potential targets for intervention.19 Therefore, this particular step has also been investigated (Figure 8). When k6 is perturbed, the transient response of M6 decreases slowly to its valley at t ) 0.05 min. Contrarily, the M7 response increases and accumulates very slowly, with only a 0.01% of increase. When the order of magnitude of response in M7 for k1, i.e., 10-5, k-1, i.e., 10-7, k2, i.e., 10-6, k3, i.e., 10-7, k4, i.e.,
Modeling of the Cytochrome P450 Cycle 10-6, k5, i.e., 10-8, k6, i.e., 10-4 was compared, respectively, k6 turns out to evoke the strongest responses. The results indicate that the formation of the product is most sensitive to a perturbation in this step (k6), as a small variation in this reaction causes the strongest effects on M7. In this case, it is reasonable to consider that the flux of the whole pathway is under the control of this step from the concept of time-varying MCA. Meanwhile, unlike most of the intermediate molecules shown above, M7 tends to go back to its steady state using a very long time (the longest is up to 0.8 min), except in the case of a perturbation in the substrate-binding step, where the system recovers extremely fast in about 10-4 min. Binding of some substrates to P450 1A2 induces a shift of the heme iron from the low- to the high-spin forms.31,32 This step is not rate-limiting, and also the high rate constant is representative for other substrates of CYP1A2.4 Accordingly, we conclude that M7 is rather insensitive to this step, since the transient effects caused by a perturbation of this step on M7 are very weak and very fast. However, the situations of long recovery (Figures 7 and 8) reveal that a small fluctuation can have an impact on a system over a long time, even up to 0.8 min. And this phenomenon might concern experimentalists; i.e., any fluctuation should be avoided whenever possible in experiments. Another interesting aspect of this work was the robustness analysis of the P450 cycle based on the sensitivity and recovery time. To our knowledge, up to now this is the first time that robustness is observed as a feature of the cytochrome P450 cycle. The response degrees of M7 and other intermediate species in all perturbations are extremely weak, with all of the response coefficients e10-4, which means that a perturbation does not cause any significant effects on the dynamic behavior of the whole system. Thus, we conclude that the P450 catalytic cycle is a robust system. Clearly, this robustness might be closely related to the biological roles of P450, i.e., the main phase I enzyme for metabolism. Although there are a variety of factors influencing the enzyme activity, the stability might be one of the key factors in ensuring the P450 natural performance. In addition, the cycle can recover to its steady state in a very fast manner after any perturbation aroused by the change of environments. In most cases, the recovery time is limited to 10-5 s and shorter, and it is the same even for M7 (Figures 2 and 3). The prompt recovery, however, also reveals the robustness of the P450 system. Robustness facilitates evolvability, and robust traits are often selected by evolution.33 Thus, the robustness of the cycle may coincide with the protection functions of cytochrome P450 enzymes that metabolize xenobiotic and endogenous compounds in the body to facilitate elimination. IV. Conclusion This paper applies a time-dependent metabolic control theory to deal with the transient-state as well as the steady-state kinetics of the reaction cycle of cytochrome P450. The evidence in this report reveals how the remote intermediates in the cycle are closely related and mutually interact in the nonsteady states. The results also show that the two electron transfers have totally different impacts on the dynamics of the cycle. The first electron transfer contributes most to the performance of the system in a
J. Phys. Chem. B, Vol. 110, No. 20, 2006 10143 nonsteady state, which needs to be concerned. By the analysis of the responses of the system, the robustness has been observed as a feature of the complex system of the P450 cycle. The finding of these properties will advance our understanding of the catalytic mechanism of cytochrome P450. Acknowledgment. The authors thank the 973 Programs (2003CCA03400 and 2003CB716005) of the Ministry of Science and Technology of China and the DUT-DICP Cooperation Fund. References and Notes (1) Guengerich, F. P. J. Biol. Chem. 1991, 266, 10019-10022. (2) Guengerich, F. P. In Cytochrome P450: Structure, Mechanisms, and Biochemistry, 2nd ed.; Ortiz de Montellano, P. R., Ed.; Plenum Press: New York, 1995; pp 473-535. (3) Yun, C.-H.; Miller, G. P.; Guengerich, F. P. Biochemistry 2001, 40, 4521-4530. (4) Guengerich, F. P.; Krauser, J. A.; Johnson. W. W. Biochemistry 2004, 43, 10775-10788. (5) Ruckpaul, K.; Rein, H.; Blank, J. Front. Biotransform. 1989, 1, 1-65. (6) Veitch, N. C.; Williams, R. J. P. Front. Biotransform. 1992, 7, 279320. (7) Imai, Y.; Sato, R.; Iyanagi, T. J. Biochem. (Tokyo) 1977, 82, 12371246. (8) Guallar, V.; Baik, M. H.; Lippard, S. J.; Friesner, R. A. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 6998-7002. (9) Denisov, I. G.; Makris, T, M.; Sligar, S. G. J. Biol. Chem. 2001, 276, 11648-11652. (10) Li, H.; Poulos, T. L. Biochim. Biophys. Acta 1999, 1441, 141149. (11) Spolitak, T.; Dawson, J. H.; Ballou, D. P. J. Biol. Chem. 2005, 280, 20300-20309. (12) Reipa, V.; Mayhew, M. P.; Vilker, V. L. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 13554-13558. (13) Schlichting, I.; Berendzen, J.; Chu, K.; Stock, A. M.; Maves, S. A.; Benson, D. E.; Sweet, R. M.; Ringe, D.; Petsko, G. A.; Sligar, S. G. Science 2000, 287, 1615-1622. (14) Kozuch, S.; Shaik, S. J. Am. Chem. Soc. 2006, 128, 3355-3365. (15) Heinrich, R.; Rapoport, T. A. Biosystems 1975, 7, 130-136. (16) Kacser, H. Biochem. Soc. Trans. 1983, 11, 35-40. (17) Reder, C. J. Theor. Biol. 1988, 135, 175-201. (18) Acerenza, L. J. Theor. Biol. 1993, 165, 63-85. (19) Cascante, M.; Boros, L. G.; Comin-Anduix, B.; de Atauri, P.; Centelles, J. J.; Lee, P. W. Nat. Biotechnol. 2002, 20, 243-249. (20) Ingalls, B. P.; Sauro, H. M. J. Theor. Biol. 2003, 222, 23-36. (21) Distlerath, L. M.; Reilly, P. E. B.; Martin, M. V.; Davis, G. G.; Wilkinson, G. R.; Guengerich, F. P. J. Biol. Chem. 1985, 260, 9057-9067. (22) Butler, M. A.; Iwasaki, M.; Guengerich, F. P.; Kadlubar, F. F. Proc. Natl. Acad. Sci. U.S.A. 1989, 86, 7696-7700. (23) Press, W. P.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes in C: The Art of Scientific Computing; Cambridge University Press: New York, 1989; pp 710-714, 734-747. (24) Shampine, L. F.; Gear, C. W. SIAM ReV. 1979, 21, 1-17. (25) Guengerich, F. P.; Johnson, W. W. Biochemistry 1997, 36, 1474114750. (26) Yun, C.-H.; Miller, G. P.; Guengerich, F. P. Biochemistry 2000, 39, 11319-11329. (27) White, R. E.; Coon, M. J. Annu. ReV. Biochem. 1980, 49, 315356. (28) Hanukoglu, I.; Rapoport, R. Endocr. Res. 1995, 21, 231-241. (29) Gutierrez, A.; Paine, M.; Wolf, C. R.; Scrutton, N. S.; Roberts, G. C. Biochemistry 2002, 41, 4626-4637. (30) Murataliev, M. B.; Feyereisen, R.; Walker, F. A. Biochim. Biophys. Acta 2004, 1698, 1-26. (31) Sandhu, P.; Guo, Z.; Baba, T.; Martin, M. V.; Tukey, R. H.; Guengerich, F. P. Arch. Biochem. Biophys. 1994, 309, 168-177. (32) Miller, G. P.; Guengerich, F. P. Biochemistry 2001, 40, 72627272. (33) Kitano, H. Nat. ReV. Genet. 2004, 5, 826-837.
