Explaining the Atypical Reaction Profiles of Heme Enzymes with a Novel Mechanistic Hypothesis and Kinetic Treatment

Many heme enzymes show remarkable versatility and atypical kinetics. The fungal extracellular enzyme chloroperoxidase (CPO) characterizes a variety of one and two electron redox reactions in the presence of hydroperoxides. A structural counterpart, found in mammalian microsomal cytochrome P450 (CYP), uses molecular oxygen plus NADPH for the oxidative metabolism (predominantly hydroxylation) of substrate in conjunction with a redox partner enzyme, cytochrome P450 reductase. In this study, we employ the two above-mentioned heme-thiolate proteins to probe the reaction kinetics and mechanism of heme enzymes. Hitherto, a substrate inhibition model based upon non-productive binding of substrate (two-site model) was used to account for the inhibition of reaction at higher substrate concentrations for the CYP reaction systems. Herein, the observation of substrate inhibition is shown for both peroxide and final substrate in CPO catalyzed peroxidations. Further, analogy is drawn in the “steady state kinetics” of CPO and CYP reaction systems. New experimental observations and analyses indicate that a scheme of competing reactions (involving primary product with enzyme or other reaction components/intermediates) is relevant in such complex reaction mixtures. The presence of non-selective reactive intermediate(s) affords alternate reaction routes at various substrate/product concentrations, thereby leading to a lowered detectable concentration of “the product of interest” in the reaction milieu. Occam's razor favors the new hypothesis. With the new hypothesis as foundation, a new biphasic treatment to analyze the kinetics is put forth. We also introduce a key concept of “substrate concentration at maximum observed rate”. The new treatment affords a more acceptable fit for observable experimental kinetic data of heme redox enzymes.


Introduction
Hemoproteins serve multiple roles in the cellular biochemistry and as a result, they are one of the well-studied proteins. Structurefunction similarities as well as disparities can be drawn between the two heme proteins, chloroperoxidase (CPO) and cytochrome P450 (CYP). The former is a highly stable glycosylated extracellular acidic protein with a constrained and polar active site [1]. The latter is a relatively sensitive microsomal membranous protein showing little post translational modifications, but with a larger hydrophobic active site [2,3]. Though both are ,45 KD mass and ,45 Å in dimensions, they bear only ,25% sequence similarities. The most important common structural element is the proximal thiolate ligand, bound to the central iron of heme (protoporphyrin IX). The formal charge on iron at the resting state is 3 + and the spin state may change based on the distal ligand and microenvironment. Both these enzymes are well-studied enzyme systems, characteristically marked for their versatility in the number of reactions they can catalyze [4][5][6][7]. Both CPO and CYPs are known for a relative lack of specificity in substrate preferences. Chloroperoxidase is a classical peroxygenase carrying out its oxidations with hydroperoxide as the ancillary activator [8]. CYP is a typical monooxygenase which requires a ternary mixture of molecular oxygen, yet another enzyme called cytochrome P450 reductase (CPR) and redox equivalents from NADPH [9].
Our recent explorations with chloroperoxidase catalyzed peroxidations had afforded some interesting and unexpected results. To account for these observations, we had reasoned out that some of the enzyme-substrate (final acceptor) interactions might not go through the typical enzyme-substrate binding [10] at a unique active site of the enzyme. As a result, they may not be defined by the classical Michaelis-Menten kinetics. While pursuing the newly discovered angles on the single electron peroxidations of CPO, we found some analogies with the two-electron CYP catalyzed oxygen insertion reactions, pertaining to the ''inhibition of reaction'' at higher substrate concentrations. Approximately 20% of the known enzymes have shown some form of substrate inhibition. Hitherto, such atypical kinetic behavior was attributed to a mechanistic scheme involving alternate substrate binding site(s) near the CYP enzyme's active site [11][12][13][14], which is a twosite binding model, as shown in Figure 1.
We present evidence and argue herein that it is highly unlikely that both CPO and the CYP family of enzymes (as exemplified by CYPs 2C9, 2E1 & 1A2) possess multiple binding sites for their diverse array of substrates. To explain for the 'substrate inhibition', we propose an alternative hypothesis which involves enzyme-free reactions of the substrates, product(s) and transient intermediate(s). We also present an alternative model for fitting the data obtained, to give meaningful indices of the reaction system.

CPO mediated peroxidations of ABTS, TMPD and Pyrogallol
To derive an overview of the steady-state reaction profiles, the substrate molecules' concentrations were varied over three decades. Kinetic data obtained for the production of stable cation radicals and condensed products were noted within the first few tens of seconds of reaction are summarized in Table 1.
For all reactions studied, increasing the final peroxidative substrates' concentration (at an initial constant peroxide concentration) generally gave an increase in the reaction rates for the submillimolar reaction range studied (Figure 2 is a salient example for ABTS, other data are shown in Table 1), which could be fit to non-linear regression of Michaelis-Menten equation, with R 2 values above 0.9. However, the data could not be transformed to fit the popular linearized models exemplified by Lineweaver-Burk or Eadie-Hofstee (results not shown). Also, incrementing the first substrate concentration by decades did not give corresponding levels of increase in second substrate conversion, as expected in Figure 1 (left side). The reaction profiles obtained by varying peroxide concentrations at constant peroxidative substrate concentration gave mixed trends (Figure 3 & Table 1 show the profile for TMPD). The increase in peroxide concentrations gave an apparent inhibition at higher concentrations, the extent of which varied with different peroxidative substrates. Again, none of these profiles could be fit to a non-linear substrate inhibition model within an extension of the Michaelis-Menten paradigm (as exemplified by the Belanger fit [15]) to give global and reproducible constants with accuracy and precision (Table 1). Figure 4 shows that a substrate like pyrogallol, which showed lower inhibitions with peroxide increments, also exhibited lowered product (purpurogallin) formation at supra-millimolar concentrations of pyrogallol. The inhibition was also seen for an active site excluded substrate like ABTS (inset of Figure 4). When the two sets of data (rates obtained by varying peroxide at constant final peroxidative substrate versus rates obtained by varying final peroxidative substrate at constant peroxide) were compared, it could be seen that increase in peroxide (at constant peroxidative substrate) had a greater effect on lowering rate. In most cases, the Belanger fit curves did not justifiably cover the data points at higher substrate concentrations (data not shown).  Table 2 depict the result when substrate effect was probed in two reaction systems-(1) employing NADPH regeneration system with enzymes to remove reduced oxygen species (ROS) and (2) directly with NADPH and without enzymes included to remove ROS. In both these reaction systems, employment of moderate amounts of Cytb 5 enhanced the product formation at lower substrate concentrations when compared to the controls. Notably, the first setup gave much higher yields of product in comparison to the second. However, incorporation of excess Cytb 5 gave similar product formations (especially at higher  Table 2. Clearly, the magnitude of K IS varied from one experiment to another significantly. The reaction profile was charted in detail by taking a 16 point curve (Figure 8), which showed that the descending part of the Belanger fit (after inflexion) significantly deviated from the experimental points. A theoretical simulation using the double hyperbolic combination showed a similar profile as the experimentally determined points ( Figure 8). Figure 9 shows the 49hydroxylated product obtained for diclofenac's reaction with two concentrations of CYP2C9. The CYP concentration was shown to have pronounced effect on the value of constants (quite like the results with CYP2E1) and the ''substrate inhibition'' was more pronounced at higher enzyme concentration. When a similar reaction setup was probed with respect to product formation at various time intervals (Figure 10), it was noted that the formed product disappeared for higher substrate concentration. Incorporation of Cytb 5 lowered the   product formation at low substrate concentrations but showed a positive effect on the yield of product at higher substrate concentrations.

CYP1A2 reactions with 7-EFC
In these reactions, quantification of both the expected product (the specifically de-ethylated substrate) and the substrate was carried out after incubation for specific times. The results are shown in Figure 11. It could be seen that the product inhibition occurred at much lower substrate concentrations. Also, the amount of specific product formed did not account for the amount of substrate depleted. Extra peaks were seen in the chromatograms of these samples (results not shown) indicating the formation of new products. These unidentified new products could account for the disappearance of excess substrate (the substrate missing and not accounted for by the formation of the expected product of 7-hydroxyfluorocoumarin).

Discussion
Some workers in the past have probed thiolate-peroxidases as a mechanistic model for CYP reactions, citing analogies and differences in their modes of action [16][17][18][19][20]. Their arguments relate to the details of the nature of the catalytic enzymatic species and the precise mechanistic chemistry involved in the reaction of the catalytic species with the substrate. Such discussions do not dictate the context of the present work. The aspect of mechanistic process probed here is if the 'spatio-temporal' idea of obstruction of the active site by higher concentration of substrates (or an allosteric modulation by excess substrate at an alternative enzyme binding site), as advocated erstwhile, and as is depicted in Figure 1, provides an adequate explanation to the 'substrate inhibition' kinetics.
The kinetic profiles obtained in this work indicate that the single electron abstractions (which have been proven to not necessarily be finally catalyzed at a unique catalytic site by CPO [10]) show a lowered yield of product upon increasing any one of its substrates. The data from this work indicates that lowering of product yields at high substrate concentrations may not be owing to a process involving interaction of the substrate and the enzyme alone, for both CPO and CYP. Evidence presented in the reactions with CYPs show that these observations could very well be owing to other factors, as is shown in Figure 12. The mechanistic route could involve: (1) A transient intermediate (either an activated enzyme or substrate species) could react with excess substrate to give an alternate product, thereby lowering the product by a competitive process. To validate this argument-(a) Schlichting et al. have already demonstrated the existence of one and two electron activated CYP species [21]. Also, Guengerich et al.
had earlier advocated a one-electron process mechanistic scheme for explaining the observations in some CYP reactions [17]. (b) Superoxide has been proposed as an essential mechanistic component (by one of us [22]) and demonstrated to exist in reaction milieu by many workers as a deleterious side-product [9]. It could react very feasibly with the substrate (which has been demonstrated earlier by one of us [22]) and reaction product on its own merit. Such a reaction would be anticipated to be a function of the substrate concentration,   which could explain the lowered yield of specific product at higher substrate concentration.
(1) OR/AND (2) The product formed could get further converted by the enzyme or yet, react with another reaction intermediate/ component present in the milieu, thereby lowering the value of estimated product in the reaction setup. This inference has been amply supported by data from this study.
In several CPO catalyzed peroxidations, the colored peroxidation product formed was depleted in due course of the reaction on its own or/and by the addition of excess of the peroxidative substrate or peroxide itself (results not shown). This makes perfect chemical sense because these reaction components are nonspecific redox sensitive molecules. CPO catalyzed chlorination reaction milieu has already been shown to possess such chemistry where peroxide serves both as activator and scavenger of reactive intermediate(s) [23]. Earlier, Cassella et al had shown that the oxidation of phenolics by CPO also exhibited a lowered product formation at higher peroxidative substrate concentration [24]. We found similar observation for various peroxidative substrates above 10 mM concentrations in our investigations (where solubility permitted, results not shown).
All these observations in steady-state kinetics of fungal CPO and microsomal CYPs indicate an analogy in the chemical reaction   phenomena. It is generally understood that both fungal CPO and microsomal CYPs catalyze via a bi-substrate route. The first process in both enzymes is assumed to involve the oxygen donor species binding at the heme and the second involves the final electron donor/acceptor substrate interaction. We know that the original activator in the CPO reaction is the redox sensitive peroxide and if we could consider superoxide as an activator for CYPs (as mooted earlier by one of us [22]), then the analogy would be explained even better. Incorporation of Cytb 5 in CYP reaction milieu (as a oneelectron redox sensitive hydrophobic macromolecule) showed clear indications that single electron processes have direct relevance to the product formation and distribution in the milieu.
Also, earlier interpretations were that Cytb 5 serves as a redox relay between CYPs and reductase, mediating the process via a proteinprotein complexation [25,26]. If that were to be the case, increase in Cytb 5 should only increase the product yield. This is not observed and therefore, the erstwhile hypothesis that ''Cytb 5 is a protein-protein redox relay between CYP and CPR'' is questionable. On the other hand, if we assume Cytb 5 to be a non-selective one-electron transient scavenger cum cycler (that affects the equilibriums involving single and two electron processes at the lipid interface) in a non-specific redox reaction setup involving superoxide, we could efficiently account for lowering or enhancement of rates in various compositions. This is especially evident as excess Cytb 5 serves well in both CYP2E1 and CYP2C9 reactions at higher substrate concentrations, under diverse conditions.
The concentration range of substrate at which the maximal rates were observed (following which increase in substrate concentrations showed a lowering in product yield) for the three CYPs ranged around 5, 25 and 125 mM for CYP1A2: 7-EFC, CYP2C9: diclofenac and CYP2E1: pNP respectively. This observation is in accordance with the chemical reactivity of the substrates. That is -the electron withdrawing nitro group and an adjacent sterically hindering hydroxyl makes pNP molecules' reaction centre to be less efficient. In comparison, the nonhindered ethoxy group's oxygen moiety's lone pair (which is conjugated to the p electron cloud in the coumarin derivative and also connected to an electron donating ethyl group) would be the most reactive and easily accessible center among the three substrates tested. In case of the peroxidation reaction with CPO, the active-site-excluded ABTS [10] (which has better electron density and donating ability) shows inhibition at lower substrate concentrations than the smaller TMPD (for a given peroxide concentration). This is yet another consideration which indicates that the ''substrate inhibition'' is not connected to a blocking of the active site.
Surely, one cannot argue that there are no multiple binding sites for the various substrates on CYP and CPO. However, it is very difficult to imagine that enzymes like CPO and CYP family have multiple binding sites for their diverse array of both their final substrates and initial activator (peroxide). As per the data reported in this study, the non-specific reaction network put forward in    Figure 12 appears more probable. Therefore, at this juncture, we express a note of caution towards the data and interpretations published in a recent article [27]. The authors therein have reported kinetic and equilibrium constants for effector site modulations (alternate term for substrate inhibitions) in the activity of CYP2E1-pNP reaction mixtures. We have exhaustively worked on the same system and ascertained that it is impossible to derive any reproducible and meaningful kinetic constants for steady state kinetics using experimental data by non-linear regression analyses with available kinetic treatments or software. As can be evident from a visual examination of Figure 2 from their communication, the theoretical fits do not do justice to the experimental data. Specifically, the rates at the point of inflexion (where maximum activities are obtained) and higher substrate concentrations (the region that the hypothesis supposedly accounts for!) clearly go out of the fit. These outliers are real and not just instances of experimental error, as hitherto considered. With much lesser standard deviations of individual points, better R 2 values than the data reported therein and with more number of points spread through the curve, the value of K IS obtained with Dynafit plots in our work ranged from ,100 mM to ,10 mM in simple control reactions that did not include any inhibitor. When molecules (inhibitors) like 4-methylpyrazole and isoquinoline were added (in our study, results not shown), the complexities for determining K I and K IS only increased manifold. The fits then pointed to an uncompetitive or noncompetitive model, at times a mixed model and in some instances, the fitted curve could hardly be called a fit! Therefore, it is our view that attempts to draw any interpretations from such poor fits and inappropriate hypothesis would only lead one to erroneous conclusions. Merely, getting an R 2 value above 0.9 is no indication that the hitherto proposed model has fidelity to the equation or mechanism. An exhaustive study of the two tables presented herewith (along with the respective figures) would convince any careful reader of the above statement.
The simulation of kinetics (and fitting thereof) could be achieved better using a biphasic treatment, with the incorporation of new meaningful constants. The fitting (for rate Y versus substrate concentration X) could be done with the following simple algorithm, using two intermediate variables (Y1 & Y2) and six true variables- The last expression is a logic statement in the algorithm used to fit data serving to demarcate the two hyperbolic phases with (X max , Y max ) as the node. Of the six true variables, V 1 & K 1 are the theoretical constants for ascending part & V 2 & K 2 are the theoretical constants for the descending part. The practically observable and ascertainable Y max (the maximum observable rate) and X max (the concentration of substrate at which maximum rate is observed) values are the new concepts introduced here. The latter values could convey more meaningful information of a given reaction system in which 'substrate inhibition' is expected or observed. The re-analyses of experimental data for CPO's reaction profile with pyrogallol ( Figure 4) with the new fitting method gave an R 2 value = 0.994. The result is shown in Figure 13. When data from Figure 8 (for CYP2E1's experimental reaction profile with pNP) was refitted using the new method, an R 2 value = 0.983 was derived with the points falling much better onto the fitted curve (results are shown in Figure 14). These show that the novel biphasic treatment gives a far more satisfactory fit, as is determined with a simple visual verification. Other details of fitting and data obtained thereof shall be discussed in a forthcoming communication.
To conclude, the hemoprotein reaction milieu with two substrates (or more) involves several competing reactions. The exact nature of the product(s) formed and their distribution thereof would be dependant on the nature of enzyme and substrates, reaction conditions and reactant concentrations. Algorithms need to be developed to predict the probabilistic course of such a reaction, given a hemoprotein reaction mixture. These efforts would have far-reaching impact in our understanding of cellular and physiological processes involving these maverick enzymes.

Materials and Methods
The chemicals and reagents used were of analytical grade, purchased from Sigma, Lancaster (USA) and SD Fine Chemicals (India). For procedural details on CPO, please refer to our recent publication [10]. The source of CYPs was either a commercial baculosome preparation from Invitrogen (PanVera) or reconstituted systems made in lab. For the production, purification and processing of CYP and associated proteins, please refer to an earlier publication [28].

General conditions
CPO reactions were carried out in open with ,20 nM CPO at ,3062uC, 100 mM phosphate buffer (Figures 1 through 6). The selection of pH value employed simple logic to optimize between autocatalytic rates and enzyme-catalyzed rates. Pyrogallol reac-tions were incubated at pH 5, ABTS [2,29-azino-bis(3-ethylbenzthiazoline-6-sulphonic acid)] reactions were incubated at pH 3.5 and tetramethyl phenylene diamine (TMPD) reactions were incubated at pH 2.75. All CYP reaction incubations were done in aerated open vials at 3761uC in 100 mM phosphate buffer, pH 7.4. Unless otherwise mentioned, reconstituted systems had 10 mg/ml of 0.2 mm vesicles of dilauryl phosphatidylcholine (DLPC, Avanti Lipids). Besides the general procedures mentioned below, specific components' concentrations and other details are mentioned in the legends to the corresponding figures.

Reactions with CYP2E1
The reactions contained 20 mM DLPC, 15 nM CYP2E1, 60 nM CPR, 0/50/500 nM cytochrome b 5 (Cytb 5 ) and the appropriate concentrations of para-nitrophenol (pNP). 200 ml of the regeneration system reaction mixture had -0.3 ml of 2 M MgCl 2 , 2.4 ml of 5 mg/ml of superoxide dismutase, 0.6 ml of 1000 Units/ml catalase, 0.6 ml of 1 Unit/ml glucose-6-phosphate dehydrogenase & 60 ml of glucose-6-phosphate. The reactions were initiated with the addition of 500 mM NADP + in the regeneration system reaction and 500 mM NADPH in another set. The HPLC protocol for quantification of product of paranitrocatechol (pNC) was similar to a procedure reported recently [27]. Aliquots of the reaction mixture were taken at 6, 12 and 18 minutes and the rate of production of pNC was calculated by the slope of linear plot obtained.

Reactions with CYP2C9
In another reaction involving reconstituted enzymes, 80 nM CYP + 80 nM CPR mixture was used. Cytb5 was in the range of 40 to 800 nM ( Figure 13). Termination of reaction for product quantification was achieved by adding 200 ml of a cold solvent mixture (94% acetonitrile + 6% acetic acid, containing tert-butyl phenol as the internal standard) to 500 ml of sample. Conversion of diclofenac (Diclof) was determined using Alltima C 18 5 m HPLC column (150 mm63.2 mm) from Alltech. The solvent system of 70% (of 30% acetonitrile in water with 1 mM perchloric acid) and 30% methanol was pumped at 0.8 ml/min. Chromatography was monitored with a UV detector at 267 and 275 nm. Elution times and areas of standard samples of diclofenac and its 39, 49 & 59 hydroxylated derivatives were used for detecting and quantifying the products. Under the conditions employed, 49hydroxydiclofenac and diclofenac eluted at ,6 and 7.5 minutes respectively.

Reactions with CYP1A2
At designated incubation intervals (5, 10 & 15 minutes), 75 ml of the reaction sample was taken and quenched with 25 ml of acetonitrile containing the internal standard and centrifuged. An appropriate amount (usually 40 ml of the supernatant) was injected for HPLC. The product formed was estimated from the slope of line formed by fitting a standard linear plot. For the quantification of 7-hydroxy trifluoromethylcoumarin (7-HFC), the de-ethylated product of CYP1A2 oxidation of 7-ethoxy trifluoromethylcoumarin (7-EFC), a Symmetry C 18 3.5 mm column from Waters was employed. A binary solvent system-solvent A = 75% of 0.1% trifluoroacetic acid in water & solvent B = acetonitrile were taken with a gradient method. The details are 0 min = 1 ml/min, 75% A + 25% B; 4 min = 1.5 ml/min, 75% A + 25% B; 9 min = 1.5 ml/min, 0% A + 100% B; 11 min = 1.5 ml/min, 75% A + 25% B & 12 min = 1 ml/min, 75% A + 25%B. A fluorescence detector with excitation and emission wavelengths set at 385 nm and 500 nm respectively was used to quantify the reactants and products. The UV absorption profiles of products were also followed in certain reactions. The analytes 7-hydroxycoumarin (an  internal standard taken at 20 mM), 7-HFC and 7-EFC eluted at ,2.6, 8.2 and 9.6 minutes respectively.

Fitting and analyses of kinetics data
Non-linear (and linear) regression analyses of enzyme kinetics were carried out using Dynafit and GraphPad Prism software for uncompetitive substrate inhibition (Belanger fit): The constraints were only experimental values were taken (0,0 excluded) and V max , K M and K IS .0. Both Dynafit and Prism outputs gave similar values of constants for all reactions studied herein and therefore, only the latter is reported. For theoretical simulation (as shown by the triangles in Figure 9), the data were derived using a fusion of two equations, in a biphasic treatment. The ascending points [until the blackened point-(75, 0.4) in Figure 9] were derived using the ascending hyperbola equation: