Substrate Channeling of Prostaglandin H2 on the Stereochemical

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Substrate Channeling of Prostaglandin H2 on the Stereochemical Control of a Cascade Cyclization Route Hsiao-Ching Yang, Yung-Chi Ge, Cheng-Han Yang, and Wei-Chih Chao ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.7b03687 • Publication Date (Web): 09 Feb 2018 Downloaded from http://pubs.acs.org on February 9, 2018

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ACS Catalysis

Substrate Channeling of Prostaglandin H2 on the Stereochemical Control of a Cascade Cyclization Route Hsiao-Ching Yang*1, Yung-Chi Ge1, Cheng-Han Yang1 and Wei-Chih Chao1 1

Department of Chemistry, Fu Jen Catholic University, New Taipei City 24205, Taiwan

*E-mail: [email protected]

interest in this subject has prompted the introduction of the nature and magnitude of the rate acceleration that may be brought about by bringing together two properly oriented reactants of substrate and enzyme via substrate channeling,9-10 the transfer of reactant from a protein surface to a buried active site in a specific pathway. Although many aspects have frequently been discussed with reference to the problem considered here,11-13 their application and quantitative significance for reactions in enzymes had been a subject of active debate. The purpose of this study is to tackle the problem head-on in diagnosing the mechanism of substrate channeling process in enzyme catalysis and efficiency. Effective rate accelerations in cyclization of the large flexible molecule PGH2 highlight kinetically supreme proficient enzymes such as cytochrome P450s.8, 14-18 A most remarkable feature of these P450s is that they all employ a conserved Cys-heme pocket wherein the Cys-ligation side is on the proximal of the heme and a distal pocket of the substance binding site to catalyze the C−H hydroxylation (Figure 1a), including a diversity of ring couplings, ring closure, and ring expansion in steroid biosynthesis and fatty acid metabolism.8, 14-16, 19 Typical P450 monooxygenase reactions are NAD(P)H and O2-dependent ones, but when the endoperoxide isomerizing P450 works as a prostacyclin synthase (PGIS) or thromboxane synthase (TXAS), it is neither NAD(P)H nor O2-dependent, and it is known generally as prostaglandin H2 (PGH2) isomerase. To illustrate the specific role of PGH2 in the P450 enzymatic reactions, Figure 1b depicts its endoperoxide structure within a strained heptane ring and two flexible arms of chiral positioned long-alkyl-chains capable of internal rotations about single bonds, leading to a diversity of isomeric conformations for catalysis. The rare event of intramolecular cyclization gives thromboxane A2 (TXA2) or prostacyclin (PGI2), which plays regulatory roles in platelet aggregation and in vaso- and bronchodilation and constriction.16-17, 20 PGH2 isomerism is proposed to involve homolytic cleavage of the 9,11-endoperoxide, with a ferryl P450 iron-bonded to one or the other of the oxygen atoms (i.e., Figure 1b) that cleaves to the alkoxy radicals.20 The mechanism utilizes the radical migration to a substrate carbon and electron transfer to the iron with carbocation formation on intermediates preceding their final rearrangement to form either PGI2 or TXA2, or fragmentation.8, 15-16, 19-20 Compared to the P450 catalytic route of mono-oxygenation via the "peroxide shunt",8, 15-16 Figure 1a, the consensus cycle is associated with the native hexacoordinate ferric form, followed by the removal of water molecule coordination from the heme to the pentacoordinate complex for substrate binding, and through forming the species of Compound 0 (Cpd 0) to yield a high-valent iron-oxygen complex Compound I (Cpd I) sequentially to oxidize the substrate.21-23 The following rates for alkyl radical rearrangement and radical recombination

Abstract Enzymes can carry out effective rate accelerations by virtue of their ability to utilize substrate-channeling forces to act as a mechanochemical valve. Such a channeling process is treated quantitatively using the key aspects of the free energy landscape; the balance between substrate positioning and conformational changes reflects the severe geometric and electronic requirements for the relatively tight transition state. The observed kcat/KM of about 106 M-1 s-1 for PGH2 cyclization has been revealed to be brought about by bringing together two properly-oriented reactants of substrate and enzyme regarding the magnitude significance of the contribution from outer- and inner-binding stereopopulation along the free energy channeling pathway, and thus shapes the cascade cyclization route, enforcing precise spatial and temporal control. The apparent constant kcat of many P450 reactions involving the heme catalytic cycle, which is often on the order of 101-102 s-1 and is usually attributed to Compound 0 to Compound I formation, may be in large part a consequence of channeling conformation changes toward the rate-limiting state that is made possible by pre-organizing the proximal hydrogen-bonding pattern of the amide groups to the cysteine sulfur, and to the push-pull modulation of the relevant heme axial ligation and activation. Keywords: Cytochrome P450; prostacyclin synthase; kcat/KM; hydrogen-bonding cysteine sulfur; heme ligation push-pull mechanism; free energy landscape; umbrella sampling potential of mean force Introduction There are several reasons for believing that the specific binding process plays an important role in reducing the free energy of activation of reactions catalyzed by enzymes.1-4 From the free energy landscape view of the hierarchical routes,4 an understanding of the conformations and the transitions among them is essential for the binding process of substrate transport. The framework of transition state theory1, 5-6 enables us to evaluate these effects on the relevant conformational transitions as coupled with the enzyme environment and the importance of interactions with specific residues that might cause the dynamical bottleneck to be effective in catalysis. Experimental studies have shown that enzymatic reactions operate with the turnover number (kcat) and the apparent binding constants of substrates (KM), yielding remarkably apparent second-order rate constant of kcat/KM, which the diffusion-controlled reactions limit at kcat/KM values of 108–109 M-1s-1; however, the vast majority of enzymes exhibit kcat/KM at mean values of 106–107 M-1 s-1, where the kcat values are in average of 101–102 s-1 and KM are around 10~100 µM.7-8 What are these kinetic parameters representing a vital feature of the “enzyme nature”, which affects the enzyme efficiency of kcat/KM? A recent renewal of

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usually occur on the order of 107–109 s-1.24-25 Another aspect suggests a “push-pull” mechanism of importance in explaining how an elaborate modulation of the Fe-S bond strength of Cys-heme complex yields the reactive intermediate to afford the rearrangement sequence of the radical chain mechanism.26-27 A more recent finding reveals that only binding of the PGH2 analogues (U51605 and U46619, Figure 1c) with long-alkyl-chains can induce the conformational change of the Cys-heme matrix in PGIS, as evidenced by resonance Raman spectra.28 Moreover, binding of PGH2 for the heme iron mediating structure will inevitably be associated with a high entropic penalty because of the lost internal rotational degrees of freedom of the long-alkyl-chains. It is well known that this entropic cost plays an important role in intramolecular cyclization reactions, which have highly confined transition-state structures.4, 29-31 The entropic penalty associated with forming a productive precyclic substrate conformation was found to be up to 43 cal mol-1K-1 (14 kcal mol-1 at 328 K), even for monocycles.31 This energy cost would slow the rate 109-fold compared to that of a reaction with activation entropy of zero. Rate measurements infer that P450 enzymatic activities convert the turnover in milliseconds to seconds.8, 15-16, 32-35 It is of particular interest to inquire why enzymes can achieve the extraordinary affinity by overcoming the entropy-enthalpy compensation and accomplishment of such precise functions to be both specific and transient.4, 29-31 Intense study of the P450 structures36 has revealed many internal channel arrangements from protein surface to heme site, suggesting that some of them do enable the transfer of reactants along the channel (see Figures. S1 and S3 in the Supporting Information (SI)). In the case of PGIS, Figure 2, it conducts PGH2 binding to the heme association.9-10 We demonstrate how the substrate-channeling process shapes the cascade cyclization route, enforcing precise spatial and temporal control, by carrying out an MD-based study of PGH2 inside PGIS and a kinetic analysis of intermediates to rate constants. Taken together, a balance exists between, on the one hand, adequate interactions that maintain an extension of the complex interface permitting the PGH2 long-alkyl-chains a cascade conformational prefold to a positioned conformation for intra-molecular ring closure and, on the other hand, interactions that convert the conformational changes in the chemical response directing precise functional heme states. This study reveals the substrate channeling effect in the evolution of enzymatic kinetic parameters, including the turnover number (kcat) and the apparent binding constants of substrates (KM), as both of these parameters, together with the enzyme effective concentration, affect the reaction rates.

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present context, hierarchical routing free energy landscape sampling computations are combined with molecular dynamics simulations to reveal the substrate channeling route of the processing of PGH2 transport in PGIS, by the established method for free energy calculations, to obtain a reliable binding free energy pathway (FEP) using Jarzynski's equality and the potential of mean force (PMF)13, 37-38 via umbrella sampling (US).39-40 We elucidate the order of binding steps and the elementary conformations along the pathway that are coupled to the channel dynamics, determine the timescale for the transition among them, and conduct comparisons with experiments. Enthalpy-Entropy Decomposition of Binding Free Energy and Binding Constant Consider the binding of a substrate (e.g., PGH2), S, to a protein receptor, E, PGIS, to form a complex ES: PGH2-PGIS. We address the system consisting of the three species of solute molecules present at concentrations [α], α = E, S, and ES. We assume that the significant interactions are between the binding molecules when complexed. The change in standard-state Gibbs free energy under constant pressure can be derived as eq. 1: ∆

.

where µα is the chemical potential of molecule α and Keq is the binding constant that determines the concentrations of the three species of molecules when the binding reaction reaches equilibrium, where the binding free energy is 0. [ ]o and [ ]eq describe the standard and equilibrium concentrations, respectively, and define ∆Gb°, the standard binding free energy. When the three species of molecules are all present at a “standard” concentration [ ]o, normally 1 M, the standard binding free energy can be obtained as eq. 1 Experimentalists often use the dissociation constant Kd, which is simply the inverse of Keq (measured as the Michaelis constant, KM). This equation enables us to convert a measured Keq or KM to estimate the standard binding free energy. Transient-state Kinetics of the Substrate Channeling and Catalytic Turnover In the present context, Scheme 1 describes the route of the substrate from bulk solvent to protein channel opening, in a sequence of fashion, wherein incorporation of the dynamics of the substrate channeling in the rate equation results in an apparent description of the substrate (S) PGH2 association to the enzyme (E) PGIS with a multi-step process, wherein the bulk aqueous medium PGH2 interacts with PGIS in a rapid bimolecular step with rate constants of k1 and k-1, followed by a series of [ES]i states in channeling with rate constants kci toward an optimal binding to the heme site [EI], termed out of the overall rate constant of k2, and the intermediate is converted into product with a rate constant of k3.

Theory and Methods MD-based methods provide a means of animating the static X-ray crystallographic structures, allowing for, e.g., the display of the entire dynamics of a substrate through the protein channel. The linkage between protein dynamics and catalysis has been demonstrated primarily on the µs–ms timescale, which correlates directly with the enzymatic turnover rate.1, 4 For a quantitative picture of substrate channeling, we turn to the developed thermo-kinetics model and computational methods for performing enhanced sampling in molecular dynamics simulations and for accelerating the process of interest in simulations. In the

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ACS Catalysis The second route is based on umbrella-sampling (US)39-40 potential of mean force (PMF)3, 12-13, 38-40, 45 calculations and requires forced extraction of the substrate channeling. To achieve convergence on accessible time scales, the route pathway takes advantage of a combined use of enhanced sampling techniques, such as grid-based molecular docking, a number of geometrical restraints, steered molecular dynamics, Jarzynski’s equality and umbrella-sampling, which handle the freedom of deeply buried flexible PGH2 to move or contort during the critical Fe-C11O separation (the pathway was stratified in 76 windows spaced at 0.5 Å in the region, covering a distance r between the C11-O atom of PGH2 and the heme iron of 2.2 to 40.2 Å) with reversible coupling/decoupling simulations in a crooked internal channel to the heme pocket. Notably, those restraints or forces were chosen speciﬁcally to reduce the conformational, orientation, and positional freedoms of the substrate and protein; any set of restraints was removed in the final calculations. The protein channel dynamics was also revealed during PGH2 migration, Figure 2c, in terms of the channel diameter evaluation, as the substrate positioning. As illustrated at positions A-RC (Figure 2d), the change apparently exhibits an association with the channel shrinkage and the steric course for a preference structure to a well-positioned cyclization, as well as the binding free energies of PGH2 passing through the protein. The accuracy of the MM-PB(GB)SA binding energy estimation, despite its complexity in terms of different approximation to the reaction field and solvent accessible born radii setting (see Table S1), is particularly sensitive to sampling conformations and helpful in providing ranking of substrate binding affinities along the channeling path. Details of the computational methodology and kinetic model are included in the Supporting Information.

In terms of k2 and k3, the overall rate constant kcat can be expressed as eq. 2,

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The rate constants of the steps in this mechanism can be approximated by introducing the ki(T) from the transition state theory (TST) framework,1, 5 which evaluates the rate constant of the ith step as eq. 3,

5 6 7 5 8 7⁄- .:;< =∆6‡ ?⁄@7A . * where kB and h are respectively the Boltzmann and Planck constants,ΔGi‡ is the free energy of activation for transitions between the elementary states at the dividing surface of substrate channeling, and ki(T) is estimated at the target temperature 300 K. Steady-state Approximation to the Elucidation of Rate Constants To examine the effect of substrate channeling with available experiments, we analyzed the mechanism with the steady-state approximation (SSA) for the mechanism of Scheme 1 in the familiar form of the Michaelis-Menten equation,41 as given in eq. 4, 5 ,DE 7 BC and B/D: 5 ,DE 7 . K F G 5* 5 $ 5 FG ∙ . M 5$ 5* 5 5 $ 5 FN . O 5 The Michaelis constant, KM, and the maximal rate, Vmax, can be readily derived from rates of catalysis measured at a variety of substrate concentrations, given in eq. 4. The maximal rate, Vmax, reveals the turnover number of an enzyme, which is the number of substrate molecules converted into product by an enzyme molecule in a unit time when the enzyme is fully saturated with substrate. Since Vmax is the reaction velocity at the saturating substrate concentration, it is equal to kcat [ES] when [ES] = [ET]. There are two distinct meanings of KM: 1) it can refer to the concentration of substrate at which half the active sites are filled, so it provides a measure of the substrate concentration required for significant catalysis to occur; 2) KM is related to the rate constants of the individual steps in the catalytic scheme defined as eq. 5. One way of looking at KM is to compare it to the dissociation constant of Kd, while altering substrate PGH2 to its analogues of U51605, U46619, and U44069 (see Figure 1c) allows examination of the analogue channeling affinity without the analogue getting catalyzed by the enzyme. We have Kd in terms of the defined rate constants, eq. 6. Because of the similarity between PGH2 and these analogue skeletons, we assume that they access the identical substrate channel in a comparable scale of bimolecular constants of k1 and k-1, and thus the channeling rate constant k2 becomes dominant for the corresponding Kd value.

Results and Discussion We begin with the free energy landscape, shown in the upper panel of Figure 3, for the complex going from bulk, revealing a flat landscape, the depth and PGH2 positioning along the channel, to the heme associative recognition, with the barrier and the relevant conformational changes, as illustrated at positions A-RC (Figure 2d). Table 1 elaborates the binding free energy in balances of favorable changes in Coulomb and van der Waals interactions and unfavorable changes in entropic cost and solvation energy. Notably, the substrate binding incurs configuration entropy penalties of -T∆S°, and the largest entropy penalty comes from the channel opening binding, from the bulk solution to protein. The measurements across the channel are 41 kcal/mol for channel opening and 39 kcal/mol for heme site, respectively. The entropy cost of 26–42 kcal/mol is generally in agreement with the estimated entropic cost of folding the 20-C polycarbon alkyl chains. This agrees well with the experimentally entropic cost of “freezing” the rotation of 15 bonds of at least 22 kcal mol-1 at 328 K.29, 31 Nevertheless, the association of PGH2 with enzyme is not driven by entropy per se. The maintenance of a conserved negative binding enthalpy is a crucial feature of the enthalpy-entropy compensation in channeling. The channel surface furnishes a cascade of substrate binding with high affinity by maximizing the binding interface. By this channel regulatory interface, the yield energy difference is associated with a change in the accessible surface area of around 70 Å2 for the bound states along the channel, varying from 385 Å2

Enhanced Sampling of Substrate Channeling Route with Free Energy Calculations For a quantitative picture of substrate channeling, we present two distinct approaches to determining the substrate channeling route and energies of the substrate, PGH2, positioning to the buried heme site of PGIS. The first route utilizes binding free energy pathway (FEP)37, 42-44 calculations with enhanced sampling to couple and decouple the substrate along the channel to the heme pocket.

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to 315 Å2 (according to the modeling software, cf. Table 1 and Figure 2d). Such a strongly enthalpy-driven transit generates a sequence of isomeric PGH2 structures exposed to the channel going over to fit the heme site. Moreover, water molecules were found to reside within the identified channels, and molecular dynamics simulations in a water box were sufficient to observe the movement of water molecules in the channels and the exchange with the heme site. This view is an extension to the observation that entropic catalysis could be achieved by expelling ordered water molecules from the active site via the channels in a manner of substrate binding.46-49

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interactions (Figures 3b and 3c). The barrier is mainly caused by the steric repulsion among the endoperoxide and the head bridge CH2 of the heptane ring, as well as the chiral-positioned hydrogen atoms with the bottleneck residues of Y460, G462, F463, L101, L105, and Y97 in very close contact of about 3Å (see Figure 3b and Table 2). The other deep basin on the profile centered at 2.2 Å corresponds to the optimal binding of PGH2 at the heme site (position RC in Figure 3b). Interestingly, the energy depth of this heme site is comparable to that of the channel doorway binding (position D); it is lower by only ~1 kcal/mol. Inspecting the atomistic details of the interactions rationalizes the sources of high binding affinity. The two arms of PGH2 adopt a parallel arrangement, in which the α-chain makes strong electrostatic interactions with residues of T338, Y97, and heme 7-propionate, and the ω-chain is mainly stabilized by the 15-OH anchoring H-bond interactions with the 6-propionate (Figure 3b). Accordingly, the endoperoxide head sits snugly on the heme site, with C11-O coordination to the iron. Further inspection shows PGH2 alkyl-chain motions coupled remarkably with the water rearrangements surrounding the channel and heme pocket, as depicted in Figures 3 and S5. We speculate that the PGH2 cyclization occurs in concert with the C-H activation, which is associated with coupling with the water-relay network and generates a transient reactive carbocationic species for the C9(O) protonation. However, this cyclization is the focus not of this work but of another ongoing work.

Substrate migration along the channeling trajectory with free energies. Comparing the FEP with PMF routes clarifies that there is a flat landscape in the bulk, and then the energy drops to ~ -20 kcal/mol (~ -4 kcal/mol for PMF) once PGH2 enters the channel interior, at r ~21 Å, followed by a shallow energy minimum at ~18 Å (position A), near the channel opening. This rise is related to the opening having a diameter of 4.5 Å, which is small as compared to the overall channel width and the buried heme site. PGH2 thus adopts a restricted conformation with two arms stretched in antiparallel orientation while it is moving from the bulk solvent to the protein channel (see Figure 3a),50-51 yielding the free energy cost associated with the loss of conformational freedom of the flexible rotamers on the long-alkyl-chains (α- and ω-chains). The intercalation at the opening via the arm of the ω-chain is associated with residues of the hydrophobic residue cluster consisting of alanines and luciens forming the groove, and the α-chain along the loop connecting the FG-loop (vide conformation A in Figure 3b). PGH2 positioning leads to the relevant channel harboring residues with significantly pre-organized motions and the decomposed energy changes as highlighted in Figure 3c and elaborated in Table 2. Along the channeling route, the GBSA free energy profile features two deep energy basins also revealed in the PMF route. The one centered at r ~13–16 Å corresponds to PGH2 stably binding to the channel doorway site, as compared to the co-crystallography structure of the U51605 position in PGIS (Figure S4). The binding affinity inside the channel is about -12 kcal/mol, where the PGH2 arms have significant interactions with the amino acid residues, in which the α-chain forms strong hydrogen-bonding interaction with R104, the endoperoxide head interacts with Y97, T338, and R362, and the ω-chain is immersed in the channel, sharing extensive van der Waals interactions with F463, Y460, etc. (vide Doorway binding conformation in Figure 3b). In the narrowest part of the channel, PGH2 experiences a barrier of ~15 kcal/mol (PMF~7.5 kcal/mol) relative to the channel opening. The independent estimate obtained from difference route calculations has revealed the significant energy barrier height separating the two basins of the channel and heme pocket. As indicated by the complex structure of the threshold (see Figure 3b), the closely-lying residues of Y97, L101, L105, R209, Y460, G462, and F463 enclose a bottleneck structure, which links two strongly-connected regions of the access channel and the heme pocket. We noted that the relatively stretched two-arm motion of PGH2 contributes to lowering of the barrier, as the steric clash between the substrate and bottleneck is largely avoided; the α-chain has strong electrostatic interactions with residues of R209 and Y97. The ω-chain of PGH2 is mainly stabilized by the 15-OH anchoring T338 and R339 with hydrogen-bonding

Substrate channeling effect on the modulation of H-bond pattern to the relevant heme axial ligation Our results reveal that the channel binding states not only operate the conformational PGH2 but also align the reactive group of the Cys-heme matrix environment (see Figures 3b and 3c). Such a substrate channeling effect on the chemical response of the reactive heme center can be traced to the loop structure connecting the distal protein channel and the proximal catalytic domain of the Cys-heme site (Figures S4 and S5). The residues of T338, R339, R362, and N419 lying on the channel wall cause the anchor interactions with the carboxyl or 15-OH groups of PGH2 stereoisomers. Thus, these elementary stages with the corresponding structural change are coupled to the proximal residues of P422, G423, and R424, which directly follow the cysteine coil (C421) around the thiolate, presenting amide N-H hydrogen bonding to the thiolate ligand (see Figure 4). It is generally recognized that the NH···S hydrogen bond pattern on the proximal side of the Cys-heme structure modulates the Fe-S bond strength, in terms of the push-pull [NH···S–Fe] relation, as for the Fe–S bond weakening by the stronger NH···S interactions. Our simulations elucidated the Fe–S dependent distribution in tuning the thiolate “push” effect to the opposite Fe-O interaction. Trajectory analyses have revealed a certain correlation between the relevant distances of Fe-S and Fe-water (O) or Fe-C11(O) during the PGH2 channeling (Figure 4a). Although the difference in Fe-S bond lengths is small, it is significant for such a bond length variation along the channeling stages. Importantly, our measurements of the Fe-S bond have a standard deviation based on the MD trajectory snapshots. Comparison revealed that the channel threshold state aligns stronger amide NH···S interactions and thus weakens the Fe-S bond, followed by the departure of the iron coordinated water to the five-coordinate high-spin iron(II) porphyrinate prior to the formation of the optimal PGH2 bound iron(III) specie as Cpd 0 (Figure 4b). 4


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ACS Catalysis culture (for the enzymes inside), and thus would give different KM (Keq) values to binding free energies (∆Gb°) (see Table 3). Therefore, a range of values for ∆Gb° is shown. The key to understanding this range is to get a sense of how the concentrations differ from standard conditions. Nevertheless, the binding energies along the protein internal channel in the present study reveal the “threshold” barrier for the turnover of substrate translocation, which is independent of the “standard” conditions because of the concentrations being effective only for the initial binding forward reaction. To put these numbers (Table 3) and energy landscape features (Figure 3) in perspective, substrate channeling exerts a driving force of a flat energy drop from the bulk to the channel intercalation and does work to surmount the barrier of 15 kcal/mol for a flexible signaling molecule of PGH2 to pass the threshold. This threshold barrier has been used to determine the rate constant of kthreshold ~ 4.6 sec-1 at the target temperature of 300 K, to be termed out of the slowest step passing the channel (Table 3). This relevant threshold state (rate-determining step) occurring in the PGH2 channeling likely reflects the experimental catalytic turnover number of PGIS with kcat of 16.3 sec-1. The same scenario can be stated for cyclooxygenase-2 (COX-2)52-53, which has revealed similar turnover with a threshold barrier (Table 3) for the arachidonic acid (AA, see Figure 1c) translocation in a channel. We furnish the means by which the P450 internal channel plays the dominant role in regulation of substrate migration. Also, a standing question is why the P450s and these lipid-derived signaling molecules were observed loci on the cell membrane and why the bulk water concentration serves much more minor roles. Moreover, incorporation of the substrate channeling dynamics in the kinetic analysis results in an apparent description of the departure of rate constant kcat, as (k2 k3)/(k2 + k3). Consider a limiting case in which k3 is much greater than k2. The product forms much more rapidly than the rate-determining step of the substrate channeling, and thus the kcat is close to the rate constant of k2 (kthreshold). When this condition is met, the Michaelis constant41 KM is feasible to represent substrate-enzyme affinity as (k2+k-1)/k1, as compared to the dissociation constant of Kd. We describe the way that the reactive turnover depends on the substrate channeling we have been discussing, and the corresponding experiments, where available, are collected in Table 4. One way to examine the effect of substrate channeling is to compare the substrate KM with its analogue Kd value, while altering substrate PGH2 to its analogues of U51605, U46619, and U44069 allows verification of the modified group interactions in channeling affinity without the analogue getting catalyzed by the enzyme. The physical basis for this comparison is the idea of these ligands sharing a similarity of skeletons; they access the identical substrate channel via the protein surface opening in a comparable scale of bimolecular constants of k1 and k-1, and thus the channeling rate constant k2 becomes dominant for the corresponding Kd value. This view is further supported by the Kd values of 1.7, 36, and >190 µM for the PGH2 analogues of U51605, U46619, and U44069, respectively, showing a significantly altered scale to the KM of 13.3 µM for substrate PGH2 (see Table 4). PGIS is therefore sensitive to modifications of the substrate for the group substitutions of 15-OH, C9-CH2, and C11-CH2 in U51605, U46619, and U44069, respectively (see Figure 1b). From a mechanistic viewpoint, the channel threshold acts as a valve in regulation of the passing; if it is slow, it will

Accordingly, the Cys-heme pocket is thus optimized for the endoperoxide binding, and the first step of the catalytic cycle of PGIS starts only when the PGH2 surmounts the channel threshold, which is accompanied by the removal of water molecule coordination to the heme iron (Figure 4b). There is accumulating evidence supporting the chemical role of heme proximal NH–S bonds in modulating the thiolate push effect for heme catalytic potential.26 Our data reveal that the distal conformational change to the Cys-heme proximal side occurs through the conjunction of key residue motifs or “molecular switches” within the protein channel. Upon substrate binding, the transitions between the catalytically component states of the P450 cycle proceed via the channeling stage. Noticeably, these defined conformational changes along the PGH2 channeling are attributed to pre-organization of the active site residues in a configuration needed to facilitate a preorganization (prerequisite) of the chemical environment prior to the reaction. Moreover, the PGIS co-crystal structure (PDB ID: 3B99),32 the substrate analogue U51605, has been found to bind at this revealed channel as the doorway structure (see Figure S4). Though the binding was initially puzzling, our study provides an examination of the substrate binding dynamics and the important function of the protein channel as a regulator, not only for enhancement of the binding affinity but also for the stepwise control of configurations for the catalytically component states to execute the P450 cycle. Elementary states along the binding dynamics with kinetic analysis The formation of sequential bound stereoisomers, as observed above, seems necessary to hold PGH2 in the channel to allow time for the structural alterations needed for stereo- and chemo-selective cyclization to occur. These dynamic components enable us to proceed with the composite time course for the transition among them and conduct comparisons with experiments. The revealed routes (Figure 3) for determining absolute free energies are underscored by the notable difference between approaches of MMGBSA binding free energy and PMF calculations. Nonetheless, the routes lead to virtually identical results in good correlations, namely the standard binding free energy (∆Gb°) and channeling threshold barrier (∆P Q , in close agreement with the experimental value (Table 3). While the dynamical events of the sequential binding process are interpreted, we elucidate the order of binding steps, Scheme 1. First is a rapid bimolecular binding step (formation of an “outside” complex, Figure 3), where the standard binding free energies given by MMGBSA and PMF calculations were ~ -20 kcal/mol and ~ -4 kcal/mol, respectively, compared to that of experimental measurement of ~ -6 kcal/mol. What follows is a stream of PGH2 conformers of the “internal” channel intercalation and conformational adjustments (stereoisomers) [ES]i to optimal binding [EI] in the buried Cys-heme site. The MMGBSA revealed the threshold barrier of ~ 14 kcal/mole, in good agreement with the experimental measurement, Figure 3 and Table 3, as compared to that of 7.5 kcal/mole given by PMF. It appears that MMGBSA is more sensitive than PMF to the protein channel environment in seeking a channeling threshold. In experiments, the calculations of ΔGb° require accurate measurement of the standard aqueous concentrations, in which such concentrations would be measured differently from the terms of isolated enzymes in aqueous and cell

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positioning and conformational change. This is treated quantitatively using calculations of the key aspects of the free energy landscape. Defined conformational changes are attributed to pre-organized heme site residues in the configuration needed to facilitate catalysis. It therefore appears that evolutionary protein channels with mechanochemidcal valves shape the kinetic parameters of enzymes and the catalytic efficiency. In spite of its obvious challenges in mapping of the substrate channeling dynamics in proteins experimentally, we suggest that global analyses of channeling residues can shed light on how evolution on the one hand and pre-organized motions on the other have molded enzyme catalysis. As more kinetic data are rapidly being gathered, the means of simulating and measuring channeling fluxes are developing and we are hopeful it will become widely available to address such a channeling function for engineering-enhanced catalysis in synthetic cascades.

reduce the entire rate, which is also reflected in the affinity values of Kd and KM. The altered Kd reflects the presence of channel threshold interactions, which are well defined in PGIS, because the closely lying residues of Y97, L101, L105, R209, G462, and F463 are operative for bottleneck regulation of the endoperoxide within a strained heptane ring bridging two chiral-positioned long-alkyl-chains in close contact (for details, see Figures S5 and S6). The magnitude of this difference in surmounting barriers is proportional to the magnitude of the increase in Kd value; for example, U44069, with much larger Kd, reflects the largely steric repulsion among the C11-CH2 and the head bridge CH2 of the heptane ring, and also the chiral-positioned hydrogen atoms with the bottleneck residues in very close contact of less than 3Å (Figure S6). Some of these channel harboring residue interactions were validated by biochemical experiments (c.f. Table 2 and Table S3). For example, the mutants indicated significantly decreased activities for PGISR219D and PGISP215R over the wild type PGIS.50 As manifested above, these identified residues do not belong to the heme site, but they indeed display a primary role in the channel regulatory transportation. This again supports the impact of the PGIS substrate channeling effect on the conformational changes and preorganization to the catalytic component formation, with stereo- and region-selectivity, which does not solely depend on the active site of heme-iron-binding to C9-O or C11-O. Comparison between the rate parameters, referring to the counter protein of TXAS and those P450s, is noteworthy. TXAS yields almost the same value of Kd for U46619 and U44069. This supports that TXAS channeling is not as sensitive as that of PGIS to substrate modifications, as evidenced by the resonance Raman spectra.25 For the case of those P450s, such as 3A4, 1A2, and 2E1, they only catalyze PGH2 fragmentation to malondialdehyde (MDA) and display an absolute apparent kcat value that is approximately 1 to 2 orders of magnitude lower than that of the PGIS enzyme (Table 4). Overall, from these studies on activity and PGH2 analogue accessibility, these P450 structures have been shown to feature substrate channel arrangements inside the protein; thus, the substrate PGH2 effectively moves through the channel into the active site of the enzyme. However, a variety of channel harboring residues do affect the selectivity and passing of reactants to produce yields of products or a desired compound. In the present study, we suggest that a high fidelity of isomerization of PGH2 into PGI2 by PGIS can be attributed to the adoption of a cascade of conformational changes via the channeling route to the buried heme site and, mainly due to the channel bottleneck stage, the preorganization of the chemical microenvironment accompanying the PGH2 passing and optimal binding to the heme site.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Simulation methods and characterization details (PDF). Author information Corresponding Author. *E-mail: [email protected] Phone: +886-2-2905-2534 ORCID Hsiao-Ching Yang : 0000-0002-7970-1357 Yung-Chi Ge : 0000-0003-1199-1500 Cheng-Han Yang : 0000-0001-7517-3799 Acknowledgments This work was supported by Grant 104-2113-M-030-009-MY3 from the Ministry of Science and Technology of the Republic of China. References (1) Garcia-Viloca, M.; Gao, J.; Karplus, M.; Truhlar, D. G., How enzymes work: analysis by modern rate theory and computer simulations. Science 2004, 303, 186-95. (2) Warshel, A.; Sharma, P. K.; Kato, M.; Xiang, Y.; Liu, H.; Olsson, M. H. M., Electrostatic Basis for Enzyme Catalysis. Chem. Rev. 2006, 106, 3210-3235. (3) Gao, J.; Ma, S.; Major, D. T.; Nam, K.; Pu, J.; Truhlar, D. G., Mechanisms and Free Energies of Enzymatic Reactions. Chem. Rev. 2006, 106, 3188-3209. (4) Henzler-Wildman, K. A.; Lei, M.; Thai, V.; Kerns, S. J.; Karplus, M.; Kern, D., A hierarchy of timescales in protein dynamics is linked to enzyme catalysis. Nature 2007, 450, 913-6. (5) Klippenstein, S. J.; Pande, V. S.; Truhlar, D. G., Chemical kinetics and mechanisms of complex systems: a perspective on recent theoretical advances. J. Am. Chem. Soc. 2014, 136, 528-46. (6) Eyring, H., The activated complex and the absolute rate of chemical reactions. Chem. Rev. 1935, 17, 65-77. (7) Bar-Even, A.; Noor, E.; Savir, Y.; Liebermeister, W.; Davidi, D.; Tawfik, D. S.; Milo, R., The moderately efficient enzyme: evolutionary and physicochemical trends shaping enzyme parameters. Biochemistry 2011, 50, 4402-4410. (8) Denisov, I. G.; Makris, T. M.; Sligar, S. G.; Schlichting, I., Structure and chemistry of cytochrome P450. Chem. Rev. 2005, 105, 2253-77. (9) Miles, E. W.; Rhee, S.; Davies, D. R., The molecular basis of substrate channeling. J. Biol. Chem. 1999, 274, 12193-6. (10) Wheeldon, I.; Minteer, S. D.; Banta, S.; Barton, S. C.; Atanassov, P.; Sigman, M., Substrate channelling as an approach to cascade reactions. Nat. Chem. 2016, 8, 299-309. (11) Gilson, M. K.; Given, J. A.; Bush, B. L.; McCammon, J. A., The

Conclusion In summary, this study presents the incorporation of substrate channeling into free energy landscape to clarify how it shapes the cascade cyclization route, enforcing precise spatial and temporal control. This channeling process plays a central role in estimation of the kcat and KM, affecting the enzyme efficiency. The present MD-based study also provides a means of animating the static X-ray crystallographic structures, allowing for, e.g., the display of an entire dynamics event of a substrate through the protein channel. The key result is the balance between substrate

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ACS Catalysis 2008, 283, 2917-2926. (33) Yeh, H. C.; Hsu, P. Y.; Wang, J. S.; Tsai, A. L.; Wang, L. H., Characterization of heme environment and mechanism of peroxide bond cleavage in human prostacyclin synthase. Biochim. Biophys. Acta. 2005, 1738, 121-32. (34) Plastaras, J. P.; Guengerich, F. P.; Nebert, D. W.; Marnett, L. J., Xenobiotic-metabolizing cytochromes P450 convert prostaglandin endoperoxide to hydroxyheptadecatrienoic acid and the mutagen, malondialdehyde. J. Biol. Chem. 2000, 275, 11784-90. (35) Hsu, P. Y.; Tsai, A. L.; Kulmacz, R. J.; Wang, L. H., Expression, purification, and spectroscopic characterization of human thromboxane synthase. J. Biol. Chem. 1999, 274, 762-9. (36) Cojocaru, V.; Winn, P. J.; Wade, R. C., The ins and outs of cytochrome P450s. Biochim. Biophys. Acta. 2007, 1770, 390-401. (37) Swanson, J. M. J.; Adcock, S. A.; McCammon, J. A., Optimized radii for Poisson. A.; calculations with the AMBER force field. J. Chem. Theory Comput. 2005, 1, 484-493. (38) Roux, B., The calculation of the potential of mean force using computer simulations. Computer Physics Communications 1995, 91, 275-282. (39) Souaille, M.; Roux, B. t., Extension to the weighted histogram analysis method: combining umbrella sampling with free energy calculations. Computer Physics Communications 2001, 135, 40-57. (40) Torrie, G. M.; Valleau, J. P., Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling. J. Comput. Phys. 1977, 23, 187-199. (41) Michaelis, L.; Menten, M. L.; Johnson, K. A.; Goody, R. S., The original Michaelis constant: translation of the 1913 Michaelis-Menten paper. Biochemistry 2011, 50, 8264-9. (42) Cramer, C. J.; Truhlar, D. G., A universal approach to solvation modeling. Accounts. Chem. Res. 2008, 41, 760-768. (43) Hawkins, G. D.; Cramer, C. J.; Truhlar, D. G., Parametrized models of aqueous free energies of solvation based on pairwise descreening of solute atomic charges from a dielectric medium. J. Phys. Chem. 1996, 100, 19824-19839. (44) Tsui, V.; Case, D. A., Molecular dynamics simulations of nucleic acids with a generalized born solvation model. J. Am. Chem. Soc. 2000, 122, 2489-2498. (45) Laio, A.; Parrinello, M., Escaping free-energy minima. Proc. Natl. Acad. Sci. U. S. A. 2002, 99, 12562-12566. (46) Young, T.; Abel, R.; Kim, B.; Berne, B. J.; Friesner, R. A., Motifs for molecular recognition exploiting hydrophobic enclosure in protein-ligand binding. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 808-13. (47) Ball, P., Water as an active constituent in cell biology. Chem Rev 2008, 108, 74-108. (48) Weber, P. C.; Wendoloski, J. J.; Pantoliano, M. W.; Salemme, F. R., Crystallographic and thermodynamic comparison of natural and synthetic ligands bound to streptavidin. J. Am. Chem. Soc. 1992, 114, 3197-3200. (49) Das, A.; Varma, S. S.; Mularczyk, C.; Meling, D. D., Functional investigations of thromboxane synthase (CYP5A1) in lipid bilayers of nanodiscs. Chembiochem 2014, 15, 892-9. (50) Deng, H.; Wu, J.; So, S. P.; Ruan, K. H., Identification of the residues in the helix F/G loop important to catalytic function of membrane-bound prostacyclin synthase. Biochemistry 2003, 42, 5609-17. (51) Chiang, C.-W.; Yeh, H.-C.; Wang, L.-H.; Chan, N.-L., Crystal Structure of the Human Prostacyclin Synthase. J. Mol. Biol. 2006, 364, 266-274. (53) Vecchio, A. J.; Orlando, B. J.; Nandagiri, R.; Malkowski, M. G., Investigating substrate promiscuity in cyclooxygenase-2: the role of Arg-120 and residues lining the hydrophobic groove. J. Bio. Chem. 2012, 287, 24619-24630. (53) Kargman, S.; Wong, E.; Greig, G. M.; Falgueyret, J. P.; Cromlish, W.; Ethier, D.; Yergey, J. A.; Riendeau, D.; Evans, J. F.; Kennedy, B.; Tagari, P.; Francis, D. A.; O'Neill, G. P., Mechanism of selective inhibition of human prostaglandin G/H synthase-1 and -2 in intact cells. Biochem Pharmacol 1996, 52, 1113-1125.

statistical-thermodynamic basis for computation of binding affinities: a critical review. Biophys. J. 1997, 72, 1047-1069. (12) Kim, Y.; Mohrig, J. R.; Truhlar, D. G., Free-energy surfaces for liquid-phase reactions and their use to study the border between concerted and nonconcerted rends shaping enzyme Parameters. asis for this compaJ. Am. Chem. Soc. 2010, 132, 11071-11082. (13) Gumbart, J. C.; Roux, B.; Chipot, C., Standard binding free energies from computer simulations: what is the best strategy? J. Chem. Theory Comput. 2013, 9, 794-802. (14) Funk, C. D., Prostaglandins and leukotrienes: advances in eicosanoid biology. Science 2001, 294, 1871-5. (15) In Cytochrome P450: Structure, Mechanism, and Biochemistry, 3rd Ed. Ortiz de Montellano P. R., Kluwer Academic/Plenum Publishers, New York,: 2005. (16) Ortiz de Montellano, P. R., Hydrocarbon hydroxylation by cytochrome P450 enzymes. Chem. Rev. 2010, 110, 932-48. (17) Collins, P. W.; Djuric, S. W., Synthesis of therapeutically useful prostaglandin and prostacyclin analogs. Chem. Rev. 1993, 93, 1533-1564. (18) Noyori, R.; Suzuki, M., Prostaglandin syntheses by three-component coupling. new synthetic methods (49). Angew. Chem. Int. Ed. Engl. 1984, 23, 847-876. (19) Green, M. T., C-H bond activation in heme proteins: the role of thiolate ligation in cytochrome P450. Curr. Opin. Chem. Biol. 2009, 13, 84-8. (20) Hecker, M.; Ullrich, V., On the mechanism of prostacyclin and thromboxane A2 biosynthesis. J. Biol. Chem. 1989, 264, 141-50. (21) Dawson, J. H., Probing structure-function relations in heme-containing oxygenases and peroxidases. Science 1988, 240, 433-9. (22) Rittle, J.; Green, M. T., Cytochrome P450 compound I: capture, characterization, and C-H bond activation kinetics. Science 2010, 330, 933-7. (23) Shaik, S.; Kumar, D.; de Visser, S. P.; Altun, A.; Thiel, W., Theoretical perspective on the structure and mechanism of cytochrome P450 enzymes. Chem. Rev. 2005, 105, 2279-328. (24) Austin, R. N.; Deng, D.; Jiang, Y.; Luddy, K.; van Beilen, J. B.; Ortiz de Montellano, P. R.; Groves, J. T., The diagnostic substrate bicyclohexane reveals a radical mechanism for bacterial cytochrome P450 in whole cells. Angew. Chem. Int. Ed. Engl. 2006, 45, 8192-4. (25) Auclair, K.; Hu, Z.; Little, D. M.; Ortiz De Montellano, P. R.; Groves, J. T., Revisiting the mechanism of P450 enzymes with the radical clocks norcarane and spiro[2,5]octane. J. Am. Chem. Soc. 2002, 124, 6020-7. (26) Groves, J. T., Enzymatic C-H bond activation: using push to get pull. Nat. Chem. 2014, 6, 89-91. (27) Krest, C. M.; Silakov, A.; Rittle, J.; Yosca, T. H.; Onderko, E. L.; Calixto, J. C.; Green, M. T., Significantly shorter Feh the radical clocks norcarane and spiro[t with greater reactivity relative to chloroperoxidase. Nat. Chem. 2015, 7, 696-702. (28) Chao, W. C.; Lu, J. F.; Wang, J. S.; Yang, H. C.; Chen, H. H.; Lan, Y. K.; Yu, Y. C.; Chou, P. T.; Wang, L. H., Probing the interaction between prostacyclin synthase and prostaglandin H2 analogues or inhibitors via a combination of resonance Raman spectroscopy and molecular dynamics simulation approaches. J. Am. Chem. Soc. 2011, 133, 18870-9. (29) Page, M. I.; Jencks, W. P., Entropic contributions to rate accelerations in enzymic and intramolecular reactions and the chelate effect. Proc. Natl. Acad. Sci. U. S. A. 1971, 68, 1678-83. (30) Manna, K.; Everett, W. C.; Schoendorff, G.; Ellern, A.; Windus, T. L.; Sadow, A. D., Highly enantioselective zirconium-catalyzed cyclization of aminoalkenes. J. Am. Chem. Soc. 2013, 135, 7235-50. (31) Chang, C.-e. A.; Chen, W.; Gilson, M. K., Ligand configurational entropy and protein binding. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 1534-1539. (32) Li, Y.-C.; Chiang, C.-W.; Yeh, H.-C.; Hsu, P.-Y.; Whitby, F. G.; Wang, L.-H.; Chan, N.-L., Structures of prostacyclin synthase and its complexes with substrate analog and inhibitor reveal a ligand-specific heme conformation change. J. Bio. Chem.

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Table 1. Energetics for the relevant PGH2 channeling conformations in PGIS, the enthalpy–entropy compensations, and the nonbonding energy contributions given at 310 K. ∆HMM

Entropyc -T∆S

Binding Free b Energy ∆Gbind

-0.17 ± 2.01

0.38 ± 0.23

42.02

42.40 ± 1.49

-8.21 ± 3.25

14.76 ± 2.78

-36.57 ± 3.51

40.67

4.14 ± 3.23

-46.05 ± 3.15

-26.06 ± 7.46

32.79 ± 5.12

-39.30 ± 5.07

40.34

1.04 ± 5.42

349.35

-51.89 ± 1.95

-28.73 ± 2.34

28.78 ± 1.65

-50.91 ± 3.08

33.61

-13.66 ± 2.32

Threshold

384.80

-27.24 ± 2.25

-4.55 ± 2.93

21.33 ± 1.95

-10.46 ± 2.81

26.45

15.99 ± 2.52

E

334.23

-50.87 ± 1.64

-22.37 ± 3.00

32.54 ± 2.28

-40.70 ± 2.87

39.44

-1.27 ± 2.51

F

315.18

-38.16 ± 2.02

-11.65 ± 1.35

25.43 ± 1.39

-24.37 ± 2.37

25.58

1.20 ± 1.83

Reactive Center

336.90

-49.87 ± 2.99

-43.93 ± 3.70

38.96 ± 2.93

-54.84 ± 2.33

39.18

-15.66 ± 3.03

PGH2 Surfacea

VDW Energy

Coulomb Energy

Solvation Energy

(Å )

∆HvdW

∆Helec

∆Gsol

Bulk Solvent

468.74

-0.22 ± 0.20

0.76 ± 2.19

A

339.39

-43.11 ± 3.32

B

347.14

Doorway

States

2

Enthalpy

a

The VDW surface of each PGH2 conformer was calculated by the software Discovery Studio. Values of binding free energy were calculated according to eqs. S(16)-S(18), details see the Supporting Information. 〈ΔPSTUV 〉 〈XPYZ[\]^_ 〉 〈P\`Za^TU 〉 〈P]TbcUV 〉 S16 〈ΔPSTUV 〉 〈Δghh 〉 〈∆PiZ] 〉 〈j∆k〉 S17 〈ΔHhh 〉 〈gTUa 〉 〈gnVo 〉 〈g^]^ 〉 S18 All values are given in kcal mol-1 c Entropy calculations were performed for 10 spaced snapshots of 1 ns production MD trajectory ( every 100 ps) with normal mode quasi-harmonic analyses. b

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ACS Catalysis

Table 2. The involved amino residues interactions during the stages of PGH2 channeling to fit the heme site binding in PGIS. PGH2 channeling stages zPGIS (hPGIS)

Reaction center

Threshold

Doorway

Channel opening

Hydrophobic residues

-

-

F45, A68-A69, L71, I73 (L44, V69-G70, R72, V74)

W38, L39, A42, F45, A68-A69, L71, I73 (W39, L40, L44, V69-G70, R72, V74)

SRS1

Y97, L101, M102 (Y99, L103, M104)

Y97, R104, I105 (Y99, R106, I107)

Y97, L101, R104 (Y99, L103, R106)

Y97, R104 (Y99, R106)

SRS2

-

K202, P205, A208-R209 (K212, P215, A218-R219)

R209-T210 (R219-T220)

R209-T210 (R219-T220)

SRS4

W272-V273, N277 (W282-V283, N287)

W272 (W282)

-

-

SRS5

I337-T338, R339 (I357-T358,R359)

A335-T338 (A355-T358)

L336, T338 (F356, T358)

L336, T338 (F356, T358)

SRS6

F463 (F483)

G462-F463 (G482-F483)

G462-F463 (G482-F483)

-

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Table 3. Summary of experimental rate constants, the inferred equilibrium binding free energy, turnover barrier and those comparative estimates from computational routes. Functional Parameters Thermodynamics Experimental Conditions (Prediction Method) PGIS-PGH233 ( MMGBSAHCT ) ( MMGBSAOBC ) ( MMPBSA ) ( PMF ) PGIS-U51605

[E]T

kon

(µM)

(M s )

-1

-1

∆qr , (∆∆qr ?

KM (analogue) Kd (substrate)c (µM)

0.05

1.4E+6

13.3 ± 1.4

0.3

-

1.7± 0.36

a

(kcal/mol)

-6.69 ( -26.57 ± 3.51 ) ( -19.74 ± 2.84 ) (4.40 ± 4.84 ) ( -4.36 ) -7.90

Kinetics

kcat (s-1) 16.7

-

b

∆qQ (∆∆qQ ,

kcat/KMe (M-1 s-1)

(kcal/mol)

15.9 (11.85 ± 3.51 ) (10.91 ± 2.84 ) (30.71 ± 4.84 ) ( 6.16 ) -

1.24E+6

-

COX2-AA ( in aqueous)52

0.02 8.4 ± 0.7 -6.96 26.7±0.5 15.6 3.22E+6 53 COX2-AA (in cell) 0.74 -8.40 a Experimentalists often use the dissociation constant Kd, which is simply the inverse of Keq (measured as the Michaelis constant, KM). The eq. 1 enables us to convert a measured Keq or KM to estimate the standard binding free energy. b The rate constants of encountered states crossing can be approximated by introducing the ki(T) from the transition state theory (TST) framework,1, 5 which evaluates the departure of the rate constant of the ith state as eq. 3. c The thermo-equilibrium KM value for the substrate PGH2 binding and the Kd value for the substrate analog U51605 to PGIS d Q 〈∆∆qr 〉 = 〈∆qr,tu0&&v wx&3&y〉 - 〈∆qr,zv {v|&1〉 and 〈∆∆qQ 〉 = 〈∆q u}~u{v 〉 - 〈∆qQ 〉. tu0&&v wx&3&y

F G { !01 ⁄ {& , if koff is much smaller than kcat, then F G { !01 ⁄5 C ≈ 5 ,DE ⁄ {& ; {& ≈ !01⁄5 G The calculations were carried out using standard state concentrations of molar volume 24.5 m3 for all species in the gas phase, 1 M for aqueous solution and 0.1 M~0.15 M for NaCl dissolved in solvent. e f

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ACS Catalysis

Table 4. The functional parameters of the P450 enzymes Enzyme

Ligand

Product

Functional parameter a

PGIS

PGH2

6-keto-PGF1

KM: 13.3 ± 1.4 µM, kcat/KM: 1.4x106 M-1s-1, kcat: 16.3s-1

PGIS

U44069

Kd: >190 µM

32

PGIS

U46619

Kd: 36 ± 2 µM

32

PGIS

U51605

Kd: 1.7 µM

This work

TXAS

PGH2

TXA2, HHT, MDA

KM: 22 µM, kcat/KM: 2.4 x 106 M-1s-1, kcat: 53.3 s-1

Reference 19, 32-33

19, 35

35

U44069

Kd: 28 ± 4µM Kd: 6 ± 3µM

37

TXAS

TXAS

U44069

Kd: 5 ± 4µM

37

TXAS

U51605

Kd: 1.1 µM

This work

35 -1

P450 3A4

PGH2

HHT +MDA

kcat: 10 ± 1 min

P450 1A2

PGH2

HHT +MDA

kcat: 0.62 ± 0.02 min-1

35

P450 2E1

PGH2

HHT +MDA

kcat: 1.0 ± 0.1 min-1

35

PGH2

KM: 26.7 ± 05 µM kcat/KM: 3.2 x 105 M-1s-1 kcat: 8.4 ± 0.7 s-1

52

COX-2

AA

a

To examine the effect of substrate channeling with available experiments, we performed analysis with the steady-state approximation for the mechanism accounting in Scheme 1, detail in the SI, as the Michaelis-Menten equation 4. The maximal rate, Vmax, reveals the turnover number of an enzyme. The Michaelis constant, KM, is related to the rate constants of the individual steps in the catalytic scheme defined as eq. 5, and compared to the dissociation constant of Kd, eq. 6.

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Figure 1. Schematic representation of (a) the C-H bond activation in P450 catalytic cycle with the peroxide shut pathway and (b) the endoperoxide PGH2 isomerization via the P450 isomerase PGIS and TXAS. (c) the PGH2 analogues. The biochemical pathways of PGH2 via the enzymatic routes14, 16, 20 lead to several classes of physiological regulators, such as the hydroxylation to prostaglandins, or by fragmentation to malondialdehyde (MDA) and 12-hydroxyheptadeca-5,8,10-trienoic acid (HHT).

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ACS Catalysis

Figure 2. Stereo view of the P450 PGIS native structure with the spatially continuous channel for substrate PGH2 access to the buried Cys-heme site. (a) Ribbon diagram of the P450 protein fold structure of PGIS (PDB 2IAG, 3B99),32-33 with a conserved orientation of the proximal helixes and loop that forms the Cys-Heme-pocket. (b) Representative configuration sampled in the channel leading to buried heme site, described by the binding conformations (lower panel) and the centers of mass (black dots) of PGH2, as well as the corresponding binding states indicated. (c) The PGH2 access to channeling stages exhibits coupling with the channel shrinkage, observed in terms of the channel length and diameter variation. (d) The isomeric configurations of PGH2 are shown in stick models; the corresponding 20 carbon atoms are colored dark green, and oxygen in red.

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Figure 3. Comparison of the FEP and PMF routes portrayed by the Fe-C11O(r) distance of the instantaneous configurations of PGH2 along the PGIS channel leading to buried heme site. (a) The evaluation value with standard deviation is associated with the conformational flexibility accounting of more than thousands of conformers in the PGH2 binding trajectory. (b) Highlight the regions for the flat landscape in the bulk, the drop and the depth with positions of binding stages, at the threshold stage the flipping of amino residues of Y97, R209, F463 leads PGH2 to a access the reaction center. PGH2 (green for carbon atoms), heme (magenta for carbon atoms) and the residues (SRS region color for carbon atoms) interacting with it are drawn as a stick model. Their oxygen and nitrogen atoms are colored red and blue, respectively. The relevant interactions are indicated by black dashed lines. (c) The decomposition energy spectra highlight the pre-organized residues (upper panel) and the region of heme proximal residues enlarged (bottom panel).

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ACS Catalysis

Figure 4. Evolution of the Cys-thiolate-ligated heme structure states along the PGH2 access path showing the different hydrogen-bonding patterns in the proximal side of the heme moiety, as the residues of P422, G423, and R424 directly following the cysteine coil around the thiolate, presenting amide N-H hydrogen bonding to the thiolate position, which affords the push-pull control for modulating the relevant Fe-S strength, as revealed by (a) the MD trajectory analyses of Fe-S distance variation and thus in regulation of the iron opposite ligation ability to water and substrate. (b) Schematic and MD snapshot views of the identified states. PGH2 (green for carbon atoms), heme (iron in ice blue and magenta for carbon atoms), the residues (sulfur in yellow and orange for carbon atoms) and the water molecules are drawn as a stick model. Their oxygen and nitrogen atoms are colored red and blue, respectively.

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Substrate Channeling of Prostaglandin H2 on the Stereochemical

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