Origin of Enzymatic Kinetic Isotope Effects in Human Purine

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On the origin of Enzymatic Kinetic Isotope Effects in Human Purine Nucleoside Phosphorylase Maite Roca, Vicent Moliner, and Iñaki Tuñón ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.7b04199 • Publication Date (Web): 13 Dec 2017 Downloaded from http://pubs.acs.org on December 13, 2017

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ACS Catalysis

On the origin of Enzymatic Kinetic Isotope Effects in Human Purine Nucleoside Phosphorylase M. Roca1,2*, V. Moliner1, I. Tuñón2*

1

Departament de Química Física i Analítica, Universitat Jaume I, 12071 Castelló, Spain

2

Departament de Química Física, Universitat de València, 46100 Burjassot, Spain

*To whom correspondence should be addressed. I. Tuñón; [email protected]. Phone (+34) 963544880. Fax (+34) 963544564 M. Roca; [email protected]. Phone: (+34) 964 728069. Fax: (+34) 964 728066

1

ACS Paragon Plus Environment

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Abstract Here we report a study of the effect of heavy isotope labeling on the reaction catalyzed by human purine nucleoside phosphorylase (hPNP) to elucidate the origin of its catalytic effect and of the enzymatic kinetic isotope effect (EKIE). Using quantum mechanical and molecular mechanical (QM/MM) molecular dynamics (MD) simulations, we study the mechanism of the hPNP enzyme and the dynamical effects by means of the calculation of the recrossing transmission coefficient. A free energy surface (FES), as a function of both a chemical and an environmental coordinate, is obtained to show the role of the environment on the chemical reaction. Analysis of reactive and nonreactive trajectories allow us to study the geometrical, dynamic and electronic changes of the chemical system. Special attention is paid to the electrostatic potential created by the environment on those atoms involved in the chemical reaction. Some amino acid residues and solvent molecules that interact with the chemical system provide a specific configuration that electrostatically favor the reaction progress, producing a reactive trajectory. The EKIE is calculated within the framework of the variational transition state theory (VTST) obtaining very good agreement with the experimental data. According to our simulations the chemical reaction is slightly slower in the heavy enzyme than in its light counterpart enzyme because protein motions coupled to the reaction coordinate are slower. Thus, protein dynamics have a small but measurable effect on the chemical reaction rate. Keywords: enzymatic kinetic isotope effect, enzyme catalysis, protein motions, QM/MM methods, variational transition state theory.

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ACS Catalysis

1. Introduction Enzymes catalyze biochemical reactions and play a major role controlling most biological processes.1,2 Thus, it is important to understand the action of enzymes on a detailed molecular level. The importance of such understanding is highlighted by the fact that many diseases can be controlled by developing drugs that block the action of enzymes in crucial biological pathways of bacteria or viruses that cause these diseases. Advances in this important field can be promoted in an efficient way by computational approaches that describe at a molecular level those effects that contribute to the catalytic process. The role of protein motions has been proposed to be at the heart of enzyme catalysis and it is a subject of heated debate among both experimentalist and theoreticians.3-10 However, identification and analysis of the so-called dynamical effects in enzyme catalyzed reactions is very challenging because experimental determinations can be often interpreted in different ways. For example, a study made by Mulholland and coworkers11 has shown that the temperature dependence of kinetic isotope effects (KIEs) could be accounted for by conformational effects instead of being considered a signature of the impact of protein motions on rate constants. Several publications tried to provide a quantification of the role of dynamics in enzyme catalysis by means of a combination of experimental and computational approaches.8-10,12,13 However, it seems that there are two different perspectives regarding the role of protein dynamics in enzyme catalysis. Some studies have indicated that enzyme catalysis is largely due to a preorganized electrostatic environment of their active sites and that protein motions do not produce significant dynamical corrections to the rate constant.1,5,8,11,12,14-23 However, the idea that protein motions are involved in enzymatic processes as the driving force in catalysis is accepted and supported by other computational and experimental studies.3,4,7,24-27 Fast promoting motions at the pico- to femtosecond timescale have been proposed to contribute to the energy-barrier crossing event.28,29 Indeed, the functional role of protein motions in enzyme catalysis has become one of the most studied topics in contemporary enzymology.

To focus more directly on the role of protein motions, entire enzymes can be isotopically substituted, with all nonexchangeable atoms of a particular type replaced by their heavier isotopes. In recent isotopic substitution studies of dihydrofolate reductase (DHFR),23,30 3


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HIV protease,31 purine nucleoside phosphorylase (PNP),29 pentaerythritol tetranitrate reductase (PETNR)32 and Lactate Dehydrogenase (LDH),33,34 the 12C, 14N and nonexchangeable 1H atoms of the enzyme were replaced with their corresponding heavy isotopes, 13C, 15N and 2H, respectively. Instead, in a study carried out for alanine racemase (AR),35 the heavy enzyme was a deuterated version of AR where all nonexchangeable hydrogens where substituted by deuterium. In all these studies, the “heavy” enzyme was compared with its “light” (natural isotopic abundance) counterpart and

shown that catalysis is usually affected by a modest reduction in the reaction rate constant of the heavy enzymes. These results have been analyzed and discussed in terms of the two different perspectives mentioned before. On the one hand, the fact that the heavy

enzyme is only slightly less active than its light counterpart shows that protein dynamics have a small effect on the chemical reaction rate due to the coupling with the motion along the reaction coordinate.8,15,17,23,36 On the other hand, in another interpretation the stress is made on the role of protein promoting vibrations that are decisive during the chemical step of the catalytic process.29,31-35 Through the study of the reaction catalyzed by human purine nucleoside phosphorylase (hPNP), Schramm and co-workers obtained rate constants of 69 s-1 and 55 s-1 for the light and heavy enzymes, respectively, using inosine as a substrate.29 The experimental enzymatic kinetic isotope effect calculated as the ratio of both rate constants (kL/kH) where L and H designates light and heavy enzymes, repectively, was 1.25. The reaction catalyzed by the heavy enzyme is slower than by the light enzyme. These researchers claim of having successfully provided evidence that supports the connection between mass-dependent vibrations and certain catalytic events of the reaction catalyzed by hPNP.29,37,38 In these studies, it was hypothesized that the femtosecond vibrational modes of these atoms decrease due to the increased mass in isotopically labelled hPNP, while electrostatic properties of the enzyme remain unchanged according to the BornOppenheimer approximation. Both global and local isotope effects were introduced by isotope specific and amino acid specific heavy atom substitutions.38 From their results, the authors concluded that the perturbation induced by heavy isotopic substitution provides support for a coupling of local catalytic site dynamics that influence the probability of transition state (TS) formation.

hPNP catalyzes the reversible phosphorolysis of 6-oxypurine nucleosides and deoxynucleosides, specifically, deoxyinosine and deoxyguanosine, to generate α-D4


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ACS Catalysis

(deoxy)ribose 1-phosphate and the corresponding purine base, hypoxanthine and guanine respectively. A genetic deficiency of hPNP causes the presence of elevated concentrations of deoxyinosine and deoxyguanosine in the blood and further reactions involving them lead to the metabolic accumulation of deoxyguanosine triphosphate (dGTP) to levels that are toxic to lymphocytes, resulting in apoptosis of dividing T-cells. Thus, hPNP is a promising target for T-cell proliferative diseases such as leukemia, lymphoma, tissue transplant rejection and autoimmune disorders including rheumatoid arthritis, among others.39-43 Consequently, hPNP is used as target for transition state analog (TSA) inhibitor design.44-47 Thus, detailed analysis of TS structures and a better understanding of enzyme dynamics will allow us to perform a rational approach to the computational design of novel and potent drugs.

The structure of hPNP is a homotrimer with the catalytic sites near the subunit interfaces. The ternary complex of hPNP includes the binding of a ligand (in this study inosine is used as substrate) and hydrogen phosphate to the active site. The reaction consists of a phosphorolysis at C1´ of inosine’s ribose with inversion of stereochemistry at this position (see Scheme 1). Reaction occurs via a SN1 like mechanism where hydrogen phosphate nucleophile and the purine base leaving group are separated from the oxocarbenium ion, defining a dissociative TS. It has to be pointed out that the reaction involves annihilation of charges in going from reactant state to product state.

The reaction mechanism of this enzyme has been computationally studied using different methods such as quantum mechanical and molecular mechanical (QM/MM) molecular dynamics (MD) simulations28,48 and empirical valence bond (EVB) simulations.49 Åqvist and coworkers, based on EVB calculations, reproduced the substrate specificity of glycosidic bond cleavage.50 They concluded that a mutation increases the reorganization energy for native substrates and the change in the electrostatic preorganization of the enzyme is revealed by a change in the activation barriers.49 Schramm and co-workers determined and analyzed in atomic detail the TS structure of hPNP, combining experimental determination of KIEs with quantum chemical models, and used it to developed tight binding transition state analogues (TSAs) to inhibit this enzyme.28,44,51-53 In a recent study, mutations of second-sphere amino acid residues were done on the heavy and light hPNP enzymes to convert the mass alteration effect on enzymatic barrier crossing rates.54 According to these authors, results from crystallographic data, 5


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mutational studies, global and local KIEs and computational analysis are consistent with enzymatic compression motions playing a significant role in forming the TS.28,37,38,48,54,55 Based on transition path sampling method, these authors observed that a motion of His257, hydrogen bonded to the 5´-hydroxyl group of inosine, pushes ribose-O5´ atom toward the ribosyl ring to cause compression between ribose-O5´ and ribose-O4´ atoms of inosine (see Scheme 1). The electronegativity of the oxygen atoms in close proximity would polarize the N-ribosidic bond yielding a fully formed oxocarbenium TS. Moreover, leaving group interactions, such as the stabilization of the protonated N7 purine base by Asn243, were also found to be essential for catalysis. These features were incorporated into the design of the stable TSAs for hPNP enzyme.52

Even though the existence of these extensive studies the origin of the catalytic effect of hPNP enzyme and, in particular, of the enzymatic kinetic isotope effects (EKIEs) remains unclear. In order to shed some light on this question, we report a study of the effect of protein heavy isotope labeling on the reaction catalyzed by hPNP within the framework of the variational transition state theory (VTST),56,57 demonstrating that the origin of catalysis and of EKIEs can be rationalized in the framework of this theory and are linked to the unique electrostatic properties of the enzymatic active site.

O H N7

NH

N9

H5ꞌO5ꞌ O4ꞌ OH

δ+

H5ꞌ O5ꞌ O4ꞌ

C1ꞌ O2ꞌ H O4 P O

OH

+

δ

H2

O4ꞌ

−

δ

P O2

N

H5ꞌ O5ꞌ

C1ꞌ O2ꞌ H

NH

N9

N

O4

O

H N7

NH

N9

N

O

O H N7

O

OH

O

C1ꞌ O2ꞌ H

O4 P O

O2

H2

O O2

H2

Scheme 1. Phosphorolysis of inosine catalyzed by hPNP to form ribose 1-phosphate and hypoxanthine.

2. Methodology 2.1. Theoretical framework. The main approximation to describe reaction kinetics in a chemical reaction, including those catalyzed by enzymes, is the transition state theory (TST),58-60 and deviations from these theory can be estimated by means of ensemble-averaged VTST (EA-VTST),61-63 6


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ACS Catalysis

𝑘𝑘 (𝑇𝑇) = Γ(𝑇𝑇, 𝑞𝑞) · 𝑘𝑘 𝑇𝑇𝑇𝑇𝑇𝑇 = Γ(𝑇𝑇, 𝑞𝑞) ·

𝑘𝑘𝐵𝐵 ·𝑇𝑇 ℎ

(𝐶𝐶 0 )1−𝑛𝑛 · 𝑒𝑒𝑒𝑒𝑒𝑒 �

Δ𝐺𝐺 ‡ (𝑇𝑇,𝑞𝑞) 𝑅𝑅𝑅𝑅

�

(1)

where ∆G‡ is the activation free energy using the reaction coordinate q, n the number of reactant species and C0 the concentration of the standard state (usually 1M), T is the temperature, R is the ideal gas constant, kB is the Boltzmann constant, h is Planck’s constant and Γ(T,q) the generalized transmission coefficient.23,64 The quasiclassical activation free energy, ∆G‡(T,q), is obtained from the classical ‡ (𝑇𝑇, 𝑞𝑞)) and including a correction for mechanical potential of mean force (PMF) (Δ𝐺𝐺𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ‡ quantizing the vibrations orthogonal to the reaction coordinate (Δ𝑊𝑊𝑣𝑣𝑣𝑣𝑣𝑣 (𝑇𝑇, 𝑞𝑞)).

‡ ‡ (𝑇𝑇, 𝑞𝑞) + Δ𝑊𝑊𝑣𝑣𝑣𝑣𝑣𝑣 Δ𝐺𝐺 ‡ (𝑇𝑇, 𝑞𝑞) = Δ𝐺𝐺𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 (𝑇𝑇, 𝑞𝑞)

(2)

The generalized transmission coefficient, Γ(T,q) , can be expressed as a product of two

contributions:60

Γ(𝑇𝑇, 𝑞𝑞) = 𝛾𝛾 (𝑇𝑇, 𝑞𝑞) · 𝜅𝜅(𝑇𝑇)

(3)

The first term is the recrossing transmission coefficient, γ(T,q), and corrects the rate

coefficient for trajectories that recross the TS dividing surface back to the reactant valley. The second term is the tunneling coefficient, κ(T), and accounts for reactive trajectories that do not reach the classical threshold energy. The former coefficient is less than or equal to 1, and its deviation to unity can arise from the coupling of the reaction coordinate to other coordinates. The latter one is larger than unity when quantum tunneling is significant. In the present work, the studied reaction does not involve any light particle transfer such as proton, hydride or hydrogen radical. Thus, for reactions not involving hydrogen atom transfers the generalized transmission coefficient is essentially due to the barrier recrossings of the system, and then only the recrossing transmission coefficient,

γ(T,q), has to be computed. This study aims to analyze the EKIE between light hPNP enzyme (isotopically unlabeled) and the heavy hPNP enzyme and to explore the origin why the heavy enzyme is slightly less active than its light counterpart. In this framework, and assuming the same force field for the heavy and light enzymes, the classical mechanical PMF is not altered if the mass of the reaction coordinate is not changed. However, increased atomic mass in hPNP alters bond vibrational modes decreasing their frequency. This can affect two terms in Eqs (1)7


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(3). On the one hand, the increase of the protein mass makes the environment slower leading to more recrossings. Thus, in the present study, where tunneling is negligible, the EKIE derived from VTST (EKIEVTST) has been obtained as the product of two contributions, the KIE due to recrossings (EKIE(γ)) and the vibrational KIE (EKIE(vib)).

𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 = 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 (𝑣𝑣𝑣𝑣𝑣𝑣)

𝑘𝑘𝑟𝑟𝐿𝐿

𝑘𝑘𝑟𝑟𝐻𝐻

≈

𝛾𝛾𝐿𝐿 (𝑇𝑇,𝑞𝑞)

𝛾𝛾𝐻𝐻 (𝑇𝑇,𝑞𝑞)

(4)

· 𝑒𝑒

−

‡,𝐿𝐿 ‡,𝐻𝐻 Δ𝑊𝑊𝑣𝑣𝑣𝑣𝑣𝑣 (𝑇𝑇,𝑞𝑞)− Δ𝑊𝑊𝑣𝑣𝑣𝑣𝑣𝑣 (𝑇𝑇,𝑞𝑞) 𝑅𝑅𝑅𝑅

= 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 (𝛾𝛾 ) ·

where L and H superscripts designate light and heavy enzymes, respectively. Because the number of recrossings increase in the heavy version, the first term is expected to result in a normal KIE (i.e. EKIE(γ) > 1). With respect to the vibrational contribution the final effect depends on whether protein vibrational modes are tighter or softer at the TS. If some protein modes present strengthened interactions with the substrate at the TS, then the associated force constant will increase and an inverse KIE would be observed (EKIE(vib) < 1). Otherwise, if the interaction with the substrate at the TS is weakened with respect to reactants, then the associated force constant will decrease and a normal KIE is expected (EKIE(vib) > 1).

2.2. Building the system. The crystal structures of hPNP in a complex with the TSA, Immucillin-H, and phosphate (PDB entry 1RR6)65 and the trimeric hPNP in a complex with DaDMe-ImmG and phosphate (3PHB as PDB code) were used to build our starting structure. One of the subunits of the trimeric hPNP (3PHB) was selected to model the Michaelis complex. With this purpose the coordinates of the phosphate molecule were taken from the 1RR6 structure, once overlapped to the selected subunit of 3PHB. The DaDMe-ImmG ligand was then replaced by the substrate inosine, which is the substrate used in this study. PROPKA3 semiempirical program66-69 was used to estimate the pKa values of the titratable protein residues to verify their protonation states at a pH of 7. According to the results, hydrogen atoms were added and assigned protonation states for all ionizable residues using fDYNAMO program70,71 assuming pH 7. A list of all the ionizable residues with their calculated pKa values is provided in the Supporting Information (Table S1). It is worth mentioning that residue Glu201 was found to be deprotonated to stabilize the purine base and His257 was neutral with the proton at NE position, leaving ND atom free

8


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ACS Catalysis

to interact with the 5´-hydroxyl group of the substrate ribose ring. From the literature, the pKa of N7 of the purine base of guanosine (similar to inosine) is 3.5 in aqueous solution. However, atom N7 was considered to be protonated as was done by Schramm and coworkers because in this way the substrate establishes a hydrogen bond interaction with the carbonyl oxygen atom of Asn243 residue, that can shift the pKa of inosine and this interaction stabilizes the leaving group at the TS.28,37,72 The system was solvated with a sphere of water molecules of 30 Å of radius centered on the C1´ atom of ribose of the substrate inosine. All the water molecules with an oxygen atom lying within 2.8 Å of any other heavy atom were deleted. Thus the final system consists of the trimeric enzyme (4394 atoms), protonated inosine substrate, hydrogen phosphate ion, and 1712 water molecules (18356 atoms in total) (see Figure S1 in the Supporting Information). The QM region consists of the protonated inosine substrate and hydrogen phosphate ion, a total of 38 atoms that were described by the semiempirical method PM373 while the atoms of the protein and water molecules were described by means of the OPLS-AA74,75 and TIP3P76 force fields, respectively. Because of the size of the system, all residues further than 25 Å from the C1´ atom were kept frozen (10329 atoms) and a buffer region was defined between 20 to 25 Å centered on the C1´ atom of the substrate where a tether constraint was applied on the heavy atoms positions using a force constant of 50 kJ · mol-1 · Å-2. To treat the nonbonding interactions, a switch function with a cutoff distance in the range 12-16 Å was used for all MM interactions (including the frozen atoms), while the QM region was allowed to interact with every flexible MM atom. The system was gradually minimized, heated and equilibrated by means of conjugate gradient optimizations and molecular dynamics (MD) simulations. First the solvent molecules were minimized and equilibrated while the rest of the system was kept fixed. Second, solvent molecules and side chains were free to be minimized and relaxed. Finally, the whole system was energy minimized and gradually heated from T=10 K to T=298 K in 100 ps before running a MD simulation at 298 K for 1 ns. A Langevin-Verlet integrator with a time a step of 1 fs was employed, using the NVT thermodynamic ensemble at a temperature of 298 K.

2.3. Free energy surfaces Once the system was equilibrated, hybrid QM/MM potential energy surface (PES) explorations and transition structure location and characterization were carried out, 9


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guided by means of the micro-macro iterations scheme.77 One of the localized transition structures is shown in Figure 1. This structure was further used as starting configuration for the two dimensional potential energy surface (2D-PES) generation in which the distances describing the breaking and forming bonds (D(N9, C1´) and D(C1´, O4), see Scheme 1) were employed as distinguished reaction coordinates. A total of 575 minimized structures were obtained and used as starting points to generate the two dimensional free energy surface (2D-FES).78 The umbrella sampling approach79 was used to constrain the system employing a force constant of 2500 kJ · mol-1 · Å-2, and the probability distributions were put together by means of the weighted histogram analysis method (WHAM)80 to obtain the full probability distribution. The values of the force constant used for the harmonic umbrella sampling were determined to allow a full overlapping of the different windows traced in the PMFs evaluation, but without losing control over the selected coordinate. The simulation windows were performed at different values of the distances that were changed using an increment of 0.1 Å between the ranges of 1.3-3.5 Å for the breaking bond distance and 1.3-3.7 Å for the forming bond distance. Each window consisted of 10 ps of equilibration followed by 20 ps of production. For all the calculations we employed the fDYNAMO library.70,71

10


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ACS Catalysis

Asn243

Glu201

Inosine

2.6 Å

His257

2.7 Å Ser220

Ser33

His86 Arg84

Figure 1. Localized transition state structure in the active site of hPNP enzyme by means of PM3/MM energy optimizations. The QM region consists of inosine substrate and hydrogen phosphate ion and are shown in a ball and sticks representation. Hydrogen bond interactions between the QM region and surrounding amino acid residues and solvent molecules are shown as dashed lines. The bond breaking and the bond forming distances are also displayed as dashed lines with distances in Å.

In this work, a FES is also obtained as a function of both a chemical and an environmental coordinate. In this case the selected chemical coordinate (q) was the antisymmetric combination of the distances describing the breaking and forming bonds (q = D(N9, C1´)D(C1´, O4)), while the difference of the electrostatic potential created by the environment (protein, solvent and counterions) on the donor and acceptor atoms (VN9 and VO4, respectively; see Scheme 1) was used as the environmental coordinate (s): 𝑗𝑗=𝑀𝑀

𝑠𝑠 = 𝑉𝑉𝑁𝑁9 − 𝑉𝑉𝑂𝑂4 = � 𝑗𝑗=1

𝑗𝑗

𝑞𝑞𝑀𝑀𝑀𝑀

�𝑟𝑟𝑗𝑗 − 𝑟𝑟𝑁𝑁9 �

𝑗𝑗=𝑀𝑀

−� 𝑗𝑗=1

𝑗𝑗

𝑞𝑞𝑀𝑀𝑀𝑀

�𝑟𝑟𝑗𝑗 − 𝑟𝑟𝑂𝑂4 �


(5) 11

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where j runs over the atoms described by MM with charge q, while the rj, rN9 and rO4 are the cartesian coordinates of atoms j, N9 and O4 respectively. This coordinate takes into account the changes in the enzymatic environment that can favour the electron transfer from the attacking to the leaving group. The environmental coordinate variation is due to the coupling of the environment to the chemical reaction when going from reactant state to product state. This FES was also obtained using umbrella sampling approach,79 applying harmonic potentials to both the chemical and environmental coordinates with force constants of 2500 kJ · mol-1 · Å-2 and 0.1 kJ-1 · mol · |e|2, respectively, as was done in previous studies.21,81,82 The joint probability distributions of the two coordinates were obtained by means of the WHAM.80 A total of 5520 MD simulation windows were run employing the same conditions described above.

2.4. Vibrational corrections. To compute zero-point energy (ZPE) corrections to the activation free energy barrier and the vibrational contribution to the EKIE by means of quantization of the vibrational frequencies, we selected 10 different configurations from QM/MM MD simulations with the chemical coordinate constrained on the reactant and TS. Each of these structures was then refined and characterized as minima and saddle points. Two different Hessian matrixes were employed to calculate the vibrational correction to the free energy (see Eq. (2)). On the one hand, structures were located and characterized including into the Hessian matrix only those atoms described by QM methods: inosine ligand and hydrogen phosphate ion. On the other hand, the Hessian was enlarged including the side chain atoms of surrounding amino acid residues that present hydrogen bond interactions with the ligand or the hydrogen phosphate ion (Gly32, Ser33, Arg84, His86, Tyr88, Glu201, Ser220, Asn243, His257 and 3 water molecules) (see Figure 2). The final vibrational corrections were obtained as an average over those structures in both, heavy and light enzymes.

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ACS Catalysis

H Asn243

N C

Glu201

H

O

C

O

O

His257

δ+

C

O N 7H

NH

CH

HN

N9

N

HC

N

H5'O5ꞌ O4ꞌ C1ꞌ

O2'H

O3'H H C

δ

−

HO P

C H

H2O

O1

NH

CH

OH

H C

Ser33 HN HC

CH2

O3

C

C

Ser220

H2O

O4

OH

HC

Tyr88

δ+

NH2 N

C

H2O C

Arg84

H2N His86

Figure 2. Scheme of the subset of atoms for the larger Hessian calculation to compute the vibrational contribution to the EKIE between the light and heavy enzymes for the TSs. This subset of atoms consists of inosine ligand, hydrogen phosphate ion and the side chain atoms of surrounding residues that establish hydrogen bond interactions with the ligand and substrate. The atoms that were replaced by their heavy isotopes are represented in red.

2.5. Rare event trajectories. Once the FESs were obtained, we carried out 800 ps long QM/MM MD simulation of the light enzyme (unlabeled enzyme) with the system restrained to remain in the TS region using the same conditions as in the preceding simulations. A harmonic potential with a force constant of 10000 kJ · mol-1 · Å-2 was applied to the antisymmetric combination of the bond breaking and bond forming distances. One structure was saved every 2 ps, resulting in 400 configurations that were used to compute free downhill trajectories. The velocity associated with the reaction coordinate is not properly thermalized in these configurations (because of the reaction coordinate restraint). Thus, following a procedure similar to that used by Gao and co-workers83 and used in our previous studies,17,18,84-86 we 13


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Page 14 of 33

selectively removed the projection of the velocity on the reaction coordinate, and added a random value taken from a Maxwell–Boltzmann distribution. For each of the saved configurations with modified velocities we ran free downhill NVE simulations integrating the equations of motion forward and backward, just changing the sign of the velocity components, to quantify recrossings through the calculation of the transmission coefficient. For the heavy enzyme, we used the same velocities for the QM atoms as in the light enzyme whereas the velocity of the MM atoms was assigned following a MaxwellBoltzmann distribution at 298K. Downhill trajectories were propagated from -4 to +4 ps in both enzymes. Two different types of trajectories were observed: (a) reactive trajectories, which present reactant-product (RP) transitions and (b) nonreactive trajectories or recrossing trajectories leading from reactants to reactants (R-R) or products to products (P-P). Both reactive and nonreactive trajectories may exhibit recrossings on the dividing surface. To compute γ(T,q) we used the “positive flux” formulation,87 by assuming that the trajectory was initiated at the barrier top with forward momentum along the reaction coordinate. For a given time t, with t=0 being the starting time for the downhill trajectory, the timedependent transmission coefficient is defined as:

γ (t ) =

j+θ [q(+ t )] −

j+θ [q(− t )]

j+

(6)

where q is the reaction coordinate, j+ represents the initially positive flux at t=0, given by q(t=0), and θ(q) is a step function equal to one in the product side of the reaction coordinate and zero on the reactant side. We analyzed the changes in the environment as the reaction proceeds by means of detailed inspection of the reactive trajectories. In these analysis t=0 indicates the passage of the system over the barrier top, negative times corresponds to the evolution of the system towards the reactant valley and positive times towards the product one.

3. Results and Discussion 3.1. The chemical free energy surface. Figure 3 shows the 2D-FES obtained for the light hPNP at the PM3/MM level as a function of the distances describing the breaking and forming bonds (D(N9, C1´) and 14


Page 15 of 33

D(C1´, O4), respectively). Free energies are expressed in kilocalories per mole. The FES shows a rather flat region around the TS with large breaking and forming bond distances. A loose or dissociative TS is then obtained in agreement with previous studies of Schramm and coworkers.28,72 In the FES is depicted in a red point the location of the TS structure localized and characterized. The free energy barrier obtained as the difference between the TS and the reactant state, corrected for the zero-point energy contribution (1.4 kcal·mol-1), is 22.9 kcal·mol-1. This result is larger from the value derived from the experimental rate constant (14.9 kcal·mol-1),29 which can be attributed to deficiencies in the semiempirical Hamiltonian (see below). The value of the antisymmetric combination of the bond breaking and bond forming distances for the TS (q‡) is -0.1 Å. This value was also determined analyzing trajectories started at q‡ = 0, -0.1 and -0.2 Å and selecting the q‡ value providing the maximum value for the transmission coefficient.

R D(C1´,O4) (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Catalysis

TS

P D(N9, C1´) (Å) Figure 3. 2D-FES for the phosphorolysis of inosine catalized by hPNP to form ribose 1phosphate and hypoxanthine as a function of the bond breaking (D(N9, C1´)) and bond forming (D(C1´, O4)) distances. Isocontour lines are drawn each 3 kcal·mol-1. R, TS and P designate the reactant state, transition state, and product state, respectively. The red point indicates the position of the localized TS structure and the dashed black line shows the TS dividing surface for a value of the antisymmetric combination of the distances 15


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Page 16 of 33

describing the breaking and forming bonds of -0.1 Å. The solid black lines are shown in order to plot the TS dividing surface.

The PM3 method for describing the QM region results in overestimated energy barriers. We then added a correction term to the activation free energy obtained as the averaged difference between the energy provided by single-point energy gas phase calculations at a high level method and by a low level method of several TS and reactant configurations using Gaussian09 package.88 The low level energies were obtained using the PM3 Hamiltonian, while the high level energies were obtained using the hybrid functional B3LYP including the Grimme empirical dispersion correction D289 as was done in a previous study.49 The basis set selected for the high level calculations was 6311+G(2df,2p). The selected QM configurations were obtained from the set of 10 TS and reactant structures localized and characterized to compute the ZPE correction to the activation free energy barrier. The corrected free energy barrier is 14.4 kcal·mol-1, in good agreement with the experimentally derived value (kcat of 69 s-1 corresponding to a free energy barrier of 14.9 kcal·mol-1).29

3.2. Role of the environment. The PM3/MM FES corresponding to the phosphorolysis of inosine substrate catalyzed by hPNP as a function of a solute coordinate (q, the antisymmetric combination of the bond forming and bond breaking distances) and an environmental coordinate (s) (calculated using Eq. (5)) is presented in Figure 4. The solute coordinate evolves from negative values at the reactant state to positive values at the product state. The environmental coordinate (s) changes from negative values at the reactant state to less negative values at the product state. In this figure, the TS dividing surface, represented in dashed blue line, is defined by the solute coordinate (-0.1Å) considering that the environment is in equilibrium. The dashed red line represents the TS dividing surface as a function of both the solute and environmental coordinates. This figure also displays the minimum free-energy path (MFEP) obtained from the gradients of the FES (solid red line) and the equilibrium free energy path, assuming that the solvent coordinate equilibrates at each value of the solute coordinate (solid blue line). The barrier obtained in Figure 4 is of 24.8 kcal·mol-1 (similar to the one obtained in Figure 3 before applying the ZPE correction, 24.3 kcal·mol-1). 16


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ACS Catalysis

As observed from Figure 4, the barrier crossing event is largely associated to changes in the solute coordinate, while the electrostatic potential essentially changes during earlier and late stages of the process. In this case VTST can provide accurate results of the rate constant through the inclusion of the transmission coefficient associated to the solute coordinate, which can be also seen as an improvement of the definition of the reaction coordinate.8,21 If the reaction coordinate were defined using a collective variable, such as the energy gap coordinate,90 enclosing the substrate and the protein degrees of freedom, the role of protein motions would be partially comprised in the activation free energy and the transmission coefficient would become closer to unity. However, our separation of solute and environmental contributions in the activation free energy and transmission coefficient offers a unique opportunity to analyze and quantify EKIEs. The appearance of a transmission coefficient lower than unity in the expression of the rate constant (Eq. (1)) can be explained in terms of the dividing surfaces obtained in the nonequilibrium and the equilibrium descriptions shown in Figure 4. The dividing surface obtained from the non-equilibrium treatment is defined in such a way that any trajectory arriving at that surface from the reactant state will continue to the product state because the free energy continuously decreases in that direction, and so the transmission coefficient would be equal to unity if the system could be described using only two coordinates. However, using the equilibrium dividing surface, some trajectories that go from reactant state to product state find a free energy barrier after crossing this surface and they could return to the reactant side. This means that, in this description, the transmission coefficient would be lower than unity. The angle between both dividing surfaces measures the deviation of the transmission coefficient to unity.91

17


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

s = VN9-VO4 (kcal·mol-1·|e|-1)

ACS Catalysis

Page 18 of 33

P

TS R

q‡ q (Å) Figure 4. 2D-FES corresponding to the enzymatic reaction catalyzed by hPNP along the solute coordinate (q) and the environmental coordinate (s). The solid red line represents the minimum free-energy path on the FES and the solid blue line corresponds to the path obtained assuming equilibrium solvation along the solute coordinate. The dashed red line corresponds to the TS dividing surface defined according to the FES along the solute and environmental coordinates. The dashed blue line corresponds to the TS dividing surface obtained when the solvent coordinate is assumed to be at equilibrium and the equilibrium plane is then defined as q‡=-0.1Å. Isocontour lines are drawn each 2 kcal·mol-1.

3.3. Time dependent transmission coefficients. After describing the reaction in terms of solute and environmental coordinates using FESs we proceed to evaluate the dynamical effects of the environment on the reaction through the transmission coefficient. This term depends on the coupling between environmental motions to the reaction coordinate and thus can be different for the heavy and light versions of the enzyme because the change in mass affects the frequencies of protein

18


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ACS Catalysis

motions. Simulations of the heavy enzyme were performed using the masses of 15N, 13C and 2H for nitrogen, carbon, and nonexchangeable hydrogen atoms in the amino acid residue atoms (see further details in “Building the heavy enzyme” section in the Supporting Information). Free downhill simulations carried out from the TS in the forward and backward directions exhibit that 34% of the total trajectories were reactive (when reactants connect to products) in the light enzyme and 32.5% in the heavy enzyme. Time-dependent transmission coefficients for the light and heavy hPNP enzymes, computed by means of Eq.6, are presented in Figure S2 in the Supporting Information. The evolution of the transmission coefficients shows a fast decay after the passage over the top of the barrier, reaching a plateau after 1.5 ps, which means that the fate of the reaction is determined after this period and no recrossings are observed afterward. The large value of the relaxation time is due to the fact that the TS region is flat and wide and then forces acting on the system can lead to fluctuations in the evolution of the reaction coordinate. The transmission coefficients arrive to a constant value of 0.46±0.02 and 0.42±0.02 for the light and heavy hPNP enzymes, respectively. Then the contribution to the EKIE due to recrossings is EKIE(γ) = γL(T,q) / γH(T,q) = 1.10 ± 0.10. This is, the transmission coefficient contributes to a normal value of the EKIE, as discussed above.

3.4. Vibrational contribution to the kinetic isotope effect. From the maximum of the PMF where the TS is located, and from the minimum valley that corresponds to the reactant state, we run long QM/MM MD simulations with the system restrained on the corresponding values of the reaction coordinate. We selected 10 structures from each MD simulation and localized them as TS and reactant state structures. Some key protein residues, those establishing hydrogen bond interactions with the chemical system, were included in the Hessian calculations (see Methods). This Hessian was then used to calculate frequencies and vibrational contributions to the activation free energy. This procedure was done for the light and heavy enzymes using the same stationary structures and changing only the mass of the substituted atoms in the enzyme. The average vibrational contributions to the activation free energy barrier ‡

(Δ𝑊𝑊𝑣𝑣𝑣𝑣𝑣𝑣 (𝑇𝑇, 𝑞𝑞)) for the light and heavy enzymes were -1.19±0.02 kcal·mol-1 and -

1.10±0.01 kcal·mol-1, respectively. Thus, the vibrational contribution to the EKIE can be obtained as follows:

19


ACS Catalysis 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 (𝑣𝑣𝑣𝑣𝑣𝑣) = 𝑒𝑒

−

‡,𝐿𝐿 ‡,𝐻𝐻 Δ𝑊𝑊𝑣𝑣𝑣𝑣𝑣𝑣 (𝑇𝑇,𝑞𝑞)− Δ𝑊𝑊𝑣𝑣𝑣𝑣𝑣𝑣 (𝑇𝑇,𝑞𝑞) 𝑅𝑅𝑅𝑅

Page 20 of 33

(6)

We obtained a normal vibrational EKIE of 1.16±0.07. According to Scheme 1, the reaction dipole associated to the charges in the reacting fragments decrease at the TS and then some protein-substrate interactions are stronger at the reactant state than at the TS. Consequently, some protein motions will be tighter at the reactant state than at the TS. This explains the normal value of the vibrational EKIE. It should be recall here that catalysis takes place with respect to the counterpart process in solution, where the differential stabilization of the reactant state can be larger due to interactions with the non-preorganized solvent dipoles.16,92

3.5. Enzymatic kinetic isotope effect Once we have obtained the vibrational contribution to the EKIE (EKIE(vib)) and the contribution due to the recrossings (EKIE(γ)), the total EKIE derived from VTST (EKIEVTST) can be calculated using Eq. 4. Table 1 shows the resulting EKIEVTST with their corresponding standard deviations. As we obtained before, both EKIEs, the vibrational one and the one due to recrossings are normal, as a result the EKIEVTST is also normal. Therefore, the light enzyme catalyzes the reaction with a rate constant slightly larger than the heavy enzyme. As observed in Table 1 our estimation for the EKIEVTST is in good agreement with the experimental value (EKIEexp). Thus, EKIE in hPNP can be fairly reproduced using VTST.

Table 1. EKIE within the framework of the VTST (EKIEVTST) calculated by the product of the vibrational KIE (EKIE(vib)) and the KIE due to recrossings (EKIE(γ)) using QM/MM methods. EKIEexp, is obtained as the ratio between the experimental rate constants of the light and heavy hPNP enzymes.29 EKIE(vib)

EKIE(γ)

EKIEVTST

EKIEexp

1.16± 0.07

1.10 ± 0.10

1.28± 0.19

1.25 ± 0.10

20


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ACS Catalysis

Our analysis of EKIEs is based on the assumption that, according to the BornOppenheimer description, the classical activation free energy along a solute coordinate is the same for the heavy and light enzymes. This is not necessarily true as far as the vibrationally averaged bond distances depend on the mass of the atoms and thus the structure of the protein could be slightly affected by mass substitution. As discussed in the Supporting Information (see in SI Text, section ‘Building the heavy enzyme’ and Figure S3) we ran additional simulations of a heavy version of the enzyme where the values of the equilibrium distances of C-H bonds were slightly decreased to represent the effect of the H/D substitution. Our simulations indicate that the structure and electrostatic properties of the light and heavy versions of the enzyme are practically indistinguishable and differences were observed only in time dependent properties (see the autocorrelation function of the electrostatic potential represented in Figure S5).

3.6. Analysis of free downhill trajectories. In order to have a better understanding on the origin of the coupling between the reaction progress and the protein environment we performed a detailed analysis of the reactive and nonreactive trajectories of both versions of the enzymes, light and heavy hPNP. From the geometrical point of view, Figure S4 in the Supporting Information shows the evolution of the distances that define the reaction coordinate, bond breaking (D(N9, C1´)) and bond forming (D(C1´, O4)) distances averaged over reactive trajectories. These distances present the expected behavior for reactive trajectories. The D(N9, C1´) distance is increasing while D(C1´, O4) distance is decreasing while going from reactants to products. Both distances start to change around 0.5 ps before crossing the TS region. From the electronic point of view, Figure 5 shows the averaged charges on N9 atom, C1´ atom of inosine, ribose-O4´ atom of inosine and O4 atom of the hydrogen phosphate ion along the reactive trajectories both in the light and heavy hPNP enzyme. The time defines the evolution of the reaction from reactant to product passing through the TS at t=0. It can be observed that the charge on the O4 atom starts to change after crossing the TS dividing surface while the charges on N9, C1´ and O4´ atoms change before crossing the TS region. The charge on the N9 atom starts to decrease at 0.75 ps before crossing the TS surface from a positive value to a negative value of charge reaching a minimum value in the TS region while the charges on C1´ and on O4´ reach a maximum value in the TS region. The charge on C1´ starts to increase from almost zero in the reactant state to a 21


ACS Catalysis

positive value in the product state. The charge on O4´ increases from a negative value in reactant state to almost zero in the TS region and then decreases again to a negative value in the product state. As explained previously, the reaction proceeds with charge separation annihilation. The inosine and the hydrogen phosphate ion have a formal charge of +1 and -1 a.u., respectively, in the reactant state and zero in the product state. The main electronic feature of the chemical reaction is the charge transfer from the O4 to the N9 atom where ionic reactants proceed toward neutral products. Furthermore, it is important to underline that the oxocarbenium TS is characterized by a maximum positive charge on the C1´ atom and an almost neutral value on the O4´ atom (see Scheme 1 and the TS region in Figure 5). This charge distribution at the TS is stabilized in the active site of hPNP by means of specific interactions with the surrounding residues (see below).

0.6 0.4

N9

C1´

0.2

Charge (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 33

0

O4´

-0.2 -0.4 -0.6 -0.8 -1

O4

-1.2 -1

-0.5

0

0.5

1

Time (ps) Figure 5. Time evolution of Mulliken charges for reactive trajectories in the light hPNP enzyme (solid lines) and in the heavy enzyme (dashed lines). The charge on the N9 atom is depicted in green, C1´ atom in red, ribose-O4átom in purple and O4 atom from hydrogen phosphate ion in blue. The vertical solid black line at t = 0 shows the position of the TS.

We have also evaluated the time evolution of intermolecular distances between key atoms of the ligand or substrate and of the amino acid residues of both the light and heavy 22


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ACS Catalysis

enzymes, averaged over the reactive trajectories. Figure 6 (a) shows that the distance between ND1 atom of His257 and the H5´ atom of 5´-hydroxyl group of inosine, depicted in blue, remains constant until the TS region and starts to increase towards products (see Scheme 1 for the atom numbering of the QM region and Figure 6 (b) for the hydrogen bond interaction pattern between the reacting system and the environment). The same trend is observed in the distance ribose-O4ánd ribose-O5átoms of inosine. According to previous studies,37,54 the motion of these atom pairs (His ND1´-inosine H5´ and inosine O5´-inosine O4´) are cooperative with the TS formation showing a compression of these distances near the TS region. From our simulations, these distances remain constant until reach the TS region without decreasing close to the TS dividing surface. Moreover, the distance between the O2 atom of the hydrogen phosphate ion and Arg84, depicted in green, increases while going from reactants to products. This change is coupled to the annihilation of the negative charge on the hydrogen phosphate ion due to the nucleophilic attack to C1´ of inosine, reflected in the decrease of the negative charge on all the oxygen atoms of hydrogen phosphate ion. For instance, the charge of O2 shifts from -0.83 a.u. at the reactant state to -0.75 a.u. at the product state. In the meantime, the positive charge on the H2 atom of the hydrogen phosphate slightly increases while going from reactants (0.20 a.u.) to products (0.25 a.u.), thus the hydrogen bond interaction established between this atom and His86 is gently stronger making the distance between them shorter as the reaction proceeds (distance depicted in purple). Another distance that elongates from reactants to products is the distance between O2´ of inosine and Met219 (distance represented in red). This change can be also explained from an electronic perspective. The charge on O2´ of inosine slightly becomes less negative (from -0.42 a.u. to -0.37 a.u.) making the hydrogen bond interaction with Met219 weaker. The evolution of the depicted distances is similar in both environments, light and heavy enzymes. In general, this analysis reveals that intermolecular interactions established between the reacting system and the environment are coupled to the charge reorganization in the reacting system.

23


ACS Catalysis

(a)

(b)

3.2 3

D(O5´ INO, O4´ INO)

Distance (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 33

2.8

His257

Met219

D(O2 HPO4-2, HH12 Arg84)

2.6

D(H2 HPO4-2, NE2 His86)

2.4

His86

2.2

D(H5´ INO, ND1 His257) D(O2´ INO, H Met219)

2

Arg84

1.8 -2

-1

0

1

2

Time (ps)

Figure 6. (a) Time evolution of intermolecular distances between key amino acid residues of the enzyme and the inosine and hydrogen phosphate ion averaged over reactive trajectories for the light (solid lines) and heavy (dash lines) enzymes. The vertical solid black line at t = 0 shows the position of the TS. (b) Transition state structure in the active site of hPNP enzyme showing the distances between the QM region and surrounding amino acid residues represented in Figure 6 (a).

We can analyze the impact of environmental motions during the reaction process by means of the time evolution of the environmental coordinate (s). Figure 7 shows the time dependent evolution of the environmental coordinate along reactive trajectories (in red for R-P trajectories, reactants connect to products) and nonreactive trajectories (in green for R-R trajectories, reactants connect to reactants and in blue for P-P trajectories, products connect to products) for the light (solid lines) and heavy (dotted lines) versions of the enzyme. This figure reveals that the type of trajectory depends on the environmental coordinate value at the TS region (t = 0). For a reactive trajectory (R-P), the environmental coordinate has to reach a specific value that does not reach a nonreactive trajectory (R-R and P-P). In the TS region, if the environmental coordinate is higher or lower the trajectory will recross to the product state or to the reactant state, respectively. Therefore, the environment has to reach a specific kind of configuration in order to produce reactive trajectories. The insert displays the time evolution of the environmental coordinate in the vicinity of the TS for the light and heavy enzymes. As can be observed, in the TS region (see the insert graphic) the change of the environmental coordinate is faster for the light enzyme than for the heavy enzyme. Thus, the light enzyme will reach more easily an 24


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ACS Catalysis

adequate electrostatic environment for the reaction to proceed and more trajectories will successfully cross the TS dividing surface for the light enzyme than for the heavy enzyme.

-70 -80 -100 -101

-90

-102 -103

-100

-104 -105 -106

-110

-107 -0.04

-0.02

0

0.02

0.04

-120 -130 -2

-1

0

1

2

Figure 7. Time evolution of the environmental coordinate defined as the difference of the electrostatic potential created by the environment on the donor and acceptor atoms averaged along the reactive trajectories R-P in red and along the nonreactive trajectories R-R and P-P in green and blue, respectively. Solid lines are for the light hPNP enzyme and dot lines for the heavy hPNP enzyme. The vertical solid black line at t = 0 shows the position of the TS. The insert shows the time evolution of the environmental coordinate averaged along the reactive trajectories in the TS region.

Time dependent evolution of the contributions to the environmental coordinate for different protein residues and water molecules averaged along the reactive trajectories are shown in Figure 8. If the evolution of the contribution of a particular residue follows the same trend as the one observed in Figure 7 for reactive trajectories (red lines), that residue will electrostatically favor the reaction progress. In Figure 8 (a) and (c) one can conclude that some neighboring amino acid residues (Ala116, Ser33, Arg84) or water molecules that interact with the oxygen atoms or with the hydroxyl group (OH) of hydrogen phosphate ion favor the reaction progress. In Figure 8 (b), the environmental coordinate created by His257 slightly increases when going from reactant state to product state. 25


ACS Catalysis

Whereas for His86 the change is gently in the opposite direction to the pattern followed by a reactive trajectory. The environmental coordinate slightly decreases from reactants to products. For other amino acid residues that establish hydrogen bond interactions with the chemical system, such as Tyr 88, Glu201, Met219, Ser220 and Asn243, the change of the environmental coordinate is almost negligible from reactants to products. (b)

-18



(a)

Ala116

-19 -20

Ser33

-21 -22

Arg84

-23 -24 -25

7 6

His86

5 4 3 2 1 0

His257

-1 -2 -3

-26 -2

-1

0

Time (ps)

1

-2

2

-1

0

1

2

Time (ps)

(c)

(d)

-35


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 33

-40 -45

His257

-50

H2O ········O4

-55

Ala116

-60 -65

Ser33

His86

-70

H2O ········OH

-75 -80

Arg84

-85 -2

-1

0

Time (ps)

1

2

Figure 8. (a-c) Time evolution of the contribution of different residues to the environmental coordinate averaged along the reactive trajectories R-P. The vertical solid black line at t = 0 shows the position of the TS. Solid lines are for the light hPNP enzyme and dot lines for the heavy hPNP enzyme. (d) Transition state structure in the active site of hPNP enzyme showing the surrounding amino acid residues and water molecules which contributions to the environmental coordinate are represented in Figure 8 (a), (b) and (c).

From these results, one can conclude that there are some important amino acid residues, such as Ala114, Ser33, Arg84 and some water molecules, that establish hydrogen bond interactions with the chemical system and electrostatically favor the reaction progress providing the suitable environment to reach the TS and then leading the system towards the formation of products.

26


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Another strategy to show that the light enzyme is slightly faster than the heavy enzyme is obtaining the autocorrelation function of the electrostatic potential created by the environment on key atoms of the chemical system at the TS structure. For this purpose, 200 ps MD simulations were run with the solute coordinate constrained at the value attained at the TS for both light and heavy versions of the enzyme. From the MD simulation, the electrostatic potential created by both environments on the donor (N9) and acceptor (O4) atoms was calculated. Figure S5 in the Supporting Information displays the autocorrelation function of the electrostatic potential created by the light and heavy enzymes on these atoms. The normalized autocorrelation functions at the TS display a very rapid relaxation in a time scale of 200 fs, approximately, in both environments, but the decay is slightly faster for the light enzyme. Thus the changes in the environment take place faster for the light enzyme than for the heavy enzyme. The effect is more pronounced on the N9 atom, because part of the coordination shell of the O4 atom is formed by water molecules that are not affected by the isotopic substitution.

4. Conclusions In this work, an exhaustive theoretical study of the reaction catalyzed by hPNP has been done by means of QM/MM MD simulations. The reaction FESs have been obtained as a function of solute and environmental coordinates in order to get a deeper insight into the participation of the environment to the real reaction coordinate. To compute the EKIE and study dynamic effects, a heavy enzyme has been designed by changing the atomic masses of some atoms by their corresponding heavy isotopes. The EKIE for hPNP has been obtained within the VTST framework in very good agreement with the experimental value. The observed normal EKIE is the result of two contributions: vibrational and dynamic. The first one is due to the fact that the chemical dipole is reduced at the TS with respect to the reactant state and then some hydrogen bond interactions between the chemical system and the enzyme are weakened, resulting in a normal vibrational contribution to the KIE. Regarding the contribution of the transmission coefficient, the heavy enzyme shows a lower value because an increase of the mass leads to a slower environment that increases the fraction of recrossing trajectories and as a result, decreases the rate constant. Both contributions have a common origin in the electrostatic coupling between the preorganized enzymatic environment and the chemical system.

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From the analysis of the free downhill trajectories, we have shown that the reaction catalyzed by hPNP consists of a charge transfer from the acceptor atom to the donor atom with a TS that presents a maximum positive charge on the C1´ atom (see Figure 5), a distinctive feature of the formation of an oxocarbenium ion. Moreover, focusing the attention on the interactions between the chemical system and the environment, it was found that there are some residues that move away from the chemical system during the reaction, such as Arg84, Met 219 and His257. However, there are other residues, such as His86, that is getting closer to the chemical system when going from reactant state to product state. All of these variations of distances between the environment and the chemical system are coupled with the charge reorganization happening while the reaction takes place, but mostly before and after the barrier crossing as shown in Figure 6. The time evolution of the environmental coordinate has a differentiated pattern depending on the type of trajectory, reactive or not. The difference between the types of trajectories comes from the value of the environmental coordinate at the TS. From our results one can conclude that the environment has to be reorganized to reach a particular electrostatic potential in order to facilitate the crossing of the TS dividing surface and reach the product region. Obviously, the time evolution of the environmental coordinate of the heavy enzyme is slower than in the light enzyme in the TS region. Thus, a larger fraction of trajectories reaches the TS (defined in terms of the solute coordinate) without an adequate value of the environmental coordinate in the heavy enzyme. As a consequence, more recrossings are present in the heavy enzyme and then a lower transmission coefficient is obtained. Finally, the contribution to the environmental coordinate due to different residues has been calculated and analyzed to reveal which residues favor electrostatically the reaction progress. In this respect, Arg84, Ser33, Ala116 and some water molecules interact electrostatically with the chemical system providing the adequate environment to reach the TS dividing surface, cross it and get products. Accordingly, these amino acid residues could be of interest in the TSA design. To sum up, protein motions on hPNP appears to have a small but measurable effect on the reaction rate. This can be adequately accounted for in the framework of VTST considering the effect of the mass substitution to the vibrational contributions to the activation barrier and to the transmission coefficient. This result is in agreement with previous conclusions derived from studies in other enzyme catalyzed reactions in our laboratories.23,93-96 28


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5. Acknowledgements The authors gratefully acknowledge financial support from the Spanish Ministerio de Economia y Competitividad and FEDER funds through CTQ2015-66223-C2 projects, from Generalitat Valenciana funds (PrometeoII/2014/022 and GV/2012/053 projects), from Universitat de València project UV-INV-AE11-40931 and Universitat Jaume I Projects P1 1B2014-26 and UJI-B2016-28. M.R. thanks Ministerio de Economía y Competitividad for a ‘Ramón y Cajal’ contract (RYC-2014-16592). The authors acknowledge the computational facilities of Universitat Jaume I and Universitat de València (Tirant Supercomputer).

Supporting Information Contents A list of all the ionizable residues with their calculated pKa values using PROPKA program is provided in Table S1 and more details about the ionization state of the residues are given. A picture of the trimeric hPNP with one of the active sites that contains inosine substrate and hydrogen phosphate ion is shown in Figure S1. Time evolution of the transmission coefficient for the phosphorolysis reaction of inosine catalyzed by hPNP for the light and heavy enzymes is plotted in Figure S2. More details about building the heavy enzyme are given in the SI. The probability density distribution of the electrostatic potential created by the environment of the heavy enzyme on the donor atom N9 and on the acceptor atom O4 with or without changes in the force field parameters is displayed in Figure S3. Average time evolution of the bond breaking and bond forming distances for the light and heavy enzymes along reactive trajectories is shown in Figure S4. Time evolution of the autocorrelation function of the electrostatic potential created by the light and heavy enzymes on the donor and acceptor atoms at the TS structure is depicted in Figure S5. The Supporting Information is available free of charge on the ACS Publications website.

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Table of Contents Graphic

Environmental coordinate

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-100 -101

TS

Light Heavy

-102 -103

Light R

His257

P

Ala116

-104 -105 -106 -107 -0.04

R Heavy R ↑ recrossing -0.02

Ser33

His86 H2O

0

0.02

0.04

Arg84

Time (ps)

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Origin of Enzymatic Kinetic Isotope Effects in Human Purine

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