Archives of Biochemistry and Biophysics xxx (2015) xxx–xxx

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Review

Nuclear quantum effects and kinetic isotope effects in enzyme reactions Alexandra Vardi-Kilshtain, Neta Nitoker, Dan Thomas Major ⇑ Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel

a r t i c l e

i n f o

Article history: Received 27 January 2015 and in revised form 2 March 2015 Available online xxxx Keywords: QM/MM Kinetic isotope effects Nuclear quantum effects Enzyme catalysis

a b s t r a c t Enzymes are extraordinarily effective catalysts evolved to perform well-defined and highly specific chemical transformations. Studying the nature of rate enhancements and the mechanistic strategies in enzymes is very important, both from a basic scientific point of view, as well as in order to improve rational design of biomimetics. Kinetic isotope effect (KIE) is a very important tool in the study of chemical reactions and has been used extensively in the field of enzymology. Theoretically, the prediction of KIEs in condensed phase environments such as enzymes is challenging due to the need to include nuclear quantum effects (NQEs). Herein we describe recent progress in our group in the development of multiscale simulation methods for the calculation of NQEs and accurate computation of KIEs. We also describe their application to several enzyme systems. In particular we describe the use of combined quantum mechanics/molecular mechanics (QM/MM) methods in classical and quantum simulations. The development of various novel path-integral methods is reviewed. These methods are tailor suited to enzyme systems, where only a few degrees of freedom involved in the chemistry need to be quantized. The application of the hybrid QM/MM quantum–classical simulation approach to three case studies is presented. The first case involves the proton transfer in alanine racemase. The second case presented involves orotidine 50 -monophosphate decarboxylase where multidimensional free energy simulations together with kinetic isotope effects are combined in the study of the reaction mechanism. Finally, we discuss the proton transfer in nitroalkane oxidase, where the enzyme employs tunneling as a catalytic fine-tuning tool. Ó 2015 Elsevier Inc. All rights reserved.

Introduction Understanding how enzymes catalyze chemical reactions in cells is a contemporary question of great importance. Indeed, enzymes are present in all organisms in nature [1], and in their absence, life as we know it would not be possible. These bio-catalysts enhance the rate of chemical reactions to values approaching the diffusion limit of bimolecular encounters in water [2]. Decades of comparisons between enzymatic reaction rates and their nonenzymatic analogues have revealed astounding rate enhancements of up to 1017-fold, as shown by Wolfenden and co-workers [3]. The ability of enzymes to lower the effective free energy barrier has been ascribed to various effects, including active site preorganization [4], reactant destabilization, desolvation [5], covalent bonding [6], quantum mechanical (QM) tunneling [7,8], and enzyme dynamics [9,10].

A simplified reaction scheme of an enzyme process is: k1

kcat

E þ S )* ES ! ESz ! EP ! E þ P k1

This process is composed of the following distinct steps: (i) initial binding of substrates to form the Michaelis complex with KM = (k1 + kcat)/k1 ffi k1/k1 (ii) catalytic step described by kcat (iii) product release. Notably, many enzymes have evolved to optimize kcat/KM, which spans a very narrow range of values [11]. However, in reality enzyme processes can be far more complex than suggested by the above scheme, making it a daunting task to delineate the intimate details of the workings of enzymes. A crucial tool in studying the intricacies of these biomachines, such as substrate binding, chemical mechanisms, and their dynamic nature is isotope effects. For each of the steps described above, there might be an associated isotope effect. An isotope effect associated with the initial

⇑ Corresponding author. E-mail address: [email protected] (D.T. Major). http://dx.doi.org/10.1016/j.abb.2015.03.001 0003-9861/Ó 2015 Elsevier Inc. All rights reserved.

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binding process is termed a binding isotope effect (BIE)1, whereas an isotope effect on the chemical step is a kinetic isotope effect (KIE). An isotope effect on the reaction equilibrium is denoted as an equilibrium isotope effect (EIE). In particular, KIE is an extremely useful tool in chemistry and biology, and has been used extensively in enzymology [12–16]. In the case of reactions with a single transition state (TS) separating reactants and products, the experimentally observed KIEs provide direct information regarding the change in bonding during the chemical event. Specifically, primary KIEs indicate which atoms are directly involved in bond making or breaking at the TS, while secondary KIEs are indicators of the location of the TS along a reaction coordinate connecting reactants and products. The KIE is defined as

KIE ¼ kL =kH

ð1Þ

where kL and kH are the rate constants for the reaction involving the light and heavy isotopologues, respectively. Numerous experimental techniques exist for determining KIEs, such as the direct method, internal competition, remote labeling, equilibrium perturbation, and intrinsic isotope effect [1]. However, in many cases there are complicating factors, and the value measured is not the intrinsic isotope effect. Two such confounding matters are substrate binding isotope effect and kinetic complexity. The former effect could arise due to differing binding constants for the two isotopomers, due to induced ligand-strain on binding or interaction with the enzyme active site matrix. Usually, this effect is presumed to be small, although it can often be non-negligible [17,18]. The latter complicating factor is the significant kinetic complexity in enzymatic reactions, which obscures the link between the measured KIE and the chemical nature of the TS. This complexity is a result of the multi-step nature of enzymatic processes, which includes multiple minima separated by TSs. For instance, conformational changes in enzymes are essential for enzyme function, and are often rate limiting in the overall process [19]. Indeed, enzymes have often evolved to a level of chemical perfection so that the chemical transformation is no longer the rate-limiting step [11]. Therefore, complexity arises due to steps that are not related directly to the chemical step of interest and are therefore not isotopically sensitive, but still mask the isotope effect on the chemical step, thus complicating the interpretation of the experimental data. This convolution may be expressed in terms of the reaction’s commitment to proceed forward (Cf) or in the reverse direction (Cr). Thus, the intrinsic KIE may be related to the observed KIE via [20]

KIEobs ¼

KIEint þ C f þ C r  EIE 1 þ Cf þ Cr

ð2Þ

where EIE is the equilibrium isotope effect and Cf and Cr are the forward and reverse commitments to catalysis, respectively. The commitment to catalysis is defined as the ratio between the isotopically sensitive rate-constant to the isotopically insensitive rate-constants affecting the observed KIE. If the reaction is essentially irreversible the KIEobs can vary from KIEint to unity (i.e. no KIE). On the other hand, if the reaction is reversible and Cf is small, the KIEobs may range from KIEint to EIE. It is of course of great importance for theoreticians to distinguish between intrinsic and observed KIEs as the computed values typically relate only to the former. 1 Abbreviations used: KIE, kinetic isotope effect; NQEs, nuclear quantum effects; QM/MM, quantum mechanics/molecular mechanics; BIE, binding isotope effect; EIE, equilibrium isotope effect; TS, transition state; TST, transition state theory; PES, potential energy surface; DFT, density functional theory; SRP, specific reaction parameter; EVB, empirical valence bond; US, umbrella sampling; QCP, quantized classical path; EA-VTST/MT, ensemble-averaged variational TST with multi-dimensional tunneling; PI–FEP, path-integral and free-energy perturbation; DHFR, dihydrofolate reductase; ADH, alcohol dehydrogenase; NAO, nitroalkane oxidase; AlaR, alanine racemase.

Theoretical approaches to kinetic isotope effects In order to compute KIEs for enzymatic reactions from first principles, the theoretical framework of transition state theory (TST) [21] or the more general generalized TST, is usually employed [5,22,23]. Within this framework, the rate constant may be expressed as follows: TST

k ¼ c  kCM

ð3Þ

TST

where kCM is the classical mechanics (CM) TST rate constant, and c TST

is a prefactor that accounts for deviations from CM TST. kCM may be obtained from classical simulations that provide the CM potential of mean force (PMF), WCM(f) [24]:

Z D E TST bW CM ðfz Þ _ kCM ¼ 1=2 jfj e = z f

fz

ebW CM ðfÞ df

ð4Þ

1

D E _ where f is the reaction coordinate, the prefactor jfj is the classiz f

cal dynamical frequency corresponding to the reaction coordinate velocity [25], b = (kBT)1, kB is Boltzmann’s constant, and T is the temperature. The prefactor c may be defined as

c¼Cjg

ð5Þ

which accounts for recrossing of the dividing surface (i.e. the TS), nuclear QM effects (NQE), and non-equilibrium distribution in phase-space, respectively. C may be computed by activated MD simulations [24], while g is often assumed to be close to unity, which is likely the case for reactions occurring in pre-organized enzyme active sites [26,27]. The QM prefactor j is defined as





TST TST kQM =kCM

¼e



 DW zQM DW zCM =RT

ð6Þ

and may be computed via a variety of methods. We note that the TST

quantum vibrational corrections may be included in kCM or in the QM prefactor. We will now describe in greater detail multiscale approaches for enzyme simulations followed by a particular approach for computing KIE, based on a path-integral (PI) formulation. Potential energy surface The potential energy surface (PES) in enzyme simulations may be treated employing a hybrid quantum mechanics–molecular mechanics (QM/MM) Hamiltonian [28,29]. In the QM/MM approach the region of chemical interest, i.e. the reacting fragment, is treated via QM while the remaining parts of the system are treated by a MM force field. The effect of the solvent and enzyme environment on the QM fragment may be included through a coupling term (i.e. electrostatic embedding). This coupling term is essential, as it accounts for the effect of the enzyme and solvent environment on the reactive fragments. Multi-scale QM/MM methods and their use have been reviewed extensively in the literature [29–34]. ^ T , in Specifically, the QM/MM Hamiltonian of the total system, H a typical molecular orbital version of the theory, can be defined by:

^T ¼ H ^ QM þ H ^ MM þ H ^ QM=MM H

ð7Þ

Here, the energy of the full system is described by adding the energy obtained from the QM calculation in the inner layer with a MM calculation in the outer layer. Furthermore, an explicit coupling term is added that describes the interaction between both layers. The coupling term is crucial, and includes the electrostatic and van der Waals interactions between the atoms in both regions.

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X ^ QM=MM ¼  H i;n

X ZN q X qn ANn BNn n  þ þ jRi  rn j N;n jRN  rn j N;n ðRN  rn Þ12 ðRN  rn Þ6

!

over the years, and we refer the interested reader elsewhere [30,51,53,54]. We note that also the EVB approach has been employed in numerous KIE studies of enzymes [55–60].

ð8Þ Here the first term accounts for the interaction between the partial charges of the MM atoms (n), qn, and the electrons of the QM region, i. The second term accounts for the interaction between the MM partial charges and the nuclei, N, of the QM region, while the final term accounts for the van-der-Waals interactions between the QM and MM atoms. This latter term is needed to account for non-electrostatic interactions between QM and MM atoms. The terms of Eq. (8) are added to the Fock matrix in wavefunction-based QM/MM methods or to the Kohn–Sham matrix in QM/MM approaches based on density functional theory (DFT). In this electrostatic embedding QM/MM approach, the wavefunction, or electron density, is polarized via the first term in Eq. (8). In wavefunction-based formalisms, the total energy may be obtained by solving the Schrödinger equation in the field of the MM partial charges

^ T W ¼ ET W H

ð9Þ

and the total potential energy is then defined as

 E D  ^  ^ V T ¼ WH QM þ HQM=MM W þ EMM

ð10Þ

Similar expressions arise for Kohn–Sham versions of DFT. The high cost of QM calculations presents a considerable challenge to current QM/MM approaches. In free energy simulations of enzyme reactions, this becomes an acute problem, as extensive sampling of conformational space is necessary to obtain converged results. However, in spite of the importance of sampling, the accuracy of the simulated enzymatic process can in principle only be as accurate as the QM method describing the active site. This is particularly true when modeling KIEs, where there is an exponential dependence between the isotope effect and the activation free energy difference between the isotopomers. It is therefore crucial to employ a reliable QM level, which might include high-level ab initio (AI) methods, DFT, and in some cases semi-empirical (SE) methods [35]. However, AI and DFT methods are often too computationally expensive, and SE approaches do not posses sufficient accuracy. It is therefore useful to adopt a more pragmatic approach, which involves fine-tuning the PES to the system at hand. This may be achieved for SE methods employing a specific reaction parameter (SRP) approach introduced by Rossi and Truhlar [36], which has been employed in numerous enzymatic reactions [37], including treatments of KIEs [8,38–43]. Another approach is to correct the SE Hamiltonian with a simple valence bond approach, and this has been done very successfully in many KIE applications [5,44–47]. Yet another economical, yet very useful approach is the SE version of DFT in the form of a self-consistent tight-binding DFT model [48,49], which has also been adopted in many enzyme studies, including isotope calculations [50]. In spite of the usefulness of molecular orbital-based methods, the QM calculation often remains the bottleneck for typical QM/ MM calculations. This may be overcome in the empirical valence bond (EVB) approach [30,51], which originates from the early construction of potential energy surfaces (e.g. LEPS [52]). The EVB method is based on a combination of classical force field (FF) and valence bond VB theory, allowing for an empirically-based QM/ MM description of chemical reactions. Specifically, this approach describes chemical reactions via a combination of diabatic states that correspond to classical VB structures. The strength of the EVB approach is its ability to treat chemistry at the cost of classical FF calculation, thus facilitating extensive sampling of the protein environment. The EVB approach has been reviewed extensively

Sampling the potential energy surface In order to sample the PES a simulation method, such as molecular dynamics (MD) or Monte Carlo (MC), is usually required. The first MD simulations of proteins were carried out in the 1970’s and focused on the hitherto unknown dynamic nature of macromolecules [61,62]. Since these early days MD simulations of proteins have become an essential tool for both theoreticians and experimentalists [63], and today, classical simulations of enzyme reactions employ almost exclusively MD simulations. However, in order to sample very rare events, such as chemical reactions, specialized methods are used to facilitate barrier climbing within reasonable simulation times [64–69]. A widely used method is the umbrella sampling (US) technique [70], which provides a simple way to model enzymatic reactions [24,71]. Other methods include free energy perturbation [72,30] thermodynamic integration, metadynamics [73], and transition path sampling [74,75]. In spite of the usefulness of classical simulation methods, these approaches cannot address questions pertaining to isotope effects. In order to treat isotopic phenomena it is necessary to employ quantum simulation methods, as the different behavior of isotopomers is due to quantum effects such as zero-point energy and tunneling. KIEs from Feynman path-integral quantum simulations Several methods have been developed to include NQE in enzyme reaction simulations. Historically, the first of these was the Feynman path-integral (PI) [76–78] quantized classical path (QCP) approach developed in the Warshel group [79,80]. Subsequently, additional approaches were introduced in the study of enzyme reactions, such as QM/MM based normal mode analysis due to Barnes and Williams [81,82], the ensemble-averaged variational TST with multi-dimensional tunneling (EA-VTST/MT) approach of Truhlar, Gao, and co-workers [22,83], and wavefunction based methods of Hammes-Schiffer and co-workers [84,85]. In our group we further developed PI approaches for enzyme reactions building on the QCP method of the Warshel-group [40,86–92], and other groups followed suit [93–96]. PIs are particularly appropriate for enzyme simulations, as they are readily applicable to multi-dimensional systems and may be employed in mixed quantum–classical systems. Generally, Feynman PIs is a less conventional formulation of quantum mechanics. It describes the probability amplitude as a quantity that takes into account all possible paths in which the system can transfer from one state to another. The quantum density matrix (DM) can be written as a PI, referring to ‘‘paths’’ by which the system can travel between initial and final configurations in an imaginary negative ‘‘time’’ domain. This formalism gives the complete statistical behavior of a QM system as a PI, as the system partition function, Q, is defined as the trace of the DM:

Q ¼ TrðqÞ ¼

Z

dxqðx; x; bÞ ¼

Z

    dx xebH x

ð11Þ

where x denotes the position of a particle in one dimension and extension to N dimensions is straightforward, and q is the thermal DM. To express the partition function as a PI, we write the density matrix operator as a product of P exponents, each representing a ‘‘time’’ slice of length s ¼ b=P:



Z

P Y   Z   dx xesH esH    esH x ¼ dx1    dxP qðxi ; xiþ1 ; sÞ i¼1

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ð12Þ

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where x1 ¼ xPþ1 . In the limit P ! 1 and s ! 0, one can use the semiclassical primitive approximation (PA):

qðxi ; xiþ1 ; sÞ ffi qPA ðxi ; xiþ1 ; sÞ ¼ qT ðxi ; xiþ1 ; sÞqPA V ðxi ; sÞ

ð13Þ

xi;L =xi;H ¼

where qT is the kinetic energy (T), i.e. free particle term:

 qT ðxi ; xiþ1 ; sÞ ffi X  exp s

m 2 2 h

2s

ðxi  xiþ1 Þ2



ð14Þ

2 1=2

where X ¼ ðm=2ps and m is the mass, while qPA is the h Þ V potential energy (V) term within the PA:

qPA V ðxi ; sÞ ¼ exp ½sVðxi Þ

ð15Þ

and Vðxi Þ is the potential at time slice i, and may be described using the hybrid QM/MM potentials described above (e.g. see Eq. (10)). The above quantum system is isomorphic to a classical system of ring polymers where each bead, i, in the polymer interacts with its neighbor, i ± 1, via a harmonic potential and experiences only a fraction, 1/P, of the full potential V (Fig. 1). The starting point for the PI approaches based on QCP is to write a QM correction to the classical partition function as follows:

R dxqQM ðx; x; bÞ Q QM ¼R Q CM dxqCM ðx; x; bÞ

ð16Þ

This expression may be written as a PI yielding

R R Q Q QM dxc dx1    dxP dðxc  xÞ Pi¼1 qT ðxi ; xiþ1 ; sÞqPA V ðxi ; sÞ ¼R R QP Q CM dxc dx1    dxP dðxc  xÞ i¼1 qT ðxi ; xiþ1 ; sÞqPA V ðxc ; sÞ

ð17Þ

where xc is the centroid coordinate. Warshel and co-workers then showed that this quantum to classical ratio might be written in the simple form [79,80]:

Q QM ¼ Q CM

** exp s

! !+ P X ðVðxi Þ  Vðxc ÞÞ i¼1

T;xc

+ ð18Þ Vðxc Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mH =mL ;

i ¼ 1; 2;    ; P

ð20Þ

where xi;L and xi;H are the coordinates for bead i of the corresponding light and heavy isotopes, respectively. This bead distribution may be computed with either the bisection or staging algorithms. The kinetic isotope effect may then be determined by the formula

D Efz f_   CL  jL  g L KIE ¼ D E Lz   f f_   CH  jH  g H

ð21Þ

H

Importantly, the ratio jL =jH is computed using mass-perturbation [87]. This greatly improved the accuracy of the computed KIE, and has been used extensively since [8,42,43,88–90,92,100– 102]. Others have also adopted mass-perturbation techniques for PI KIE in the study of small molecules [103,104]. To further enhance the efficiency of the PI simulations, one may use higher order factorizations of the DM operator. Specifically, in our group we adopted the approach of Chin [105–107] and generated a higher order version of the QCP method, which converges at a considerably lower number of beads, at the cost of computing the potential gradient, rV, in addition to the potential, V [89,91,92,108]. This approach may also be combined with the mass-perturbation approach, to efficiently compute the KIE [43,92]. As a final note in this section, it is important to realize that when comparing theoretical and experimental KIEs it is critical to distinguish between observed and intrinsic isotope effects (see Eq. (2)). Theory computes the latter directly, and usually cannot estimate kinetic complexity. Multiscale KIE applications

The external average represents a CM average while the inner average is a so-called free particle average yielding a delocalized QM description. In this approach, the classical simulation is performed separately from the quantum simulation. We may then write the quantum correction to the CM TST rate constant (Eq. (6)):

  Q zQM =Q zCM j ¼  RS RS  Q QM =Q CM

where the light atom of mass mL is replaced by a heavier isotope of mass mH, one can show that the two bead-distributions differ only by the ratio of the corresponding masses (Fig. 1) [87,89]:

ð19Þ

where the quantum correction is computed at the reactant state and transition state. A well-known problem with PI simulations is the difficulty in sampling the polymer ring due the harmonic coupling between the beads [77]. Our initial attempts to implement the QCP approach clearly demonstrated this issue, and we turned our focus to combining QCP with enhanced sampling methods. We therefore combined QCP with the bisection sampling algorithm developed by Pollock and Ceperley [40,86,97,98], and later we also coupled the method with the staging algorithm [89,99]. In spite of the greatly improved convergence of the QCP approach with the bisection or staging algorithms, the approach was not efficient enough to accurately predict KIEs. KIE are due to minute differences in free energy, and specialized techniques are required to obtain quantitative results. This is essential in order to remove sampling noise, which is inherent to simulation methods. We therefore developed a mass-perturbation technique, termed path-integral and free-energy perturbation (PI–FEP), wherein the free energy difference between the different isotopes is computed directly [87,89]. Considering an atom transfer reaction

Historical perspective The first case where a multiscale simulation technique was employed to compute KIE was in the classical work by Warshel and Bromberg in 1970 [109]. In this work they employed a QM + MM strategy (the ‘‘+’’ indicates that there was no coupling ^ QM=MM term was not between the QM and MM regions, i.e. the H included in Eqs. (7) and (8)) to study the KIE in the oxidation of 4a,4b-dihydrophenanthrenes. The authors found that a large KIE was due to QM tunneling and loss of zero-point energy at the TS, and additionally observed a reduction in the KIE with increasing temperature. Interestingly, it was only much later, in 1996 that a QM/MM study incorporating KIE calculations appeared in the literature [81,82], about 20 years after the advent of the QM/MM approach [28]. In this series of papers, Barnes and Williams presented their pioneering work for a solution and an enzyme reaction using multiscale modeling [81,82]. In an initial study of an acidcatalyzed glycoside hydrolysis in solution the authors found that both stepwise and concerted mechanisms were possible, based on a QM/MM potential energy reaction profile [81]. The difference between the barriers for the two reactions paths was negligible (0.05 kcal/mol), although the TS structures were markedly different. The authors then computed 14C, 15N, and secondary b-2H and a-3H KIEs, and found that for the latter isotopic substitution at the a-position, a significant difference between the mechanisms was found. Indeed, the computed a-3H KIEs was in agreement only with the stepwise process. Subsequently, the same methodology was applied to the glycoside hydrolysis reaction in the enzyme sialidase [82]. The mechanistic questions in this enzyme reaction

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A

5

B

Fig. 1. (A) An illustration of the classical (red circle) and PI quantum (blue ring polymer) representations. In the classical case, the particle in the reactant state has no zeropoint energy. To allow barrier crossing through the transition state the particle must have total energy greater than that of the barrier height. In the quantum case, the particle is replaced by a polymer ring, which possesses zero-point energy and has a finite probability of penetrating the barrier, due to its delocalized description. Example depicts the enzyme alanine racemase wherein a proton transfers between donor (D) and acceptor (A). (B) Mass perturbation where a heavy mass (mH, top) is perturbed to a light mass (mL, bottom).

were substantial: Are the reactions stepwise or concerted; do they occur with retention or inversion of configuration at the anomeric site? In this work, which addressed the influenza B and Salmonella typhimurium sialidases, all computed KIEs were in close agreement with experiment, but still left room for improvement, in particular for a more accurate potential energy function. The strength of the strategy introduced by Barnes and Williams of combining hybrid simulation methods with the computation of KIEs was succinctly stated in their work [82]: ‘‘Comparison of calculated KIEs with experimental values provides a very stern test, and their use provides a very strong anchor to prevent theoretical modeling from drifting into unreality’’. Since these early studies, there has been significant progress in simulation methodologies, and multiscale KIE techniques have been applied to a wide range of enzymes. A non-exhaustive list of such enzyme studies includes dihydrofolate reductase (DHFR) [41,46,56,90,102,110–114], alcohol dehydrogenase (ADH) [50,83,115,116], lipoxygenase [55,59,117–119], methylamine dehydrogenase [115,120–124], thymidylate synthase [125,126], chorismate mutase [127–129], several decarboxylases [43,100,101,130], methylmalonyl-CoA mutase [131,132], alanine racemase [39,100,133], formate dehydrogenase [42,134], nitroalkane oxidase [8,108,135], morphinone reductase [116], and glyoxalase [134,136]. In the following we will focus on some examples of work performed in our group, with which we are most familiar. Intrinsic kinetic isotope effects in alanine racemase Alanine racemase (AlaR) is a PLP-dependent enzyme, which catalyzes the interconversion between L-Ala and D-Ala (Scheme 1). AlaR presents an important antibiotic target due to its role in bacterial synthesis. Prior studies of AlaR have largely focused on enzyme inhibition and several potent inhibitors have been found [137]. The mechanistic aspects of the racemization reaction have been studied extensively by experimental methods [138–148], and it has been demonstrated by mutagenesis [142–144] and based on several crystal structures [140,141,145] that catalysis is performed by the acid-base pair Tyr2650 (prime indicates residues from the second subunit) and Lys39. This acid-base pair is located on opposite sides of the PLP conjugated plane, in ideal position for a two-step proton transfer (Fig. 2). The key steps of the racemization reaction (e.g. L ? D isomerization) involve (Scheme 1) (1)

Binding of L-Ala to the enzyme in an internal aldimine state with the PLP-cofactor bound via a Schiff base to Lys39. (2) L-Ala formation of an external aldimine with the PLP-cofactor (Ala-PLP) by displacing Lys39 (3) Tyr2650 abstraction of a proton from LAla forming a quinonoid intermediate (4) reprotonation by Lys39 to form D-Ala linked to PLP in an external aldimine form (5) Lys39 displacing D-Ala to form an internal aldimine and subsequent release of D-Ala. The proton abstraction reaction is believed to be the principle rate-limiting step based on mutational analysis and KIE measurements, although the rate of the preceding transaldimination is very similar [142–144,146,147]. Toney and co-workers have presented a detailed free-energy profile for this reaction [147,148]. In this work we employed a hybrid QM(AM1-SRP)/MM Hamiltonian, wherein the standard AM1 method [149] was re-optimized to fit the chemistry of racemase reactions. The computed free energy profile was found to be in fair agreement with the experimentally determined one, and brought further support for the two-base mechanism [133]. Key findings in this work were the prediction of a stable intermediate, which suggests a stepwise proton shuffling, as well as the role of near and distant amino-acid residues in stabilizing the TS. In particular, the relative catalytic role of the PLP-cofactor and the enzyme environment was delineated. These findings are similar to those recently found for the related serine racemase enzyme [150]. To bring further support for the reaction mechanism and validate the computational procedure, KIEs were computed and compared with the work of Spies and Toney [146,148]. The experimentally determined KIEs were 1.66 and 1.57 for the reaction in the L ? D and D ? L directions, respectively, which is significantly lower than the semi-classical limit. These values were interpreted within the framework of Westheimer–Melander theory, which predicts that the magnitude of the intrinsic primary KIE varies with both the extent of H-transfer at the TS as well as the angle between the donor-H-acceptor. Thus, very small KIEs can occur when the TS is highly non-linear or with a very early or late TS. Based on the QM/MM studies of AlaR neither of these conditions seemed to be met, and indeed the computed KIEs using our PI approach were 4.21 for the a-proton abstraction in the L ? D alanine conversion and in the opposite direction we predicted a range from 3.06 to 4.60, depending on the kinetic scheme. These values were corroborated using the very different EA-VTST/MT approach and the

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H 3N Lys 39

Tyr265'-O H 3C L-Ala + E-PLP

H O O P O O

H N

N

H 3C

COO H O CH 3

H 3N Lys 39

Tyr265'-OH

O O P O O

COO N

H

N

H 3C H

H O CH 3

H 2N Lys 39

Tyr265'-OH

O O P O O

H N

N

COO H O

D-Ala + E-PLP

CH 3

Scheme 1. The racemization reaction, L-Ala ¢ D-Ala, catalyzed by AlaR.

respective KIEs were 3.97 for the L ? D alanine conversion and in the D ? L direction we predicted a range from 2.65 to 3.33, depending on the kinetic scheme. In the case of the AlaR reaction, we found that the dominant quantum mechanical contribution is due to the change in zero-point energy in going from the reactant state to the transition state, and that proton tunneling is negligible with an average transmission factor of 1.14 and 1.31 for the proton and deuteron, respectively in the step performed by Tyr2650 . In addition, we found that the average recrossing transmission factors, C, are close to unity with values of 0.96 and 0.94 for the hydrogen and deuterium transfers, respectively. Thus, the reaction rate difference between the different isotopomers may largely be ascribed to differences in zero-point energy change in climbing from the RS to the TS. The origin of the discrepancy between the experimental and computed KIEs is not clear, although several factors may be envisaged. In addition to uncertainties in the computational modeling, we note that there is considerable complexity involved in the analysis of the experimental kinetic data, in particular due to multiple steps with similar rates, and it is possible that the experimental KIE was not exactly equal to the intrinsic value. It is worth noting that an earlier study utilizing the Lys39Ala mutant showed a greater primary KIE of 5.4, in which the small molecule methylamine was employed as an enzymerescuing agent. It is assumed that such a mutation-rescue scheme might raise the proton transfer barrier, and thereby unmask the chemical step [144]. Heavy-atom kinetic isotope effects as a mechanistic tool in orotidine decarboxylase Orotidine 50 -monophosphate (OMP) decarboxylase (ODC) is a highly efficient enzyme, which catalyzes the decarboxylation of OMP to uridine 50 -monophosphate (UMP) (Scheme 2) [151]. ODC catalyzes the crucial final step in the pyrimidine biosynthetic pathway, and presents a significant target in the development of anti-malaria and cancer drugs [152,153]. Interestingly, ODC is among the most proficient enzymes known. The non-enzymatic rate constant extrapolated to 25 °C is ca. 1016 s1, corresponding to a half-life of 78 million years. The ODC catalyzed reaction has a turnover rate of 39 s1, yielding a rate enhancement of ca. 1017 [151]. The catalytic mechanism of ODC has been subject to numerous investigations by both experimental [154–164] and computational [156,165–172] means. In particular, Rishavy and Cleland employed 13C and 15N KIEs to elucidate the mechanism [164], and concluded that the most likely pathway involves a direct decarboxylation with an anionic intermediate [162,173]. In addition, multiple isotope effect experiments were employed to determine whether protonation occurs in concert with decarboxylation for the ODC reaction [174]. Therein the 13C isotope effects did not increase when the aqueous solvent for the reaction was replaced with D2O, showing that no protonation occurs as the C–C bond is cleaved, pointing to a stepwise mechanism. The stepwise decarboxylation followed by protonation by an active site Lys residue [175] has received accruing support by a series of NMR studies by Richard and co-workers [173,176–178]. The direct

Fig. 2. Active site in alanine racemase in the carbanion intermediate state.

decarboxylation followed by C6-protonation mechanism has gained acceptance in recent years based on a series of QM/MM studies [156,166,169], although none of the early studies on this system studied the proton transfer explicitly (Fig. 3). In our investigation of this system, we initially used the decarboxylation of 1-methyl orotate in various protonation states in explicit sulfolane solvent as a test case for the ODC catalysis of OMP to UMP. This study included free-energy profiles as well as calculation of heavy-atom KIE using a high-order Trotter factorization of the thermal DM in conjunction with our PI–FEP massperturbation approach and a hybrid QM(AM1)/MM PES [92]. Decarboxylation reactions constitute a family of reactions treated rather well by the standard SE AM1 Hamiltonian [149], and no further fine-tuning of the method was necessary. We computed 13C and 15N KIE for the 1-methyl orotate decarboxylation reaction, and the computed KIE results were in good agreement with the available experimental data [179]. Subsequently, we employed hybrid QM/MM simulations to investigate the catalytic mechanism of ODC, focusing on the decarboxylation of OMP and 5-fluoro-OMP (5-F-OMP) by ODC [43]. In this work, we calculated for the first time a complete free energy landscape for the ODC catalyzed decarboxylation reaction of OMP and 5-F-OMP, including the proton transfer step (Fig. 3). We concluded that decarboxylation of OMP/5-F-OMP is the ratedetermining step with free energy barriers of 14.9 kcal/mol and 14.0 kcal/mol, respectively. These results are in fairly good agreement with the experimentally estimated values of 16.4 kcal/mol for OMP and 14.2 for 5-F-OMP based on the observed rates [180]. The difference between OMP and 5-F-OMP is due to the inductive effect of fluorine, which stabilizes the carbanion intermediate.

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A. Vardi-Kilshtain et al. / Archives of Biochemistry and Biophysics xxx (2015) xxx–xxx O4 2 -2

O

O3 PO

O

HO OMP

1 N 6 CO2-

HN ODCase H+

OH

Table 1 Comparison between the computed and experimental intrinsic kinetic isotope effect values for the decarboxylation reaction in ODC at 298 K.

O 5

3 HN

-2

O

O3 PO

O

N

HO

+

KIE

CO2

OH

UMP

Scheme 2. Decarboxylation of OMP by ODC.

Calcd.a

Exp.

OMP CO2 N1 O2 O4

1.050 ± 0.006 1.003 ± 0.005 0.998 ± 0.005 1.004 ± 0.007

1.0494 ± 0.0006 [154,164] 1.0068 ± 0.0003 [164] 0.983 ± 0.001 [163]

5-Fluoro-OMP CO2 N1 O2 O4

1.047 ± 0.009 1.004 ± 0.006 0.998 ± 0.005 1.001 ± 0.005

1.0356 ± 0.0001 [162]

a The computed KIEs, with accompanying statistical uncertainties, were obtained with path-integral PI–FEP simulations.

O RCH2NO2 + O2 + OH-

NAO

R C H

+ NO2- + H2O2

Scheme 3. The oxidation reaction catalyzed by NAO.

Fig. 3. Active site in ODC at the OMP-decarboxylation transition state. The decarboxylation and proton transfer coordinates are marked with a dotted, green line.

Furthermore, we established that the subsequent proton transfer step by an active site Lys residue occurs after completion of the decarboxylation step, supporting a decoupling of the C-C bond breakage and the C-H bond formation. To facilitate further direct comparison with experiment we computed the KIEs for the enzyme-catalyzed reactions using the PI–FEP approach. The computed KIEs were in good agreement with experiment and provided further support for a direct decarboxylation mechanism (Table 1), which has been proposed by numerous other researchers [156,162,164,166,169,178,181]. In particular, a large experimental 13 C KIE of 1.0494 for the carboxylate carbon [164], which may be compared to the computed value of 1.050, is in agreement with the notion that decarboxylation is rate limiting. Interestingly, a mechanism involving pre-protonation of the O2 OMP oxygen has been substantiated based on an inverse 18O2 KIE [163]. However, our PI–FEP simulated 18O2 KIE also exhibited an inverse effect for the direct decarboxylation mechanism, suggesting that the observed inverse oxygen KIE is due to changes in H-bonding rather than protonation.

Tunneling in nitroalkane oxidase – insights from KIEs Nitroalkane oxidase (NAO) catalyzes the proton transfer reaction between nitroethane and Asp402 in the flavoenzyme nitroalkane oxidase (NAO) to yield the corresponding aldehyde (Scheme 3). The NAO-catalyzed reaction was studied both experimentally [182] and computationally [8] and compared to an analogous, uncatalyzed process, involving the same substrate with an acetate ion in an aqueous solution [38]. Kinetic measurements have shown that the abstraction of the a-proton from nitroethane by the carboxylate group is rate-limiting in NAO, and is accelerated by a factor of 109 over the corresponding reaction in water [182]. Importantly, this reaction is a rare case where the chemistry in the model reaction and the enzymatic counterpart is identical [10]. In this study we employed a hybrid QM(AM1-SRP)/MM Hamiltonian in conjunction with path-integral and free-energy

perturbation (i.e. PI–FEP) simulations to estimate the role of NQEs (Fig. 4). The computed free energies of activation and reaction in the enzyme and in solution were in agreement with experiments [182]. In particular, the enzyme was found to reduce the barrier height relative to the non-enzymatic reaction through stabilization of the transition state by 8.5 kcal/mol, compared with 10.8 kcal/mol from experiment. This effect may be ascribed to electrostatic stabilization. The overall contribution of NQE (zero-point energies and tunneling contributions) to barrier reduction of the proton transfer was shown to be greater in the enzyme than in water (3.4 vs. 3.0 kcal/mol, respectively), thus constituting a small catalytic effect. Further, the presence of the enzyme increased the difference in the free-energy barrier between proton and deuteron transfer, compared with that computed in solution. In line with this finding, the computed primary KIE on the proton abstraction step was elevated in NAO (8.36) relative to the uncatalyzed reaction (6.63), again in agreement with experiment. While these findings clearly point to a differential NQE between the enzymatic and solution-phase processes, a key aspect of this work concerned the explicit participation of tunneling in catalysis. This was initially probed by calculating the Swain-Schaad exponent [183] for mixed-labeling competitive experiments. Deviation from semi-classical Swain-Schaad exponents have been suggested as a sensitive indicator of tunneling [184,185]. The mass-perturbation approach embedded in the PI–FEP method allowed us to determine these secondary KIEs efficiently and accurately. The mixed Swain-Schaad exponential relationship is defined as the ratio of the natural logarithms of mixed-labeling KIEs, where breakdown of the semiclassical prediction (3.3) may serve as evidence for tunneling. An inflated exponent (4.3) was obtained for the reaction in NAO compared with that in solution without a catalyst (3.5), indicative of a differential tunneling effect for the NAO-catalyzed and uncatalyzed proton transfer reactions. To get a direct estimation of the tunneling transmission coefficient, the tunneling contribution should be separated from the overall NQEs. The extent of tunneling was obtained using the EA-VTST/ MT approach [22,83]. We obtained tunneling transmission coefficients of 3.5 and 1.3 for the enzymatic and the solution phase reactions, respectively, suggesting a catalytic tunneling effect enhancing the rate by a factor of 2.7. This enzyme enhanced tunneling is due to a narrowing of the adiabatic potential energy surface and of the PMF in the enzyme relative to the solution phase

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although in these simulations the isotope effect was treated within a classical framework [112]. Acknowledgments This research has been supported by the Israel Science Foundation and the Binational Science Foundation. References

Fig. 4. Proton abstraction of nitroethane by acetate ion in water. The transferring proton, as well as the donor and acceptor atoms, is treated as a path-integral ringpolymer.

reaction. Additionally, the enzyme PMF is considerably more symmetric than in the solution phase. The combined catalytic effect due to tunneling is small, but non-negligible, and may be considered catalytic fine-tuning. We note that this finding is in overall agreement with that of Hwang and Warshel, i.e. that NQE make small contributions to catalysis [186].

Summary and outlook In the current review, we presented an overview of the simulation methods developed in our group for the prediction of KIEs and strategies employed in our studies of enzyme catalysis. The overall mode of work is multi-scale, wherein both the PES and nuclear motion are treated at different levels of accuracy. The PES is described by a hybrid QM/MM Hamiltonian, and the QM level is determined by the chemistry involved in the particular enzyme. Typically, free energy profiles are obtained for the enzymes using classical simulation techniques. However, in order to predict KIEs or treat transfer of light particles such as H+/H/ H, quantum simulation methods must be employed, and in such cases we employ various PI strategies. The multi-scale approach has been successfully applied to numerous enzymes, and in this review we presented three of these enzyme reactions, AlaR, ODC, and NAO. In spite of the success in the area of in silico estimation of KIEs using multiscale methods, significant challenges lie ahead. For instance the temperature dependence of the KIEs in a large number of enzymes show very complex trends as a function of mutations. This peculiar behavior has been linked to a hierarchy of thermodynamically equilibrated states that control the hydrogen donor and acceptor distance as well as active-site electrostatics, and thereby creating an ensemble of conformations that are suitable for H-tunneling [187,188]. Although several reports have managed to reproduce some temperature dependent behavior [55,56,59,60,126,189–191], this remains a challenge [56]. An additional challenge relates to protein isotope effects, or so-called heavy-enzyme dynamics. In such experiments, some or all non-exchangeable atoms are replaced by their heavy isotopomer, hence increasing the weight of the enzyme, but without perturbing the Born–Oppenheimer PES [192]. Also in this case some initial reports have shown successful simulations of the heavy-enzyme dynamics,

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Nuclear quantum effects and kinetic isotope effects in enzyme reactions.

Enzymes are extraordinarily effective catalysts evolved to perform well-defined and highly specific chemical transformations. Studying the nature of r...
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