Heavy enzymes — experimental and computational insights in enzyme dynamics

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ScienceDirect Heavy enzymes — experimental and computational insights in enzyme dynamics Katarzyna S´widerek1,2, J Javier Ruiz-Pernı´a3, Vicent Moliner3 and In˜aki Tun˜o´n1 The role of protein motions in the chemical step of enzymecatalyzed reactions is the subject of an open debate in the scientific literature. The systematic use of isotopically substituted enzymes has been revealed as a useful tool to quantify the role of these motions. According to the Born– Oppenheimer approximation, changing the mass of the protein does not change the forces acting on the system but alters the frequencies of the protein motions, which in turn can affect the rate constant. Experimental and theoretical studies carried out in this field are presented in this article and discussed in the framework of Transition State Theory. Addresses 1 Departamento de Quı´mica Fı´sica, Universitat de Vale`ncia, 46100 Burjassot, Spain 2 Institute of Applied Radiation Chemistry, Lodz University of Technology, 90-924 Lodz, Poland 3 Departamento de Quı´mica Fı´sica y Analı´tica, Universitat Jaume I, 12071 Castello´n, Spain Corresponding authors: Moliner, Vicent ([email protected]) and Tun˜o´n, In˜aki ([email protected])

Current Opinion in Chemical Biology 2014, 21:11–18 This review comes from a themed issue on Mechanisms Edited by AnnMarie C O’Donoghue and Shina CL Kamerlin

1367-5931/$ – see front matter, # 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cbpa.2014.03.005

Introduction Nowadays many of the basic physical principles that explain the enormous catalytic power of enzymes are well-understood. The seminal Pauling’s proposal has been now rationalized by molecular simulations in terms of the electrostatic stabilization that the active site provides for the transient structures that appear during the transformation of reactants into products and, in particular, for the transition state (TS) [1]. This knowledge has been used to guide the redesign of new functions into existing enzymes or the de novo design of new enzymes [2]. Nevertheless, the moderate success obtained until now using this strategy has reignited the debate about the origin of the catalytic power of natural enzymes [3,4]. Enzymes are flexible entities with active motions before, after and during the chemical transformation [5]. In fact, www.sciencedirect.com

enzymes must be stable enough to retain their threedimensional structure but flexible enough to change among the different conformations relevant at each step of the catalytic cycle [6,7]. The explicit consideration of different reactive conformations is a requisite to explain some experimental results such as the kinetic disorder observed in single-molecule experiments [8] or the temperature dependence of kinetic isotope effects (KIEs) [9]. A controversial subject is the proposal about the active role played by some protein motions driving the conversion of substrates into products. This proposal comprises both slow conformational changes, related with protein loop motions [10], and fast vibrational motions, termed as promoting vibrations [11,12]. These proposals are often presented under the denomination of ‘dynamical effects’. Although this is an ambiguous term, since any chemical reaction involves dynamics, the meaning becomes clearer by contrast to statistical rate theories. Transition State Theory (TST), in its conventional [13] or generalized formulation [14] provides a theoretical framework to study enzyme catalyzed reactions [15]. TST can be formulated as a quasi-equilibrium approximation to the calculation of the reactive flux [16]. When applying TST, the coordinates of the system are divided in two sub-sets: the reaction coordinate, or RC (j), that describes the advance of the system along trajectories connecting reactants and products states, and the remaining coordinates. The free energy profile along the RC is obtained assuming that these remaining coordinates are in their equilibrium (Boltzmann) distributions at any value of the RC. Protein motions relevant for the chemical step can usually equilibrate at the reactant state, except for very fast processes or for weakly coupled degrees of freedom [17]. However, barrier crossing takes place in the femtosecond time scale and the participation of protein motions in this event could lead to deviations from the equilibrium treatment. It is then obvious that the selection of the RC becomes critical when applying TST to study enzymatic reactions. Free energy surfaces as a function of substrate and protein degrees of freedom can be used to analyze the participation of the environment in the RC [18,19]. In this regard, different scenarios can be obtained depending on the participation of the substrate (q) and protein (s) degrees of freedom into the RC (j(s,q)) as illustrated in Fig. 1. Only in the case represented in Current Opinion in Chemical Biology 2014, 21:11–18

12 Mechanisms

Enzyme isotope effects

Figure 1

(b)

(a)

s

s

R

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P R q

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(d) s

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q Current Opinion in Chemical Biology

Simplified picture of the free energy surfaces corresponding to four possible scenarios of enzyme catalyzed reactions depending on the participation of the substrate (q) and protein (s) degrees of freedom into the RC (j(s,q)): (a) the RC is described exclusively in terms of substrate coordinates; (b) moderate participation of protein motions in the RC; (c) significant participation of protein motions in the definition of the RC; and (d) the RC is described exclusively in terms of protein coordinate. The red dashed line represents the location of the Transition State dividing surface.

Fig. 1a the RC can be described exclusively in terms of substrate coordinates. The opposite situation, where the process is completely driven by protein motions, is represented in Fig. 1d. Some electron transfer processes correspond to this kind of representation [20]. Fig. 1b and c represents intermediate situations with moderate (b) or significant (c) participation of protein motions in the definition of the RC. Fig. 1b represents an interesting case observed in simulations of enzymatic processes [19,21,22]. Protein motions participate in the RC but crossing the dividing surface is largely defined by changes in the substrate coordinates. In these cases TST can render accurate results through the inclusion of a transmission coefficient, which is equivalent to an improvement of the definition of the RC [23]. The RC can be defined using collective variables depending on both the protein and the substrate degrees of freedom, such as the energy gap coordinate [24]. In this case the role of protein motions is also incorporated in the activation free energy and the transmission coefficient becomes closer to unity. The RC can be also determined after inspection of unbiased reactive trajectories generated by means of Transition Path Sampling (TPS) [25] or minimum free energy paths located on multidimensional surfaces [26]. Current Opinion in Chemical Biology 2014, 21:11–18

Isotopic substitutions of atoms involved in a chemical reaction are traditionally used as a potent tool to know about the characteristics of the TS and, consequently, to study reaction mechanisms [27]. A change in atomic masses alters the vibrational frequencies while the underlying Potential Energy Surface (PES) remains unaltered according to the Born–Oppenheimer approximation. Isotopic substitution modifies the vibrational contributions to the activation free energy and quantum tunnel probabilities, affecting thus the rate constants. A similar strategy has been proposed to analyze the role of protein motions in the chemical step of enzyme catalyzed processes. In 1969 Rokop et al. reported a kinetic study of a deuterated version of Alkaline Phosphatase, where all non-exchangeable hydrogens were substituted by deuterium, showing a decrease in vmax by a factor equal to 1.8 with respect to the ordinary version of the enzyme [28]. This difference was attributed to the diminution of the vibrational energy available in the active site of the deuterated enzyme. Later, in 2007 a deuterated version of human Arginase I showed a reduction of 1.3 in the reaction rate while the structure was shown to be identical to the natural enzyme [29]. In 2011 Schramm and coworkers [30] measured the enzyme isotope effect on the rate constant of the chemical step for a version of human Purine Nucleoide Phosphorylase (hPNP). In this study the normal isotopic distribution of the protein atoms was modified replacing all carbon, nitrogen and nonexchangeable hydrogen atoms by 13C, 15N and 2H, respectively. The so-called ‘heavy enzyme’ or ‘Born– Oppenheimer enzyme’ showed a diminution in the rate constant of the chemical step relative to the ‘light enzyme’ (the isotopically unlabeled counterpart), which was interpreted as a dynamical link between mass-dependent bond vibrations of the protein and events in the RC. In principle, there are several factors that can contribute to the variation of the rate constant of the chemical step with protein isotopic substitution. First, a change in the vibrational frequencies of the protein can modify the position and/or the orientation of the TS dividing surface. Obviously this is not the case of Fig. 1a, where the TS is defined exclusively in terms of the substrate coordinates, but in any other situation enzyme KIEs different to unity can indicate participation of protein motions in the RC. This effect can be estimated within the theoretical framework of TST obtaining the free energy profile along a properly defined RC or by means of the evaluation of the transmission coefficient associated to a substrate coordinate [31]. In addition to this ‘classical’ effect of the change in the protein mass, it must be also considered that quantization of protein motions may affect the activation free energy in the heavy and light enzymes in a slightly different way, the same as observed for substrate secondary KIEs. One www.sciencedirect.com

Heavy enzymes and dynamics Javier Ruiz-Pernı´a et al. 13

could also hypothesize that the change in the vibrational motions of the environment modify tunneling probabilities in the case of reactions involving the transfer of light particles (H, H+ or H). Finally, keeping in mind the amount of hydrogens atoms present in an enzyme, perdeuteration may slightly affect the structure and stability of the protein, which could also have consequences on reactivity. In fact, changes in denaturation temperatures [32] and protein hydrophobicity [33] have been reported. A brief overview of recent studies based on enzyme KIEs is detailed next. The corresponding reactions are shown in Fig. 2.

Schramm and co-workers analyzed the HIV-1 protease catalytic process showing that steady-state rate is dominated by the chemical step, which is assumed to correspond to peptide C-N bond breaking. The circular dichroism spectra for light and heavy enzymes showed that the isotopologues were structurally identical. Interestingly, significant differences in the KM constant between the light and heavy versions were reported in this work. Measurements of the rate constants (see Table 1) resulted in a normal isotope effect of 1.19  0.05. The observed reduction in the value of the rate constant for the heavy enzyme supported the hypothesis of the active role played by femtosecond time scale protein motions in TS formation.

Purine nucleoside phosphorylase

Pentaerythritol tetranitrate reductase

PNP catalyzes the reversible phosphorolysis of 6-oxypurine (20 deoxy)-b-D-ribonucleosides to (2-deoxy)-a-Dribose 1-phosphate and purine base in the presence of inorganic orthophosphate. In 2011 Schramm and coworkers characterized the kinetics of the heavy version of human PNP, obtained by replacing 12C, 14N and nonexchangeable 1H by 13C, 14N and 2H [30]. The increased mass (9.9%) had no consequences on the steady-state kinetics of the reaction with inosine and guanosine: KM and kcat remained unchanged with respect to the light enzyme. The values of these constants are dominated by substrate binding and product release, respectively, indicating that these processes are unaffected by the change in the protein mass. The intrinsic KIEs are also identical, within the experimental error, in the heavy and light enzymes, reflecting an unaltered geometry of the TS. However, single-turnover rate constant, which correspond to the chemical step, differ up to 20% and 27% between light and heavy PNPs, for inosine and guanosine, respectively (see Table 1). This was attributed to an alteration of femtosecond protein motions that contribute to barrier-crossing pathways, where all favorable interactions between reactant and active site residues are required.

Flavin mononucleotide (FMN)-dependent PETNR catalyzes hydride transfer from NADH or NADPH to FMN. This transfer has been proposed to take place, mainly, by quantum tunneling [36]. Previous stopped-flow studies carried out by Hay, Scrutton and co-workers indicated that primary 2H KIEs for FMN reduction are temperature-dependent with NADPH but, within experimental error, temperature-independent with NADH [36]. The authors considered this different behavior as a definitive probe of a stronger coupling of fast motions with the RC when NADPH was the cofactor. More recently, same authors have adapted the approach designed by Schramm and co-workers to investigate the possible relationship between fast protein motions and temperature dependence of KIEs with heavy and light forms of PETNR [37]. The observed rate constants (see Table 1) render enzyme KIEs of 1.11  0.09 and 1.29  0.02 for the hydride transfer from NADH and NADPH, respectively. The rate constants were higher in the light enzyme than in the heavy enzyme at various temperatures ranging from 5 to 35 8C. This work also analyzed enzyme KIEs for deuteride transfer, obtaining inverse values (lower than unity) for all the studied temperatures when the cofactor was NADH. While not discussing this intriguing temperature dependency, authors claimed that the observed temperature dependence of the KIE was a consequence of the coupling between the hydride transfer and the motions of the protein.

A subsequent theoretical work studied reactive trajectories in the heavy and light enzymes [34]. The analysis of these unbiased reactive trajectories, generated using TPS, showed how some vibrational motions were delayed in the heavy enzyme. This theoretical work confirmed the role of femtosecond mass-dependent protein motions in the chemical step, although did not offer a quantification of the effect on the rate constant.

Alanine racemase

HIV-1 protease

AR is a homodimer that catalyzes the interconversion of L-alanine and D-alanine, an essential process required in the formation of the peptidoglycan layer of bacteria cell wall. At high pH, the chemical reaction step, involving two proton transfers, is rate-limiting.

Almost at the same time of publication of the paper on PNP, Schramm and co-workers published the study on Human immunodeficiency virus type 1 protease (HIV-1 protease) [35]. The main role of HIV-1 protease is to recognize the peptide structure and to catalyze the hydrolysis of the peptide bond.

Toney and co-workers measured enzyme KIEs using a deuterated version of AR where all the non-exchangeable hydrogens where substituted by deuterium, resulting in a 5.5% increase of the protein mass. The rate constant for Lalanine and D-alanine were reduced in a factor equal to

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Current Opinion in Chemical Biology 2014, 21:11–18

14 Mechanisms

Figure 2

O H N

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Reactions catalyzed by enzymes for which the enzyme isotope effect has been measured.

1.32  0.04 and 1.21  0.03, respectively [38]. Interestingly, enzymes KIEs were shown to be significantly larger for the deuterated substrate; 1.67  0.05 and 1.40  0.04 for 2-2H-L-alanine and D-alanine, respectively. On the other side, primary substrate KIEs were also larger in perdeuterated AR. The observation that enzyme and substrate isotope effects were not independent of each other was attributed to the coupling of protein motions and proton transfer in the rate-limiting event. The authors also suggest that protein motions may be involved in promoting proton tunneling in both proton transfers. Current Opinion in Chemical Biology 2014, 21:11–18

Wild-type dihydrofolate reductase DHFR is one of the most popular systems in the debate about the relationship between enzyme dynamics and catalysis. DHFR catalyzes a hydride transfer from NADPH to 7,8-dihydrofolate (H2F) to form 5,6,7,8-tetrahydrofolate (THF). It has been proved that DHFR from Escherichia coli (EcDHFR) adopts two major conformations depending on the relative position of the M20 loop and the active site; a closed conformation in reactant complex and an occluded conformation in the product complexes [39,40]. Results for mutants of DHFR [10,41] www.sciencedirect.com

Heavy enzymes and dynamics Javier Ruiz-Pernı´a et al. 15

Table 1 Summary of enzyme KIEs (kL/kH). Values in parenthesis correspond to QM/MM calculations. kcat (s1)

Reactant

Enzyme

13

Light PNP HIV-1 PR PETNR AR wt-DHFR N23PP/S148A -DHFR a b

Inosine Guanosine Aminobenzoyl-Thr-Ile-Nle* pNO2-Phe-Gln-Arg-NH2 Flavin mononucleotide + NADH Flavin mononucleotide + NADPH L-Alanine D-Alanine 7,8-Dihydrofolate 7,8-Dihydrofolate

kL/k H

Heavy ( C,

69  3 26  1 3.28  0.08

15

Ref.

1.25  0.07 b 1.37  0.09 b 1.19  0.05

25 25 25

[30]

1.11  0.09 b 1.29  0.02 b 1.32  0.04 1.21  0.03 1.10  0.04 (1.16  0.04) 1.37  0.03 (1.26  0.04)

25 25 25 25 30 (27) 30 (27)

[37] [37] [38]

N, H)

55  2 19  1 2.75  0.08

1.99  0.02 33.5  0.2 1030  20 750  10 209.1  5.0 (219) 47.23  1.28 (8.0)

T (8C)

2

1.80  0.14 25.9  0.4 780  20 a 620  20 a 190.1  8.5 (188) 34.44  1.18 (6.3)

[35]

[31] [22]

Enzyme isotope effects were measured by substituting only the non-exchangeable hydrogen atoms by 2H. Error bars calculated from the standard errors provided for the rate constants of the light and heavy enzymes.

have been interpreted as showing a central role for protein dynamics in catalysis. However, strong evidences also exist against a direct coupling of large-scale millisecond protein motions to the RC during hydride transfer from NADPH to H2F derived from simulations [42,43,44] and experiments [45,46]. This controversial debate stimulated the use of enzyme KIEs on the chemical step of EcDHFR [31]. The combination of experimental results, quantum mechanics/molecular mechanics simulations, and theoretical analyses identified the observed differences in reactivity between a heavy wt-EcDHFR (prepared as in Schramm and coworkers protocol) and the natural light wt-EcDHFR. Experiments and simulations provided enzyme KIEs in good agreement, 1.10  0.04 and 1.16  0.04, respectively (see Table 1). Normal enzyme KIEs were attributed to the smaller value of the transmission coefficient in the heavy enzyme [31]. Importantly, other contributions to the rate constant, the free energy barrier and quantum tunneling, were not affected by isotopic substitution, indicating no significant role for ‘promoting motions’ in driving tunneling or modulating the barrier. The study concluded that the heavy enzyme presents a larger fraction of trajectories recrossing because protein adaptation to changes in the chemical system is slower than in the light enzyme. Protein dynamics would have a small, but measurable, effect on the chemical reaction rate, which can be accurately reproduced by TST.

EcDHFR-N23PP/S148A A recent analysis of enzyme KIEs has been performed on a catalytically compromised variant of EcDHFR, EcDHFR-N23PP/S148A [22]. A previous report had showed that this mutant is unable to adopt the occluded conformation and that millisecond to microsecond time scale motions observed in the M20 loop of wild type EcDHFR are suppressed in the variant [10]. This ‘dynamic knockout’ mutant displayed a reduced hydride transfer rate constant, and it was concluded that protein www.sciencedirect.com

motions lost in EcDHFR-N23PP/S148A are involved in promoting hydride transfer [10]. Nevertheless, this proposal was not supported by EVB calculations [42]. As in the previous study performed on wt-EcDHFR [31], a heavy EcDHFR-N23PP/S148A was prepared and enzyme KIE was measured as 1.37  0.02 at pH 7 while the computationally predicted value was 1.26  0.04 (see Table 1) [22]. Simulations showed that the variant enzyme is less well set up to accommodate the chemical reaction and that a higher degree of reorganization is required to go from reactants to TS. This effect provokes a slightly larger participation of protein motions in the RC, as reflected in the smaller value of the transmission coefficient. Thus, the reduction of the rate constant of the chemical step in the EcDHFR-N23PP/ S148A catalyzed reaction was proposed to be essentially a consequence of an increase of the quasi-classical free energy barrier and, to a minor extent, an increased number of trajectories recrossing the TS dividing surface. The increased dynamic coupling to the chemical coordinate would be in fact detrimental to catalysis.

Conclusions and remarks Preparation of heavy enzymes, where the normal isotopic distribution of protein atoms is modified, has been shown to be an efficient tool to shed light into the controversial debate on the role of protein dynamics in the chemical reaction step. Since the seminal work of Rokop et al. [28] where the kinetics of two fully deuterated enzymes were measured, until the most recent studies in which all carbon, nitrogen and non-exchangeable hydrogen atoms are replaced by 13C, 15N and 2H, studies on heavy enzymes show negligible effects on protein structure and a small but measurable change in the rate of catalysis. In general, normal enzyme KIEs (a decline in the rate constant of the heavy versions) are observed. These enzyme KIEs have been most of the times interpreted Current Opinion in Chemical Biology 2014, 21:11–18

16 Mechanisms

as a dynamical link between mass-dependent protein vibrations and barrier crossing. Theoretical studies based on TST have allowed quantifying enzyme KIEs suggesting that, in the case of EcDHFR, the reduced reaction rate constant in the heavy enzyme reflects differences in environmental coupling to the hydride transfer step, with no effects on the barrier and quantum tunneling contribution [22,31]. The rate constant of the chemical step would be smaller in the heavy enzyme because protein motions coupled to the RC are slower, favoring the recrossing of some trajectories. TST can be also used to interpret the unexpected inverse enzyme KIEs obtained by Hay, Scrutton and coworkers in PETNR when the transferred particle was a deuteride [37]. In this case, when the motion along the RC is slower, and/or the temperature is higher, the equilibrium approximation can work better and then enzyme KIEs could be dominated by changes in the quantized protein vibrational levels. Tighter interactions at the TS would produce inverse secondary KIEs. A different interpretation was derived from calculations based on TPS for heavy and light versions of PNP [34] and Lactate Dehydrogenase [47]. Despite the effect of the mass change on the rate constant was not quantified with this technique, an increase in the time of barrier crossing in the heavy enzymes was associated with the existence of important promotion vibrations. As a final summary, kinetic studies of heavy enzymes, combined with computer simulations, can be considered an excellent tool to study the impact of protein motions in the chemical step. These techniques are not obviously unique, since kinetic studies on designed mutants [10,41,48] or the study of temperature dependent KIEs [9,36,45,46,48–50] are useful tools that have been also applied to shed some light in this debate. Further studies will be necessary in the future to reach a consensus in the scientific community about the role of protein motions in catalysis.

Acknowledgments This work was supported by the Spanish Ministerio de Economı´a y Competitividad and FEDER funds for project CTQ2012-36253; Generalitat Valenciana for Prometeo/2009/053 project; the Polish National Science Center (NCN) for grant 2011/02/A/ST4/00246 and Universitat Jaume I for project P11B2011-23.

References and recommended reading Papers of particular interest, published within the period of review, have been highlighted as:  of special interest  of outstanding interest 1.

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9. Glowacki DR, Harvey JN, Mulholland AJ: Taking Ockham’s razor  to enzyme dynamics and catalysis. Nat Chem 2012, 4:169-176. This contribution makes a very clear presentation of ‘dynamical effects’ hypothesis in the context of statistical rate theories. It is shown that some experimental evidences that are usually interpreted as a sign of these effects in enzymatic reactions can be alternatively explained within Transition State Theory. In particular, some observations about temperature dependence of rate constants and Kinetic Isotopic Effects may be explained admitting conformational diversity of the enzyme at the reactants state. 10. Bhabha G, Lee J, Ekiert DC, Gam J, Wilson IA, Dyson HJ,  Benkovic SJ, Wright PE: A dynamic knockout reveals that conformational fluctuations influence the chemical step of enzyme catalysis. Science 2011, 332:234-238. This works analysis the kinetic constant of a ‘dynamical-knockout’ designed mutant of EcDHFR. Mutations introduced in the M20 loop suppress its mobility as determined by NMR measurements. These mutations reduce the rate constant while the structure of the protein, as determined by X-ray crystallography, remains unaltered. The authors conclude that although the active site of the mutant is fully preorganized, millisecond-time-scale fluctuations of the active site are restricted so that the enzyme cannot efficiently sample higher-energy conformational substates that are conductive to formation of the transition state. 11. Antoniou D, Caratzoulas S, Kalyanaraman C, Mincer JS, Schwartz SD: Barrier passage and protein dynamics in enzymatically catalyzed reactions. Eur J Biochem 2002, 269:3103-3112. 12. Hay S, Scrutton NS: Good vibrations in enzyme-catalysed reactions. Nat Chem 2012, 4:161-168. 13. Eyring H, Stearn AE: The application of the theory of absolute reaction rates to proteins. Chem Rev 1939, 24:253-270. 14. Truhlar DG, Hase WL, Hynes JT: The current status of transition state theory. J Phys Chem 1983, 87:2664-2682 Erratum: 1983;87:5523. 15. Gao J, Ma S, Major DT, Nam K, Pu J, Truhlar DG: Mechanisms and free energies of enzymatic reactions. Chem Rev 2006, 106:3188-3209. 16. Fernandez-Ramos A, Ellingson BA, Garrett BC, Truhlar DG: Variational transition state theory with multidimensional tunneling. Rev Comput Chem 2007, 23:125-232. 17. Peters B: Transition state theory, dynamics, and narrow timescale separation in the rate promoting vibrations model of enzyme catalysis. J Chem Theor Comp 2010, 6:1447-1454. 18. Bertran J, Burgos FS: The question of equilibrium in transition state solvation. J Chem Educ 1984, 61:416-417. 19. Olsson MH, Warshel A: Solute solvent dynamics and energetics in enzyme catalysis: the S(N)2 reaction of dehalogenase as a general benchmark. J Am Chem Soc 2004, 126:15167-15179. 20. Marcus RA: Electron transfer reactions in chemistry. Theory and experiment. Rev Mod Phys 1993, 65:599-610. 21. Garcı´a-Meseguer R, Martı´ S, Ruiz-Pernı´a JJ, Moliner V, Tun˜o´n I: Studying the role of protein dynamics in an SN2 enzyme reaction using free-energy surfaces and solvent coordinates. Nat Chem 2013, 5:566-571. www.sciencedirect.com

Heavy enzymes and dynamics Javier Ruiz-Pernı´a et al. 17

22. Ruiz-Pernia JJ, Luk LYP, Garcı´a-Meseguer R, Martı´ S,  Loveridge EJ, Tun˜o´n I, Moliner V, Allemann RK: Increased dynamic effects in a catalytically compromised variant of Escherichia coli dihydrofolate reductase. J Am Chem Soc 2013, 135:18689-18696. Enzyme Kinetic Isotope Effects for the dynamically compromised mutant of EcDHFR presented in Ref. [10] are experimentally measured and computationally reproduced by means of the evaluation of the transmission coefficient. Experiments and simulations are compatible with a scenario where the ‘dynamical knock-out’ mutant presents in fact more ‘dynamical effects’ in the chemical step (‘dynamical knock-in’). Mutations lead to a slightly less efficient active site that must suffer more reorganization during the chemical step to stabilize efficiently the TS. This larger participation of protein motions compared to the wild-type enzyme lead to a greater value of enzyme KIEs. 23. Klippenstein SJ, Pande VS, Truhlar DG: Chemical kinetics and mechanisms of complex systems: a perspective on recent  theoretical advances. J Am Chem Soc 2014, 136:528-546. This perspective article reviews the current state in the theoretical understanding of complex chemical reactions, including the enzymatic ones. Some key concepts for understanding theoretical approaches to enzymatic reactions, such as free energy surfaces, reaction coordinates and non-equilibrium effects, are clearly presented. 24. Warshel A: Dynamics of reactions in polar solvents. Semiclassical trajectory studies of electron-transfer and proton-transfer reactions. J Phys Chem 1982, 86:2218-2224. 25. Bolhuis PG, Chandler D, Dellago C, Geissler PL: Transition path sampling: throwing ropes over rough mountain passes, in the dark. Annu Rev Phys Chem 2002, 53:291-318. 26. Zinovjev K, Ruiz-Pernı´a JJ, Tun˜o´n I: Toward an automatic determination of enzymatic reaction mechanisms and their activation free energies. J Chem Theor Comput 2013, 9:37403749. 27. Kohen A, Limbach HH: Isotope effects in chemistry and biology. Boca Raton, FL: CRC Press; 2006, . 28. Rokop S, Gajda L, Parmerter S, Crespi HL, Katz JJ: Purification and characterization of fully deuterated enzymes. Biochim  Biophys Acta 1969, 191:707-715. Authors characterize two fully deuterated enzymes, an Alkaline Phosphatase and a Ribonuclease. The deuterated Alkaline Phospatase showed a decrease in the reaction rate by a factor of 1.8. The difference in vmax was attributed to the modification of the vibrational frequencies and the subsequent diminution in the vibrational energy available in the heavy enzyme. 29. Di Costanzo L, Moulin M, Haertlein M, Meilleur F, Christianson DW: Expression, purification, assay, and crystal structure of perdeuterated human arginase I. Arch Biochem Biophys 2007, 465:82-89. 30. Silva RG, Murkin AS, Schramm VL: Femtosecond dynamics  coupled to chemical barrier crossing in a Born–Oppenheimer enzyme. Proc Natl Acad Sci U S A 2011, 108:18661-18665. This seminal paper analyzes the consequences of the change in protein mass on the kinetic parameters of human PNP. A heavy version of human-PNP was obtained substituting C, N and non-exchangeable H atoms by the heavier isotopes: 13C, 15N and 2H. Interestingly substrate KIEs and steady-state kinetic parameters were equal (within experimental error) in both enzymes, indicating that substrate binding and product release are unaltered by the change in mass. However, the single-turnover rate constant, which corresponds to the chemical step, was found to be smaller in the heavy enzyme. This reduced probability of barrier crossing was interpreted as a sign of the participation of protein femtosecond vibrational motions in the passage over the barrier. 31. Luk LY, Javier Ruiz-Pernı´a J, Dawson WM, Roca M, Loveridge EJ,  Glowacki DR, Harvey JN, Mulholland AJ, Tun˜o´n I, Moliner V, Allemann RK: Unraveling the role of protein dynamics in dihydrofolate reductase catalysis. Proc Natl Acad Sci U S A 2013, 110:16344-16349. This paper analyzes Enzyme KIEs in EcDHFR combining three different strategies: experimental measurements, theoretical analysis of temperature-dependence and computer simulations in the framework of Transition State Theory. This is the first paper in which Enzyme KIEs are theoretically determined. The reduction of the rate constant in the heavy enzyme was reproduced by an increase in the number of recrossing trajectories and then the diminution of the fraction of successful ones. The reduction of vibrational frequencies in the active site of the heavy www.sciencedirect.com

enzymes makes this slower, diminishing the ability to follow the changes in the chemical system, reason why some trajectories crossing the dividing surface returns to the reactants valley. 32. Chen C-H, Liu IW, MacColl R, Berns DS: Differences in structure and stability between normal and deuterated proteins (phycocyanin). Biopolymers 2014, 22:1223-1233. 33. Liu X, Hanson BL, Langan P, Viola RE: The effect of deuteration on protein structure: a high-resolution comparison of hydrogenous and perdeuterated haloalkane dehalogenase. Acta Cryst 2007, D63:1000-1008. 34. Antoniou D, Ge X, Schramm VL, Schwartz SD: Mass modulation of  protein dynamics associated with barrier crossing in purine nucleoside phosphorylase. J Phys Chem Lett 2012, 3:3538-3544. Transition Path Sampling (TPS) is used to generate a set of reactive trajectories in light and heavy versions of human-PNP using QM/MM hybrid methods. The advantage of this technique is that no assumption about the nature of the reaction coordinate is required a priori and all the degrees of freedom of the system can be, in principle, treated in an equalstep basis. The analysis of reactive trajectories showed the participation of some protein motions in the chemical event. In particular, ribosyl group compression by His257 has been proposed to play a significant role polarizing the ribosidic bond favoring bond-breaking. This vibrational motion is delayed in the heavy enzyme. Another vibrational motion, involving Asn243, was suggested to play a role stabilizing the leaving group. This motion also presents a greater time-lag with respect to bond breaking and forming processes in the heavy version of the enzyme. This theoretical work confirmed the role of femtosecond mass-dependent protein motions in the chemical step. 35. Kipp DR, Silva RG, Schramm VL: Mass-dependent bond  vibrational dynamics influence catalysis by HIV-1 protease. J Am Chem Soc 2011, 133:19358-19361. This paper represents the second contribution of the group of Schramm and co-workers to the study of the role of mass-dependent bond vibrational dynamics on enzyme catalyzed reactions based on measurements of rate constant in light and heavy enzymes. Circular dichroism spectra for both enzymes showed that the isotopologues are structurally identical while normal isotope effect is interpreted as another demonstration of the active role of enzyme motions in the femtosecond time scale during the formation of TS. 36. Pudney CR, Hay S, Levy C, Pang J, Sutcliffe MJ, Leys D, Scrutton NS: Evidence to support the hypothesis that promoting vibrations enhance the rate of an enzyme catalyzed H-tunneling reaction. J Am Chem Soc 2009, 131:17072-17073. 37. Pudney CR, Guerriero A, Baxter NJ, Johannissen LO, Waltho JP,  Hay S, Scrutton NS: Fast protein motions are coupled to enzyme H-transfer reactions. J Am Chem Soc 2013, 135:2512-2517. In this paper, the methodology used by Silva and co-workers (Ref. [30]) is applied to investigate the impact of fast protein motions on the temperature dependence of KIEs in the H-transfer reaction catalyzed by pentaerythritol tetranitrate reductase (PETNR) with two different cofactors, NADH and NADPH. Authors also studied the transfer of deuteride obtaining enzyme KIEs at different temperatures, which is a solid tool to analyze tunneling effects on enzymes. According to the authors, comparison of the KIE temperature dependence in light and heavy enzyme demonstrate a direct link between (promoting) vibrations in the protein and the chemical step. 38. Toney MD, Castro JN, Addington TA: Heavy-enzyme kinetic  isotope effects on proton transfer in alanine racemase. J Am Chem Soc 2013, 135:2509-2511. This work focuses on the dependence between substrate and enzyme KIEs as a tool to evidence the coupling between their vibrational motions at the reaction TS. Kinetic measurements were performed on Alanine Racemase from Geobacillus stearothermophilus and its perdeuterated version (with a mass increase of 5.5%). First, enzymes KIEs were shown to be significantly larger with deuterated than with protiated substrates and second, primary substrate KIEs were also found to be larger in perdeuterated than in conventional AR. The violation of the rule of the geometric mean in KIEs was attributed to the coupling of protein motions and proton transfer in the rate-limiting event. The authors also suggest that protein motions may be involved in promoting proton tunneling in both proton transfers, although recognizing that the results are not conclusive at this respect. 39. Fierke CA, Johnson KA, Benkovic SJ: Construction and evaluation of the kinetic scheme associated with dihydrofolate reductase from Escherichia coli. Biochemistry 1987, 26:4085-4092. Current Opinion in Chemical Biology 2014, 21:11–18

18 Mechanisms

40. Sawaya MR, Kraut J: Loop and subdomain movements in the mechanism of Escherichia coli dihydrofolate reductase: crystallographic evidence. Biochemistry 1997, 36:586-603. 41. Wang L, Tharp S, Selzer T, Benkovic SJ, Kohen A: Effects of a distal mutation on active site chemistry. Biochemistry 2006, 45:1383-1392. 42. Adamczyk AJ, Cao J, Kamerlin SC, Warshel A: Catalysis by  dihydrofolate reductase and other enzymes arises from electrostatic preorganization, not conformational motions. Proc Natl Acad Sci U S A 2011, 108:14115-14120. This work presents a computational study, based on empirical valence bond calculations, on the wild type and two dihydrofolate reductase (EcDHFR) mutants, that contradict the conclusions presented in the paper of Bhabha et al. (Ref. [10]) The results suggest that dynamics do not contribute to catalysis, but rather that the reorganization free energy (which basically results from electrostatic contributions) can rationalize the entire effect of the mutants. In this paper, Warshel and co-workers stress the need of distinguishing between orthogonal conformational fluctuations and those toward the chemical TS, with the contribution to catalysis of the former being negligible. 43. Boekelheide N, Salomo´n-Ferrer R, Miller TF III: Dynamics and dissipation in enzyme catalysis. Proc Natl Acad Sci U S A 2011, 108:16159-16163. 44. Fan Y, Cembran A, Ma S, Gao J: Connecting protein conformational dynamics with catalytic function as illustrated in dihydrofolate reductase. Biochemistry 2013, 52:2036-2049.

Current Opinion in Chemical Biology 2014, 21:11–18

45. Loveridge EJ, Behiry EM, Guo J, Allemann RK: Evidence that a ‘dynamic knockout’ in Escherichia coli dihydrofolate reductase does not affect the chemical step of catalysis. Nat Chem 2012, 4:292-297. 46. Loveridge EJ, Tey LH, Behiry EM, Dawson WM, Evans RM, Whittaker SB, Gu¨nther UL, Williams C, Crump MP, Allemann RK: The role of large-scale motions in catalysis by dihydrofolate reductase. J Am Chem Soc 2011, 133:2056120570. 47. Masterson JE, Schwartz SD: Changes in protein architecture and subpicosecond protein dynamics impact the reaction catalyzed by lactate dehydrogenase. J Phys Chem A 2013, 117:7107-7113. 48. Singh PN, Sen A, Francis K, Kohen A: Extension and limits of the network of coupled motions correlated to hydride transfer in dihydrofolate reductase. J Am Chem Soc 2014, 136:2575-2582. 49. Francis K, Stojkovic V, Kohen A: Preservation of protein dynamics in dihydrofolate reductase evolution. J Biol Chem 2013, 288:35961-35968. 50. Stojkovic V, Perissinotti LL, Willmer D, Benkovic DJ, Kohen A: Effects of the donor–acceptor distance and dynamics on hydride tunneling in the dihydrofolate reductase catalyzed reaction. J Am Chem Soc 2012, 134:1738-1745.

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