Electrostatic basis for enzyme catalysis

The role of higher CO-multipole moments in understanding the dynamics of photodissociated carbonmonoxide in myoglobin

The influence of electrostatic multipole moments up to hexadecapole on the dynamics of photodissociated carbon monoxide (CO) in myoglobin is investigated. The CO electrostatic potential is expressed as an expansion into atomic multipole moments of increasing order up to octopole which are obtained from a distributed multipole analysis. Three models with increasingly accurate molecular multipoles (accurate quadrupole, octopole, and hexadecapole moments, respectively) are developed and used in molecular dynamics simulations. All models with a fluctuating quadrupole moment correctly describe the location of the B-state whereas the sign of the octopole moment differentiates between the Fe...CO and Fe...OC orientation. For the infrared spectrum of photodissociated CO, considerable differences between the three electrostatic models are found. The most detailed electrostatic model correctly reproduces the splitting, shift, and width of the CO spectrum in the B-state. From an analysis of the trajectories, the spectroscopic B(1) and B(2) states are assigned to the Fe...CO and Fe...OC substates, respectively.

Second step of hydrolytic dehalogenation in haloalkane dehalogenase investigated by QM/MM methods

Mechanistic studies on the hydrolytic dehalogenation catalyzed by haloalkane dehalogenases are of importance for environmental and industrial applications. Here, Car-Parrinello (CP) and ONIOM hybrid quantum-mechanical/molecular mechanics (QM/MM) are used investigate the second reaction step of the catalytic cycle, which comprises a general base-catalyzed hydrolysis of an ester intermediate (EI) to alcohol and free enzyme. We focus on the enzyme LinB from Sphingomonas paucimobilis UT26, for which the X-ray structure at atomic resolution is available. In agreement with previous proposals, our calculations suggest that a histidine residue (His272), polarized by glutamate (Glu132), acts as a base, accepting a proton from the catalytic water molecule and transferring it to an alcoholate ion. The reaction proceeds through a metastable tetrahedral intermediate, which shows an easily reversed reaction to the EI. In the formation of the products, the protonated aspartic acid (Asp108) can easily adopt conformation of the relaxed state found in the free enzyme. The overall free energy barrier of the reaction calculated by potential of the mean force integration using CP-QM/MM calculations is equal to 19.5 +/- 2 kcal . mol(-1). The lowering of the energy barrier of catalyzed reaction with respect to the water reaction is caused by strong stabilization of the reaction intermediate and transition state and their preorganization by electrostatic field of the enzyme.

Free energies of chemical reactions in solution and in enzymes with ab initio quantum mechanics/molecular mechanics methods

Combined quantum mechanics/molecular mechanics (QM/MM) methods provide an accurate and efficient energetic description of complex chemical and biological systems, leading to significant advances in the understanding of chemical reactions in solution and in enzymes. Here we review progress in QM/MM methodology and applications, focusing on ab initio QM-based approaches. Ab initio QM/MM methods capitalize on the accuracy and reliability of the associated quantum-mechanical approaches, however, at a much higher computational cost compared with semiempirical quantum-mechanical approaches. Thus reaction-path and activation free-energy calculations based on ab initio QM/MM methods encounter unique challenges in simulation timescales and phase-space sampling. This review features recent developments overcoming these challenges and enabling accurate free-energy determination for reaction processes in solution and in enzymes, along with applications.

Substrate polarization in enzyme catalysis: QM/MM analysis of the effect of oxaloacetate polarization on acetyl-CoA enolization in citrate synthase

Citrate synthase is an archetypal carbon-carbon bond forming enzyme. It promotes the conversion of oxaloacetate (OAA) to citrate by catalyzing the deprotonation (enolization) of acetyl-CoA, followed by nucleophilic attack of the enolate form of this substrate on OAA to form a citryl-CoA intermediate and subsequent hydrolysis. OAA is strongly bound to the active site and its alpha-carbonyl group is polarized. This polarization has been demonstrated spectroscopically, [(Kurz et al., Biochemistry 1985;24:452-457; Kurz and Drysdale, Biochemistry 1987;26:2623-2627)] and has been suggested to be an important catalytic strategy. Substrate polarization is believed to be important in many enzymes. The first step, formation of the acetyl-CoA enolate intermediate, is thought to be rate-limiting in the mesophilic (pig/chicken) enzyme. We have examined the effects of substrate polarization on this key step using quantum mechanical/molecular mechanical (QM/MM) methods. Free energy profiles have been calculated by AM1/CHARMM27 umbrella sampling molecular dynamics (MD) simulations, together with potential energy profiles. To study the influence of OAA polarization, profiles were calculated with different polarization of the OAA alpha-carbonyl group. The results indicate that OAA polarization influences catalysis only marginally but has a larger effect on intermediate stabilization. Different levels of treatment of OAA are compared (MM or QM), and its polarization in the protein and in water analyzed at the B3LYP/6-31+G(d)/CHARMM27 level. Analysis of stabilization by individual residues shows that the enzyme mainly stabilizes the enolate intermediate (not the transition state) through electrostatic (including hydrogen bond) interactions: these contribute much more than polarization of OAA.

The mutability of enzyme active-site shape determinants

Investigations of enzyme action typically focus on elucidating the catalytic roles of hydrogen bonding interactions between polar active-site residues and substrate molecules. Less clear is the importance of non-hydrogen bonding contacts to enzymatic rate accelerations. To investigate the importance of such interactions in a model system, six residues that participate in van der Waals contacts with substrate glucose within the active site of Escherichia coli glucokinase were individually randomized via site-directed mutagenesis. In vivo selection in a glucokinase-deficient bacterium was employed to identify amino acid substitutions that were complicit with enzyme activity. The results suggest that small residues, such as alanine and glycine, are largely immutable, whereas larger amino acids are more tolerant of diverse substitution patterns. Surprisingly, a glucokinase variant that contains glycine in place of six non-hydrogen bonding contacts retains approximately 1% of the wild-type activity. These findings establish non-hydrogen bonding shape determinants as highly appealing targets for widespread substitution during efforts to redesign the catalytic properties of natural enzymes.

On the relationship between thermal stability and catalytic power of enzymes

The possible relationship between the thermal stability and the catalytic power of enzymes is of great current interest. In particular, it has been suggested that thermophilic or hyperthermophilic (Tm) enzymes have lower catalytic power at a given temperature than the corresponding mesophilic (Ms) enzymes, because the thermophilic enzymes are less flexible (assuming that flexibility and catalysis are directly correlated). These suggestions presume that the reduced dynamics of the thermophilic enzymes is the reason for their reduced catalytic power. The present paper takes the specific case of dihydrofolate reductase (DHFR) and explores the validity of the above argument by simulation approaches. It is found that the Tm enzymes have restricted motions in the direction of the folding coordinate, but this is not relevant to the chemical process, since the motions along the reaction coordinate are perpendicular to the folding motions. Moreover, it is shown that the rate of the chemical reaction is determined by the activation barrier and the corresponding reorganization energy, rather than by dynamics or flexibility in the ground state. In fact, as far as flexibility is concerned, we conclude that the displacement along the reaction coordinate is larger in the Tm enzyme than in the Ms enzyme and that the general trend in enzyme catalysis is that the best catalyst involves less motion during the reaction than the less optimal catalyst. The relationship between thermal stability and catalysis appears to reflect the fact that to obtain small electrostatic reorganization energy it is necessary to invest some folding energy in the overall preorganization process. Thus, the optimized catalysts are less stable. This trend is clearly observed in the DHFR case.

Probing the two-metal ion mechanism in the restriction endonuclease BamHI

The choreography of restriction endonuclease catalysis is a long-standing paradigm in molecular biology. Bivalent metal ions are required almost for all PD..D/ExK type enzymes, but the number of cofactors essential for the DNA backbone scission remained ambiguous. On the basis of crystal structures and biochemical data for various restriction enzymes, three models have been developed that assign critical roles for one, two, or three metal ions during the phosphodiester hydrolysis. To resolve this apparent controversy, we investigated the mechanism of BamHI catalysis using quantum mechanical/molecular mechanical simulation techniques and determined the activation barriers of three possible pathways that involve a Glu-113 or a neighboring water molecule as a general base or an external nucleophile that penetrated from bulk solution. The extrinsic mechanism was found to be the most favorable with an activation free energy of 23.4 kcal/mol, in reasonable agreement with the experimental data. On the basis of the effect of the individual metal ions on the activation barrier, metal ion A was concluded to be pivotal for the reaction, while the enzyme lacking metal ion B still has moderate efficiency. Thus, we propose that the catalytic scheme of BamHI does not involve a general base for nucleophile generation and requires one obligatory metal ion for catalysis that stabilizes the attacking nucleophile and coordinates it throughout the nucleophilic attack. Such a model may also explain the variation in the number of metal ions in the crystal structures and thus could serve as a framework for a unified catalytic scheme of type II restriction endonucleases.

Dielectric dispersion interpretation of single enzyme dynamic disorder, spectral diffusion, and radiative fluorescence lifetime

A formulation based on measurable dielectric dispersion of enzymes is developed to estimate fluctuations in electrostatic interaction energy on time scales as long as milliseconds to seconds at a local site in enzymes. Several single molecule experimental obsevations occur on this time scale, currently unreachable by real time computational trajectory simulations. We compare the experimental results on the autocorrelation function of the fluctuations of catalysis rate with the calculations using the dielectric dispersion formulation. We also discuss the autocorrelation functions of the fluorescence lifetime and of spectral diffusion. We use a previously derived relation between the observables and the electric field fluctuations and calculate the latter using dielectric dispersion data for the proteins and the Onsager regression hypothesis.

An interpretation of fluctuations in enzyme catalysis rate, spectral diffusion, and radiative component of lifetimes in terms of electric field fluctuations

Time-dependent fluctuations in the catalysis rate (deltak(t)) observed in single-enzyme experiments were found in a particular study to have an autocorrelation function decaying on the same time scale as that of spectral diffusion deltaomega(0)(t). To interpret this similarity, the present analysis focuses on a factor in enzyme catalysis, the local electrostatic interaction energy (E) at the active site and its effect on the activation free energy barrier. We consider the slow fluctuations of the electrostatic interaction energy (deltaE(t)) as a contributor to deltak(t) and relate the latter to deltaomega(0)(t). The resulting relation between deltak(t) and deltaomega(0)(t) is a dynamic analog of the solvatochromism used in interpreting solvent effects on organic reaction rates. The effect of the postulated deltaE(t) on fluctuations in the radiative component (deltagamma(r)(-1)(t)) of the fluorescence decay of chromophores in proteins also is examined, and a relation between deltagamma(r)(-1)(t) and deltaomega(0)(t) is obtained. Experimental tests will determine whether the correlation functions for deltak(t), deltaomega(0)(t), and deltagamma(r)(-1) are indeed similar for any enzyme. Measurements of dielectric dispersion, epsilon(omega), for the enzyme discussed elsewhere will provide further insight into the correlation function for deltaE(t). They also will determine whether fluctuations in the nonradiative component gamma(nr)(-1) of the lifetime decay has a different origin, fluctuations in distance for example.

Screening of the active site from water by the incoming ligand triggers catalysis and inhibition in serine proteases

The pKa of the catalytic His57 N(epsilon)H in the tetrahedral complex (TC) of chymotrypsin with trifluoromethyl ketone inhibitors is 4-5 units higher relative to the free enzyme (FE). Such stable TC's, formed with transition state (TS) analog inhibitors, are topologically similar to the catalytic TS. Thus, analysis of this pKa shift may shed light on the role of water solvation in the general base catalysis by histidine. We applied our QM/SCRF(VS) approach to study this shift. The method enables explicit quantum mechanical DFT calculations of large molecular clusters that simulate chemical reactions at the active site (AS) of water solvated enzymes. We derived an analytical expression for the pKa dependence on the degree of water exposure of the ionizable group, and on the total charge in the enzyme AS, Q(A) and Q(B), when the target ionizable functional group (His57 in this study) is in the acidic (A) and basic (B) forms, respectively. Q2(B) > Q2(A) both in the FE and in the TC of chymotrypsin. Therefore, water solvation decreases the relative stability of the protonated histidine in both. Ligand binding reduces the degree of water solvation of the imidazole ring, and consequently elevates the histidine pKa. Thus, the binding of the ligand plays a triggering role that switches on the cascade of catalytic reactions in serine proteases.

Design-atom approach for the quantum mechanical/molecular mechanical covalent boundary: a design-carbon atom with five valence electrons

A critical issue underlying the accuracy and applicability of the combined quantum mechanical/molecular mechanical (QM/MM) methods is how to describe the QM/MM boundary across covalent bonds. Inspired by the ab initio pseudopotential theory, here we introduce a novel design atom approach for a more fundamental and transparent treatment of this QM/MM covalent boundary problem. The main idea is to replace the boundary atom of the active part with a design atom, which has a different number of valence electrons but very similar atomic properties. By modifying the Troullier-Martins scheme, which has been widely employed to construct norm-conserving pseudopotentials for density functional calculations, we have successfully developed a design-carbon atom with five valence electrons. Tests on a series of molecules yield very good structural and energetic results and indicate its transferability in describing a variety of chemical bonds, including double and triple bonds.

OMP decarboxylase--An enigma persists

In 1995, Radzicka and Wolfenden reported that the rate enhancement produced by orotidine 5'-phosphate decarboxylase (ODCase) approaches 10(17), making this enzyme the most effective pure protein catalyst known in Nature [A. Radzicka, R. Wolfenden, Science 267 (1995) 90-93]. Over the last 12 years, there have been many hypotheses put forward to explain that impressive effect. In this perspective, we provide a summary of the reaction pathways under consideration for ODCase, highlight the supporting and refuting data, and suggest experiments designed to further test each of the candidate pathways.

What is the role of the helical domain of Gsalpha in the GTPase reaction?

Structural analysis of Gsalpha shows that it is composed of two domains: the ras-like domain (RD) that is conserved in all members of the GTPase superfamily and is homologous to the monomeric G-proteins (e.g., p21ras) and an alpha-helical domain (HD) that is unique to heterotrimeric G-proteins. Little is known about the function of the HD. Recent experiments by Bourne and co-workers, who expressed both the RD and the HD of Gsalpha separately and found that GTP hydrolysis is very slow if only recombinant RD is present but is accelerated when the HD is added, suggest that the HD serves as an intrinsic GTPase-activating protein (GAP). In this work, the GTP hydrolysis in Gsalpha was studied. The results obtained by calculating catalytic effects with and without the HD provide evidence for the role of the HD as a GAP. It is demonstrated that a major part of the catalysis is obtained because of an allosteric influence of the HD on the RD. Structural as well as energetic considerations suggest that the HD confines the RD to a more compact conformation, pushing the phosphate into an orientation where it is further stabilized, thus lowering the overall reaction barrier. The resemblance between the behavior of rasGAP and the HD suggests that the conclusion may be a general conclusion, applicable for all of the G-protein members.

Analysis of Classical and Quantum Paths for Deprotonation of Methylamine by Methylamine Dehydrogenase

The hydrogen-transfer reaction catalysed by methylamine dehydrogenase (MADH) with methylamine (MA) as substrate is a good model system for studies of proton tunnelling in enzyme reactions--an area of great current interest--for which atomistic simulations will be vital. Here, we present a detailed analysis of the key deprotonation step of the MADH/MA reaction and compare the results with experimental observations. Moreover, we compare this reaction with the related aromatic amine dehydrogenase (AADH) reaction with tryptamine, recently studied by us, and identify possible causes for the differences observed in the measured kinetic isotope effects (KIEs) of the two systems. We have used combined quantum mechanics/molecular mechanics (QM/MM) techniques in molecular dynamics simulations and variational transition state theory with multidimensional tunnelling calculations averaged over an ensemble of paths. The results reveal important mechanistic complexity. We calculate activation barriers and KIEs for the two possible proton transfers identified-to either of the carboxylate oxygen atoms of the catalytic base (Asp428beta)-and analyse the contributions of quantum effects. The activation barriers and tunnelling contributions for the two possible proton transfers are similar and lead to a phenomenological activation free energy of 16.5+/-0.9 kcal mol(-1) for transfer to either oxygen (PM3-CHARMM calculations applying PM3-SRP specific reaction parameters), in good agreement with the experimental value of 14.4 kcal mol(-1). In contrast, for the AADH system, transfer to the equivalent OD1 was found to be preferred. The structures of the enzyme complexes during reaction are analysed in detail. The hydrogen bond of Thr474beta(MADH)/Thr172beta(AADH) to the catalytic carboxylate group and the nonconserved active site residue Tyr471beta(MADH)/Phe169beta(AADH) are identified as important factors in determining the preferred oxygen acceptor. The protein environment has a significant effect on the reaction energetics and hence on tunnelling contributions and KIEs. These environmental effects, and the related clearly different preferences for the two carboxylate oxygen atoms (with different KIEs) in MADH/MA and AADH/tryptamine, are possible causes of the differences observed in the KIEs between these two important enzyme reactions.

The Cooperative Effect Between Active Site Ionized Groups and Water Desolvation Controls the Alteration of Acid/Base Catalysis in Serine Proteases

What is the driving force that alters the catalytic function of His57 in serine proteases between general base and general acid in each step along the enzymatic reaction? The stable tetrahedral complexes (TC) of chymotrypsin with trifluoromethyl ketone transition state analogue inhibitors are topologically similar to the catalytic transition state. Therefore, they can serve as a good model to study the enzyme catalytic reaction. We used DFT quantum mechanical calculations to analyze the effect of solvation and of polar factors in the active site of chymotrypsin on the pKa of the catalytic histidine in FE (the free enzyme), EI (the noncovalent enzyme inhibitor complex), and TC. We demonstrated that the acid/base alteration is controlled by the charged groups in the active site--the catalytic Asp102 carboxylate and the oxyanion. The effect of these groups on the catalytic His is modulated by water solvation of the active site.

Protein Environment Facilitates O2 Binding in Non-Heme Iron Enzyme. An Insight from ONIOM Calculations on Isopenicillin N Synthase (IPNS)

Binding of dioxygen to a non-heme enzyme has been modeled using the ONIOM combined quantum mechanical/molecular mechanical (QM/MM) method. For the present system, isopenicillin N synthase (IPNS), binding of dioxygen is stabilized by 8-10 kcal/mol for a QM:MM (B3LYP:Amber) protein model compared to a quantum mechanical model of the active site only. In the protein system, the free energy change of O2 binding is close to zero. Two major factors consistently stabilize O2 binding. The first effect, evaluated at the QM level, originates from a change in coordination geometry of the iron center. The active-site model artificially favors the deoxy state (O2 not bound) because it allows too-large rearrangements of the five-coordinate iron site. This error is corrected when the protein is included. The corresponding effect on binding energies is 3-6 kcal/mol, depending on the coordination mode of O2 (side-on or end-on). The second major factor that stabilizes O2 binding is van der Waals interactions between dioxygen and the surrounding enzyme. These interactions, 3-4 kcal/mol at the MM level, are neglected in models that include only the active site. Polarization of the active site by surrounding amino acids does not have a significant effect on the binding energy in the present system.

Origin of the Temperature Dependence of Isotope Effects in Enzymatic Reactions: The Case of Dihydrofolate Reductase

The origin of the temperature dependence of kinetic isotope effects (KIEs) in enzyme reactions is a problem of general interest and a major challenge for computational chemistry. The present work simulates the nuclear quantum mechanical (NQM) effects and the corresponding KIE in dihydrofolate reductase (DHFR) and two of its mutants by using the empirical valence bond (EVB) and the quantum classical path (QCP) centroid path integral approach. Our simulations reproduce the overall observed trend while using a fully microscopic rather than a phenomenological picture and provide an interesting insight. It appears that the KIE increases when the distance between the donor and acceptor increases, in a somewhat counter intuitive way. The temperature dependence of the KIE appears to reflect mainly the temperature dependence of the distance between the donor and acceptor. This trend is also obtained from a simplified vibronic treatment, but as demonstrated here, the vibronic treatment is not valid at short and medium distances, where it is essential to use the path integral or other approaches capable of moving seamlessly from the adiabatic to the diabatic limits. It is pointed out that although the NQM effects do not contribute to catalysis in DHFR, the observed temperature dependence can be used to refine the potential of mean force for the donor and acceptor distance and its change due to distanced mutations.

'In-line attack' conformational effect plays a modest role in an enzyme-catalyzed RNA cleavage: a free energy simulation study

Since the proposal of 'in-line attack' conformation as a possibly important intermediate in RNA cleavage, its structure has been captured in various protein and RNA enzymes; these structures strengthen the belief that this conformation plays an essential role in the catalysis of RNA cleavage. As generally discussed, this intermediate structure can be involved in energy barrier reduction in two possible ways, e.g. through either conformational effect or electrostatic effect. In order to quantitatively elucidate the contribution of conformational effect in this type of enzyme catalysis, free energy simulations were performed on the RNA structures both in a splicing endonuclease complex and in the aqueous solution. Our free energy simulation results revealed that the 'in-line attack' conformational effect plays a modest role in facilitating the reaction rate enhancement (approximately 12-fold) compared with the overall 10(12)-fold rate increase. The close agreement between the present computational estimation and an experimental measurement on the spontaneous RNA cleavage in an in vitro evolved ATP aptamer motives us to realize that the conformation distribution of an enzyme substrate prior to rather than after its binding determines the upper bound of the rate enhancement ability through the conformational strategy.

A new paradigm for electrostatic catalysis of radical reactions in vitamin B12 enzymes

The catalytic power of enzymes containing coenzyme B(12) cofactor has been, in some respects, the "last bastion" for the strain hypothesis. The present work explores the origin of this effect by using simulation methods that overcome the sampling difficulties of previous energy minimization studies. It is found that the major part of the catalytic effect is due to the electrostatic interaction between the ribose and the protein, and that the strain contribution is very small. Remarkably, enzymes can use electrostatic effects even in a radical process, when the charge distribution of the reacting fragments does not change significantly during the reaction. Electrostatic catalysis can, in such cases, be obtained by attaching a polar group to the leaving fragment and designing an active site that interacts more strongly with this group in the product state than in the reactant state. The finding that evolution had to use this trick provides further evidence to the observation that it is extremely hard to catalyze enzymatic reactions by nonelectrostatic factors. The trick used by B(12) enzymes may, in fact, be a very powerful new strategy in enzyme design.

Femtochemistry in enzyme catalysis: DNA photolyase

Photolyase uses light energy to split UV-induced cyclobutane pyrimidine dimers in damaged DNA. This photoenzyme encompasses a series of elementary dynamical processes during repair function from early photoinitiation by a photoantenna molecule to enhance repair efficiency, to in vitro photoreduction through aromatic residues to reconvert the cofactor to the active form, and to final photorepair to fix damaged DNA. The corresponding series of dynamics include resonance energy transfer, intraprotein electron transfer, and intermolecular electron transfer, bond breaking-making rearrangements and back electron return, respectively. We review here our recent direct studies of these dynamical processes in real time, which showed that all these elementary reactions in the enzyme occur within subnanosecond timescale. Active-site solvation was observed to play a critical role in the continuous modulation of catalytic reactions. As a model system for enzyme catalysis, we isolated the enzyme-substrate complex in the transition-state region and mapped out the entire evolution of unmasked catalytic reactions of DNA repair. These observed synergistic motions in the active site reveal a perfect correlation of structural integrity and dynamical locality to ensure maximum repair efficiency on the ultrafast time scale.

H and other transfers in enzymes and in solution: theory and computations, a unified view. 2. Applications to experiment and computations

Equations obtained in part I for the free-energy barrier to one-step enzymatic reactions between bound reactants are discussed. The rate is expressed in terms of lambdao (protein reorganization energy), DeltaG(o) (standard free energy of reaction of the H-transfer step), bond breaking/bond forming term, w (work terms), and H-transmission property. Two alternative approximations for the coupling of the bond breaking/bond forming and protein are distinguished experimentally in favorable cases by the DeltaG(o) where the maximum deuterium kinetic isotope effect occurs. Plots of log rate versus DeltaG(o) and properties such as DeltaS* and DeltaS(o) are discussed. The weak or zero T-dependence of the kinetic isotope effect for wild-type enzymes operating under physiological conditions is interpreted in terms of vanishing (or isotopically insensitive) w plus transfer from the lowest H-state. Static and dynamic protein flexibility is discussed. While the many correlations accessible for electron transfers are not available for H-transfers in enzymes, a combination of experiment, computation, and analytical approaches can assist in evaluating the utility of the present equations and in suggesting further experiments and computations. A protein reorganization energy lambdao is obtained in the literature from the extended valence bond formalism where diabatic electronic states are used. A method is suggested for extracting it when instead a bond distance difference coordinate is used. The results may provide a bridge between the two approaches.

A Transition Path Sampling Study of the Reaction Catalyzed by the Enzyme Chorismate Mutase

The study of the chemical steps in enzyme-catalyzed reactions represents a challenge for molecular simulation techniques. One concern is how to calculate paths for the reaction. Common techniques include the definition of a reaction coordinate in terms of a small set of (normally) geometrical variables or the determination of minimum energy paths on the potential energy surface of the reacting system. Both have disadvantages, the former because it presupposes knowledge of which variables are likely to be important for reaction and the latter because it provides a static picture and dynamical effects are ignored. In this paper, we employ the transition path sampling method developed by Chandler and co-workers, which overcomes some of these limitations. The reaction that we have chosen is the chorismate-mutase-catalyzed conversion of chorismate into prephenate, which has become something of a test case for simulation studies of enzyme mechanisms. We generated an ensemble of approximately 1000 independent transition paths for the reaction in the enzyme and another approximately 500 for the corresponding reaction in solution. A large variety of analyses of these paths was performed, but we have concentrated on characterizing the transition state ensemble, particularly the flexibility of its structures with respect to other ligands of the enzyme and the time evolution of various geometrical and energetic properties as the reaction proceeds. We have also devised an approximate technique for locating transition state structures along the paths.

The Catalytic Effect of Dihydrofolate Reductase and Its Mutants Is Determined by Reorganization Energies

The effect of distant mutations on the catalytic reaction of dihydrofolate reductase (DHFR) is reexamined by empirical valence bond simulations. The simulations reproduce for the first time the changes in the observed rate constants (without the use of adjustable parameters for this purpose) and show that the changes in activation barriers are strongly correlated with the corresponding changes in the reorganization energy. The preorganization of the polar groups of enzymes is the key catalytic factor, and anticatalytic mutations destroy this preorganization. Some anticatalytic mutations in DHFR also increase the distance between the donor and acceptor, but this effect is not directly related to catalysis since the native enzyme and the uncatalyzed reaction in water have similar average donor-acceptor distances. Insight into the effect of a mutation is provided by constructing the relevant free energy surfaces in terms of the generalized solute-solvent coordinates. It is shown how the mutations change the reaction coordinate and the activation barrier, and it is clarified that the corresponding changes do not reflect dynamical effects. It is also pointed out that all reactions in a condensed phase involve correlated motions (both in enzymes and in solution) and that the change of such motions upon mutations is a result of the change in the shape of the multidimensional reaction path on the solute-solvent surface, rather than the reason for the change in rate constant. Thus, as far as catalysis is concerned, the change in the activation barrier is due to the change in the electrostatic preorganization energy.

Ab initio quantum mechanical/molecular mechanical molecular dynamics simulation of enzyme catalysis: the case of histone lysine methyltransferase SET7/9

To elucidate enzyme catalysis through computer simulation, a prerequisite is to reliably compute free energy barriers for both enzyme and solution reactions. By employing on-the-fly Born-Oppenheimer molecular dynamics simulations with the ab initio quantum mechanical/molecular mechanical approach and the umbrella sampling method, we have determined free energy profiles for the methyl-transfer reaction catalyzed by the histone lysine methyltransferase SET7/9 and its corresponding uncatalyzed reaction in aqueous solution, respectively. Our calculated activation free energy barrier for the enzyme catalyzed reaction is 22.5 kcal/mol, which agrees very well with the experimental value of 20.9 kcal/mol. The difference in potential of mean force between a corresponding prereaction state and the transition state for the solution reaction is computed to be 30.9 kcal/mol. Thus, our simulations indicate that the enzyme SET7/9 plays an essential catalytic role in significantly lowering the barrier for the methyl-transfer reaction step. For the reaction in solution, it is found that the hydrogen bond network near the reaction center undergoes a significant change, and there is a strong shift in electrostatic field from the prereaction state to the transition state, whereas for the enzyme reaction, such an effect is much smaller and the enzyme SET7/9 is found to provide a preorganized electrostatic environment to facilitate the methyl-transfer reaction. Meanwhile, we find that the transition state in the enzyme reaction is a little more dissociative than that in solution.

Bridging from molecular simulation to biochemical networks

How can we make the connection between the three-dimensional structures of individual proteins and understanding how complex biological systems involving many proteins work? The modelling and simulation of protein structures can help to answer this question for systems ranging from multimacromolecular complexes to organelles and cells. On one hand, multiscale modelling and simulation techniques are advancing to permit the spatial and temporal properties of large systems to be simulated using atomic-detail structures. On the other hand, the estimation of kinetic parameters for the mathematical modelling of biochemical pathways using protein structure information provides a basis for iterative manipulation of biochemical pathways guided by protein structure. Recent advances include the structural modelling of protein complexes on the genomic level, novel coarse-graining strategies to increase the size of the system and the time span that can be simulated, and comparative molecular field analyses to estimate enzyme kinetic parameters.

Ultrafast catalytic processes in enzymes

The study of biocatalysis and biotransformation in the transition-state region has been challenging and difficult, but recent advances on two important photoenzymes in nature, DNA photolyase and protochlorophyllide oxidoreductase, have enabled the investigation of their catalytic processes in real time. By following the entire evolution of substrate transformation, the functional dynamics constituting a series of elementary reactions have been mapped out. The five fundamental reactions in the enzymes, namely electron transfer, bond breaking and making, proton and hydride transfer, all occur ultrafast within subnanosecond. The direct clocking of catalytic transition states probes central, unmasked chemical processes and provides mechanistic insights into the role of the dynamics in enzyme function, which not only facilitates the formation of the enzyme-substrate complex in the transition-state configurations, but also modulates the subsequent catalytic reactions for maximum biotransformation efficiency.

Tunneling and Classical Paths for Proton Transfer in an Enzyme Reaction Dominated by Tunneling: Oxidation of Tryptamine by Aromatic Amine Dehydrogenase

Proton tunneling dominates the oxidative deamination of tryptamine catalyzed by the enzyme aromatic amine dehydrogenase. For reaction with the fast substrate tryptamine, a H/D kinetic isotope effect (KIE) of 55 +/- 6 has been reported-one of the largest observed in an enzyme reaction. We present here a computational analysis of this proton-transfer reaction, applying combined quantum mechanics/molecular mechanics (QM/MM) methods (PM3-SRP//PM3/CHARMM22). In particular, we extend our previous computational study (Masgrau et al. Science 2006, 312, 237) by using improved energy corrections, high-level QM/MM methods, and an ensemble of paths to estimate the tunneling contributions. We have carried out QM/MM molecular dynamics simulations and variational transition state theory calculations with small-curvature tunneling corrections. The results provide detailed insight into the processes involved in the reaction. Transfer to the O2 oxygen of the catalytic base, Asp128beta, is found to be the favored reaction both thermodynamically and kinetically, even though O1 is closer in the reactant complex. Comparison of quantum and classical models of proton transfer allows estimation of the contribution of hydrogen tunneling in lowering the barrier to reaction in the enzyme. A reduction of the activation free energy due to tunneling of 3.1 kcal mol-1 is found, which represents a rate enhancement due to tunneling by 2 orders of magnitude. The calculated KIE of 30 is significantly elevated over the semiclassical limit, in agreement with the experimental observations; a semiclassical value of 6 is obtained when tunneling is omitted. A polarization of the C-H bond to be broken is observed due to the close proximity of the catalytic aspartate and the (formally) positively charged imine nitrogen. A comparison is also made with the related quinoprotein methylamine dehydrogenase (MADH)-the much lower KIE of 11 that we obtain for the MADH/methylamine system is found to arise from a more endothermic potential energy surface for the MADH reaction.

QM/MM studies of enzymes

Combined quantum-mechanics/molecular-mechanics (QM/MM) methods are making rapid progress both methodologically and with respect to their range of application. Mechanistic studies on enzymes, including contributions towards the understanding of enzyme catalysis, continue to be a major target. They are joined by calculations of pK(a) values, redox properties, ground- and excited-state spectroscopic parameters, and excited-state dynamics. Methodological advances include improved QM/MM schemes, in particular new approaches for an effective treatment of the QM-MM electrostatic interactions, and the incorporation of new efficient and accurate QM methods in QM/MM schemes.

Electrostatic Contributions to Binding of Transition State Analogues Can Be Very Different from the Corresponding Contributions to Catalysis: Phenolates Binding to the Oxyanion Hole of Ketosteroid Isomerase

The relationship between binding of transition state analogues (TSAs) and catalysis is an open problem. A recent study of the binding of phenolate TSAs to ketosteroid isomerase (KSI) found a small change in the binding energy with a change in charge delocalization of the TSAs. This has been taken as proof that electrostatic effects do not contribute in a major way to catalysis. Here we reanalyze the relationship between the binding of the TSAs and the chemical catalysis by KSI as well as the binding of the transition state (TS), by computer simulation approaches. Since the simulations reproduce the relevant experimental results, they can be used to quantify the different contributions to the observed effects. It is found that the binding of the TSA and the chemical catalysis represent different thermodynamic cycles with very different electrostatic contributions. While the binding of the TSA involves a small electrostatic contribution, the chemical catalysis involves a charge transfer process and a major electrostatic contribution due to the preorganization of the active site. Furthermore, it is found that the electrostatic preorganization contributions to the binding of the enolate intermediate of KSI and the TS are much larger than the corresponding effect for the binding of the TSAs. This reflects the dependence of the preorganization on the orientation of the nonpolar form of the TSAs relative to the oxyanion hole. It seems to us that this work provides an excellent example of the need for computational studies in analyzing key experimental findings about enzyme catalysis.

Enzymatic catalysis and transfers in solution. I. Theory and computations, a unified view

The transfer of hydride, proton, or H atom between substrate and cofactor in enzymes has been extensively studied for many systems, both experimentally and computationally. A simple equation for the reaction rate, an analog of an equation obtained earlier for electron transfer rates, is obtained, but now containing an approximate analytic expression for the bond rupture-bond forming feature of these H transfers. A "symmetrization," of the potential energy surfaces is again introduced [R. A. Marcus, J. Chem. Phys. 43, 679 (1965); J. Phys. Chem. 72, 891 (1968)], together with Gaussian fluctuations of the remaining coordinates of the enzyme and solution needed for reaching the transition state. Combining the two expressions for the changes in the difference of the two bond lengths of the substrate-cofactor subsystem and in the fluctuation coordinates of the protein leading to the transition state, an expression is obtained for the free energy barrier. To this end a two-dimensional reaction space (m,n) is used that contains the relative coordinates of the H in the reactants, the heavy atoms to which it is bonded, and the protein/solution reorganization coordinate, all leading to the transition state. The resulting expression may serve to characterize in terms of specific parameters (two "reorganization" terms, thermodynamics, and work terms), experimental and computational data for different enzymes, and different cofactor-substrate systems. A related characterization was used for electron transfers. To isolate these factors from nuclear tunneling, when the H-tunneling effect is large, use of deuterium and tritium transfers is of course helpful, although tunneling has frequently and understandably dominated the discussions. A functional form is suggested for the dependence of the deuterium kinetic isotope effect (KIE) on DeltaG degrees and a different form for the 13C KIE. Pressure effects on deuterium and 13C KIEs are also discussed. Although formulated for a one-step transfer of a light particle in an enzyme, the results would also apply to single-step transfers of other atoms and groups in enzymes and in solution.

Coordinated effects of distal mutations on environmentally coupled tunneling in dihydrofolate reductase

One of the most intriguing questions in modern enzymology is whether enzyme dynamics evolved to enhance the catalyzed chemical transformation. In this study, dihydrofolate reductase, a small monomeric protein that catalyzes a single C-H-C transfer, is used as a model system to address this question. Experimental and computational studies have proposed a dynamic network that includes two residues remote from the active site (G121 and M42). The current study compares the nature of the H-transfer step of the WT enzyme, two single mutants, and their double mutant. The contribution of quantum mechanical tunneling and enzyme dynamics to the H-transfer step was examined by determining intrinsic kinetic isotope effects, their temperature dependence, and activation parameters. Different patterns of environmentally coupled tunneling were found for these four enzymes. The findings indicate that the naturally evolved WT dihydrofolate reductase requires no donor-acceptor distance fluctuations (no gating). Both single mutations affect the rearrangement of the system before tunneling, so some gating is required, but the overall nature of the environmentally coupled tunneling appears similar to that of the WT enzyme. The double mutation, on the other hand, seems to cause a major change in the nature of H transfer, leading to poor reorganization and substantial gating. These findings support the suggestion that these distal residues synergistically affect the H transfer at the active site of the enzyme. This observation is in accordance with the notion that these remote residues are part of a dynamic network that is coupled to the catalyzed chemistry.

Modeling electrostatic effects in proteins

Electrostatic energies provide what is perhaps the most effective tool for structure-function correlation of biological molecules. This review considers the current state of simulations of electrostatic energies in macromolecules as well as the early developments of this field. We focus on the relationship between microscopic and macroscopic models, considering the convergence problems of the microscopic models and the fact that the dielectric 'constants' in semimacroscopic models depend on the definition and the specific treatment. The advances and the challenges in the field are illustrated considering a wide range of functional properties including pK(a)'s, redox potentials, ion and proton channels, enzyme catalysis, ligand binding and protein stability. We conclude by pointing out that, despite the current problems and the significant misunderstandings in the field, there is an overall progress that should lead eventually to quantitative descriptions of electrostatic effects in proteins and thus to quantitative descriptions of the function of proteins.