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MM studies of enzymes
QM/MM studies of enzymes Hans Martin Senn and Walter Thiel 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 pKa 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. Addresses Max-Planck-Institut fu¨r Kohlenforschung, D-45470 Mu¨lheim an der Ruhr, Germany Corresponding author: Thiel, Walter ([email protected])
Current Opinion in Chemical Biology 2007, 11:182–187 This review comes from a themed issue on Biocatalysis and biotransformation Edited by Bernhard Hauer and Manfred T Reetz Available online 16th February 2007 1367-5931/$ – see front matter # 2006 Elsevier Ltd. All rights reserved. DOI 10.1016/j.cbpa.2007.01.684
Introduction For the modelling of enzymatic reactions and other biomolecular processes that involve changes in the electronic structure, such as charge transfer or electronic excitation, quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice. The basic idea is to use a QM method for the chemically active region (e.g. substrates and cofactors) and combine it with an MM treatment for the surroundings (e.g. the full protein and solvent). Because the two regions generally (strongly) interact, it is not possible to write the total energy of the entire system simply as the sum of the energies of the subsystems. Coupling terms have to be considered, and it is necessary to take precautions at the boundary between the subsystems, especially if it cuts through covalent bonds. The exact form of the coupling terms and the details of the boundary treatment define a specific QM/MM scheme. Since the seminal contribution by Warshel and Levitt thirty years ago [1], the development of improved methods and the ever-increasing availability of computing resources Current Opinion in Chemical Biology 2007, 11:182–187
have greatly inspired the field. The range of applications has continuously been extended from structural aspects over energetics to dynamics and spectroscopic properties. The present review covers the period from 2004 to September 2006. It illustrates the vitality of the field by highlighting selected methodological advances as well as different types of applications. For a more comprehensive treatment we refer to recent review articles [2,3,4,5,6,7,8].
Methods QM/MM schemes
A variety of approaches deals with the problem of covalent bonds across the QM–MM boundary. The most popular choice is probably the use of ‘link atoms’: the dangling bond of the QM system is saturated by an additional QM atom, most commonly hydrogen, placed along the bond between the frontier QM and MM atoms. One issue of this scheme is that the link atom is in close proximity to the frontier MM atom and, thus, the MM point charges can overpolarize the QM density. This can be alleviated by deleting or redistributing the point charges in the boundary region. Two studies [9,10] carefully evaluated existing and new treatments. The main conclusion is that it is crucial to preserve the total charge and the dipoles at the boundary (‘charge shift’, ‘redistributed charge and dipoles’ schemes). The performance of link-atom methods that implement such refined boundary treatments is overall on par with more rigorous, but also technically more involved, procedures using frozen hybrid orbitals or specially parameterized boundary atoms to saturate the QM part [5]. An accurate description of the electrostatic forces on the QM subsystem due to the MM environment is essential for a reliable modelling of biomolecules. The standard approach is to let the MM point charges polarize the QM electron density (‘electrostatic embedding’). Including all the electrostatic interactions explicitly is computationally challenging, and QM–MM electrostatic cutoffs are problematic. Recent studies [11–13] have confirmed that electrostatic cutoffs can introduce significant artefacts and that it is important to treat the MM–MM and QM–MM electrostatics in a balanced manner. We highlight here some developments in the area of long-range QM–MM electrostatic interactions. York and co-workers [11] presented a linear-scaling Ewald method for semi-empirical QM/MM simulations under periodic boundary conditions. This method uses the particle–mesh Ewald technique for the interaction www.sciencedirect.com
QM/MM studies of enzymes Senn and Thiel 183
between the MM charges and a point-charge representation of the QM density. A linear-scaling real-space multigrid approach was introduced by Laino et al. [14,15], which represents the MM charges by Gaussian charge distributions and their potential by sums of Gaussians (Gaussian expansion of the electrostatic potential). The scheme was implemented within density-functional theory (DFT) for the QM part and has been extended to include periodic boundary conditions [15]. The generalized solvent boundary potential (GSBP) method, adapted for QM/MM simulations by Cui and co-workers [12,16], takes a different approach. Only a comparably small region around the QM part is treated explicitly, whereas the remainder of the system is kept fixed and is described in terms of a solvent-shielded static field and a Poisson–Boltzmann reaction field. QM methods used in QM/MM
The QM/MM formalism as such is flexible enough to accommodate almost any QM method. However, we point out two developments in the present context. The first is the SCC-DFTB (self-consistent charge density-functional tight-binding) method, a semi-empirical, DFT-inspired approach developed by Elstner, Frauenheim and collaborators. It promises, within the validity domain of the parameterization, an accuracy comparable to DFT at the cost of semi-empirical methods. Although not new, its use in biomolecular QM/MM simulations has gained considerable momentum thanks to several attractive application and method-oriented studies [4,9,13,16–19]. The second development is the family of ‘local’ correlated ab initio methods, exemplified by the LMP2 (local secondorder Møller–Plesset perturbation theory) and LCCSD (local coupled-cluster singles and doubles) approaches developed by Werner, Schu¨tz and collaborators. They take advantage of the short-ranged nature of electron correlation to achieve a linear scaling of the computational cost with system size. The superior accuracy of such high-level methods can therefore now be exploited also for biomolecular QM/MM studies [20], certainly at the level of energy calculations at fixed geometries (i.e. single points). Optimization and free-energy methods
The Yang group [21–25] has been active in adapting optimization and sampling techniques for the use with QM/MM methods. They presented an implementation of the nudged-elastic-band (NEB) approach for finding the minimum-energy path (MEP) [21] that includes in the path definition only selected degrees of freedom and makes sure that the environment follows the reaction smoothly. They also adapted the path-optimization procedure by Ayala and Schlegel, again by restricting the degrees of freedom considered in the definition of the distance between configurations [22]. They combined www.sciencedirect.com
the two methods into a two-step procedure for the determination of reaction paths in enzymatic systems [23]. Given the QM/MM MEP, they constructed a reactionpath potential using the energies, vibrational frequencies and electronic response properties of the QM region along the path [24]. One crucial approximation in these schemes is the replacement of the QM density by ESP charges (atomic charges fitted to the electrostatic potential) in the evaluation of the electrostatic QM–MM coupling. This approximation also forms the basis for the QM/MM free-energy perturbation (FEP) method to calculate free-energy differences along a reaction path [25]. The molecular-dynamics (MD) sampling along the path, which is predetermined by QM/MM optimizations, can be performed effectively at the MM level; the QM part is kept fixed. Related QM/MM FEP schemes were presented by Rod and Ryde [26,27] and by Ka¨stner et al. [28]. The latter also carefully validated the ESP and other approximations used. QM/MM structure refinement
A promising technique pioneered by Ryde et al. [29] exploits the QM/MM method to refine structural data from single-crystal X-ray diffraction [30], NMR [31] or EXAFS [32] measurements. The basic idea is to use a QM/MM, rather than a pure MM, model that is refined against the experimental data. This very much alleviates the problem that the quality of experimental structures is less reliable in and around the active site because of the MM models being carefully tuned to describe the protein but being less reliable for substrates and cofactors (generally, non-protein parts of the structure). Merz and coworkers [33] recently presented a similar approach.
Applications Reactivity
Enzymatic reactions have been the primary target of QM/MM studies. From the vast variety of systems studied, we have selected two examples: chorismate mutase and cytochrome P450. Chorismate mutase catalyses the Claisen rearrangement of chorismate to prephenate (Figure 1a), a key step of the shikimate pathway for the synthesis of aromatic amino acids in plants, fungi and bacteria. This reaction, a rare example of a pericyclic reaction in biochemistry, has been the subject of numerous theoretical studies dealing with the structure of the enzyme–substrate complex, reaction pathways and the role of specific residues in transition-state (TS) stabilization. It has served as an important case for testing and developing theories on the origin of enzymatic catalysis. Mulholland and collaborators [34] reported Hartree–Fock/MM reaction-path optimizations, corrected with DFT and MP2 single-point calculations, and compared the reaction in the enzyme and in continuum solvent. Current Opinion in Chemical Biology 2007, 11:182–187
184 Biocatalysis and biotransformation
Figure 1
Schematics of the main mechanistic features of the enzyme reactions discussed in this review. (a) Claisen-type rearrangement of chorismate to prephenate in chorismate mutase. The allyl vinyl ether unit rearranging to a 3,4-unsaturated ketone is highlighted in red. Note the 6-ring chair-type transition state. (b) Hydroxylation of an aliphatic hydrocarbon RH in cytochrome P450. The heme Fe(III) hydroperoxo complex (Compound 0) loses water upon protonation to generate the reactive Fe(IV) oxo species (Compound I). Compound I is able to abstract a hydrogen atom from the substrate, yielding an alkyl radical and the Fe(III) hydroxo complex, which recombine to form the product R–OH, still coordinated to the Fe(III) centre.
They concluded that electrostatic TS stabilization is the major contribution to catalysis in this case. They also calculated the free energy required to generate ‘near attack conformations’ (NACs) [35], showing that these conformations cannot account for catalysis by themselves. Using the differential TS stabilization approach, they analysed the contributions of specific residues [36]. To assess the influence of variations in the environment on the reaction barrier, they calculated reaction paths starting from 16 snapshots taken from QM/MM MD simulations [37]. They explained the overall catalytic effect by an about equal combination of the cost of forming a NAC in the enzyme and TS stabilization. The reason why the enzyme binds to NACs was proposed to be their similarity to the TS. As the enzyme is adapted to bind to the TS, it also binds to the closely resembling NACs. However, Bruice and co-workers [38], who advanced the NAC proposal as the dominant effect in enzyme catalysis, attributed only about 10% of the catalytic effect to TS stabilization. A unifying perspective from the kinetic point of view is provided in [39]. The cytochrome P450 enzymes constitute a superfamily of monooxygenases that perform a variety of essential functions, such as detoxification and biosynthesis, in nearly all living species. They catalyze many types of reactions including aliphatic and aromatic hydroxylation, epoxidation and heteroatom oxidation. The extensive theoretical work on these enzymes has been reviewed [40], but there are many new QM/MM studies that focus on different aspects of P450 reactivity. The crucial reactive intermediate in the catalytic cycle is generally Current Opinion in Chemical Biology 2007, 11:182–187
accepted to be an iron(IV)-oxo species (Compound I, see Figure 1b) with three unpaired electrons that give rise to almost degenerate doublet and quartet states. Early DFT/MM calculations have established that the enzyme environment controls and tunes the spin density distribution in the porphyrin and sulfur ligands of Compound I through hydrogen-bonding to sulfur [40]. DFT/ MM studies on camphor hydroxylation by Compound I support the two-state rebound mechanism that had previously been proposed on the basis of QM model calculations: the initial hydrogen abstraction encounters similar barriers in both spin states (slightly lower in the doublet), whereas the subsequent rebound step is essentially barrierless in the doublet but has to surmount a nonnegligible barrier in the quartet [41]. This two-state reactivity scenario provides a unifying picture for P450 reactivity [40]. In another DFT/MM work, it has been suggested that the quartet TS for hydrogen abstraction in P450cam is stabilized by remote effects, in particular by favourable electrostatic interactions between a porphyrin propionate sidechain and a neighbouring arginine residue [42]. However, this unusual TS stabilization mechanism could not be confirmed in a subsequent DFT/MM work [43], which uncovered a different catalytic effect: a single water molecule (e.g. the one liberated during the formation of Compound I from Compound 0) can significantly lower the barrier to hydrogen abstraction because its hydrogen bond to the oxo atom of Compound I becomes stronger in the TS [43,44]. Compound I formation is usually formulated as a heterolytic process, with the addition of a proton to the hydroperoxo ligand of Compound 0 being followed by dissociation of water. www.sciencedirect.com
QM/MM studies of enzymes Senn and Thiel 185
However, recent DFT/MM calculations indicate [45] that a quasi-homolytic pathway might be more favourable: the initial O–O bond cleavage in Compound 0 is followed by a concomitant proton and electron transfer to yield Compound I and water in an overall heterolytic fashion. These few examples of QM/MM studies on P450cam illustrate the mechanistic insights that can be gained, and the extension of such work to other related enzymes will be of obvious value. We note two such examples: DFT/MM calculations on three human subfamilies of cytochrome P450 show that Compound I is electronically similar in all three isoforms [46], and DFT/MM methods have also been used for an in silico design of a mutant of cytochrome P450 containing selenocystein, in which Compound I is predicted to be formed faster and to be consumed more slowly during C–H hydroxylation than in the wild-type species [47].
simulations. QM/MM molecular dynamics together with modern sampling techniques to explore free-energy surfaces will probably become more widely used. Concomitant with the methodological improvements, the application of the QM/MM approach will continue to be extended from ground-state structure and reactivity to pKa and redox calculations, spectroscopic properties, and excited-state structure, dynamics and reactivity.
Excited states, spectroscopy
1.
QM/MM methods are applicable not only to ground-state structures and energetics, but also to electronically excited states and spectroscopic properties. As an example of recent work on excited-state reactivity, we mention the simulations on the photoactivated trans-to-cis isomerization of the p-coumaric acid chromophore in the photoactive yellow protein (PYP) [48]. The photoreaction was simulated using excited-states dynamics with a surface-hopping procedure at the multi-reference ab initio/MM level.
Acknowledgements This work was supported by the Volkswagenstiftung.
References and recommended reading Papers of particular interest, published within the period of review, have been highlighted as: of special interest of outstanding interest
Friesner RA, Guallar V: Ab initio quantum chemical and mixed quantum mechanics/molecular mechanics (QM/MM) methods for studying enzymatic catalysis. Annu Rev Phys Chem 2005, 56:389-427. Compact overview of QM, MM and QM/MM methodology with detailed discussion of selected QM/MM applications to enzymatic reactions. The authors also discuss the understanding of enzyme catalysis and the performance of QM/MM models in general.
2.
3.
Vertical electronic excitation energies were reported for the green fluorescent protein (GFP) [49], the retinal chromophore in rhodopsins [18,50] and the copperprotein plastocyanin [51]. Examples for the calculation of magnetic-resonance properties include: retinal in rhodopsins (NMR chemical shifts) [18,50]; the ferryl heme-iron unit of cytochrome P450 (EPR g-values, hyperfine-coupling tensors, zero-field splittings) [52]; and plastocyanin (EPR g- and hyperfine-coupling tensors) [51]. The P450 study reported also Mo¨ssbauer parameters and Heisenberg exchange-coupling constants [52]. The calculation of these properties, especially for transitionmetal systems, is highly involved. QM methods applied include correlated multi-reference methods [18,49,52] and time-dependent DFT [50,51,52].
5.
Conclusions
7.
QM/MM calculations have provided significant contributions to the understanding of structure, reactivity and spectroscopic properties of enzymes in recent years. Improved QM methods within QM/MM have extended the range of applicability and enabled sophisticated property calculations in the protein environment. The importance of electrostatics in enzymatic processes is reflected in efficient and accurate approaches to treat the QM–MM electrostatic coupling, and we anticipate further developments, stimulated not the least by the extensive consideration of this topic in classical www.sciencedirect.com
Warshel A, Levitt M: Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J Mol Biol 1976, 103:227-249.
Bruice TC: Computational approaches: reaction trajectories, structures, and atomic motions. Enzyme reactions and proficiency. Chem Rev 2006, 106:3119-3139.
4.
Riccardi D, Schaefer P, Yang Y, Yu H, Ghosh N, Prat-Resina X, Ko¨nig P, Li G, Xu D, Guo H et al.: Development of effective quantum mechanical/molecular mechanical (QM/MM) methods for complex biological processes. J Phys Chem B 2006, 110:6458-6469. Summary of methodological advances (SCC-DFTB, QM–MM coupling, free-energy methods) illustrated by applications to pKa calculations and proton-transport processes. Lin H, Truhlar DG: QM/MM: what have we learned, where are we, and where do we go from here? Theor Chem Acc, Epub ahead of print, DOI:10.1007/s00214-006-0143-z. Succinct review of current methodological issues of the QM/MM approach.
6.
Senn HM, Thiel W: QM/MM methods for biological systems. In Atomistic Approaches in Modern Biology. (Topics in Current Chemistry, Vol 268). Edited by Reiher M. Berlin: Springer; 2007:173-290. Extensive review of the state of the art of the QM/MM method, including its use in optimization and simulation schemes. Tabular survey of biomolecular applications covering the period 2000 to mid-2006. Garcia-Viloca M, Gao J, Karplus M, Truhlar DG: How enzymes work: analysis by modern rate theory and computer simulations. Science 2004, 303:186-195.
8.
Warshel A, Sharma PK, Kato M, Xiang Y, Liu H, Olsson MHM: Electrostatic basis for enzyme catalysis. Chem Rev 2006, 106:3210-3235. Systematic presentation of the arguments supporting the concept of electrostatic transition-state stabilization to rationalize enzyme catalysis. Alternative proposals are summarized and held against transition-state stabilization. 9.
Ko¨nig PH, Hoffmann M, Frauenheim T, Cui Q: A critical evaluation of different QM/MM frontier treatments with SCC-DFTB as the QM method. J Phys Chem B 2005, 109:9082-9095.
10. Lin H, Truhlar DG: Redistributed charge and dipole schemes for combined quantum mechanical and molecular Current Opinion in Chemical Biology 2007, 11:182–187
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mechanical calculations. J Phys Chem A 2005, 109:3991-4004.
umbrella sampling: application to an enzymatic reaction. J Chem Theory Comput 2006, 2:452-461.
11. Nam K, Gao J, York DM: An efficient linear-scaling Ewald method for long-range electrostatic interactions in combined QM/MM calculations. J Chem Theory Comput 2005, 1:2-13.
29. Ryde U, Olsen L, Nilsson K: Quantum chemical geometry optimizations in proteins using crystallographic raw data. J Comput Chem 2002, 23:1058-1070.
12. Schaefer P, Riccardi D, Cui Q: Reliable treatment of electrostatics in combined QM/MM simulation of macromolecules. J Chem Phys 2005, 123: 014905/1–14.
30. Rulı´sˇek L, Ryde U: Structure of reduced and oxidized manganese superoxide dismutase: a combined computational and experimental approach. J Phys Chem B 2006, 110:11511-11518.
13. Riccardi D, Schaefer P, Cui Q: pKa calculations in solution and proteins with QM/MM free energy perturbation simulations: a quantitative test of QM/MM protocols. J Phys Chem B 2005, 109:17715-17733. 14. Laino T, Mohamed F, Laio A, Parrinello M: An efficient real space multigrid QM/MM electrostatic coupling. J Chem Theory Comput 2005, 1:1176-1184. 15. Laino T, Mohamed F, Laio A, Parrinello M: An efficient linear-scaling electrostatic coupling for treating periodic boundary conditions in QM/MM simulations. J Chem Theory Comput 2006, 2:1370-1378. 16. Ko¨nig PH, Ghosh N, Hoffmann M, Elstner M, Tajkhorshid E, Frauenheim T, Cui Q: Toward theoretical analysis of long-range proton transfer kinetics in biomolecular pumps. J Phys Chem A 2006, 110:548-563. 17. Banerjee A, Yang W, Karplus M, Verdine GL: Structure of a repair enzyme interrogating undamaged DNA elucidates recognition of damaged DNA. Nature 2005, 434:612-618. 18. Hoffmann M, Wanko M, Strodel P, Ko¨nig PH, Frauenheim T, Schulten K, Thiel W, Tajkhorshid E, Elstner M: Color tuning in rhodopsins: the mechanism for the spectral shift between bacteriorhodopsin and sensory rhodopsin II. J Am Chem Soc 2006, 128:10808-10818. 19. Elstner M: The SCC-DFTB method and its application to biological systems. Theor Chem Acc 2006, 116:316-325. 20. Claeyssens F, Harvey JN, Manby FR, Mata RA, Mulholland AJ, Ranaghan KE, Schu¨tz M, Thiel S, Thiel W, Werner H-J: High-accuracy computation of reaction barriers in enzymes. Angew Chem Int Ed 2006, 45:6856-6859. Demonstration of the use of modern correlated ab initio methods in QM/MM calculations of enzymatic reaction barriers. LCCSD(T0) yields essentially chemical accuracy for the enzymes chorismate mutase and p-hydroxybenzoate hydroxylase. 21. Xie L, Liu H, Yang W: Adapting the nudged elastic band method for determining minimum-energy paths of chemical reactions in enzymes. J Chem Phys 2004, 120:8039-8052. 22. Liu H, Lu Z, Cisneros GA, Yang W: Parallel iterative reaction path optimization in ab initio quantum mechanical/molecular mechanical modeling of enzyme reactions. J Chem Phys 2004, 121:697-706. 23. Cisneros GA, Liu H, Lu Z, Yang W: Reaction path determination for quantum mechanical/molecular mechanical modeling of enzyme reactions by combining first order and second order ‘chain-of-replicas’ methods. J Chem Phys 2005:122. 114502/1–7. 24. Lu Z, Yang W: Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations. J Chem Phys 2004, 121:89-100. 25. Zhang Y, Liu H, Yang W: Free energy calculation on enzyme reactions with an efficient iterative procedure to determine minimum energy paths on a combined ab initio QM/MM potential energy surface. J Chem Phys 2000, 112:3483-3492. 26. Rod TH, Ryde U: Quantum mechanical free energy barrier for an enzymatic reaction. Phys Rev Lett 2005, 94: 138302/1-4. 27. Rod TH, Ryde U: Accurate QM/MM free energy calculations of enzyme reactions: methylation by catechol Omethyltransferase. J Chem Theory Comput 2005, 1:1240-1251. 28. Ka¨stner J, Senn HM, Thiel S, Otte N, Thiel W: QM/MM free-energy perturbation compared to thermodynamic integration and Current Opinion in Chemical Biology 2007, 11:182–187
31. Hsiao Y-W, Drakenberg T, Ryde U: NMR structure determination of proteins supplemented by quantum chemical calculations: detailed structure of the Ca2+ sites in the EGF34 fragment of protein S. J Biomol NMR 2005, 31:97-114. 32. Hsiao Y-W, Ryde U: Interpretation of EXAFS spectra for sitting-atop complexes with the help of computational methods. Inorg Chim Acta 2006, 359:1081-1092. 33. Yu N, Hayik SA, Wang B, Liao N, Reynolds CH, Merz KM Jr: Assigning the protonation states of the key aspartates in b-secretase using QM/MM X-ray structure refinement. J Chem Theory Comput 2006, 2:1057-1069. 34. Ranaghan KE, Ridder L, Szefczyk B, Sokalski WA, Hermann JC, Mulholland AJ: Transition state stabilization and substrate strain in enzyme catalysis: ab initio QM/MM modelling of the chorismate mutase reaction. Org Biomol Chem 2004, 2:968-980. 35. Ranaghan KE, Mulholland AJ: Conformational effects in enzyme catalysis: QM/MM free energy calculation of the ‘NAC’ contribution in chorismate mutase. Chem Commun 2004: 1238-1239. 36. Szefczyk B, Mulholland AJ, Ranaghan KE, Sokalski WA: Differential transition-state stabilization in enzyme catalysis: quantum chemical analysis of interactions in the chorismate mutase reaction and prediction of the optimal catalytic field. J Am Chem Soc 2004, 126:16148-16159. 37. Claeyssens F, Ranaghan KE, Manby FR, Harvey JN, Mulholland AJ: Multiple high-level QM/MM reaction paths demonstrate transition-state stabilization in chorismate mutase: correlation of barrier height with transition-state stabilization. Chem Commun 2005:5068-5070. Multiple reaction profiles obtained at the B3LYP/CHARMM level support the concept of transition-state stabilization for the Claisen rearrangement in chorismate mutase. 38. Zhang X, Zhang X, Bruice TC: A definitive mechanism for chorismate mutase. Biochemistry 2005, 44:10443-10448. 39. Giraldo J, Roche D, Rovira X, Serra J: The catalytic power of enzymes: conformational selection or transition state stabilization? FEBS Lett 2006, 580:2170-2177. A kinetic view on enzyme catalysis. Catalytic proposals are connected with kinetic expressions representing the effect of conformational states and the rate constants in the enzyme and in solution. Chorismate mutase serves as illustrative example. 40. Shaik S, Kumar D, de Visser SP, Altun A, Thiel W: Theoretical perspective on the structure and mechanism of cytochrome P450 enzymes. Chem Rev 2005, 105:2279-2328. Comprehensive review. 41. Scho¨neboom JC, Cohen S, Lin H, Shaik S, Thiel W: Quantum mechanical/molecular mechanical investigation of the mechanism of C–H hydroxylation of camphor by cytochrome P450cam: theory supports a two-state rebound mechanism. J Am Chem Soc 2004, 126:4017-4034. 42. Guallar V, Friesner RA: Cytochrome P450CAM enzymatic catalysis cycle: a quantum mechanics/molecular mechanics study. J Am Chem Soc 2004, 126:8501-8508. 43. Altun A, Guallar V, Friesner RA, Shaik S, Thiel W: The effect of heme environment on the hydrogen abstraction reaction of camphor in P450cam catalysis: a QM/MM study. J Am Chem Soc 2006, 128:3924-3925. 44. Altun A, Shaik S, Thiel W: Systematic QM/MM investigation of factors that affect the cytochrome P450-catalyzed hydrogen abstraction of camphor. J Comput Chem 2006, 27:1324-1337. www.sciencedirect.com
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Technically detailed report highlighting the possible pitfalls in QM/MM studies on enzyme reactivity. 45. Zheng J, Wang D, Thiel W, Shaik S: QM/MM study of mechanisms for Compound I formation in the catalytic cycle of cytochrome P450cam. J Am Chem Soc 2006, 128:13204-13215. 46. Bathelt CM, Zurek J, Mulholland AJ, Harvey JN: Electronic structure of Compound I in human isoforms of cytochrome P450 from QM/MM modeling. J Am Chem Soc 2005, 127:12900-12908. 47. Cohen S, Kumar D, Shaik S: In silico design of a mutant of cytochrome P450 containing selenocysteine. J Am Chem Soc 2006, 128:2649-2653. 48. Groenhof G, Bouxin-Cademartory M, Hess B, de Visser SP, Berendsen HJC, Olivucci M, Mark AE, Robb MA: Photoactivation of the photoactive yellow protein: why photon absorption triggers a trans-to-cis isomerization of the chromophore in the protein. J Am Chem Soc 2004, 126:4228-4233. The excited-states dynamics of the photoactivated trans-to-cis isomerization of the PYP chromophore is investigated at the CASSCF/MM level using a surface-hopping algorithm. The reactivity after the photoevent is followed with classical MD and semi-empirical QM/MM. Results include
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quantum yields, fluorescence lifetimes and mechanistic insights, such as the preferential electrostatic stabilization of the chromophore’s excited state in the active site. 49. Sinicropi A, Andruniow T, Ferre´ N, Basosi R, Olivucci M: Properties of the emitting state of the green fluorescent protein resolved at the CASPT2//CASSCF/CHARMM level. J Am Chem Soc 2005, 127:11534-11535. 50. Gasco´n JA, Sproviero EM, Batista VS: Computational studies of the primary phototransduction event in visual rhodopsin. Acc Chem Res 2006, 39:184-193. Summary of advances towards a molecular understanding of the primary photoevent in rhodopsin. Covered are mechanistic and spectroscopic QM/MM studies. The latter include calculations of electronic excitation energies at the TDDFT//DFT/MM and CASPT2//CASSCF/MM levels and of 1H and 13C NMR chemical shifts. 51. Sinnecker S, Neese F: QM/MM calculations with DFT for taking into account protein effects on the EPR and optical spectra of metalloproteins. Plastocyanin as a case study. J Comput Chem 2006, 27:1463-1475. 52. Scho¨neboom JC, Neese F, Thiel W: Toward identification of the Compound I reactive intermediate in cytochrome P450 chemistry: a QM/MM study of its EPR and Mo¨ssbauer parameters. J Am Chem Soc 2005, 127:5840-5853.
Current Opinion in Chemical Biology 2007, 11:182–187
Current Opinion in Chemical Biology 2007, 11:182–187 This review comes from a themed issue on Biocatalysis and biotransformation Edited by Bernhard Hauer and Manfred T Reetz Available online 16th February 2007 1367-5931/$ – see front matter # 2006 Elsevier Ltd. All rights reserved. DOI 10.1016/j.cbpa.2007.01.684
Introduction For the modelling of enzymatic reactions and other biomolecular processes that involve changes in the electronic structure, such as charge transfer or electronic excitation, quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice. The basic idea is to use a QM method for the chemically active region (e.g. substrates and cofactors) and combine it with an MM treatment for the surroundings (e.g. the full protein and solvent). Because the two regions generally (strongly) interact, it is not possible to write the total energy of the entire system simply as the sum of the energies of the subsystems. Coupling terms have to be considered, and it is necessary to take precautions at the boundary between the subsystems, especially if it cuts through covalent bonds. The exact form of the coupling terms and the details of the boundary treatment define a specific QM/MM scheme. Since the seminal contribution by Warshel and Levitt thirty years ago [1], the development of improved methods and the ever-increasing availability of computing resources Current Opinion in Chemical Biology 2007, 11:182–187
have greatly inspired the field. The range of applications has continuously been extended from structural aspects over energetics to dynamics and spectroscopic properties. The present review covers the period from 2004 to September 2006. It illustrates the vitality of the field by highlighting selected methodological advances as well as different types of applications. For a more comprehensive treatment we refer to recent review articles [2,3,4,5,6,7,8].
Methods QM/MM schemes
A variety of approaches deals with the problem of covalent bonds across the QM–MM boundary. The most popular choice is probably the use of ‘link atoms’: the dangling bond of the QM system is saturated by an additional QM atom, most commonly hydrogen, placed along the bond between the frontier QM and MM atoms. One issue of this scheme is that the link atom is in close proximity to the frontier MM atom and, thus, the MM point charges can overpolarize the QM density. This can be alleviated by deleting or redistributing the point charges in the boundary region. Two studies [9,10] carefully evaluated existing and new treatments. The main conclusion is that it is crucial to preserve the total charge and the dipoles at the boundary (‘charge shift’, ‘redistributed charge and dipoles’ schemes). The performance of link-atom methods that implement such refined boundary treatments is overall on par with more rigorous, but also technically more involved, procedures using frozen hybrid orbitals or specially parameterized boundary atoms to saturate the QM part [5]. An accurate description of the electrostatic forces on the QM subsystem due to the MM environment is essential for a reliable modelling of biomolecules. The standard approach is to let the MM point charges polarize the QM electron density (‘electrostatic embedding’). Including all the electrostatic interactions explicitly is computationally challenging, and QM–MM electrostatic cutoffs are problematic. Recent studies [11–13] have confirmed that electrostatic cutoffs can introduce significant artefacts and that it is important to treat the MM–MM and QM–MM electrostatics in a balanced manner. We highlight here some developments in the area of long-range QM–MM electrostatic interactions. York and co-workers [11] presented a linear-scaling Ewald method for semi-empirical QM/MM simulations under periodic boundary conditions. This method uses the particle–mesh Ewald technique for the interaction www.sciencedirect.com
QM/MM studies of enzymes Senn and Thiel 183
between the MM charges and a point-charge representation of the QM density. A linear-scaling real-space multigrid approach was introduced by Laino et al. [14,15], which represents the MM charges by Gaussian charge distributions and their potential by sums of Gaussians (Gaussian expansion of the electrostatic potential). The scheme was implemented within density-functional theory (DFT) for the QM part and has been extended to include periodic boundary conditions [15]. The generalized solvent boundary potential (GSBP) method, adapted for QM/MM simulations by Cui and co-workers [12,16], takes a different approach. Only a comparably small region around the QM part is treated explicitly, whereas the remainder of the system is kept fixed and is described in terms of a solvent-shielded static field and a Poisson–Boltzmann reaction field. QM methods used in QM/MM
The QM/MM formalism as such is flexible enough to accommodate almost any QM method. However, we point out two developments in the present context. The first is the SCC-DFTB (self-consistent charge density-functional tight-binding) method, a semi-empirical, DFT-inspired approach developed by Elstner, Frauenheim and collaborators. It promises, within the validity domain of the parameterization, an accuracy comparable to DFT at the cost of semi-empirical methods. Although not new, its use in biomolecular QM/MM simulations has gained considerable momentum thanks to several attractive application and method-oriented studies [4,9,13,16–19]. The second development is the family of ‘local’ correlated ab initio methods, exemplified by the LMP2 (local secondorder Møller–Plesset perturbation theory) and LCCSD (local coupled-cluster singles and doubles) approaches developed by Werner, Schu¨tz and collaborators. They take advantage of the short-ranged nature of electron correlation to achieve a linear scaling of the computational cost with system size. The superior accuracy of such high-level methods can therefore now be exploited also for biomolecular QM/MM studies [20], certainly at the level of energy calculations at fixed geometries (i.e. single points). Optimization and free-energy methods
The Yang group [21–25] has been active in adapting optimization and sampling techniques for the use with QM/MM methods. They presented an implementation of the nudged-elastic-band (NEB) approach for finding the minimum-energy path (MEP) [21] that includes in the path definition only selected degrees of freedom and makes sure that the environment follows the reaction smoothly. They also adapted the path-optimization procedure by Ayala and Schlegel, again by restricting the degrees of freedom considered in the definition of the distance between configurations [22]. They combined www.sciencedirect.com
the two methods into a two-step procedure for the determination of reaction paths in enzymatic systems [23]. Given the QM/MM MEP, they constructed a reactionpath potential using the energies, vibrational frequencies and electronic response properties of the QM region along the path [24]. One crucial approximation in these schemes is the replacement of the QM density by ESP charges (atomic charges fitted to the electrostatic potential) in the evaluation of the electrostatic QM–MM coupling. This approximation also forms the basis for the QM/MM free-energy perturbation (FEP) method to calculate free-energy differences along a reaction path [25]. The molecular-dynamics (MD) sampling along the path, which is predetermined by QM/MM optimizations, can be performed effectively at the MM level; the QM part is kept fixed. Related QM/MM FEP schemes were presented by Rod and Ryde [26,27] and by Ka¨stner et al. [28]. The latter also carefully validated the ESP and other approximations used. QM/MM structure refinement
A promising technique pioneered by Ryde et al. [29] exploits the QM/MM method to refine structural data from single-crystal X-ray diffraction [30], NMR [31] or EXAFS [32] measurements. The basic idea is to use a QM/MM, rather than a pure MM, model that is refined against the experimental data. This very much alleviates the problem that the quality of experimental structures is less reliable in and around the active site because of the MM models being carefully tuned to describe the protein but being less reliable for substrates and cofactors (generally, non-protein parts of the structure). Merz and coworkers [33] recently presented a similar approach.
Applications Reactivity
Enzymatic reactions have been the primary target of QM/MM studies. From the vast variety of systems studied, we have selected two examples: chorismate mutase and cytochrome P450. Chorismate mutase catalyses the Claisen rearrangement of chorismate to prephenate (Figure 1a), a key step of the shikimate pathway for the synthesis of aromatic amino acids in plants, fungi and bacteria. This reaction, a rare example of a pericyclic reaction in biochemistry, has been the subject of numerous theoretical studies dealing with the structure of the enzyme–substrate complex, reaction pathways and the role of specific residues in transition-state (TS) stabilization. It has served as an important case for testing and developing theories on the origin of enzymatic catalysis. Mulholland and collaborators [34] reported Hartree–Fock/MM reaction-path optimizations, corrected with DFT and MP2 single-point calculations, and compared the reaction in the enzyme and in continuum solvent. Current Opinion in Chemical Biology 2007, 11:182–187
184 Biocatalysis and biotransformation
Figure 1
Schematics of the main mechanistic features of the enzyme reactions discussed in this review. (a) Claisen-type rearrangement of chorismate to prephenate in chorismate mutase. The allyl vinyl ether unit rearranging to a 3,4-unsaturated ketone is highlighted in red. Note the 6-ring chair-type transition state. (b) Hydroxylation of an aliphatic hydrocarbon RH in cytochrome P450. The heme Fe(III) hydroperoxo complex (Compound 0) loses water upon protonation to generate the reactive Fe(IV) oxo species (Compound I). Compound I is able to abstract a hydrogen atom from the substrate, yielding an alkyl radical and the Fe(III) hydroxo complex, which recombine to form the product R–OH, still coordinated to the Fe(III) centre.
They concluded that electrostatic TS stabilization is the major contribution to catalysis in this case. They also calculated the free energy required to generate ‘near attack conformations’ (NACs) [35], showing that these conformations cannot account for catalysis by themselves. Using the differential TS stabilization approach, they analysed the contributions of specific residues [36]. To assess the influence of variations in the environment on the reaction barrier, they calculated reaction paths starting from 16 snapshots taken from QM/MM MD simulations [37]. They explained the overall catalytic effect by an about equal combination of the cost of forming a NAC in the enzyme and TS stabilization. The reason why the enzyme binds to NACs was proposed to be their similarity to the TS. As the enzyme is adapted to bind to the TS, it also binds to the closely resembling NACs. However, Bruice and co-workers [38], who advanced the NAC proposal as the dominant effect in enzyme catalysis, attributed only about 10% of the catalytic effect to TS stabilization. A unifying perspective from the kinetic point of view is provided in [39]. The cytochrome P450 enzymes constitute a superfamily of monooxygenases that perform a variety of essential functions, such as detoxification and biosynthesis, in nearly all living species. They catalyze many types of reactions including aliphatic and aromatic hydroxylation, epoxidation and heteroatom oxidation. The extensive theoretical work on these enzymes has been reviewed [40], but there are many new QM/MM studies that focus on different aspects of P450 reactivity. The crucial reactive intermediate in the catalytic cycle is generally Current Opinion in Chemical Biology 2007, 11:182–187
accepted to be an iron(IV)-oxo species (Compound I, see Figure 1b) with three unpaired electrons that give rise to almost degenerate doublet and quartet states. Early DFT/MM calculations have established that the enzyme environment controls and tunes the spin density distribution in the porphyrin and sulfur ligands of Compound I through hydrogen-bonding to sulfur [40]. DFT/ MM studies on camphor hydroxylation by Compound I support the two-state rebound mechanism that had previously been proposed on the basis of QM model calculations: the initial hydrogen abstraction encounters similar barriers in both spin states (slightly lower in the doublet), whereas the subsequent rebound step is essentially barrierless in the doublet but has to surmount a nonnegligible barrier in the quartet [41]. This two-state reactivity scenario provides a unifying picture for P450 reactivity [40]. In another DFT/MM work, it has been suggested that the quartet TS for hydrogen abstraction in P450cam is stabilized by remote effects, in particular by favourable electrostatic interactions between a porphyrin propionate sidechain and a neighbouring arginine residue [42]. However, this unusual TS stabilization mechanism could not be confirmed in a subsequent DFT/MM work [43], which uncovered a different catalytic effect: a single water molecule (e.g. the one liberated during the formation of Compound I from Compound 0) can significantly lower the barrier to hydrogen abstraction because its hydrogen bond to the oxo atom of Compound I becomes stronger in the TS [43,44]. Compound I formation is usually formulated as a heterolytic process, with the addition of a proton to the hydroperoxo ligand of Compound 0 being followed by dissociation of water. www.sciencedirect.com
QM/MM studies of enzymes Senn and Thiel 185
However, recent DFT/MM calculations indicate [45] that a quasi-homolytic pathway might be more favourable: the initial O–O bond cleavage in Compound 0 is followed by a concomitant proton and electron transfer to yield Compound I and water in an overall heterolytic fashion. These few examples of QM/MM studies on P450cam illustrate the mechanistic insights that can be gained, and the extension of such work to other related enzymes will be of obvious value. We note two such examples: DFT/MM calculations on three human subfamilies of cytochrome P450 show that Compound I is electronically similar in all three isoforms [46], and DFT/MM methods have also been used for an in silico design of a mutant of cytochrome P450 containing selenocystein, in which Compound I is predicted to be formed faster and to be consumed more slowly during C–H hydroxylation than in the wild-type species [47].
simulations. QM/MM molecular dynamics together with modern sampling techniques to explore free-energy surfaces will probably become more widely used. Concomitant with the methodological improvements, the application of the QM/MM approach will continue to be extended from ground-state structure and reactivity to pKa and redox calculations, spectroscopic properties, and excited-state structure, dynamics and reactivity.
Excited states, spectroscopy
1.
QM/MM methods are applicable not only to ground-state structures and energetics, but also to electronically excited states and spectroscopic properties. As an example of recent work on excited-state reactivity, we mention the simulations on the photoactivated trans-to-cis isomerization of the p-coumaric acid chromophore in the photoactive yellow protein (PYP) [48]. The photoreaction was simulated using excited-states dynamics with a surface-hopping procedure at the multi-reference ab initio/MM level.
Acknowledgements This work was supported by the Volkswagenstiftung.
References and recommended reading Papers of particular interest, published within the period of review, have been highlighted as: of special interest of outstanding interest
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2.
3.
Vertical electronic excitation energies were reported for the green fluorescent protein (GFP) [49], the retinal chromophore in rhodopsins [18,50] and the copperprotein plastocyanin [51]. Examples for the calculation of magnetic-resonance properties include: retinal in rhodopsins (NMR chemical shifts) [18,50]; the ferryl heme-iron unit of cytochrome P450 (EPR g-values, hyperfine-coupling tensors, zero-field splittings) [52]; and plastocyanin (EPR g- and hyperfine-coupling tensors) [51]. The P450 study reported also Mo¨ssbauer parameters and Heisenberg exchange-coupling constants [52]. The calculation of these properties, especially for transitionmetal systems, is highly involved. QM methods applied include correlated multi-reference methods [18,49,52] and time-dependent DFT [50,51,52].
5.
Conclusions
7.
QM/MM calculations have provided significant contributions to the understanding of structure, reactivity and spectroscopic properties of enzymes in recent years. Improved QM methods within QM/MM have extended the range of applicability and enabled sophisticated property calculations in the protein environment. The importance of electrostatics in enzymatic processes is reflected in efficient and accurate approaches to treat the QM–MM electrostatic coupling, and we anticipate further developments, stimulated not the least by the extensive consideration of this topic in classical www.sciencedirect.com
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