- Email: [email protected]
Quantum mechanical calculations on biological systems
257
Quantum mechanical calculations on biological systems Richard A Friesner* and Michael D Beachy Improvements in quantum chemical methods have led to increased applications to biological problems, including the development of potential energy functions for molecular mechanics and modeling of the reactive chemistry in enzyme active sites, with particularly interesting progress being made for metal-containing systems. An important direction is the development and application of hybrid quantum chemicalmolecular mechanics methods. Addresses
Department of Chemistry, Columbia University,3000 Broadway, Mail Code 3110, New York, NY 10027, USA *e-mail: [email protected] Current Opinion in Structural Biology 1998, 8:257-262
http://biomednet.com/elecref/O959440XO0800257 © Current Biology Ltd ISSN 0959-440X Abbreviations CPU central processing unit density functional theory DFT molecular dynamics MD MM molecular mechanical MMFF Merck molecular force field second order Meller-Plesset perturbation MP2 quantum mechanical QM self-consistent reaction field SCRF Introduction
This review will be concerned with the application of quantum chemical methods to the modeling of biomolecular systems. T h e rapid increases in computing power and the capability of theoretical methods and software have led to significant increases in the utility of quantum chemical approaches over the past decade; the most recent methodoh)gical advances will be briefly discussed below. T h e remainder of the review will describe a wide range of results obtained for specific biological problems. This discussion is organized into two sections: an overview covering a wide range of different types of studies is presented first, followed by a more detailed focus on a smaller number of selected areas. Overview
In principle, the solution of Schrodinger's equation completely specifies the chemical behavior of all molecular systems. In practice, the quantity most relevant to the theoretical modeling of complex systems, such as those found in biology; is the energy of a given molecular structure as a fimction of the position of the atoms, that is, the potential energy surface. Q u a n t u m chemical computer programs can now calculate such energies rather accurately for systems with the order of 20-50 atoms (and, arguably, for systems as large as 100 atoms). T h e results of these calculations can then be used either to directly investigate biochemical processes (via a truncated model of the system) or to
develop empirical potential energy functions that reproduce the quantum chemical energetics at a much lower computational cost, via parametrization of molectdar modeling furce fields. T h e quantum chemical studies we shall be considering can be divided into a number of distinct classes. At the most general level, virtually all modern biomolecular modeling force fields utilize some parametrization from quantum chemical data. Similarly, quantum chemistry can be used to derive specific force-field parameters, for example, for a novel pharmaceutical c o m p o u n d [1,2",3,4]. Parameters of interest include atomic charges, conformational energies (which are often fit to torsional potentials), and relative tautomer energies. Finall>; quantum chemical methods can be used to test the accuracy of force field structures and energetics. Specific application of quantum chemical calculations to biological models takes several different forms. T h e most common approach is to construct a small molecule model of an enzymatic reaction, typically 10-30 atoms, and calculate the reactant, product, and transition state energies in the gas phase [1,2,5-11,12°',13",14"]. Q u a n t u m chemical methods used range from the semiempirical to the ab initio with very high levels of electron correlation. A recent trend has been to augment this approach (construction of a small molecule model) with a continuum treatment of solvation, often via self-consistent reaction field (SCRF) methodologies [14",15,16]. One recent example of this trend is the work of I,ee and Houk [12"°], in which a novel mechanism for the enzymatic decarboxylation of orotidine raonophosphate was proposed. A variety of modeling assumptions were used and the dramatic acceleration observed in the enzymatic reaction was obtained in the calculations. A second example is calculations by Florifin and Warshel [13"], demonstrating that an 0¢ hydroxyl group can attack a phosphate monomethyl ester with a relatively low activation barrier (correcting erroneous conclusions drawn from experimental studies of the trimethyl ester). T h e y suggest that such a mechanism is implicated in the biologically important process of enzyme catalyzed phosphate hydrolysis. Increases in the capabilities of ab initio quantum chemical methods have permitted more ambitious undertakings in which a significant fraction of an enzyme's active site is included in the quantum mechanical model. Two such examples are work by Wladkowski et al. [17°], a study of the acylation of ~-lactams by class A I]-lactamase (in which four active site residues were explicitly included in the calculations) and by Nederkoorn et a]. [18"], an investigation of the binding of histamine to an oligopeptide model (containing five residues) of the histamine H e receptor. While
258 Theoryand simulation
there are as yet relatively few calculations of this type, and these often require compromises in the level of quantum chemical theory, such as the use of small basis sets and less accurate approximation, trends in this direction are certain to continue as the cost of computing decreases. %.
T h e most satisfactory level of modeling of an enzymatic reaction involves some representation of the macromolecular environment. T h e most popular approach at present is the so-called hybrid or mixed quantum mechanical/molecular mechanical (QM/MM) methodology T h e s e methods retain the advantage of treating only a small core of the system via quantum chemical methods, while allowing the remainder to be modeled at the molecular mechanics level; thus, the computational effort is not much greater than for a small model quantum chemical computation, but the condensed phase environment is represented in a reasonably accurate fashion. An increasing number of papers in this area are appearing, each with a unique implementation. On the one hand, the proliferation of novel methods makes evaluation of the reliability of each calculation quite difficult, but on the other it displays the vigor and excitement of this research direction. Finally, it is possible to carry out quantum molecular dynamics (MD) on a large model of a biological system in an attempt to simulate reactive chemistry. T h e only tool for which this is presently viable utilizes the Car-Parinello density functional theory ( D F T ) methodology, which was used by Sagnella et a]. [19"] to study proton transfer in a model ion channel. Severe computational requirements limit calculations to only a very short timescale, although one can again expect this to be lengthened in fl~tt~re work. F o c u s o n p r o g r e s s in s p e c i f i c a r e a s A b iniUo quantum chemical methods T h e development of ab initio quantum chemical methods
relevant to biological simulation and modeling have been focused on two areas. First, D F T approaches, based upon breakthroughs by Becke over the past decade [20-23] (with important contributions from Pople and co-workers [24-26]), have been increasingly applied to incorporate electron correlation effects at a reasonable computational cost. For large systems, a version of D F T based upon Becke's gradient correction scheme can be made to scale linearly with system size through the use of fast multipole techniques and other numerical algorithms [27"]. Linear scaling D F T methods are still in the development phase, so few practical applications have been reported as yet. A second approach is the use of localized correlation methods, pioneered originally by Saeb6 and Pulay [28] and by Pulay and co-workers [29]. Although these methods are typically somewhat more expensive than D F T approaches and the computational expense scales in the NZ-N -~ range (where N is the number of atoms in the system) for tractable calculations, they arc capable of greater accuracy than current D F T approaches for certain problems, such as
those involving dispersive interactions or conformational energetics [30]. A localized second order M~ller-Plesset perturbation (MP2) method has been demonstrated that is quite competitive in central processing unit (CPU) time with D F T calculations for medium to large systems [30]. For highly accurate results, a multireference version of local MP2 methods [31"] has recently been shown to provide exceptionally reliable results for conformational energetics when compared to a 36 molecule experimental database assembled by Halgren and co-workers [32]. Force field development N e w protein and nucleic acid force fields make increasing use of quantum chemical calculations for parameter development. Recent examples of force fields include the Merck molecular force field ( M M F F ) [33",34-37], O P L S - A A [38"'], A M B E R [39] and C H A R M m [40]. Typically, calculations carried out in order to model torsional parameters, atomic charges, and hydrogen bonding interactions are performed with a basis set of only moderate size (6-31G ~) at the H a r t r e e - F o c k level, although M M F F utilizes some larger (triple zeta) basis set level MP2 calculations in its torsional fitting efforts. At the same time, the n u m b e r of molecules included in the parametrization database of many of these force fields has been significantly expanded, leading to greater accuracy for a wider range of structures. Because the nonbonded interactions must yield correct condensed phase behavior, force field parametrization cannot be carried out exclusively through fitting to quantum chemistry; van der \¥aals' parameters and, often, atomic charges are adjusted to reproduce experimental liquid state data. T h e resulting procedures are therefore heuristic and must be tested for transferability to modeling larger systems. One important way of doing this is to carry out accurate quantum chemical calculations for representative large systems and to compare the predictions of the force fields for relative conformational energies. Recently, calculations at the local MP2 level using a high quality triple zeta basis set have been performed for the alanine tetrapeptide [41"] and used to assess the performance uf most of the widely used molecular mechanics protein force fields. Significant differences in force field accuracy for both structures and energies were observed. This work demonstrates that accurate quantum chemical conformational energies can be obtained for molecules in the -50 atom size range, and it is likely that such calculations will increasingly be used to calibrate force fields used in biomolecular simulations. Modeling of enzyme active sites containing transition metals Transition metal containing systems have traditionally been much harder to treat with ab initio quantum chemical methods than, for example, organic molecules containing exclusively first row atoms. T h e r e are many reasons for this: it is more difficult to converge self-consistent field
Quantum mechanical calculations of biological systems Friesnerand Beachy 959
(SCF) calculations and geometry optimizations; Hartree-Fock methods provide a poorer zero-order description for metal-containing molecules (thus requiring the use of expensive electron correlation methods); significant issues arise concerning spin states, distribution of charge in the molecule, and organization ofdelectrons; and in many cases, the chemistry is not well understood even for simple model systems, making it difficult to tell when the modeling effort has been successful. The recent advent of improved D F T methods, however, has provided a much more satisfactory description of metal-containing systems at a relatively low additional cost. This, combined with the increased computing power available, has led to the study of models for the catalytic active site of several metalloenzymes that are substantially more realistic than models in previous work. Systems studied include models for the active sites of blue copper proteins [42"], the watersplitting enzyme in photosystem II [43"], superoxide dismutase [44], methane monooxygenase [45"], and the dicopper core of oxyhemocyanin [46"]. As an example, we shall briefly discuss the methane monoxygenase studies of Siegbahn and Crabtree [45"]. The active site of the native enzyme is a di-iron complex that catalyzes the conversion of methane and oxygen to methanol and water. In [45°'], the active site model contained the di-iron core but replaced amino acid sidechain ligands with hydroxyl groups. A variety of stationary points and transitions states, representing proposed reactants, products, and intermediates in the catalytic process, were examined. The B3-LYP hybrid D F T method was used in all calculations [23,26]. Geometry optimizations were carried out using a double zeta basis set followed by single point calculations using an extended basis set containing more than 400 basis functions. On the basis of these calculations, a proposal for the reaction mechanism was put forward. There are numerous potential problems with the above work, including size of the basis set, inadequate representation of protein ligands, uncertainty about the accuracy of the B3-[XP methodology for transition metal-containing systems, and failure to filly examine the multidimensional potential surface to locate all relevant energy minima. Nevertheless, the calculations represent a significant advance over previously published work on systems of this type. Future studies will undoubtedly include a much larger fraction of the active site and address the methodological issues raised above. Mixed Q M / M M
calculations
During the past year, QM/MM modeling of various types was applied to an impressive number of diverse enzymatic systems: carbonic anhydrase [47,48"], triose phosphate isomerase [49], aspartylglucosamidase [50"], alcohol dehydrogenase [51], lactate dehydrogenase [52,53], malate dehydrogenase [54], chorismate mutase [55"], and HIV protease [56]. Quantum chemical methods ranged from semiempirical methods (typically AMI or PM3) to correlated ah initio computations.
Using semiempirical methods, it is possible to carry out actual dynamical runs in which the quantum chemistry is evaluated at every step. The accuracy of semiempirical quantum chemistry, however, is typically not quantitative. If one is asking qualitative questions concerning alternative mechanisms in which the proposed pathways display large differences in energetics, then it may be possible to draw substantive conclusions despite this difficulty. Alternatively, one can try to specifically reparametrize the semiempirical model to yield accurate results for a particular set of molecular structures [54]. With ab initio methods (which can of course still contain errors in the predicted energetics), direct MD simulations perse are not yet feasible, so one has to resort to procedures that examine the dynamics less directly. Such procedures include determination of stationary points, or alternation of QM and MM calculations in which the QM results are used to constrain the MD simulations and starting guesses at MD structures are then used for QM/MM optimization of stationary points [50°]. A systematic realization of this approach is construction of a series of QM/MM energies along a reaction coordinate from which one can extract an approximation for the reaction kinetics [55"]. For the MM part of the calculations, a wide variety of force fields were employed, ranging from the well known protein molecular models (CHARMm, AMBER and GROMOS) to specially devised new models [47]. Finally, some calculations [50"] utilized continuum solvent methods to treat the surrounding aqueous medium. There are still significant methodological questions concerning how QM/MM calculations should be carried out. For example, what is the correct approach to defining the interactions of the QM and MM subsystems at the boundary between them? These questions are being actively studied in model systems [57]. The most commonly used methods at present employ link atoms, as seen in the early work of Karplus and co-workers [58]. More generally, if one wishes to achieve quantitatively reliable results, one should be aware that there are issues concerning parametrization specific to the QM/MM model. While the protocols in current use appear to be qualitatively reasonable, there is not yet sufficient quantitative comparison with experimental data to provide rigorous validation of any specific implementation. Consequently, the papers cited above typically explore qualitative issues, in many cases with apparent success. These successes include selecting proposed catalytic reaction pathways and elucidating the role of the enzyme environment in catalysis (e.g. in lowering barriers to reaction). Future work will build closer connections between theory and experiment, allowing better calibration of the various components of the methodology; this in turn will allow improvement of the methods. Conclusions
The development of greatly improved quantum chemical methods, coupled with robust QM/MM implementations,
260
Theory and simulation
offers, fi~r the first time, the promise of being able to reliably model enzymatic reactions. At the same time, improvement of force fields by fitting to accurate quantum chemistry will increase reliability in the nonreactive parts nf the calculation; a key step needed here is explicit inclusion of polarizability, which correctly reproduces many body energy terms. Finally, development of quantitative semiempitical methods is important for actually carrying out simulations of reactive dynamics, a particularly crucial step when the reaction coordinate is in serious doubt. The past year reflects significant prngress in all of these areas; it is likely that on a five 3:ear timescale, high quality calculations along these lines will bc carried out on a routine basis. When this point is reached, the impact of (luantunl chemical calculations on biological problems will be suhstantiallx/enhanced.
Acknowledgements RAt: ac'knowledgcs support by National hlsdtutes or" Hcaldr grant 5-R01GM40526.
References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as: • of special interest • • of outstanding interest 1.
Hernandez B, Orozco M, Luque FJ: Role of the tautomerism of 2azaadenine and 2-azahypoxanthine in substrate recognition by xanthine oxidase. J Comput Aided Mol Des 1997, 11:153-162.
2.
Davidson MM, Guest JM, Craw JS, Hillier IH, Vincent MA: Conformational and solvation aspects of the chorismateperphenate rearrangement studies by ab inifio electronic structure and simulation methods. J Chem Soc Perkin Trans 1997, 2:1395-1400. This paper compares the results of continuum and explicit solvation on the conformational energetics and activation barrier of the Claisen rearrangment of chorismate to prephenate. The detailed comparison of quantum and classical simulation results, and the succesful comparison with experiments, are of significant interest. 3.
Smith B J: A conformational study of 2-oxanoh insight into the role of ring distortion on enzyme-catalyzed glycosidic bond cleavage. J Am Chem Soc 199"7, 119:2699-2706.
4.
Murcko MA: Conformational analysis of carbonic anhydrase inhibitors using ab initio molecular orbital methods. 1. Rotational isomerism in methane sulfonamide anion, CH3-SO2-NH. Theor Chem Ace 1997, 96:56-60.
5.
George P, Glusker JP, Bock CW: An ab initio computational molecular orbital study of radical, protonated radical (radical cation), and carbocation species that have been proposed in mechanisms for the transfer process in the enzyme-coenzyme B12 -catalyzed dehydration of 1,2-dihydroxyethane. J Am Chem Soc 1997, 1 "19:7065-7074.
6.
7.
8.
9.
Pitarch J, Ruiz-Lopez MF, PascuaI-Ahuir J-L, Silla E, Tur~6n h Ab initio calculations on neutral and alkaline hydrolyses of ~-Iactam antibiotics. A theoretical study including solvent effects. J Phys Chem B 1997, 101:3581-3588. Zheng Y-J, Ornstein RL: Role of active site tyrosine in glutathion Stransferase: insights from a theoretical study of model systems. JAm Chem Soc 1997, 119:1523-1528. Zheng Y-J, Bruice TO: A Theoretical examination of the factors controlling the catalytic efficiency of a transmethylation enzyme: cathechol O-methyltransferase. J Am Chem Soc 1997, 119:81378145. Zheng Y-J, Bruice TC: On the dehalogenation mechanism of 4chlorobenzoyl CoA by 4-chlorobenzoyl CoA dehalogenase: insight from study based on the nonenzymatic reaction. J Am Chem Soc 1997, 119:3868-3877.
10.
Per~kyl~M: Triosephosphate isomerase (TI M)-catalysed proton abstraction from carbon acid: an analysis on the origin of the catalytic activity. Chem Cornmun 1996, 361-362.
11. Thomson C, Zwaans R: Ab initio calculations on 2-, 3- and 4substituted quinolines in relation with their activity as protein tyrosine kinase inhibitors. J Mo/Struct 1996, 362:51-68. 12. Lee JK, Houk KN: A proficient enzyme revisited: the predicted oo mechanism for orotidine monophosphate decarboxylase. Science 1997, 276:942-945. This paper proposes a specific mechanistic explanation using quantum chemical modeling for a reaction that is dramatically accelerated by the enzyme. Although the quantum chemistry is not particularly high level, nor on a large model of the enzyme active site, the mechanistic proposal is an interesting one that can be tested experimentally. 13. Florian J, Warshel A: A fundamental assumption about OH- attack in phosphate ester hydrolysis is not fully justified. J Am Chem Soc 1997, 119:5473-5474. This paper investigates phosphate ester hydrolysis using ab initio quantum chemical techniques and shows that the proposed pathway is inconsistent with these calculations. Of interest here is the use of calculations in order to rule out a proposed mechanistic pathway for a biologically important system. 14. Marten B, Kim K, Cortis C, Friesner RA, Murphy RB, Ringnalda MN, Sitkoff D, Honig B: New model for calculation of solvation free energies: correction of self-consistent reaction field continuum dielectric theory for short range hydrogen bonding effects. J Phys Chem 1996, 100:11775-11788. This paper shows that dielectric continuum methods have systematic inaccuracies due to the incorrect treatment of hydrogen bonding, and develops a systematic empirical protocol to correct this deficiency. The same problems can also be observed in molecular mechanics force fietds, which rely primarily on an electrostatic description of hydrogen bonding. 15. Cortis C, Langlois JM, Beachy M, Friesner R: Quantum mechanical geometry optimization in solution using a finite element continuum electrostatics method. J Chem Phys 1996, 105:54725484. 16. Tomasi J, Persico M: Molecular interactions in solution: an overview of methods based on continuous distributions of the solvent. Chem Rev 1994, 94:2027-2094. 17.
Wladkowski BD, Chenoweth SA, Sanders J N, Krauss M, Stevens WJ: Acylation of ~-Iactarnase: an ab initio theoretical study on the effects of the oxy-anion hole. J Am Chem Soc 1997, 119:64236431. This paper incorporates explicit amino acid residues from the active site into the quantum chemical model and calculates the activation energy for the proposed enzymatic pathway at the Hartree-Fock level. The paper is noteworthy for the large size of the quantum chemical model. 18. Nederkoorn PHJ, van Lenthe JH, van der Goot H, Donne-Op den Kelder GM, Timmerman H: The agonistic binding site at the histamine H 2 receptor. I. Theoretical investigations of histamine binding to an oligopeptide mimicking a part of the fifth transmembrane 0~-helix. J Comput Aided Mol Des 1996, 10:461-478. This paper presents ab initio modeling of receptor-ligand binding using quite a large model, by current literature standards, for the receptor active site. From the calculations, a proposal for the binding site of the ligand is presented. 19. Sagnella DE, Laasonen K, Klein ML: Ab initio molecular dynamics study of proton transfer in a polyglycine analog of the ion channel gramicidin A. Biophys J 1996, 71:1172-1178. This paper describes a state of the art ab initio molecular dynamics calculation on a biologically relevant system, specifically investigating proton transfer in an ion channel. 20. Becke AD: Density-functional thermochemistry. (I.) The effect of the exchange-only gradient correction. J Chem Phys 1992, 96:2155-2160. 21.
Becke AD: Density-functional thermochemistry. (11.) The effect of the Perdew-Wang generalized gradient correlation correction. J Chem Phys 1992, 97:9173-9177.
22. Becke AD: Density-functional thermochemistry. (111.)The role of exact exchange. J Chem Phys 1993, 98:5648-5652. 23.
Becke, AD: A new mixing of Hartree-Fock and local densityfunctional theories. J Chem Phys 1993, 98:1372-1377.
24. Curtiss LA, Raghavachari K, Redfern PC, Pople JA: Investigation of the use of B3LYP zero-point energies and geometries in the
Quantum mechanical calculations of biological systems Friesner and Beachy
calculation of enthalpies of formation. Chem Phys Lett 1997, 270:419-426. 25. Curtiss LA, Raghavachari K, Redfern PC, Pople JA: Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation. J Chern Phys 199"7, 106:1063-1079. 26. Johnson BG, Gill PMW, Pople JA: The performance of a family of density functional methods. J Chem Phys 1993, 98:5612-5626. White CA, Johnson BG, Gill PMW, Head Gordon M: Linear scaling density functional calculations via the continuous fast multipole method. Chem Phys Lett 1996, 253:268-278. This is the first paper on linear scaling density functional theory (DFT), which has the potential to extend DFT to very large systems. The paper is primarily technical, but will be of interest to readers who want to understand what is involved in using quantum chemisty for ultralarge computations. 27.
28.
Saebo S, Pulay P: The local correlation treatmenL I1. Implementation and tests. J Chem Phys 1988, 88:1884-1890.
29. Wolinski K, Sellers H, Pulay P: Consistent generalization of the M~ller-Plesset partitioning to open-shell and multiconfigurational SCF reference states in many-body perturbation theory. Chern Phys Lett 198?, 140:225-231. 30.
Murphy M, Beachy MD, Friesner RA, Ringnalda MN: Pseudospectral localized Meller-Plesset methods: theory and calculation of conformational energies. J Chem Phys 1996, 103:1481-1490.
Murphy RB, Pollard VVT, Friesner RA: Pseudospectral localized generalized Meller-Plesset methods with a generalized valence bond reference wave function: theory and calculation of conformational energies. J Chem Phys 1997, 106:5073-5084. This paper demonstrates a quantum chemical method, based upon multireference perturbation theory, with N 3 scaling, that provides uniformly high accuracies for conformational energies. Such methods will be crucial in designing the next generation of force fields in which quantitative agreement with quantum chemical data is enforced. 31.
32.
St-Amant A, Cornell WD, Kollman PA, Halgren TA: Calculation of molecular geometries, relative conformational energies, dipole moments, and molecular electrostatic potential fitted charges of small organic molecules of biochemical interest by density functional theory. J Comput Chem 1995, 16:1483-1506.
Halgren TA: Merck Molecular Force Field. I. Basis, form, scope, parameterization, and performance of MMFF94. J Comput Chem 1996, 17:490-519. This paper describes a new molecular modeling force field, MMFF, with wide coverage of pharmaceutical compounds, using extensive fitting to good quality quantum chemical data. The MMFF force field is one of the two best performers in the tests carried out in [41"] concerning the prediction of tetrapeptide energetics. 33.
34.
Halgren TA: Merck Molecular Force Field. I1. MMFF94 van der Waals and electrostatic parameters for intermolecular interactions. J Comput Chem 1996, 17:520-552.
35.
Halgren TA: Merck Molecular Force Field. II1. Molecular geometrics and vibrational frequencies for MM FF94. J Comput Chem 1996, 17:553-586.
36.
Halgren TA, Nachbar RB: Merck Molecular Force Field. IV. Conformational Energies and Geometries for M MFF94. J Comput Chem 1996, 17:587-615.
37.
Halgren TA: Merck Molecular Force Field. V. Extension of MMFF94 using experimental data, additional computational data, and empirical rules. J Comput Chem 1996, 17:616-641.
Beachy M, Chasman D, Murphy R, Halgren T, Friesner R: Accurate ab initio quantum chemical determination of the relative energetics of peptide conformations and assessment of empirical force fields. J Am Chem Soc 1997, 119:5908-5920. This paper tests the transferability of protein force fields with large scale accurate quantum chemistry calculations. The energies of 10 conformations of an alanine tetrapeptide were computed at a accurate quantum chemical level and the results compared against a comprehensive list of protein molecular mechanics force fields. A preliminary assessment of the accuracy of the force fields tested is provided. 41. •.
Ryde U, Olsson MHM, Pierloot K, RoDS B e : the cupric geometry of blue copper proteins is not strained. J Mol Biol 1996, 261:586-596. This paper presents ab initio quantum chemical calculations on an active site model for blue copper proteins, using both density functional theory and multireference perturbation theory methods, and concludes that the active site geometry around the copper center is not strained. The use of multireference perturbation theory, a highly accurate quantum chemical method, on a reasonable size active site model, is particulary noteworthy here. 42.
43.
Blomberg MRA, Siegbahn PEM, Styring S, Babcock GT, Akermaker B, Korall P: A quantum chemical study of hydrogen abstraction from manganese-coordinated water by a tyrosyl radical: a model for water oxidation in photosystem I1. J Am Chem Soc 1997, 119:8285-8292. This paper provides ab initio quantum chemical calculations on a large transition metal active site model using density functional theory, with a specific mechanism proposed for key steps of water oxidation in photosystem II. This is a biologically important problem and the calculations provide support for a proposed physical mechanism. 44.
39.
Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM Jr, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA: A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J Am Chem Soc 1995, 117:5179-5197.
40.
Mackerell AD Jr, Wiorkiewicz-Kuczera J, Karplus M: An all-atom empirical energy function for the simulation of nucleic acids..I Am Chem Soc 1995, 117:11946-11975.
Fisher CL, Chen, J-L, Li J, Bashford D, Noodleman L: Densityfunctional and electrostatic calculations for a model of a manganese superoxide dismutase active site in aqueous solution, J Phys Chem 1996, 100:13498-13505.
Siegbahn PEM, Crabtree RH: Mechanism of C-H activation by diiron methane monoxygenases: quantum chemical studies, J Am Chem Soc 1997, 119:3103-3113. This paper presents ab initio quantum chemical calculations on a large transition metal active site model of methane monooxygenase using density functional theory, with proposals for the pathway by which the enzyme catalyzes the transformation of methane to methanol. Particularly noteworthy here is the use of large basis sets for the DFT calculations. This is a major step forward in obtaining more reliable results for energetics as compared to previous work in the literature. 45 •o
Cramer CJ, Smith BA, Tolman WB: Ab initio characterization of the isomerism between the H-n2:n2-peroxo- and bis(u-oxo)dicopper cores. J Am Chem Soc 1996, 118:11283-1128?. This paper describes ab initio quantum chemical calculations on small active site models of the conformational energetics of dicopper cores. The calculations use multireference perturbation theory, and are thus high quality calculations, and also a dielectric continuum solvation model. 46
4?.
38. Jorgensen WL, Maxwell DS, TiradoRives J: Development and testing •. of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J Am Chern Soc 1996, 118:1122511236. This paper describes a new molecular modeling force field, OPLS-AA, which is extensively fit to both quantum chemical data and liquid state thermodynamics. OPLS-AA is one of the two best performers in the tests carried out in [41"'], and simultaneously provides excellent prediction of liquid state properties.
261
Garmer DR: Carbonic anhydrase reactivity, mutation, and inhibition probed with a model of ab initio quantum chemistry within a protein. J Phys Chem 199?, 101:2945-2953.
48. Merz Jr KM, Banci L: Binding of bicarbonate to human carbonic anhydrase Ih a continuum of binding states. J Am Chem Soc 1997, 119: 863-871. This paper presents Q M / M M simulations using a semi-empirical QM Hamiltonian on the binding of bicarbonate to carbonic anhydrase. It is a good example of how a Q M / M M calculation can address qualitative questions reasonably well, even though the model is probably not highly precise. With a transition metal-binding site, conventional force fields are problematic, and Q M / M M even at the semi-empirical level is likely the best alternative. 49. Alagona G, Ghio C, Kollman PA: Chemical reaction mechanisms in vacuo, in solution and in enzyme fields: isomerization catalyzed by triose phosphate- isomerase (TIM). J Mol Struct 1996, 371:287298. 50. Per~kyl~ M, Kollman PA: A simulation of the catalytic mechanism of aspartylglucosaminidase using ab initio quantum mechanics and molecular dynamics. J Am Chem Soc 199"7, 119:1189-1196. This paper uses a Q M / M M approach in which simulations are carried out at the MD level. Key structures are then extracted from the simulations and calculated at the QM level using Hartree-Fock and MP2 levels of theory, treating the protein environment as point charges and using a continuum model for solvation. The QM calculations allow an evaluation of transition state energetics that would be unavailable from the MM force field. An explanation of the catalytic mechanism is provided from the calculations.
262
Theory and simulation
51. Ryde U: The coordination of the catalytic zinc ion in alcohol dehydrogenase studied by combined quantum-chemical and molecular mechanics calculations. J Comput Aided Mo/ Des 1996, 10:153-164. 52. Moliner V, Turner A J, Williams IH: Transition-state structural refinement with GRACE and CHARMm: realistic modelling of lactate dehydrogenase using a combined quantum/classical method. Chem Commun 1997, 1271-1272. 53. Ranganathan S, Gready JE: Hybrid quantum and molecular mechanical ( Q M / M M ) studies on the pyruvate to L-lactate intemonversion in L-lactate dehydrogenase. J Phys Chem B 199?, 101:5614-5618. 54. Cunningham MA, Ho LL, Nguyen DT, Gillilan RE, Bash PA: Simulation of the enzyme mechanism of malate dehydrogenase. Biochemistry 1997, 36:4800-4816. 55. Davidson MM, Gould IR, Hillier IH: The mechanism of the catalysis • of the Claisen rearrangement of chorismate to perphenate by the chorismate mutase from Bacillus subtilis. A molecular mechanics
and hybrid quantum mechanical/molecular mechanical study. J Chem Soc Perkin Trans 1996, 2:525-532. This paper investigates the role of the active site of the enzyme chorismate mutase in catalyzing the Claisen rearrangement of chorismate to prephenate. Here, QM structures (computed at the Hartree-Fock level) along the reaction path are docked into the active site and the energies are evaluated via a mixed QM/MM Hamiltonian. This is yet another approach to deploying QM/MM technology, and leads to reasonable qualitative agreement with experiments in terms of the ability of the enzyme to lower the barrier to reaction.
56. Liu H, ML~ller-PlatheF, van Gunsteren WF: A combined quantum/classical molecular dynamics study of the catalytic mechanism of HIV protease. J Mol Biol 1996, 261:454-469. 57. EureniusKP, Chatfield DC, Brooks BR, Hodoscek M: Enzyme mechanisms with hybrid quantum and molecular mechanical potentials. I. Theoretical considerations. Int J Quantum Chem 1996, 60:1189-1200. 58. Bash PA, Field MJ, Karplus M: Free energy perturbation method for chemical reactions in the condensed phase: a dynamical approach based on a combined quantum and molecular mechanics potential. J Am Chem Soc 1987, 109:8092-8094.
Quantum mechanical calculations on biological systems Richard A Friesner* and Michael D Beachy Improvements in quantum chemical methods have led to increased applications to biological problems, including the development of potential energy functions for molecular mechanics and modeling of the reactive chemistry in enzyme active sites, with particularly interesting progress being made for metal-containing systems. An important direction is the development and application of hybrid quantum chemicalmolecular mechanics methods. Addresses
Department of Chemistry, Columbia University,3000 Broadway, Mail Code 3110, New York, NY 10027, USA *e-mail: [email protected] Current Opinion in Structural Biology 1998, 8:257-262
http://biomednet.com/elecref/O959440XO0800257 © Current Biology Ltd ISSN 0959-440X Abbreviations CPU central processing unit density functional theory DFT molecular dynamics MD MM molecular mechanical MMFF Merck molecular force field second order Meller-Plesset perturbation MP2 quantum mechanical QM self-consistent reaction field SCRF Introduction
This review will be concerned with the application of quantum chemical methods to the modeling of biomolecular systems. T h e rapid increases in computing power and the capability of theoretical methods and software have led to significant increases in the utility of quantum chemical approaches over the past decade; the most recent methodoh)gical advances will be briefly discussed below. T h e remainder of the review will describe a wide range of results obtained for specific biological problems. This discussion is organized into two sections: an overview covering a wide range of different types of studies is presented first, followed by a more detailed focus on a smaller number of selected areas. Overview
In principle, the solution of Schrodinger's equation completely specifies the chemical behavior of all molecular systems. In practice, the quantity most relevant to the theoretical modeling of complex systems, such as those found in biology; is the energy of a given molecular structure as a fimction of the position of the atoms, that is, the potential energy surface. Q u a n t u m chemical computer programs can now calculate such energies rather accurately for systems with the order of 20-50 atoms (and, arguably, for systems as large as 100 atoms). T h e results of these calculations can then be used either to directly investigate biochemical processes (via a truncated model of the system) or to
develop empirical potential energy functions that reproduce the quantum chemical energetics at a much lower computational cost, via parametrization of molectdar modeling furce fields. T h e quantum chemical studies we shall be considering can be divided into a number of distinct classes. At the most general level, virtually all modern biomolecular modeling force fields utilize some parametrization from quantum chemical data. Similarly, quantum chemistry can be used to derive specific force-field parameters, for example, for a novel pharmaceutical c o m p o u n d [1,2",3,4]. Parameters of interest include atomic charges, conformational energies (which are often fit to torsional potentials), and relative tautomer energies. Finall>; quantum chemical methods can be used to test the accuracy of force field structures and energetics. Specific application of quantum chemical calculations to biological models takes several different forms. T h e most common approach is to construct a small molecule model of an enzymatic reaction, typically 10-30 atoms, and calculate the reactant, product, and transition state energies in the gas phase [1,2,5-11,12°',13",14"]. Q u a n t u m chemical methods used range from the semiempirical to the ab initio with very high levels of electron correlation. A recent trend has been to augment this approach (construction of a small molecule model) with a continuum treatment of solvation, often via self-consistent reaction field (SCRF) methodologies [14",15,16]. One recent example of this trend is the work of I,ee and Houk [12"°], in which a novel mechanism for the enzymatic decarboxylation of orotidine raonophosphate was proposed. A variety of modeling assumptions were used and the dramatic acceleration observed in the enzymatic reaction was obtained in the calculations. A second example is calculations by Florifin and Warshel [13"], demonstrating that an 0¢ hydroxyl group can attack a phosphate monomethyl ester with a relatively low activation barrier (correcting erroneous conclusions drawn from experimental studies of the trimethyl ester). T h e y suggest that such a mechanism is implicated in the biologically important process of enzyme catalyzed phosphate hydrolysis. Increases in the capabilities of ab initio quantum chemical methods have permitted more ambitious undertakings in which a significant fraction of an enzyme's active site is included in the quantum mechanical model. Two such examples are work by Wladkowski et al. [17°], a study of the acylation of ~-lactams by class A I]-lactamase (in which four active site residues were explicitly included in the calculations) and by Nederkoorn et a]. [18"], an investigation of the binding of histamine to an oligopeptide model (containing five residues) of the histamine H e receptor. While
258 Theoryand simulation
there are as yet relatively few calculations of this type, and these often require compromises in the level of quantum chemical theory, such as the use of small basis sets and less accurate approximation, trends in this direction are certain to continue as the cost of computing decreases. %.
T h e most satisfactory level of modeling of an enzymatic reaction involves some representation of the macromolecular environment. T h e most popular approach at present is the so-called hybrid or mixed quantum mechanical/molecular mechanical (QM/MM) methodology T h e s e methods retain the advantage of treating only a small core of the system via quantum chemical methods, while allowing the remainder to be modeled at the molecular mechanics level; thus, the computational effort is not much greater than for a small model quantum chemical computation, but the condensed phase environment is represented in a reasonably accurate fashion. An increasing number of papers in this area are appearing, each with a unique implementation. On the one hand, the proliferation of novel methods makes evaluation of the reliability of each calculation quite difficult, but on the other it displays the vigor and excitement of this research direction. Finally, it is possible to carry out quantum molecular dynamics (MD) on a large model of a biological system in an attempt to simulate reactive chemistry. T h e only tool for which this is presently viable utilizes the Car-Parinello density functional theory ( D F T ) methodology, which was used by Sagnella et a]. [19"] to study proton transfer in a model ion channel. Severe computational requirements limit calculations to only a very short timescale, although one can again expect this to be lengthened in fl~tt~re work. F o c u s o n p r o g r e s s in s p e c i f i c a r e a s A b iniUo quantum chemical methods T h e development of ab initio quantum chemical methods
relevant to biological simulation and modeling have been focused on two areas. First, D F T approaches, based upon breakthroughs by Becke over the past decade [20-23] (with important contributions from Pople and co-workers [24-26]), have been increasingly applied to incorporate electron correlation effects at a reasonable computational cost. For large systems, a version of D F T based upon Becke's gradient correction scheme can be made to scale linearly with system size through the use of fast multipole techniques and other numerical algorithms [27"]. Linear scaling D F T methods are still in the development phase, so few practical applications have been reported as yet. A second approach is the use of localized correlation methods, pioneered originally by Saeb6 and Pulay [28] and by Pulay and co-workers [29]. Although these methods are typically somewhat more expensive than D F T approaches and the computational expense scales in the NZ-N -~ range (where N is the number of atoms in the system) for tractable calculations, they arc capable of greater accuracy than current D F T approaches for certain problems, such as
those involving dispersive interactions or conformational energetics [30]. A localized second order M~ller-Plesset perturbation (MP2) method has been demonstrated that is quite competitive in central processing unit (CPU) time with D F T calculations for medium to large systems [30]. For highly accurate results, a multireference version of local MP2 methods [31"] has recently been shown to provide exceptionally reliable results for conformational energetics when compared to a 36 molecule experimental database assembled by Halgren and co-workers [32]. Force field development N e w protein and nucleic acid force fields make increasing use of quantum chemical calculations for parameter development. Recent examples of force fields include the Merck molecular force field ( M M F F ) [33",34-37], O P L S - A A [38"'], A M B E R [39] and C H A R M m [40]. Typically, calculations carried out in order to model torsional parameters, atomic charges, and hydrogen bonding interactions are performed with a basis set of only moderate size (6-31G ~) at the H a r t r e e - F o c k level, although M M F F utilizes some larger (triple zeta) basis set level MP2 calculations in its torsional fitting efforts. At the same time, the n u m b e r of molecules included in the parametrization database of many of these force fields has been significantly expanded, leading to greater accuracy for a wider range of structures. Because the nonbonded interactions must yield correct condensed phase behavior, force field parametrization cannot be carried out exclusively through fitting to quantum chemistry; van der \¥aals' parameters and, often, atomic charges are adjusted to reproduce experimental liquid state data. T h e resulting procedures are therefore heuristic and must be tested for transferability to modeling larger systems. One important way of doing this is to carry out accurate quantum chemical calculations for representative large systems and to compare the predictions of the force fields for relative conformational energies. Recently, calculations at the local MP2 level using a high quality triple zeta basis set have been performed for the alanine tetrapeptide [41"] and used to assess the performance uf most of the widely used molecular mechanics protein force fields. Significant differences in force field accuracy for both structures and energies were observed. This work demonstrates that accurate quantum chemical conformational energies can be obtained for molecules in the -50 atom size range, and it is likely that such calculations will increasingly be used to calibrate force fields used in biomolecular simulations. Modeling of enzyme active sites containing transition metals Transition metal containing systems have traditionally been much harder to treat with ab initio quantum chemical methods than, for example, organic molecules containing exclusively first row atoms. T h e r e are many reasons for this: it is more difficult to converge self-consistent field
Quantum mechanical calculations of biological systems Friesnerand Beachy 959
(SCF) calculations and geometry optimizations; Hartree-Fock methods provide a poorer zero-order description for metal-containing molecules (thus requiring the use of expensive electron correlation methods); significant issues arise concerning spin states, distribution of charge in the molecule, and organization ofdelectrons; and in many cases, the chemistry is not well understood even for simple model systems, making it difficult to tell when the modeling effort has been successful. The recent advent of improved D F T methods, however, has provided a much more satisfactory description of metal-containing systems at a relatively low additional cost. This, combined with the increased computing power available, has led to the study of models for the catalytic active site of several metalloenzymes that are substantially more realistic than models in previous work. Systems studied include models for the active sites of blue copper proteins [42"], the watersplitting enzyme in photosystem II [43"], superoxide dismutase [44], methane monooxygenase [45"], and the dicopper core of oxyhemocyanin [46"]. As an example, we shall briefly discuss the methane monoxygenase studies of Siegbahn and Crabtree [45"]. The active site of the native enzyme is a di-iron complex that catalyzes the conversion of methane and oxygen to methanol and water. In [45°'], the active site model contained the di-iron core but replaced amino acid sidechain ligands with hydroxyl groups. A variety of stationary points and transitions states, representing proposed reactants, products, and intermediates in the catalytic process, were examined. The B3-LYP hybrid D F T method was used in all calculations [23,26]. Geometry optimizations were carried out using a double zeta basis set followed by single point calculations using an extended basis set containing more than 400 basis functions. On the basis of these calculations, a proposal for the reaction mechanism was put forward. There are numerous potential problems with the above work, including size of the basis set, inadequate representation of protein ligands, uncertainty about the accuracy of the B3-[XP methodology for transition metal-containing systems, and failure to filly examine the multidimensional potential surface to locate all relevant energy minima. Nevertheless, the calculations represent a significant advance over previously published work on systems of this type. Future studies will undoubtedly include a much larger fraction of the active site and address the methodological issues raised above. Mixed Q M / M M
calculations
During the past year, QM/MM modeling of various types was applied to an impressive number of diverse enzymatic systems: carbonic anhydrase [47,48"], triose phosphate isomerase [49], aspartylglucosamidase [50"], alcohol dehydrogenase [51], lactate dehydrogenase [52,53], malate dehydrogenase [54], chorismate mutase [55"], and HIV protease [56]. Quantum chemical methods ranged from semiempirical methods (typically AMI or PM3) to correlated ah initio computations.
Using semiempirical methods, it is possible to carry out actual dynamical runs in which the quantum chemistry is evaluated at every step. The accuracy of semiempirical quantum chemistry, however, is typically not quantitative. If one is asking qualitative questions concerning alternative mechanisms in which the proposed pathways display large differences in energetics, then it may be possible to draw substantive conclusions despite this difficulty. Alternatively, one can try to specifically reparametrize the semiempirical model to yield accurate results for a particular set of molecular structures [54]. With ab initio methods (which can of course still contain errors in the predicted energetics), direct MD simulations perse are not yet feasible, so one has to resort to procedures that examine the dynamics less directly. Such procedures include determination of stationary points, or alternation of QM and MM calculations in which the QM results are used to constrain the MD simulations and starting guesses at MD structures are then used for QM/MM optimization of stationary points [50°]. A systematic realization of this approach is construction of a series of QM/MM energies along a reaction coordinate from which one can extract an approximation for the reaction kinetics [55"]. For the MM part of the calculations, a wide variety of force fields were employed, ranging from the well known protein molecular models (CHARMm, AMBER and GROMOS) to specially devised new models [47]. Finally, some calculations [50"] utilized continuum solvent methods to treat the surrounding aqueous medium. There are still significant methodological questions concerning how QM/MM calculations should be carried out. For example, what is the correct approach to defining the interactions of the QM and MM subsystems at the boundary between them? These questions are being actively studied in model systems [57]. The most commonly used methods at present employ link atoms, as seen in the early work of Karplus and co-workers [58]. More generally, if one wishes to achieve quantitatively reliable results, one should be aware that there are issues concerning parametrization specific to the QM/MM model. While the protocols in current use appear to be qualitatively reasonable, there is not yet sufficient quantitative comparison with experimental data to provide rigorous validation of any specific implementation. Consequently, the papers cited above typically explore qualitative issues, in many cases with apparent success. These successes include selecting proposed catalytic reaction pathways and elucidating the role of the enzyme environment in catalysis (e.g. in lowering barriers to reaction). Future work will build closer connections between theory and experiment, allowing better calibration of the various components of the methodology; this in turn will allow improvement of the methods. Conclusions
The development of greatly improved quantum chemical methods, coupled with robust QM/MM implementations,
260
Theory and simulation
offers, fi~r the first time, the promise of being able to reliably model enzymatic reactions. At the same time, improvement of force fields by fitting to accurate quantum chemistry will increase reliability in the nonreactive parts nf the calculation; a key step needed here is explicit inclusion of polarizability, which correctly reproduces many body energy terms. Finally, development of quantitative semiempitical methods is important for actually carrying out simulations of reactive dynamics, a particularly crucial step when the reaction coordinate is in serious doubt. The past year reflects significant prngress in all of these areas; it is likely that on a five 3:ear timescale, high quality calculations along these lines will bc carried out on a routine basis. When this point is reached, the impact of (luantunl chemical calculations on biological problems will be suhstantiallx/enhanced.
Acknowledgements RAt: ac'knowledgcs support by National hlsdtutes or" Hcaldr grant 5-R01GM40526.
References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as: • of special interest • • of outstanding interest 1.
Hernandez B, Orozco M, Luque FJ: Role of the tautomerism of 2azaadenine and 2-azahypoxanthine in substrate recognition by xanthine oxidase. J Comput Aided Mol Des 1997, 11:153-162.
2.
Davidson MM, Guest JM, Craw JS, Hillier IH, Vincent MA: Conformational and solvation aspects of the chorismateperphenate rearrangement studies by ab inifio electronic structure and simulation methods. J Chem Soc Perkin Trans 1997, 2:1395-1400. This paper compares the results of continuum and explicit solvation on the conformational energetics and activation barrier of the Claisen rearrangment of chorismate to prephenate. The detailed comparison of quantum and classical simulation results, and the succesful comparison with experiments, are of significant interest. 3.
Smith B J: A conformational study of 2-oxanoh insight into the role of ring distortion on enzyme-catalyzed glycosidic bond cleavage. J Am Chem Soc 199"7, 119:2699-2706.
4.
Murcko MA: Conformational analysis of carbonic anhydrase inhibitors using ab initio molecular orbital methods. 1. Rotational isomerism in methane sulfonamide anion, CH3-SO2-NH. Theor Chem Ace 1997, 96:56-60.
5.
George P, Glusker JP, Bock CW: An ab initio computational molecular orbital study of radical, protonated radical (radical cation), and carbocation species that have been proposed in mechanisms for the transfer process in the enzyme-coenzyme B12 -catalyzed dehydration of 1,2-dihydroxyethane. J Am Chem Soc 1997, 1 "19:7065-7074.
6.
7.
8.
9.
Pitarch J, Ruiz-Lopez MF, PascuaI-Ahuir J-L, Silla E, Tur~6n h Ab initio calculations on neutral and alkaline hydrolyses of ~-Iactam antibiotics. A theoretical study including solvent effects. J Phys Chem B 1997, 101:3581-3588. Zheng Y-J, Ornstein RL: Role of active site tyrosine in glutathion Stransferase: insights from a theoretical study of model systems. JAm Chem Soc 1997, 119:1523-1528. Zheng Y-J, Bruice TO: A Theoretical examination of the factors controlling the catalytic efficiency of a transmethylation enzyme: cathechol O-methyltransferase. J Am Chem Soc 1997, 119:81378145. Zheng Y-J, Bruice TC: On the dehalogenation mechanism of 4chlorobenzoyl CoA by 4-chlorobenzoyl CoA dehalogenase: insight from study based on the nonenzymatic reaction. J Am Chem Soc 1997, 119:3868-3877.
10.
Per~kyl~M: Triosephosphate isomerase (TI M)-catalysed proton abstraction from carbon acid: an analysis on the origin of the catalytic activity. Chem Cornmun 1996, 361-362.
11. Thomson C, Zwaans R: Ab initio calculations on 2-, 3- and 4substituted quinolines in relation with their activity as protein tyrosine kinase inhibitors. J Mo/Struct 1996, 362:51-68. 12. Lee JK, Houk KN: A proficient enzyme revisited: the predicted oo mechanism for orotidine monophosphate decarboxylase. Science 1997, 276:942-945. This paper proposes a specific mechanistic explanation using quantum chemical modeling for a reaction that is dramatically accelerated by the enzyme. Although the quantum chemistry is not particularly high level, nor on a large model of the enzyme active site, the mechanistic proposal is an interesting one that can be tested experimentally. 13. Florian J, Warshel A: A fundamental assumption about OH- attack in phosphate ester hydrolysis is not fully justified. J Am Chem Soc 1997, 119:5473-5474. This paper investigates phosphate ester hydrolysis using ab initio quantum chemical techniques and shows that the proposed pathway is inconsistent with these calculations. Of interest here is the use of calculations in order to rule out a proposed mechanistic pathway for a biologically important system. 14. Marten B, Kim K, Cortis C, Friesner RA, Murphy RB, Ringnalda MN, Sitkoff D, Honig B: New model for calculation of solvation free energies: correction of self-consistent reaction field continuum dielectric theory for short range hydrogen bonding effects. J Phys Chem 1996, 100:11775-11788. This paper shows that dielectric continuum methods have systematic inaccuracies due to the incorrect treatment of hydrogen bonding, and develops a systematic empirical protocol to correct this deficiency. The same problems can also be observed in molecular mechanics force fietds, which rely primarily on an electrostatic description of hydrogen bonding. 15. Cortis C, Langlois JM, Beachy M, Friesner R: Quantum mechanical geometry optimization in solution using a finite element continuum electrostatics method. J Chem Phys 1996, 105:54725484. 16. Tomasi J, Persico M: Molecular interactions in solution: an overview of methods based on continuous distributions of the solvent. Chem Rev 1994, 94:2027-2094. 17.
Wladkowski BD, Chenoweth SA, Sanders J N, Krauss M, Stevens WJ: Acylation of ~-Iactarnase: an ab initio theoretical study on the effects of the oxy-anion hole. J Am Chem Soc 1997, 119:64236431. This paper incorporates explicit amino acid residues from the active site into the quantum chemical model and calculates the activation energy for the proposed enzymatic pathway at the Hartree-Fock level. The paper is noteworthy for the large size of the quantum chemical model. 18. Nederkoorn PHJ, van Lenthe JH, van der Goot H, Donne-Op den Kelder GM, Timmerman H: The agonistic binding site at the histamine H 2 receptor. I. Theoretical investigations of histamine binding to an oligopeptide mimicking a part of the fifth transmembrane 0~-helix. J Comput Aided Mol Des 1996, 10:461-478. This paper presents ab initio modeling of receptor-ligand binding using quite a large model, by current literature standards, for the receptor active site. From the calculations, a proposal for the binding site of the ligand is presented. 19. Sagnella DE, Laasonen K, Klein ML: Ab initio molecular dynamics study of proton transfer in a polyglycine analog of the ion channel gramicidin A. Biophys J 1996, 71:1172-1178. This paper describes a state of the art ab initio molecular dynamics calculation on a biologically relevant system, specifically investigating proton transfer in an ion channel. 20. Becke AD: Density-functional thermochemistry. (I.) The effect of the exchange-only gradient correction. J Chem Phys 1992, 96:2155-2160. 21.
Becke AD: Density-functional thermochemistry. (11.) The effect of the Perdew-Wang generalized gradient correlation correction. J Chem Phys 1992, 97:9173-9177.
22. Becke AD: Density-functional thermochemistry. (111.)The role of exact exchange. J Chem Phys 1993, 98:5648-5652. 23.
Becke, AD: A new mixing of Hartree-Fock and local densityfunctional theories. J Chem Phys 1993, 98:1372-1377.
24. Curtiss LA, Raghavachari K, Redfern PC, Pople JA: Investigation of the use of B3LYP zero-point energies and geometries in the
Quantum mechanical calculations of biological systems Friesner and Beachy
calculation of enthalpies of formation. Chem Phys Lett 1997, 270:419-426. 25. Curtiss LA, Raghavachari K, Redfern PC, Pople JA: Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation. J Chern Phys 199"7, 106:1063-1079. 26. Johnson BG, Gill PMW, Pople JA: The performance of a family of density functional methods. J Chem Phys 1993, 98:5612-5626. White CA, Johnson BG, Gill PMW, Head Gordon M: Linear scaling density functional calculations via the continuous fast multipole method. Chem Phys Lett 1996, 253:268-278. This is the first paper on linear scaling density functional theory (DFT), which has the potential to extend DFT to very large systems. The paper is primarily technical, but will be of interest to readers who want to understand what is involved in using quantum chemisty for ultralarge computations. 27.
28.
Saebo S, Pulay P: The local correlation treatmenL I1. Implementation and tests. J Chem Phys 1988, 88:1884-1890.
29. Wolinski K, Sellers H, Pulay P: Consistent generalization of the M~ller-Plesset partitioning to open-shell and multiconfigurational SCF reference states in many-body perturbation theory. Chern Phys Lett 198?, 140:225-231. 30.
Murphy M, Beachy MD, Friesner RA, Ringnalda MN: Pseudospectral localized Meller-Plesset methods: theory and calculation of conformational energies. J Chem Phys 1996, 103:1481-1490.
Murphy RB, Pollard VVT, Friesner RA: Pseudospectral localized generalized Meller-Plesset methods with a generalized valence bond reference wave function: theory and calculation of conformational energies. J Chem Phys 1997, 106:5073-5084. This paper demonstrates a quantum chemical method, based upon multireference perturbation theory, with N 3 scaling, that provides uniformly high accuracies for conformational energies. Such methods will be crucial in designing the next generation of force fields in which quantitative agreement with quantum chemical data is enforced. 31.
32.
St-Amant A, Cornell WD, Kollman PA, Halgren TA: Calculation of molecular geometries, relative conformational energies, dipole moments, and molecular electrostatic potential fitted charges of small organic molecules of biochemical interest by density functional theory. J Comput Chem 1995, 16:1483-1506.
Halgren TA: Merck Molecular Force Field. I. Basis, form, scope, parameterization, and performance of MMFF94. J Comput Chem 1996, 17:490-519. This paper describes a new molecular modeling force field, MMFF, with wide coverage of pharmaceutical compounds, using extensive fitting to good quality quantum chemical data. The MMFF force field is one of the two best performers in the tests carried out in [41"] concerning the prediction of tetrapeptide energetics. 33.
34.
Halgren TA: Merck Molecular Force Field. I1. MMFF94 van der Waals and electrostatic parameters for intermolecular interactions. J Comput Chem 1996, 17:520-552.
35.
Halgren TA: Merck Molecular Force Field. II1. Molecular geometrics and vibrational frequencies for MM FF94. J Comput Chem 1996, 17:553-586.
36.
Halgren TA, Nachbar RB: Merck Molecular Force Field. IV. Conformational Energies and Geometries for M MFF94. J Comput Chem 1996, 17:587-615.
37.
Halgren TA: Merck Molecular Force Field. V. Extension of MMFF94 using experimental data, additional computational data, and empirical rules. J Comput Chem 1996, 17:616-641.
Beachy M, Chasman D, Murphy R, Halgren T, Friesner R: Accurate ab initio quantum chemical determination of the relative energetics of peptide conformations and assessment of empirical force fields. J Am Chem Soc 1997, 119:5908-5920. This paper tests the transferability of protein force fields with large scale accurate quantum chemistry calculations. The energies of 10 conformations of an alanine tetrapeptide were computed at a accurate quantum chemical level and the results compared against a comprehensive list of protein molecular mechanics force fields. A preliminary assessment of the accuracy of the force fields tested is provided. 41. •.
Ryde U, Olsson MHM, Pierloot K, RoDS B e : the cupric geometry of blue copper proteins is not strained. J Mol Biol 1996, 261:586-596. This paper presents ab initio quantum chemical calculations on an active site model for blue copper proteins, using both density functional theory and multireference perturbation theory methods, and concludes that the active site geometry around the copper center is not strained. The use of multireference perturbation theory, a highly accurate quantum chemical method, on a reasonable size active site model, is particulary noteworthy here. 42.
43.
Blomberg MRA, Siegbahn PEM, Styring S, Babcock GT, Akermaker B, Korall P: A quantum chemical study of hydrogen abstraction from manganese-coordinated water by a tyrosyl radical: a model for water oxidation in photosystem I1. J Am Chem Soc 1997, 119:8285-8292. This paper provides ab initio quantum chemical calculations on a large transition metal active site model using density functional theory, with a specific mechanism proposed for key steps of water oxidation in photosystem II. This is a biologically important problem and the calculations provide support for a proposed physical mechanism. 44.
39.
Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM Jr, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA: A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J Am Chem Soc 1995, 117:5179-5197.
40.
Mackerell AD Jr, Wiorkiewicz-Kuczera J, Karplus M: An all-atom empirical energy function for the simulation of nucleic acids..I Am Chem Soc 1995, 117:11946-11975.
Fisher CL, Chen, J-L, Li J, Bashford D, Noodleman L: Densityfunctional and electrostatic calculations for a model of a manganese superoxide dismutase active site in aqueous solution, J Phys Chem 1996, 100:13498-13505.
Siegbahn PEM, Crabtree RH: Mechanism of C-H activation by diiron methane monoxygenases: quantum chemical studies, J Am Chem Soc 1997, 119:3103-3113. This paper presents ab initio quantum chemical calculations on a large transition metal active site model of methane monooxygenase using density functional theory, with proposals for the pathway by which the enzyme catalyzes the transformation of methane to methanol. Particularly noteworthy here is the use of large basis sets for the DFT calculations. This is a major step forward in obtaining more reliable results for energetics as compared to previous work in the literature. 45 •o
Cramer CJ, Smith BA, Tolman WB: Ab initio characterization of the isomerism between the H-n2:n2-peroxo- and bis(u-oxo)dicopper cores. J Am Chem Soc 1996, 118:11283-1128?. This paper describes ab initio quantum chemical calculations on small active site models of the conformational energetics of dicopper cores. The calculations use multireference perturbation theory, and are thus high quality calculations, and also a dielectric continuum solvation model. 46
4?.
38. Jorgensen WL, Maxwell DS, TiradoRives J: Development and testing •. of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J Am Chern Soc 1996, 118:1122511236. This paper describes a new molecular modeling force field, OPLS-AA, which is extensively fit to both quantum chemical data and liquid state thermodynamics. OPLS-AA is one of the two best performers in the tests carried out in [41"'], and simultaneously provides excellent prediction of liquid state properties.
261
Garmer DR: Carbonic anhydrase reactivity, mutation, and inhibition probed with a model of ab initio quantum chemistry within a protein. J Phys Chem 199?, 101:2945-2953.
48. Merz Jr KM, Banci L: Binding of bicarbonate to human carbonic anhydrase Ih a continuum of binding states. J Am Chem Soc 1997, 119: 863-871. This paper presents Q M / M M simulations using a semi-empirical QM Hamiltonian on the binding of bicarbonate to carbonic anhydrase. It is a good example of how a Q M / M M calculation can address qualitative questions reasonably well, even though the model is probably not highly precise. With a transition metal-binding site, conventional force fields are problematic, and Q M / M M even at the semi-empirical level is likely the best alternative. 49. Alagona G, Ghio C, Kollman PA: Chemical reaction mechanisms in vacuo, in solution and in enzyme fields: isomerization catalyzed by triose phosphate- isomerase (TIM). J Mol Struct 1996, 371:287298. 50. Per~kyl~ M, Kollman PA: A simulation of the catalytic mechanism of aspartylglucosaminidase using ab initio quantum mechanics and molecular dynamics. J Am Chem Soc 199"7, 119:1189-1196. This paper uses a Q M / M M approach in which simulations are carried out at the MD level. Key structures are then extracted from the simulations and calculated at the QM level using Hartree-Fock and MP2 levels of theory, treating the protein environment as point charges and using a continuum model for solvation. The QM calculations allow an evaluation of transition state energetics that would be unavailable from the MM force field. An explanation of the catalytic mechanism is provided from the calculations.
262
Theory and simulation
51. Ryde U: The coordination of the catalytic zinc ion in alcohol dehydrogenase studied by combined quantum-chemical and molecular mechanics calculations. J Comput Aided Mo/ Des 1996, 10:153-164. 52. Moliner V, Turner A J, Williams IH: Transition-state structural refinement with GRACE and CHARMm: realistic modelling of lactate dehydrogenase using a combined quantum/classical method. Chem Commun 1997, 1271-1272. 53. Ranganathan S, Gready JE: Hybrid quantum and molecular mechanical ( Q M / M M ) studies on the pyruvate to L-lactate intemonversion in L-lactate dehydrogenase. J Phys Chem B 199?, 101:5614-5618. 54. Cunningham MA, Ho LL, Nguyen DT, Gillilan RE, Bash PA: Simulation of the enzyme mechanism of malate dehydrogenase. Biochemistry 1997, 36:4800-4816. 55. Davidson MM, Gould IR, Hillier IH: The mechanism of the catalysis • of the Claisen rearrangement of chorismate to perphenate by the chorismate mutase from Bacillus subtilis. A molecular mechanics
and hybrid quantum mechanical/molecular mechanical study. J Chem Soc Perkin Trans 1996, 2:525-532. This paper investigates the role of the active site of the enzyme chorismate mutase in catalyzing the Claisen rearrangement of chorismate to prephenate. Here, QM structures (computed at the Hartree-Fock level) along the reaction path are docked into the active site and the energies are evaluated via a mixed QM/MM Hamiltonian. This is yet another approach to deploying QM/MM technology, and leads to reasonable qualitative agreement with experiments in terms of the ability of the enzyme to lower the barrier to reaction.
56. Liu H, ML~ller-PlatheF, van Gunsteren WF: A combined quantum/classical molecular dynamics study of the catalytic mechanism of HIV protease. J Mol Biol 1996, 261:454-469. 57. EureniusKP, Chatfield DC, Brooks BR, Hodoscek M: Enzyme mechanisms with hybrid quantum and molecular mechanical potentials. I. Theoretical considerations. Int J Quantum Chem 1996, 60:1189-1200. 58. Bash PA, Field MJ, Karplus M: Free energy perturbation method for chemical reactions in the condensed phase: a dynamical approach based on a combined quantum and molecular mechanics potential. J Am Chem Soc 1987, 109:8092-8094.