An all atom force field for simulations of proteins and nucleic acids.
TL;DR: An all atom potential energy function for the simulation of proteins and nucleic acids and the first general vibrational analysis of all five nucleic acid bases with a molecular mechanics potential approach is presented.
Abstract: We present an all atom potential energy function for the simulation of proteins and nucleic acids. This work is an extension of the CH united atom function recently presented by S.J. Weiner et al. J. Amer. Chem. Soc., 106, 765 (1984). The parameters of our function are based on calculations on ethane, propane, n−butane, dimethyl ether, methyl ethyl ether, tetrahydrofuran, imidazole, indole, deoxyadenosine, base paired dinucleoside phosphates, adenine, guanine, uracil, cytosine, thymine, insulin, and myoglobin. We have also used these parameters to carry out the first general vibrational analysis of all five nucleic acid bases with a molecular mechanics potential approach.
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TL;DR: An N⋅log(N) method for evaluating electrostatic energies and forces of large periodic systems is presented based on interpolation of the reciprocal space Ewald sums and evaluation of the resulting convolutions using fast Fourier transforms.
Abstract: An N⋅log(N) method for evaluating electrostatic energies and forces of large periodic systems is presented. The method is based on interpolation of the reciprocal space Ewald sums and evaluation of the resulting convolutions using fast Fourier transforms. Timings and accuracies are presented for three large crystalline ionic systems.
24,332 citations
TL;DR: A general Amber force field for organic molecules is described, designed to be compatible with existing Amber force fields for proteins and nucleic acids, and has parameters for most organic and pharmaceutical molecules that are composed of H, C, N, O, S, P, and halogens.
Abstract: We describe here a general Amber force field (GAFF) for organic molecules. GAFF is designed to be compatible with existing Amber force fields for proteins and nucleic acids, and has parameters for most organic and pharmaceutical molecules that are composed of H, C, N, O, S, P, and halogens. It uses a simple functional form and a limited number of atom types, but incorporates both empirical and heuristic models to estimate force constants and partial atomic charges. The performance of GAFF in test cases is encouraging. In test I, 74 crystallographic structures were compared to GAFF minimized structures, with a root-mean-square displacement of 0.26 A, which is comparable to that of the Tripos 5.2 force field (0.25 A) and better than those of MMFF 94 and CHARMm (0.47 and 0.44 A, respectively). In test II, gas phase minimizations were performed on 22 nucleic acid base pairs, and the minimized structures and intermolecular energies were compared to MP2/6-31G* results. The RMS of displacements and relative energies were 0.25 A and 1.2 kcal/mol, respectively. These data are comparable to results from Parm99/RESP (0.16 A and 1.18 kcal/mol, respectively), which were parameterized to these base pairs. Test III looked at the relative energies of 71 conformational pairs that were used in development of the Parm99 force field. The RMS error in relative energies (compared to experiment) is about 0.5 kcal/mol. GAFF can be applied to wide range of molecules in an automatic fashion, making it suitable for rational drug design and database searching.
13,615 citations
TL;DR: The results demonstrate that use of ab initio structural and energetic data by themselves are not sufficient to obtain an adequate backbone representation for peptides and proteins in solution and in crystals.
Abstract: New protein parameters are reported for the all-atom empirical energy function in the CHARMM program. The parameter evaluation was based on a self-consistent approach designed to achieve a balance between the internal (bonding) and interaction (nonbonding) terms of the force field and among the solvent−solvent, solvent−solute, and solute−solute interactions. Optimization of the internal parameters used experimental gas-phase geometries, vibrational spectra, and torsional energy surfaces supplemented with ab initio results. The peptide backbone bonding parameters were optimized with respect to data for N-methylacetamide and the alanine dipeptide. The interaction parameters, particularly the atomic charges, were determined by fitting ab initio interaction energies and geometries of complexes between water and model compounds that represented the backbone and the various side chains. In addition, dipole moments, experimental heats and free energies of vaporization, solvation and sublimation, molecular volume...
13,164 citations
TL;DR: In this article, the parametrization and testing of the OPLS all-atom force field for organic molecules and peptides are described, and the parameters for both torsional and non-bonded energy properties have been derived, while the bond stretching and angle bending parameters have been adopted mostly from the AMBER force field.
Abstract: The parametrization and testing of the OPLS all-atom force field for organic molecules and peptides are described. Parameters for both torsional and nonbonded energetics have been derived, while the bond stretching and angle bending parameters have been adopted mostly from the AMBER all-atom force field. The torsional parameters were determined by fitting to rotational energy profiles obtained from ab initio molecular orbital calculations at the RHF/6-31G*//RHF/6-31G* level for more than 50 organic molecules and ions. The quality of the fits was high with average errors for conformational energies of less than 0.2 kcal/mol. The force-field results for molecular structures are also demonstrated to closely match the ab initio predictions. The nonbonded parameters were developed in conjunction with Monte Carlo statistical mechanics simulations by computing thermodynamic and structural properties for 34 pure organic liquids including alkanes, alkenes, alcohols, ethers, acetals, thiols, sulfides, disulfides, a...
12,024 citations
TL;DR: The Weighted Histogram Analysis Method (WHAM) as mentioned in this paper is an extension of Ferrenberg and Swendsen's multiple histogram technique for complex biomolecular Hamiltonians.
Abstract: The Weighted Histogram Analysis Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomolecular Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free-energy and Potential of Mean Force calculations. This algorithm possesses the following advantages over methods that are currently employed: (1) It provides a built-in estimate of sampling errors thereby yielding objective estimates of the optimal location and length of additional simulations needed to achieve a desired level of precision; (2) it yields the “best” value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addition to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better estimates of the free-energy differences. By recasting the Ferrenberg–Swendsen Multiple Histogram equations in a form suitable for molecular mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine. © 1992 by John Wiley & Sons, Inc.
5,784 citations
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TL;DR: The CHARMM (Chemistry at Harvard Macromolecular Mechanics) as discussed by the authors is a computer program that uses empirical energy functions to model macromolescular systems, and it can read or model build structures, energy minimize them by first- or second-derivative techniques, perform a normal mode or molecular dynamics simulation, and analyze the structural, equilibrium, and dynamic properties determined in these calculations.
Abstract: CHARMM (Chemistry at HARvard Macromolecular Mechanics) is a highly flexible computer program which uses empirical energy functions to model macromolecular systems. The program can read or model build structures, energy minimize them by first- or second-derivative techniques, perform a normal mode or molecular dynamics simulation, and analyze the structural, equilibrium, and dynamic properties determined in these calculations. The operations that CHARMM can perform are described, and some implementation details are given. A set of parameters for the empirical energy function and a sample run are included.
14,725 citations
TL;DR: In this article, a unique mean plane is defined for a general monocyclic puckered ring, which is described by amplitude and phase coordinates which are generalizations of those introduced for cyclopentane by Kilpatrick, Pitzer, and Spitzer.
Abstract: A unique mean plane is defined for a general monocyclic puckered ring. The geometry of the puckering relative to this plane is described by amplitude and phase coordinates which are generalizations of those introduced for cyclopentane by Kilpatrick, Pitzer, and Spitzer. Unlike earlier treatments based on torsion angles, no mathematical approximations are involved. A short treatment of the four-, five-, and six-membered ring demonstrates the usefulness of this concept. Finally, an example is given of the analysis of crystallographic structural data in terms of these coordinates. Although the nonplanar character of closed rings in many cyclic compounds has been widely recognized for many years, there remain some difficulties in its quantitative specification. An important first step was taken by Kilpatrick, Pitzer, and Spitzer in their 1947 discussion of the molecular structure of cyclopentane.' Starting with the normal modes of out-of-plane motions of a planar regular pentagon,* they pointed out that displacement of the j t h carbon atom perpendicular to the plane could be written 2 112 zj = (/'SI 4 COS (2+ + 4 n ( j 11/51 (11 where q is a puckering amplitude and $ is a phase angle describing various kinds of puckering. By considering changes in an empirical potential energy for displacements perpendicular to the original planar form, they gave reasons to believe that the lowest energy was obtained for a nonzero value of q (finite puckering) but that this minimum was largely independent of $. Motion involving a change in fi at constant q was described as pseudorotation. Subsequent refinement of this work has involved models in which constraints to require constant bond lengths are imposed3q4 and extensions to larger rings5-' and some heterocyclic systems are considered.* Although the correctness of the model of Kilpatrick, et a f . , I and the utility of the (q. $) coordinate system is generally accepted, application to a general five-membered ring with unequal bond lengths and angles is not straightforward. Given the Cartesian coordinates for the five atoms (as from a crystal structure), determination of puckering displacements z, requires specification of the plane z = 0. A least-squares choice (minimization of Zz i2) is one possibility, but the five displacements relative to this plane cannot generally be expressed in terms of two parameters q and $ according to eq 1. An attempt to define a generalized set of puckering cordinates which avoids these difficulties was made by Geise, Altona, Romers, and S~ndara l ingam.~l ' Their quantitative description of puckering in five-membered rings involves the five torsion angles 0, rather than displacements perpendicular to some plane. These torsion angles are directly derivable from the atomic coordinates and are all zero in the planar form. They proposed a relationship of the form\
6,526 citations
TL;DR: In this paper, a force field for simulation of nucleic acids and proteins is presented, which is based on the ECEPP, UNECEPP, and EPEN energy refinement software.
Abstract: We present the development of a force field for simulation of nucleic acids and proteins. Our approach began by obtaining equilibrium bond lengths and angles from microwave, neutron diffraction, and prior molecular mechanical calculations, torsional constants from microwave, NMR, and molecular mechanical studies, nonbonded parameters from crystal packing calculations, and atomic charges from the fit of a partial charge model to electrostatic potentials calculated by ab initio quantum mechanical theory. The parameters were then refined with molecular mechanical studies on the structures and energies of model compounds. For nucleic acids, we focused on methyl ethyl ether, tetrahydrofuran, deoxyadenosine, dimethyl phosphate, 9-methylguanine-l-methylcytosine hydrogen-bonded complex, 9-methyladenine-l-methylthymine hydrogen-bonded complex, and 1,3-dimethyluracil base-stacked dimer. Bond, angle, torsional, nonbonded, and hydrogen-bond parameters were varied to optimize the agreement between calculated and experimental values for sugar pucker energies and structures, vibrational frequencies of dimethyl phosphate and tetrahydrofuran, and energies for base pairing and base stacking. For proteins, we focused on 4>,'lt maps of glycyl and alanyl dipeptides, hydrogen-bonding interactions involving the various protein polar groups, and energy refinement calculations on insulin. Unlike the models for hydrogen bonding involving nitrogen and oxygen electron donors, an adequate description of sulfur hydrogen bonding required explicit inclusion of lone pairs. There are two fundamental problems in simulating the struc tural and energetic properties of molecules: the first is how to choose an analytical been placed E(R) which correctly describes the energy of the system in terms of its 3N degrees of freedom. The second is how the simulation can search or span conforma tional space (R) in order to answer questions posed by the scientist interested in the properties of the system. For complex systems, solution to the first problem are an es sential first step in attacking the second problem, and thus, considerable effort has been placed in developing analytical functions that are simple enough to allow one to simulate the properties of complex molecules yet accurate enough to obtain meaningful estimates for structures and energies. In the case of the structures and thermodynamic stabilities of saturated hydrocarbons in inert solvents or the gas phase, the first problem has been essentially solved by molecular mechanics ap proaches of Allinger, I Ermer and Lifson,2 and their co-workers. However, for polar and ionic molecules in condensed phases, unsolved questions remain as to the best form of the analytical function E(R). In the area of proteins and peptides, seminal work has come from the Scheraga 3 and Lifson 4 schools. The Scheraga group has used both crystal packing (intermolecular) and con formational properties of peptides to arrive at force fields ECEPP, UNECEPP, and EPEN for modeling structural and thermodynamic properties of peptides and proteins. Levitt, using the energy refinement software developed in the Lifson group, has proposed a force field for proteins based on calculations on lysozyme,S and Gelin and Karplus have adapted this software along with many parameters from the Scheraga studies to do molecular dynamics
4,340 citations
TL;DR: An improved force field for molecular mechanics calculations of the structures and energies of hydrocarbons is presented in this paper, where the problem of simultaneously obtaining a sufficiently large gauche butane interaction energy while keeping the hydrogens small enough for good structural predictions was solved with the aid of onefold and twofold rotational barriers.
Abstract: An improved force field for molecular mechanics calculations of the structures and energies of hydrocarbons is presented. The problem of simultaneously obtaining a sufficiently large gauche butane interaction energy while keeping the hydrogens small enough for good structural predictions was solved with the aid of onefold and twofold rotational barriers. The structural results are competitive with the best of currently available force fields, while the energy calculations are superior to any previously reported. For a list of 42 selected diverse types of hydrocarbons, the standard deviation between the calculated and experimental heats of formation is 0.42 kcal/mol, compared with an average reported experimental error for the same group of compounds of 0.40 kcal/mol. I t has been now amply demonstrated that force field calculations offer the method of choice for the determination of the structures and energies of molecules under many circums t a n c e ~ . ~ ~ While many previously published force fields are very good, they do contain errors which are sufficiently large as to be worrisome to those wishing to utilize them to the fullest possible extent. While the organic chemist is primarily interested in compounds which contain functional groups, since the fundamental structure of organic molecules in general is hydrocarbon in character, a high degree of accuracy in the hydrocarbon part of the force field is crucial. “First generation” force fields showed that one could indeed calculate accurate structures and energies, although the fit to experiment was in some cases less good than one would desire. There has been some difficulty in ascertaining exactly where the force fields were in error, and in which cases the experimental data were less accurate than the probable errors indicated. This question is still not fully answerable but, clearly, more and better data have become available in the last several years. The best we can do is to utilize the existing data, and point out where we feel that there may be errors. We will discuss herein three of the earlier force fields. These are our earlier force field M M l ( 1973)3 and the most recent force fields by Schleyer (EAS)5b and Bartell (MUB-2).6 For all of their usefulness and accuracy, these force fields contained various flaws which showed up in different ways. In an effort to minimize the discrepancy between calculations and experiment, the van der Waals characteristics of atoms were important quantities to be evaluated. In Figure 1 is shown a graph taken mainly from a recent paper by Bartel16 in which the force exerted by a pair of atoms as a function of distance is plotted for several different force fields including MUB-2, EAS, and M M I . For present purposes we will define a “hard” atom as one for which the plot of the force vs. distance for the repulsive part of the curve shows a steep slope (as the dashed C/C line in the figure), and a “soft” atom as one where this slope is more gentle (as the solid line). We will also define a “bigger” atom as one where the line is slid farther to the right, and a “smaller” atom as one for which it is slid to the left. With this terminology, it is seen from the graph that in M M I we used a hydrogen atom which was both rather hard and large compared to that used by Bartell (and other workers), while we used a carbon atom which was small. The “hardness” of our curves was determined by the Hill equation, which is known to fit well for interactions between rare gases.’ There is no assurance that such curves are ideal for carbon and hydrogen atoms which are covalently bound. However, they seemed like a reasonable choice in the absence of definite information. Bartell, mainly on the basis of theory, chose a much softer hydrogen.8 Most other workers have been inclined to follow Bartell’s lead. Bartell’s more recent choice (bVIUB-2) is based on theoretical calculations by Kochanski9 on the Hz molecule. His new hydrogen is larger but softer than the old one. In our early worki0 we noticed that we could not fit adequately to the axial-equatorial methylcyclohexane energy difference using Bartell’s hydrogen, and varying the other parameters that it seemed one might reasonably vary. We therefore continued to use the hard Hill-type hydrogens. Bartell was less anxious to fit this energy difference, and felt he could do a better overall job with structure using soft hydrogens. In each case, the C /H interaction was taken to be the mean of the H / H and C/C interactions. White has also pointed out in a recent paper that our hydrogens are too hard to explain certain data .” We too regard the cyclodecane case which he discusses as a key case, because of the data now available, and it will be discussed below. We
3,313 citations
TL;DR: In this article, an approach for deriving net atomic charges from ab initio quantum mechanical calculations using a least squares fit of the quantum mechanically calculated electrostatic potential to that of the partial charge model is presented.
Abstract: We present an approach for deriving net atomic charges from ab initio quantum mechanical calculations using a least squares fit of the quantum mechanically calculated electrostatic potential to that of the partial charge model. Our computational approach is similar to those presented by Momany [J. Phys. Chem., 82, 592 (1978)], Smit, Derissen, and van Duijneveldt [Mol. Phys., 37, 521 (1979)], and Cox and Williams [J. Comput. Chem., 2, 304 (1981)], but differs in the approach to choosing the positions for evaluating the potential. In this article, we present applications to the molecules H2O, CH3OH, (CH3)2O, H2CO, NH3, (CH3O)2PO, deoxyribose, ribose, adenine, 9-CH3 adenine, thymine, 1-CH3 thymine, guanine, 9-CH3 guanine, cytosine, 1-CH3 cytosine, uracil, and 1-CH3 uracil. We also address the question of inclusion of “lone pairs,” their location and charge.
2,976 citations