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.

Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems

NAMD is a parallel molecular dynamics code designed for high-performance simulation of large biomolecular systems. NAMD scales to hundreds of processors on high-end parallel platforms, as well as tens of processors on low-cost commodity clusters, and also runs on individual desktop and laptop computers. NAMD works with AMBER and CHARMM potential functions, parameters, and file formats. This article, directed to novices as well as experts, first introduces concepts and methods used in the NAMD program, describing the classical molecular dynamics force field, equations of motion, and integration methods along with the efficient electrostatics evaluation algorithms employed and temperature and pressure controls used. Features for steering the simulation across barriers and for calculating both alchemical and conformational free energy differences are presented. The motivations for and a roadmap to the internal design of NAMD, implemented in C++ and based on Charm++ parallel objects, are outlined. The factors affecting the serial and parallel performance of a simulation are discussed. Finally, typical NAMD use is illustrated with representative applications to a small, a medium, and a large biomolecular system, highlighting particular features of NAMD, for example, the Tcl scripting language. The article also provides a list of the key features of NAMD and discusses the benefits of combining NAMD with the molecular graphics/sequence analysis software VMD and the grid computing/collaboratory software BioCoRE. NAMD is distributed free of charge with source code at www.ks.uiuc.edu.

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Scalable molecular dynamics with NAMD

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.

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Development and testing of a general amber force field.

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Scalable Molecular Dynamics with NAMD

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...

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All-atom empirical potential for molecular modeling and dynamics studies of proteins.

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

A new force field for molecular mechanical simulation of nucleic acids and proteins

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.

An all atom force field for simulations of proteins and nucleic acids.

Simulation of formamide hydrolysis by hydroxide ion in the gas phase and in aqueous solution

We present the results of molecular dynamics simulations on d(C-G-C-G-A) X d(T-C-G-C-G) with fully charged phosphates with and without inclusion of counterions. The average structures found in the two simulations are similar, but the simulation with counterions does give an average helix repeat, tilt, and twist in better agreement with those found in the x-ray structure of d(C-G-C-G-A-A-T-T-C-G-C-G)2. The average sugar pucker phases and amplitudes are in qualitative agreement with those found in NMR studies of double-helical DNA, and a number of examples of sugar repuckering from C2' endo to C3' endo carbon conformations in the sugar ring are found. The hydrogen bond correlations as well as torsion correlations are analyzed, and some interesting long-range correlations between dihedral angles are found.

S. J. Weiner

Papers

A new force field for molecular mechanical simulation of nucleic acids and proteins

An all atom force field for simulations of proteins and nucleic acids.

A new force field for molecular mechanical simulation of nucleic acids and proteins

Simulation of formamide hydrolysis by hydroxide ion in the gas phase and in aqueous solution

Molecular dynamics simulations of d(C-G-C-G-A) X d(T-C-G-C-G) with and without "hydrated" counterions