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.

CHARMM: A program for macromolecular energy, minimization, and dynamics calculations

Protein structure and dynamics can be characterized on the atomistic level with both nuclear magnetic resonance (NMR) experiments and molecular dynamics (MD) simulations. Here, we quantify the ability of the recently presented CHARMM36 (C36) force field (FF) to reproduce various NMR observables using MD simulations. The studied NMR properties include backbone scalar couplings across hydrogen bonds, residual dipolar couplings (RDCs) and relaxation order parameter, as well as scalar couplings, RDCs, and order parameters for side-chain amino- and methyl-containing groups. It is shown that the C36 FF leads to better correlation with experimental data compared to the CHARMM22/CMAP FF and suggest using C36 in protein simulations. Although both CHARMM FFs contains the same nonbond parameters, our results show how the changes in the internal parameters associated with the peptide backbone via CMAP and the χ1 and χ2 dihedral parameters leads to improved treatment of the analyzed nonbond interactions. This highlights the importance of proper treatment of the internal covalent components in modeling nonbond interactions with molecular mechanics FFs. © 2013 Wiley Periodicals, Inc.

CHARMM36 all-atom additive protein force field: Validation based on comparison to NMR data

After an outline of work on rare-gas systems, which serves as a target for parallel work on alkali halides, and an initial brief survey of those parts of this parallel work for which results have been obtained, interionic potential models for alkali halides are considered in some detail. The rigid ion potentials of Fumi and Tosi are discussed and then a major part of the section is devoted to deriving a new set of polarizable ion potentials, which incorporate the ideas behind the lattice dynamical shell model. Extensions which include many-body terms in the potentials are considered briefly and finally the information which can be obtained from alkali halide diatomic molecules is discussed. In the third section methods of computer simulation for ionic liquids are outlined, concentrating on the molecular dynamics method, and some of the properties which can be obtained by analysing the ion trajectories are listed. Results from simulations, including some new work on LiF, NaCl and RbI, are reviewed.

Interionic potentials in alkali halides and their use in simulations of the molten salts

We present an all-atom additive empirical force field for the hexopyranose monosaccharide form of glucose and its diastereomers allose, altrose, galactose, gulose, idose, mannose, and talose. The model is developed to be consistent with the CHARMM all-atom biomolecular force fields, and the same parameters are used for all diastereomers, including both the alpha- and beta-anomers of each monosaccharide. The force field is developed in a hierarchical manner and reproduces the gas-phase and condensed-phase properties of small-molecule model compounds corresponding to fragments of pyranose monosaccharides. The resultant parameters are transferred to the full pyranose monosaccharides, and additional parameter development is done to achieve a complete hexopyranose monosaccharide force field. Parametrization target data include vibrational frequencies, crystal geometries, solute-water interaction energies, molecular volumes, heats of vaporization, and conformational energies, including those for over 1800 monosaccharide conformations at the MP2/cc-pVTZ//MP2/6-31G(d) level of theory. Although not targeted during parametrization, free energies of aqueous solvation for the model compounds compare favorably with experimental values. Also well-reproduced are monosaccharide crystal unit cell dimensions and ring pucker, densities of concentrated aqueous glucose systems, and the thermodynamic and dynamic properties of the exocyclic torsion in dilute aqueous systems. The new parameter set expands the CHARMM additive force field to allow for simulation of heterogeneous systems that include hexopyranose monosaccharides in addition to proteins, nucleic acids, and lipids.

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Additive empirical force field for hexopyranose monosaccharides.

The growing adoption of generalized-ensemble algorithms for biomolecular simulation has resulted in a resurgence in the use of the weighted histogram analysis method (WHAM) to make use of all data generated by these simulations. Unfortunately, the original presentation of WHAM by Kumar et al. is not directly applicable to data generated by these methods. WHAM was originally formulated to combine data from independent samplings of the canonical ensemble, whereas many generalized-ensemble algorithms sample from mixtures of canonical ensembles at different temperatures. Sorting configurations generated from a parallel tempering simulation by temperature obscures the temporal correlation in the data and results in an improper treatment of the statistical uncertainties used in constructing the estimate of the density of states. Here we present variants of WHAM, STWHAM and PTWHAM, derived with the same set of assumptions, that can be directly applied to several generalized ensemble algorithms, including simulated tempering, parallel tempering (better known as replica-exchange among temperatures), and replica-exchange simulated tempering. We present methods that explicitly capture the considerable temporal correlation in sequentially generated configurations using autocorrelation analysis. This allows estimation of the statistical uncertainty in WHAM estimates of expectations for the canonical ensemble. We test the method with a one-dimensional model system and then apply it to the estimation of potentials of mean force from parallel tempering simulations of the alanine dipeptide in both implicit and explicit solvent.

Use of the Weighted Histogram Analysis Method for the Analysis of Simulated and Parallel Tempering Simulations.

: In using a computer experiment to calculate the time correlation function of some dynamical variable, the ensemble average over an equilibrium distribution in phase space often is replaced by a time average over a finite interval T. It is shown here that the statistical uncertainty due to this kind of average is of the order of 1/the square root of T. The coefficient of the square root is related to a characteristic relaxation time of the correlation function. If only time averaging is performed, the resulting statistical uncertainty in typical computer experiments may be of the order of twenty percent. (Author)

Statistical error due to finite time averaging in computer experiments.

A generalization of the Navier-Stokes equation, valid for wavelengths and times of a molecular order of magnitude, is discussed on the basis of viscoelastic behavior of simple classical liquids. In this theory, transport coefficients are replaced by appropriate viscoelastic memory functions. The theory is verified by analyzing the data on current-correlation functions obtained from computer experiments. Three different models for the time dependence of the viscoelastic memory are investigated, namely, a single-exponential decay, a modified-exponential decay, and a Gaussian decay. It is obsrved that the memory functions are approximately Gaussian, at least for times of the order of one or two relaxation times. This is in agreement with a conjecture of Forster, Martin, and Yip. The wave-number dependence of the half-width of the Gaussian decay, and of the longitudinal- and shear-viscosity coefficients, are found from computer experiments. The extrapolated values of these transport coefficients, in the limit $k\ensuremath{\rightarrow}0$, are in good agreement with experiments on liquid argon.

Generalized Hydrodynamics and Analysis of Current Correlation Functions

Hydrodynamics and Collective Angular-Momentum Fluctuations in Molecular Fluids

A hydrodynamic solution for the decay of the angular momentum of an initially moving volume element in an otherwise stationary, compressible, viscous fluid predicts a long time decay of the angular momentum autocorrelation function which behaves as [ηst / Mρ]−(d+2)/2 where ηs is the shear viscosity, Mρ is the mass density, and d is the dimension of the system. This slow decay, which would not lead to the divergence of the rotational diffusion coefficient, or of the spin–rotation relaxation time, is caused by a vortex field which results from the interaction between a structured particle and host fluid. This result is analogous to the long time tail in the linear momentum autocorrelation function recently reported by Alder and Wainwright.

Cooperative Phenomena and the Decay of the Angular Momentum Correlation Function at Long Times

Recent light-scattering experiments which have investigated the splittings in the depolarized Rayleigh spectrum of certain nonassociated liquids are discussed in the context of generalized hydrodynamics. It is shown that a purely hydrodynamic or viscoelastic theory does not account for important features of the observed spectrum. However, if angular momentum fluctuations are considered, many of the features of the observed spectra can be accounted for. Moreover, a theory due to Rytov is discussed and studied in the context of generalized hydrodynamics.

Narinder K. Ailawadi

Papers

Statistical error due to finite time averaging in computer experiments.

Generalized Hydrodynamics and Analysis of Current Correlation Functions

Hydrodynamics and Collective Angular-Momentum Fluctuations in Molecular Fluids

Cooperative Phenomena and the Decay of the Angular Momentum Correlation Function at Long Times

Light Scattering from Shear Waves: The Role of Angular Momentum Fluctuations in Light Scattering