Richard W. Pastor

CHARMM: The biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model‐building capabilities. The CHARMM program is applicable to problems involving a much broader class of many‐particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical‐molecular mechanical force fields, to all‐atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Constant pressure molecular dynamics simulation: The Langevin piston method

A new method for performing molecular dynamics simulations under constant pressure is presented. In the method, which is based on the extended system formalism introduced by Andersen, the deterministic equations of motion for the piston degree of freedom are replaced by a Langevin equation; a suitable choice of collision frequency then eliminates the unphysical ‘‘ringing’’ of the volume associated with the piston mass. In this way it is similar to the ‘‘weak coupling algorithm’’ developed by Berendsen and co‐workers to perform molecular dynamics simulation without piston mass effects. It is shown, however, that the weak coupling algorithm induces artifacts into the simulation which can be quite severe for inhomogeneous systems such as aqueous biopolymers or liquid/liquid interfaces.

Update of the CHARMM all-atom additive force field for lipids: Validation on six lipid types

A significant modification to the additive all-atom CHARMM lipid force field (FF) is developed and applied to phospholipid bilayers with both choline and ethanolamine containing head groups and with both saturated and unsaturated aliphatic chains. Motivated by the current CHARMM lipid FF (C27 and C27r) systematically yielding values of the surface area per lipid that are smaller than experimental estimates and gel-like structures of bilayers well above the gel transition temperature, selected torsional, Lennard-Jones and partial atomic charge parameters were modified by targeting both quantum mechanical (QM) and experimental data. QM calculations ranging from high-level ab initio calculations on small molecules to semiempirical QM studies on a 1,2-dipalmitoyl-sn-phosphatidylcholine (DPPC) bilayer in combination with experimental thermodynamic data were used as target data for parameter optimization. These changes were tested with simulations of pure bilayers at high hydration of the following six lipids: DPPC, 1,2-dimyristoyl-sn-phosphatidylcholine (DMPC), 1,2-dilauroyl-sn-phosphatidylcholine (DLPC), 1-palmitoyl-2-oleoyl-sn-phosphatidylcholine (POPC), 1,2-dioleoyl-sn-phosphatidylcholine (DOPC), and 1-palmitoyl-2-oleoyl-sn-phosphatidylethanolamine (POPE); simulations of a low hydration DOPC bilayer were also performed. Agreement with experimental surface area is on average within 2%, and the density profiles agree well with neutron and X-ray diffraction experiments. NMR deuterium order parameters (S(CD)) are well predicted with the new FF, including proper splitting of the S(CD) for the aliphatic carbon adjacent to the carbonyl for DPPC, POPE, and POPC bilayers. The area compressibility modulus and frequency dependence of (13)C NMR relaxation rates of DPPC and the water distribution of low hydration DOPC bilayers also agree well with experiment. Accordingly, the presented lipid FF, referred to as C36, allows for molecular dynamics simulations to be run in the tensionless ensemble (NPT), and is anticipated to be of utility for simulations of pure lipid systems as well as heterogeneous systems including membrane proteins.

An analysis of the accuracy of Langevin and molecular dynamics algorithms

Analytic expressions for mean squared positions and velocities of a harmonic oscillator are derived for Langevin dynamics algorithms valid in the high and low friction limits, and for the Verlet algorithm. For typical values of the parameters, errors in the positions are small. However, if the velocity is defined by the usual Verlet form, kinetic energies (and therefore calculated temperatures) can be in error by several per cent for the Langevin algorithms. If the Bunger-Brooks-Karplus algorithm is used to calculate positions, a simple redefinition of the velocity results greatly in improved kinetic energies. In addition, due to cancellation of errors in the velocities and the positions, the correct virial is obtained. The effect of including the force derivative in diffusive algorithms is examined. Positional and velocity averages are calculated for the Verlet algorithm for arbitrary initial conditions, and errors in the total energy and virial are analysed. Connection is made with the Langevin algorith...

Additive empirical force field for hexopyranose monosaccharides

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 α‐ and β‐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.

Molecular Dynamics Studies of Polyethylene Oxide and Polyethylene Glycol: Hydrodynamic Radius and Shape Anisotropy

A revision (C35r) to the CHARMM ether force field is shown to reproduce experimentally observed conformational populations of dimethoxyethane. Molecular dynamics simulations of 9, 18, 27, and 36-mers of polyethylene oxide (PEO) and 27-mers of polyethylene glycol (PEG) in water based on C35r yield a persistence length lambda = 3.7 A, in quantitative agreement with experimentally obtained values of 3.7 A for PEO and 3.8 A for PEG; agreement with experimental values for hydrodynamic radii of comparably sized PEG is also excellent. The exponent upsilon relating the radius of gyration and molecular weight (R(g) proportional, variantM(w)(upsilon)) of PEO from the simulations equals 0.515 +/- 0.023, consistent with experimental observations that low molecular weight PEG behaves as an ideal chain. The shape anisotropy of hydrated PEO is 2.59:1.44:1.00. The dimension of the middle length for each of the polymers nearly equals the hydrodynamic radius R(h)obtained from diffusion measurements in solution. This explains the correspondence of R(h) and R(p), the pore radius of membrane channels: a polymer such as PEG diffuses with its long axis parallel to the membrane channel, and passes through the channel without substantial distortion.

A Coarse-Grained Model for Polyethylene Oxide and Polyethylene Glycol: Conformation and Hydrodynamics

A coarse-grained (CG) model for polyethylene oxide (PEO) and polyethylene glycol (PEG) developed within the framework of the MARTINI CG force field (FF) using the distributions of bonds, angles, and dihedrals from the CHARMM all-atom FF is presented. Densities of neat low molecular weight PEO agree with experiment, and the radius of gyration R(g) = 19.1 A +/- 0.7 for 76-mers of PEO (M(w) approximately 3400), in excellent agreement with neutron scattering results for an equal sized PEG. Simulations of 9, 18, 27, 36, 44, 67, 76, 90, 112, 135, and 158-mers of the CG PEO (442 < M(w) < 6998) at low concentration in water show the experimentally observed transition from ideal chain to real chain behavior at 1600 < M(w) < 2000, in excellent agreement with the dependence of experimentally observed hydrodynamic radii of PEG. Hydrodynamic radii of PEO calculated from diffusion coefficients of the higher M(w) PEO also agree well with experiment. R(g) calculated from both all-atom and CG simulations of PEO76 at 21 and 148 mg/cm(3) are found to be nearly equal. This lack of concentration dependence implies that apparent R(g) from scattering experiments at high concentration should not be taken to be the chain dimension. Simulations of PEO grafted to a nonadsorbing surface yield a mushroom to brush transition that is well described by the Alexander-de Gennes formalism.

Molecular dynamics simulation of unsaturated lipid bilayers at low hydration: parameterization and comparison with diffraction studies

A potential energy function for unsaturated hydrocarbons is proposed and is shown to agree well with experiment, using molecular dynamics simulations of a water/octene interface and a dioleoyl phosphatidylcholine (DOPC) bilayer. The simulation results verify most of the assumptions used in interpreting the DOPC experiments, but suggest a few that should be reconsidered. Comparisons with recent results of a simulation of a dipalmitoyl phosphatidylcholine (DPPC) lipid bilayer show that disorder is comparable, even though the temperature, hydration level, and surface area/lipid for DOPC are lower. These observations highlight the dramatic effects of unsaturation on bilayer structure.

Constant surface tension simulations of lipid bilayers: The sensitivity of surface areas and compressibilities

Eight molecular dynamics simulations of a hydrated lipid bilayer have been carried out differing only in the applied surface tension, γ, defining the boundary conditions of the periodic cell. The calculated surface area per molecule and deuterium order parameter profile are found to depend strongly on γ. We present several methods to calculate the area compressibility modulus, KA, from the simulations. Equivalence between the constant area and constant surface tension ensembles is investigated by comparing the present simulations with earlier work from our laboratories and we find simulation results to depend much more strongly on the specified surface area or surface tension than on the ensemble employed.

Computer simulation of liquid/liquid interfaces. I. Theory and application to octane/water

Statistical ensembles for simulating liquid interfaces at constant pressure and/or surface tension are examined, and equations of motion for molecular dynamics are obtained by various extensions of the Andersen extended system approach. Valid ensembles include: constant normal pressure and surface area; constant tangential pressure and length normal to the interface; constant volume and surface tension; and constant normal pressure and surface tension. Simulations at 293 K and 1 atm normal pressure show consistent results with each other and with a simulation carried out at constant volume and energy. Calculated surface tensions for octane/water (61.5 dyn/cm), octane/vacuum (20.4 dyn/cm) and water/vacuum (70.2 dyn/cm) are in very good agreement with experiment (51.6, 21.7, and 72.8 dyn/cm, respectively). The practical consequences of simulating with two other approaches commonly used for isotropic systems are demonstrated on octane/water: applying equal normal and tangential pressures leads to an instabil...