Explicit-solvent molecular dynamics simulations of a DNA tetradecanucleotide duplex: lattice-sum versus reaction-field electrostatics

Five long-timescale (10 ns) explicit-solvent molecular dynamics simulations of a DNA tetradecanucleotide dimer are performed using the GROMOS 45A4 force field and the simple-point-charge water model, in order to investigate the effect of the treatment of long-range electrostatic interactions as well as of the box shape and size on the structure and dynamics of the molecule (starting from an idealised B-DNA conformation). Long-range electrostatic interactions are handled using either a lattice-sum (LS) method (particle–particle–particle–mesh; one simulation performed within a cubic box) or a cutoff-based reaction-field (RF) method (four simulations, with long-range cutoff distances of 1.4 or 2.0 nm and performed within cubic or truncated octahedral periodic boxes). The overall double-helical structure, including Watson–Crick (WC) base-pairing, is well conserved in the simulation employing the LS scheme. In contrast, the WC base-pairing is nearly completely disrupted in the four simulations employing the RF scheme. These four simulations result in highly distorted compact (cutoff distance of 1.4 nm) or extended (cutoff distance of 2 nm) structures, irrespective of the shape and size of the computational box. These differences observed between the two schemes seem correlated with large differences in the radial distribution function between charged entities (backbone phosphate groups and sodium counterions) within the system.     

Analysis and evaluation of channel models: simulations of alamethicin

Alamethicin is an antimicrobial peptide that forms stable channels with well-defined conductance levels. We have used extended molecular dynamics simulations of alamethicin bundles consisting of 4, 5, 6, 7, and 8 helices in a palmitoyl-oleolyl-phosphatidylcholine bilayer to evaluate and analyze channel models and to link the models to the experimentally measured conductance levels. Our results suggest that four helices do not form a stable water-filled channel and might not even form a stable intermediate. The lowest measurable conductance level is likely to correspond to the pentamer. At higher aggregation numbers the bundles become less symmetrical. Water properties inside the different-sized bundles are similar. The hexamer is the most stable model with a stability comparable with simulations based on crystal structures. The simulation was extended from 4 to 20 ns or several times the mean passage time of an ion. Essential dynamics analyses were used to test the hypothesis that correlated motions of the helical bundles account for high-frequency noise observed in open channel measurements. In a 20-ns simulation of a hexameric alamethicin bundle, the main motions are those of individual helices, not of the bundle as a whole. A detailed comparison of simulations using different methods to treat long-range electrostatic interactions (a twin range cutoff, Particle Mesh Ewald, and a twin range cutoff combined with a reaction field correction) shows that water orientation inside the alamethicin channels is sensitive to the algorithms used. In all cases, water ordering due to the protein structure is strong, although the exact profile changes somewhat. Adding an extra 4-nm layer of water only changes the water ordering slightly in the case of particle mesh Ewald, suggesting that periodicity artifacts for this system are not serious.     

Cutoff size need not strongly influence molecular dynamics results for solvated polypeptides

The correct treatment of van der Waals and electrostatic nonbonded interactions in molecular force fields is essential for performing realistic molecular dynamics (MD) simulations of solvated polypeptides. The most computationally tractable treatment of nonbonded interactions in MD utilizes a spherical distance cutoff (typically, 8-12 A) to reduce the number of pairwise interactions. In this work, we assess three spherical atom-based cutoff approaches for use with all-atom explicit solvent MD: abrupt truncation, a CHARMM-style electrostatic shift truncation, and our own force-shifted truncation. The chosen system for this study is an end-capped 17-residue alanine-based alpha-helical peptide, selected because of its use in previous computational and experimental studies. We compare the time-averaged helical content calculated from these MD trajectories with experiment. We also examine the effect of varying the cutoff treatment and distance on energy conservation. We find that the abrupt truncation approach is pathological in its inability to conserve energy. The CHARMM-style shift truncation performs quite well but suffers from energetic instability. On the other hand, the force-shifted spherical cutoff method conserves energy, correctly predicts the experimental helical content, and shows convergence in simulation statistics as the cutoff is increased. This work demonstrates that by using proper and rigorous techniques, it is possible to correctly model polypeptide dynamics in solution with a spherical cutoff. The inherent computational advantage of spherical cutoffs over Ewald summation (and related) techniques is essential in accessing longer MD time scales.     

Long-range electrostatic interactions in molecular dynamics: an endothelin-1 case study

An extensive conformational search in explicit solvent was performed in order to compare the influence of different long-range electrostatic interaction treatments in molecular dynamics. The short peptide endothelin-1 was selected as the subject of molecular dynamics studies that started from both X-ray and NMR obtained structures. Electrostatic interactions were treated using two of the most common methods--residue-based cutoff and particle mesh Ewald (PME). Analyses of free energy calculations (MM-PBSA method used), secondary structure elements and hydrogen bonds were performed, and there suggested that there is no unambiguous conclusion about which of the two methods of long-range electrostatics treatment should be used in MD simulations in this case. The most reliable data was provided by a trajectory that started with the NMR structure and used the cutoff method to treat electrostatic interactions. This leads to a recommendation that the choice of electrostatics treatment should be made carefully and not automatically by choosing the PME method simply because it is the most widely used.     

On the Ewald artifacts in computer simulations. The test-case of the octaalanine peptide with charged termini

The treatment of electrostatic interactions in molecular simulations is of fundamental importance. Ewald and related methods are being increasingly used to the detriment of cutoff schemes, which are known to produce several artifacts. A potential drawback of the Ewald method is the spatial periodicity that is imposed to the system, which could produce artifacts when applied in the simulation of liquids. In this work we analyze the octaalanine peptide with charged termini in explicit solvent, for which severe effects due to the use of Ewald sums were predicted using continuum electrostatics. Molecular Dynamics simulations for a total of 158 nanoseconds were performed in cells of different sizes. From the comparison of the results of different system sizes, no significant periodicity-induced artifacts were observed. It is argued that in current biomolecular simulations, the incomplete sampling is likely to affect the results to a larger extent than the artifacts induced by the use of Ewald sums.     

Long-range Electrostatic Interactions in Molecular Dynamics: An Endothelin-1 Case Study

Abstract

An extensive conformational search in explicit solvent was performed in order to compare the influence of different long-range electrostatic interaction treatments in molecular dynamics. The short peptide endothelin-1 was selected as the subject of molecular dynamics studies that started from both X-ray and NMR obtained structures. Electrostatic interactions were treated using two of the most common methods—residue-based cutoff and particle mesh Ewald (PME). Analyses of free energy calculations (MM-PBSA method used), secondary structure elements and hydrogen bonds were performed, and there suggested that there is no unambiguous conclusion about which of the two methods of long-range electrostatics treatment should be used in MD simulations in this case. The most reliable data was provided by a trajectory that started with the NMR structure and used the cutoff method to treat electrostatic interactions. This leads to a recommendation that the choice of electrostatics treatment should be made carefully and not automatically by choosing the PME method simply because it is the most widely used.     

On the Ewald Artifacts in Computer Simulations. The Test-Case of the Octaalanine Peptide With Charged Termini

Abstract

The treatment of electrostatic interactions in molecular simulations is of fundamental importance. Ewald and related methods are being increasingly used to the detriment of cutoff schemes, which are known to produce several artifacts. A potential drawback of the Ewald method is the spatial periodicity that is imposed to the system, which could produce artifacts when applied in the simulation of liquids. In this work we analyze the octaalanine peptide with charged termini in explicit solvent, for which severe effects due to the use of Ewald sums were predicted using continuum electrostatics. Molecular Dynamics simulations for a total of 158 nanoseconds were performed in cells of different sizes. From the comparison of the results of different system sizes, no significant periodicity-induced artifacts were observed. It is argued that in current biomolecular simulations, the incomplete sampling is likely to affect the results to a larger extent than the artifacts induced by the use of Ewald sums.     

Parameterization of Coulomb interaction in three-dimensional periodic systems

A simple method is proposed to calculate Coulomb interactions in three-dimensional periodic cubic systems. It is based on the parameterization of the interaction on polynomials and rational functions. The parameterized functions are compared to tabulation methods, to the Ewald calculations and cubic harmonic function fits found in the literature. Our parameterizations are computationally more efficient than, the use of tabulations at all cases and seem to be more efficient than the cubic harmonic parameterizations in the case of simultaneous potential energy and force calculations. In comparison to the Ewald method, it is feasible to use the parameterizations on small systems and on systems, where pair-wise additive short-range interactions are dominant. One also may prefer the parameterizations to the Ewald method for large systems, if limited accuracy is needed. The embedding of the method into existing molecular dynamics and Monte Carlo simulation codes is very simple. The presented investigation contains some numerical experimental data to support the correct theoretical partition of potential energy in periodic systems, as well.     

Molecular dynamics simulations of a protein-protein dimer: particle-mesh Ewald electrostatic model yields far superior results to standard cutoff model.

In this article we present two 1000 ps molecular dynamics simulations on the rat micro-glutathione S-transferase dimeric enzyme in complex with the product 1-(S-glutathionyl)-2,4-dinitrobenzene, in a periodic box with explicit solvent molecules, and investigate the effect of long-range electrostatics models on the structure and dynamics of the dimer and its components. One simulation used the standard cutoff method (10A), whilst the other used the particle-mesh Ewald (PME) method. We monitored the root mean-square atomic deviation (RMSD) from the initial crystal structure to examine the convergence of both simulations, as well as several other structural parameters such as the distance between active sites, rigid body rotation between domains in subunits, radius of gyration, B-factors, number of hydrogen bonds and salt bridges and solvent-accessible surface area. For example, with the PME method, the dimer structure remains much closer to the initial crystallographic structure with an average RMSD of 1.3A +/- 0.1A and 1.0A +/- 0.1A for all heavy and backbone atoms, respectively, in the last 200 ps; the respective values for the cutoff simulation are 4.7A +/- 0.3A and 4.2A +/- 0.3A. The large deviations observed in the cutoff simulation severely affected the stability of the enzyme dimer and its complex with the bound product. This finding is contrary to that found in a similar study of the monomeric protein ubiquitin [Fox, T. & Kollman, P. A. Proteins Struct. Func. Genet. 25, 315-334 (1996)]. Unlike the earlier published work, the present study provides evidence that the standard cutoff method is not generally valid for the study of protein complexes, or their subunits.     

Molecular dynamics simulations of lipid bilayers: major artifacts due to truncating electrostatic interactions

We study the influence of truncating the electrostatic interactions in a fully hydrated pure dipalmitoylphosphatidylcholine (DPPC) bilayer through 20 ns molecular dynamics simulations. The computations in which the electrostatic interactions were truncated are compared to similar simulations using the particle-mesh Ewald (PME) technique. All examined truncation distances (1.8-2.5 nm) lead to major effects on the bilayer properties, such as enhanced order of acyl chains together with decreased areas per lipid. The results obtained using PME, on the other hand, are consistent with experiments. These artifacts are interpreted in terms of radial distribution functions g(r) of molecules and molecular groups in the bilayer plane. Pronounced maxima or minima in g(r) appear exactly at the cutoff distance indicating that the truncation gives rise to artificial ordering between the polar phosphatidyl and choline groups of the DPPC molecules. In systems described using PME, such artificial ordering is not present.     

Structure and dynamics of calcium-activated calmodulin in solution.

Two 4-ns molecular dynamics simulations of calcium loaded calmodulin in solution have been performed, using both standard nonbonded cutoffs and Ewald summation to treat electrostatic interactions. Our simulation results are generally consistent with solution experimental studies of calmodulin structure and dynamics, including NMR, cross-linking, fluorescence and x-ray scattering. The most interesting result of the molecular dynamics simulations is the detection of large-scale structural fluctuations of calmodulin in solution. The globular N- and C-terminal domains tend to move approximately like rigid bodies, with fluctuations of interdomain distances within a 7 A range and of interdomain angles by up to 60 deg. Essential dynamics analysis indicates that the three dominant types of motion involve bending of the central helix in two perpendicular planes and a twist in which the domains rotate in opposite directions around the central helix. In the more realistic Ewald trajectory the protein backbone remains mostly within a 2-3 A root-mean-square distance from the crystal structure, the secondary structure within the domains is conserved and middle part of the central helix becomes disordered. The central helix itself exhibits limited fluctuations, with its bend angle exploring the 0-50 degrees range and the end-to-end distance falling in 39-43 A. The results of the two simulations were similar in many respects. However, the cutoff trajectory exhibited a larger deviation from the crystal, loss of several helical hydrogen bonds in the N-terminal domain and lack of structural disorder in the central helix.     

On the truncation of long-range electrostatic interactions in DNA

Long-range interactions are known to play an important role in highly polar biomolecules like DNA. In molecular dynamics simulations of nucleic acids and proteins, an accurate treatment of the long-range interactions are crucial for achieving stable nanosecond trajectories. In this report, we evaluate the structural and dynamic effects on a highly charged oligonucleotide in aqueous solution from different long-range truncation methods. Two group-based truncation methods, one with a switching function and one with a force-switching function were found to fail to give accurate stable trajectories close to the crystal structure. For these group-based truncation methods, large root mean square (rms) deviations from the initial structure were obtained and severe distortions of the oligonucleotide were observed. Another group-based truncation scheme, which used an abrupt truncation at 8. 0 A or at 12.0 A was also investigated. For the short cutoff distance, the conformations deviated far away from the initial structure and were significantly distorted. However, for the longer cutoff, where all necessary electrostatic interactions were included, the trajectory was quite stable. For the particle mesh Ewald (PME) truncation method, a stable DNA simulation with a heavy atom rms deviation of 1.5 A was obtained. The atom-based truncation methods also resulted in stable trajectories, according to the rms deviation from the initial B-DNA structure, of between 1.5 and 1.7 A for the heavy atoms. In these stable simulations, the heavy atom rms deviations were approximately 0.6-1.0 A lower for the bases than for the backbone. An increase of the cutoff radius from 8 to 12 A decreased the rms deviation by approximately 0.2 A for the atom-based truncation method with a force-shifting function, but increased the computational time by a factor of 2. Increasing the cutoff from 12 to 18 A for the atom-based truncation method with a force-shifting function requires 2-3 times more computational time, but did not significantly change the rms deviation. Similar rms deviations from the initial structure were found for the atom-based method with a force-shifting function and for the PME method. The computational cost was longer for the PME method with a cutoff of 12. 0 A for the direct space nonbonded calculations than for the atom-based truncation method with a force-shifting function and a cutoff of 12.0 A. If a nonperiodic boundary, e.g., a spherical boundary, was used, a considerable speedup could be achieved. From the rms fluctuations, the terminal nucleotides and especially the cytidines were found to be more flexible than the nonterminal nucleotides. The B-DNA form of the oligonucleotide was maintained throughout the simulations and is judged to depend on the parameters of the energy function and not on the truncation method used to handle the long-range electrostatic interactions. To perform accurate and stable simulations of highly charged biological macromolecules, we recommend that the atom-based force-shift method or the PME method should be used for the long-range electrostatics interactions.     

Molecular dynamics study of complexes of poly(glutamate) and dodecyltrimethylammonium

The supramolecular organization of self-assembled stoichiometric complexes formed by dodecyltrimethylammonium cations and ionized poly(gamma-glutamic) acid has been investigated in chloroform solution. Atomistic molecular dynamics simulations have been performed considering three different starting conformations for the polyelectrolyte chain, two sets of electrostatic parameters, and two methods for evaluating the electrostatic interactions. Results indicate that the polypeptide chain tends to adopt an alpha-like helix conformation similar to that obtained in aqueous solution for the un-ionized poly(gamma-glutamic) acid. On the other hand, both surfactant...amide and surfactant...carboxylate interactions were identified in the complex, this multiple pattern being previously observed in other surfactant...polypeptide complexes. Although the influence of the force-field in the results has been found to be negligible, the method used to evaluate the electrostatic interactions affects significantly the dynamics of the system. The more important differences between the results obtained using the spherical cutoff and Particle Mesh Ewald methods are discussed.     

The range and shielding of dipole-dipole interactions in phospholipid bilayers

In molecular dynamics simulations of lipid bilayers, the structure is sensitive to the precise treatment of electrostatics. The dipole-dipole interactions between headgroup dipoles are not long-ranged, but the area per lipid and, through it, other properties of the bilayer are very sensitive to the detailed balance between the perpendicular and in-plane components of the headgroup dipoles. This is affected by the detailed properties of the cutoff scheme or if long-range interactions are included by Ewald or particle-mesh Ewald techniques. Interaction between the in-plane components of the headgroup dipoles is attractive and decays as the inverse sixth power of distance. The interaction is screened by the square of a dielectric permittivity close to the value for water. Interaction between the components perpendicular to the membrane plane is repulsive and decays as the inverse third power of distance. These interactions are screened by a dielectric permittivity of the order 10. Thus, despite the perpendicular components being much smaller in magnitude than the in-plane components, they will dominate the interaction energies at large distances.     

Study of the electrostatics treatment in molecular dynamics simulations

This article considers the treatment of long-range interactions in molecular dynamics simulations. We investigate the effects of using different cutoff distances, constant versus distance-dependent dielectric, and different smoothing methods. In contrast to findings of earlier studies, we find that increasing the cutoff over 8 A does not significantly improve the accuracy (Arnold and Ornstein, Proteins 1994;18:19-33), and using a distance-dependent dielectric instead of a constant dielectric also does not improve accuracy (Guenot and Kollman, Protein Sci 1992;1:1185-1205). This might depend on differences in simulation protocols or force fields, or both, because we use the CHARMM22 force field with stochastic boundary conditions, whereas earlier studies used other protocols and energy functions. We also note that the stability of the simulations is highly dependent on the starting structure, showing that accurate molecular simulations not only depend on a realistic simulation protocol but also on correct initial conditions.     

Molecular dynamics simulations of the ErbB-2 transmembrane domain within an explicit membrane environment: comparison with vacuum simulations

Two 500-ps molecular dynamics simulations performed on the single transmembrane domain of the ErbB-2 tyrosine kinase receptor immersed in a fully solvated dilauroylphosphatidyl-ethanolamine bilayer (DLPE) are compared to vacuum simulations. One membrane simulation shows that the initial alpha helix undergoes a local pi helix conversion in the peptide part embedded in the membrane core similar to that found in simulation vacuum. Lipid/water/peptide interaction analysis shows that in the helix core, the intramolecular peptide interactions are largely dominant compared to the interactions with water and lipids whereas the helix extremities are much more sensitive to these interactions at the membrane interfaces. Our results suggest that simulations in a lipid environment are required to understand the dynamics of transmembrane helices, but can be reasonably supplemented by in vacuo simulations to explore rapidly its conformational space and to describe the internal deformation of the hydrophobic core.     

The consistency of large concerted motions in proteins in molecular dynamics simulations.

A detailed investigation is presented into the effect of limited sampling time and small changes in the force field on molecular dynamics simulations of a protein. Thirteen independent simulations of the B1 IgG-binding domain of streptococcal protein G were performed, with small changes in the simulation parameters in each simulation. Parameters studied included temperature, bond constraints, cut-off radius for electrostatic interactions, and initial placement of hydrogen atoms. The essential dynamics technique was used to reveal dynamic differences between the simulations. Similar essential dynamics properties were found for all simulations, indicating that the large concerted motions found in the simulations are not particularly sensitive to small changes in the force field. A thorough investigation into the stability of the essential dynamics properties as derived from a molecular dynamics simulation of a few hundred picoseconds is provided. Although the definition of the essential modes of motion has not fully converged in these short simulations, the subspace in which these modes are confined is found to be reproducible.     

Peptide folding driven by Van der Waals interactions

Contrary to the widespread view that hydrogen bonding and its entropy effect play a dominant role in protein folding, folding into helical and hairpin-like structures is observed in molecular dynamics (MD) simulations without hydrogen bonding in the peptide-solvent system. In the widely used point charge model, hydrogen bonding is calculated as part of the interaction between atomic partial charges. It is removed from these simulations by setting atomic charges of the peptide and water to zero. Because of the structural difference between the peptide and water, van der Waals (VDW) interactions favor peptide intramolecular interactions and are a major contributing factor to the structural compactness. These compact structures are amino acid sequence dependent and closely resemble standard secondary structures, as a consequence of VDW interactions and covalent bonding constraints. Hydrogen bonding is a short range interaction and it locks the approximate structure into the specific secondary structure when it is included in the simulation. In contrast to standard molecular simulations where the total energy is dominated by charge-charge interactions, these simulation results will give us a new view of the folding mechanism.