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.     

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.     

Effect of periodic box size on aqueous molecular dynamics simulation of a DNA dodecamer with particle-mesh Ewald method

The particle-mesh Ewald (PME) method is considered to be both efficient and accurate for the evaluation of long-range electrostatic interactions in large macromolecular systems being studied by molecular dynamics simulations. This method assumes "infinite" periodic boundary conditions resembling the symmetry of a crystal environment. Can such a "solid-state" method accurately portray a macromolecular solute such as DNA in solution? To address this issue, we have performed three 1500-ps PME molecular dynamics (MD) simulations, each with a different box size, on the d(CGCGA6CG)-(CGT6CGCG) DNA dodecamer. The smallest box had the DNA solvated by a layer of water molecules of at least 5 A along each orthogonal direction. The intermediate size box and the largest box had the DNA solvated by a layer of water molecules of at least 10 A and 15 A, respectively, along each orthogonal direction. The intermediate size box in the present study is similar to the box size currently chosen by most workers in the field. Based on a comparison of RMSDs and curvature for this single DNA dodecamer sequence, the larger two box sizes do not appear to afford any extra benefit over the smallest box. The implications of this finding are briefly discussed.     

Structure and dynamics of the conserved protein GPI anchor core inserted into detergent micelles

A suitable approach which combines nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations have been used to study the structure and the dynamics of the glycosylphosphatidylinositol (GPI) anchor Manalphal-2Manalpha1-6Manalphal -4GlcNalpha1-6myo-inositol-1-OPO(3)-sn-1,2-dimyristoylglycerol (1) incorporated into dodecylphosphatidylcholine (DPC) micelles. The results have been compared to those previously obtained for the products obtainable from (1) after phospholipase cleavage, in aqueous solution. Relaxation and diffusion NMR experiments were used to establish the formation of stable aggregates and the insertion of (1) into the micelles. MD calculations were performed including explicit water, sodium and chloride ions and using the Particle Mesh Ewald approach for the evaluation of the electrostatic energy term. The MD predicted three dimensional structure and dynamics were substantiated by nuclear overhauser effect (NOE) measurements and relaxation data. The pseudopentasaccharide structure, which was not affected by incorporation of (1) into the micelle, showed a complex dynamic behaviour with a faster relative motion at the terminal mannopyranose unit and decreased mobility close to the micelle. This motion may be better described as an oscillation relative to the membrane rather than a folding event.     

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.     

Analysis of the effect of electrostatic energy truncation in molecular dynamics simulations of immunoglobulin G light chain dimer

Molecular dynamics (MD) simulations of immunoglobulin G (IgG) light chain dimer using particle mesh Ewald (PME) and cutoff methods of treating electrostatic interactions were performed. The results indicate that structural parameters (RMSD, radius of gyration, solvent accessible surface) are very similar for both schemes; however, PME simulation shows increased mobility of side chains. This leads to larger fluctuations in the distance between the monomers in the dimer molecule, and, as a consequence, results in decreased number of interactions across the dimer interface. The wall clock time of the simulations was also compared. It was shown that the PME method is approximately 30% faster than the cutoff method for the system studied on a single processor.Figure Backbone order parameters for PME (red) and cutoff (green) calculations. Thick, horizontal lines show stable secondary structures     

Molecular dynamics simulation study of DNA triplex formed by mixed sequences in solution

The unrestrained molecular dynamics simulation of the triple helical DNA with mix sequences d(GACTGGTGAC).d(CTGACCACTG)*d (GACTGGTGAC), using the particle mesh Ewald sum, is presented here. The Ewald summation method effectively eliminates the usualcut-of of the long range interactions and allowed us to evaluate the full effect of the electrostatic forces. The AMBER5.0 force field has been used during the simulation in solvent. The MD results support a dynamically stable model of DNA triplex over the entire length of the trajectory. The duplex structure assumes the conformation, which is very close to B-DNA. In mixed sequences the purine bases occurs in both strand of DNA duplex. The bases of third strand do not favor the Hoogsteen or/and reverse Hoogsteen type of Hydrogen bonding but they form hydrogen bonds with the bases of both the strand of DNA duplex. The orientation of the third strand is parallel to one of the strand of duplex and all nucleotides (C, A, G & T) show isomorphic behavior with respect to the DNA duplex. The conformation of all the three strands is almost same except few exceptions. Due to interaction of third strand the conformational change in the duplex structure and a finite amount of displacement in the W-C base pairs have been observed. The conformational variation of the back bone torsion angles and helicoidal parameters, groove widths have been discussed. The sequence dependent effects on local conformation, helicoidal and morphological structure, width of the grooves of DNA helix may have important implication for understanding the functional energetics and specificity of interactions of DNA and its triplexes with proteins, pharmaceutical agents and other ligands.     

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.     

A 5-nanosecond molecular dynamics trajectory for B-DNA: analysis of structure, motions, and solvation.

We report the results of four new molecular dynamics (MD) simulations on the DNA duplex of sequence d(CGCGAATTCGCG)2, including explicit consideration of solvent water, and a sufficient number of Na+ counterions to provide electroneutrality to the system. Our simulations are configured particularly to characterize the latest MD models of DNA, and to provide a basis for examining the sensitivity of MD results to the treatment of boundary conditions, electrostatics, initial placement of solvent, and run lengths. The trajectories employ the AMBER 4.1 force field. The simulations use particle mesh Ewald summation for boundary conditions, and range in length from 500 ps to 5.0 ns. Analysis of the results is carried out by means of time series for conformationalm, helicoidal parameters, newly developed indices of DNA axis bending, and groove widths. The results support a dynamically stable model of B-DNA for d(CGCGAATTCGCG)2 over the entire length of the trajectory. The MD results are compared with corresponding crystallographic and NMR studies on the d(CGCGAATTCGCG)2 duplex, and placed in the context of observed behavior of B-DNA by comparisons with the complete crystallographic data base of B-form structures. The calculated distributions of mobile solvent molecules, both water and counterions, are displayed. The calculated solvent structure of the primary solvation shell is compared with the location of ordered solvent positions in the corresponding crystal structure. The results indicate that ordered solvent positions in crystals are roughly twice as structured as bulk water. Detailed analysis of the solvent dynamics reveals evidence of the incorporation of ions in the primary solvation of the minor groove B-form DNA. The idea of localized complexation of otherwise mobile counterions in electronegative pockets in the grooves of DNA helices introduces an additional source of sequence-dependent effects on local conformational, helicoidal, and morphological structure, and may have important implications for understanding the functional energetics and specificity of the interactions of DNA and RNA with regulatory proteins, pharmaceutical agents, and other ligands.     

Restrained molecular dynamics of solvated duplex DNA using the particle mesh Ewald method

Restrained and unrestrained aqueous solution molecular dynamics simulations applying the particle mesh Ewald (PME) method to DNA duplex structures previously determined via in vacuo restrained molecular dynamics with NMR-derived restraints are reported. Without experimental restraints, the DNA decamer, d(CATTTGCATC)d(GATGCAAATG) and trisdecamer, d(AGCTTGCCTTGAG)d(CTCAAGGCAAGCT), structures are stable on the nanosecond time scale and adopt conformations in the B-DNA family. These free DNA simulations exhibit behavior characteristic of PME simulations previously performed on DNA sequences, including a low helical twist, frequent sugar pucker transitions, BI- BII(–) transitions and coupled crankshaft (–) motion. Refinement protocols similar to the original in vacuo restrained molecular dynamics (RMD) refinements but in aqueous solution using the Cornell et al. force field [Cornell et al. (1995) J. Am. Chem. Soc., 117, 5179–5197] and a particle mesh Ewald treatment produce structures which fit the restraints very well and are very similar to the original in vacuo NMR structure, except for a significant difference in the average helical twist. Figures of merit for the average structure found in the RMD PME decamer simulations in solution are equivalent to the original in vacuo NMR structure while the figures of merit for the free MD simulations are significantly higher. The free MD simulations with the PME method, however, lead to some sequence-dependent structural features in common with the NMR structures, unlike free MD calculations with earlier force fields and protocols. There is some suggestion that the improved handling of electrostatics by PME improves long-range structural aspects which are not well defined by the short-range nature of NMR restraints.     

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.     

Importance of explicit salt ions for protein stability in molecular dynamics simulation.

The accurate and efficient treatment of electrostatic interactions is one of the challenging problems of molecular dynamics simulation. Truncation procedures such as switching or shifting energies or forces lead to artifacts and significantly reduced accuracy. The particle mesh Ewald (PME) method is one approach to overcome these problems by providing a computationally efficient means of calculating all long-range electrostatic interactions in a periodic simulation box by use of fast Fourier transformation techniques. For the application of the PME method to the simulation of a protein with a net charge in aqueous solution, counterions are added to neutralize the system. The usual procedure is to add charge-balancing counterions close to charged residues to neutralize the protein surface. In the present article, we show that for MD simulation of a small protein of marginal stability, the YAP-WW domain, explicit modeling of 0.2 M ionic strength (in addition to the charge-balancing counterions) is necessary to maintain a stable protein structure. Without explicit ions throughout the periodic simulation box, the charge-balancing counterions on the protein surface diffuse away from the protein, resulting in destruction of the beta-sheet secondary structure of the WW domain.     

Hydration effects on the electrostatic potential around tuftsin

The electrostatic potential and component dielectric constants from molecular dynamics (MD) trajectories of tuftsin, a tetrapeptide with the amino acid sequence Thr–Lys–Pro–Arg in water and in saline solution are presented. The results obtained from the analysis of the MD trajectories for the total electrostatic potential at points on a grid using the Ewald technique are compared with the solution to the Poisson–Boltzmann (PB) equation. The latter was solved using several sets of dielectric constant parameters. The effects of structural averaging on the PB results were also considered. Solute conformational mobility in simulations gives rise to an electrostatic potential map around the solute dominated by the solute monopole (or lowest order multipole). The detailed spatial variation of the electrostatic potential on the molecular surface brought about by the compounded effects of the distribution of water and ions close to the peptide, solvent mobility, and solute conformational mobility are not qualitatively reproducible from a reparametrization of the input solute and solvent dielectric constants to the PB equation for a single structure or for structurally averaged PB calculations. Nevertheless, by fitting the PB to the MD electrostatic potential surfaces with the dielectric constants as fitting parameters, we found that the values that give the best fit are the values calculated from the MD trajectories. Implications of using such field calculations on the design of tuftsin peptide analogues are discussed. © 1999 John Wiley & Sons, Inc. Biopoly 50: 133–143, 1999     

Molecular Dynamics Simulation Study of DNA Triplex Formed by Mixed Sequences in Solution

Abstract

The unrestrained molecular dynamics simulation of the triple helical DNA with mix sequences d(GACTGGTGAC)?d(CTGACCACTG)*d (GACTGGTGAC), using the particle mesh Ewald sum, is presented here. The Ewald summation method effectively eliminates the usual “cut-off” of the long—range interactions and allowed us to evaluate the full effect of the electrostatic forces. The AMBER5.0 force field has been used during the simulation in solvent. The MD results support a dynamically stable model of DNA triplex over the entire length of the trajectory. The duplex structure assumes the conformation, which is very close to B-DNA. In mixed sequences the purine bases occurs in both strand of DNA duplex. The bases of third strand do not favor the Hoogsteen or/and reverse Hoogsteen type of Hydrogen bonding but they form hydrogen bonds with the bases of both the strand of DNA duplex. The orientation of the third strand is parallel to one of the strand of duplex and all nucleotides (C, A, G & T) show isomorphic behavior with respect to the DNA duplex. The conformation of all the three strands is almost same except few exceptions. Due to interaction of third strand the conformational change in the duplex structure and a finite amount of displacement in the W-C base pairs have been observed. The conformational variation of the back bone torsion angles and helicoidal parameters, groove widths have been discussed. The sequence—dependent effects on local conformation, helicoidal and morphological structure, width of the grooves of DNA helix may have important implication for understanding the functional energetics and specificity of interactions of DNA and its triplexes with proteins, pharmaceutical agents and other legends.     

Application of isotropic periodic sum method for 4-pentyl-4′-cyanobiphenyl liquid crystal

In future large-scale molecular dynamics (MD) simulations that will use parallel computing, the isotropic periodic sum (IPS) method is expected to effectively reduce the cost of interaction calculations while maintaining adequate accuracy. To assess the accuracy of this method in estimating low-charge-density polymer systems, we performed atomistic MD simulations of the bulk state of liquid crystal systems based on 4-pentyl-4′-cyanobiphenyl (5CB). In conditions of 270 K ≤ T ≤ 320 K and a normal pressure, the temperature dependence of the density, potential energy and order parameter was estimated using the IPS and Ewald sum method. The results of the IPS method and Ewald sum were consistent within the range of error. In conditions close to the phase transition point, however, the averaged values of potential energy and order parameter had a small difference. We concluded that the fundamental physical properties for the bulk state of 5CB systems are determined reasonably by using the IPS method, at least in conditions that are not close to the phase transition point.     

DNA structure: what's in charge?

DNA structure is well known to be sensitive to hydration and ionic strength. Recent theoretical predictions and experimental observations have raised the idea of the intrusion of monovalent cations into the minor groove spine of hydration in B-form DNA. To investigate this further, extensions and further analysis of molecular dynamics (MD) simulations on d(CGCCGAATTCGCG), d(ATAGGCAAAAAATAGGCAAAAATGG) and d(G(5)-(GA(4)T(4)C)(2)-C(5)), including counterions and water, have been performed. To examine the effective of minor groove ions on structure, we analyzed the MD snapshots from a 15 ns trajectory on d(CGCGAATTCGCG) as two subsets: those exhibiting a minor groove water spine and those with groove-bound ions. The results indicate that Na(+) at the ApT step of the minor groove of d(CGCCGAATTCGCG) makes only small local changes in the DNA structure, and these changes are well within the thermal fluctuations calculated from the MD. To examine the effect of ions on the differential stability of a B-form helix, further analysis was performed on two longer oligonucleotides, which exhibit A-tract-induced axis bending localized around the CpG step in the major groove. Plots of axis bending and proximity of ions to the bending locus were generated as a function of time and revealed a strong linear correlation, supporting the idea that mobile cations play a key role in local helix deformations of DNA and indicating ion proximity just precedes the bending event. To address the issue of "what's in charge?" of DNA structure more generally, the relative free energy of A and B-form d(CGCGAATTCGCG) structures from MD simulations under various environmental circumstances were estimated using the free energy component method. The results indicate that the dominant effects on conformational stability come from the electrostatic free energy, but not exclusively from groove bound ions per se, but from a balance of competing factors in the electrostatic free energy, including phosphate repulsions internal to the DNA, the electrostatic component of hydration (i.e. solvent polarization), and electrostatic effects of the counterion atmosphere. In summary, free energy calculations indicate that the electrostatic component is dominant, MD shows temporal proximity of mobile counterions to be correlated with A-track-induced bending, and thus the mobile ion component of electrostatics is a significant contributor. However, the MD structure of the dodecamer d(CGCGAATTCGCG) is not highly sensitive to whether there is a sodium ion in the minor groove.     

Electrostatic interactions play an essential role in DNA repair and cold-adaptation of Uracil DNA glycosylase

Life has adapted to most environments on earth, including low and high temperature niches. The increased catalytic efficiency and thermoliability observed for enzymes from organisms living in constantly cold regions when compared to their mesophilic and thermophilic cousins are poorly understood at the molecular level. Uracil DNA glycosylase (UNG) from cod (cUNG) catalyzes removal of uracil from DNA with an increased k_cat and reduced K_m relative to its warm-active human (hUNG) counterpart. Specific issues related to DNA repair and substrate binding/recognition (K_m) are here investigated by continuum electrostatics calculations, MD simulations and free energy calculations. Continuum electrostatic calculations reveal that cUNG has surface potentials that are more complementary to the DNA potential at and around the catalytic site when compared to hUNG, indicating improved substrate binding. Comparative MD simulations combined with free energy calculations using the molecular mechanics-Poisson Boltzmann surface area (MM-PBSA) method show that large opposing energies are involved when forming the enzyme-substrate complexes. Furthermore, the binding free energies obtained reveal that the Michaelis-Menten complex is more stable for cUNG, primarily due to enhanced electrostatic properties, suggesting that energetic fine-tuning of electrostatics can be utilized for enzymatic temperature adaptation. Energy decomposition pinpoints the residual determinants responsible for this adaptation. Figure Electrostatic isosurfaces of cod uracil DNA glycosylase in complex with double stranded DNA     

Cytosine ribose flexibility in DNA: a combined NMR 13C spin relaxation and molecular dynamics simulation study

Using (13)C spin relaxation NMR in combination with molecular dynamic (MD) simulations, we characterized internal motions within double-stranded DNA on the pico- to nano-second time scale. We found that the C-H vectors in all cytosine ribose moieties within the Dickerson-Drew dodecamer (5'-CGCGAATTCGCG-3') are subject to high amplitude motions, while the other nucleotides are essentially rigid. MD simulations showed that repuckering is a likely motional model for the cytosine ribose moiety. Repuckering occurs with a time constant of around 100 ps. Knowledge of DNA dynamics will contribute to our understanding of the recognition specificity of DNA-binding proteins such as cytosine methyltransferase.     

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.