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 artificial periodicity in simulations of biomolecules under Ewald boundary conditions: a continuum electrostatics study.

Ewald and related methods are nowadays routinely used in explicit-solvent simulations of biomolecules, although they impose an artificial periodicity in systems which are inherently non-periodic. The consequences of this approximation should be assessed, since they may crucially affect the reliability of computer simulations under Ewald boundary conditions. In the present study we use a method based on continuum electrostatics to investigate the nature and magnitude of possible periodicity-induced artifacts on the potentials of mean force for conformational equilibria in biomolecules. Three model systems and pathways are considered: polyalanine oligopeptides (unfolding), a DNA tetranucleotide (separation of the strands), and the protein Sac7d (conformations from a molecular dynamics simulation). Artificial periodicity may significantly affect these conformational equilibria, in each case stabilizing the most compact conformation of the biomolecule. Three factors enhance periodicity-induced artifacts: (i) a solvent of low dielectric permittivity; (ii) a solute size which is non-negligible compared to the size of the unit cell; and (iii) a non-neutral solute. Neither the neutrality of the solute nor the absence of charge pairs at distances exceeding half the edge of the unit cell do guarantee the absence of artifacts.     

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.     

Monte-Carlo simulations of strongly interacting dipolar fluids between two conducting walls

We report Monte-Carlo simulation results for a strongly interacting dipolar soft sphere (DSS) fluid confined between two conducting, planar walls. The long-range dipolar interactions, including contributions from the “image dipoles” in the metal, are handled by mapping onto a problem with three-dimensional (3d) periodicity which can be treated by conventional Ewald summation methods. Considering two different wall separations our results indicate the occurence of wall-induced local and long-range ordering very similar to the related case of insulating walls. To understand this behavior we present ground-state (lattice) calculations on the basis of the Ewald sums, as well as simple macroscopic arguments appropriate for dipolar systems between conducting walls.     

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.     

Molecular Dynamics Simulations of Double-Stranded DNA in an Explicit Solvent Model with the Zero-Dipole Summation Method

Molecular dynamics (MD) simulations of a double-stranded DNA with explicit water and small ions were performed with the zero-dipole summation (ZD) method, which was recently developed as one of the non-Ewald methods. Double-stranded DNA is highly charged and polar, with phosphate groups in its backbone and their counterions, and thus precise treatment for the long-range electrostatic interactions is always required to maintain the stable and native double-stranded form. A simple truncation method deforms it profoundly. On the contrary, the ZD method, which considers the neutralities of charges and dipoles in a truncated subset, well reproduced the electrostatic energies of the DNA system calculated by the Ewald method. The MD simulations using the ZD method provided a stable DNA system, with similar structures and dynamic properties to those produced by the conventional Particle mesh Ewald method.     

The influence of the simulation box geometry in solid-state molecular simulations: phase behaviour of lithium iodide in a dynamic Monte Carlo simulation

In thermodynamic computer simulations, it is common to use cubic simulation boxes, which are then regarded as unit cells of an infinitely large cubic lattice. While this approach is adequate for gases and liquids at low densities, for dense liquids and solid cuboid boxes forming an orthorhombic lattice or parallelepiped boxes forming a triclinic lattice are shown to be advantageous, because they do not predetermine the structure of the simulated system. In this work, an extension of the Ewald summation formalism towards a parallelepiped lattice symmetry is given. Monte Carlo simulations of lithium iodide with cubic, cuboid and parallelepiped box geometries are reported; the latter is found to offer little improvement over the cuboid geometry. The existence of two hexagonal solid phases is discussed.     

Parametric dependence on shear viscosity of SPC/E water from equilibrium and non-equilibrium molecular dynamics simulations

A parametric dependent study is crucial for the accurate determination of transport coefficients such as shear viscosity. In this study, we calculate the shear viscosity of extended simple point charge water using a transverse current auto-correlation function (TCAF) from equilibrium molecular dynamics (EMD) and the periodic perturbation method from non-equilibrium molecular dynamics (NEMD) simulations for varying coupling time and system sizes. Results show that the shear viscosity calculated using EMD simulations with different thermostats varies significantly with coupling times and system size. The use of Berendsen and velocity-rescale thermostats in NEMD simulations generates a significant drift from the target temperature and results in an inconsistent shear viscosity with coupling time and system size. The use of Nosé–Hoover thermostat in NEMD simulations offers thermodynamic stability which results in a consistent shear viscosity for various coupling times and system sizes.     

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.     

Testing demographic models of effective population size

Due to practical difficulties in obtaining direct genetic estimates of effective sizes, conservation biologists have to rely on so-called 'demographic models' which combine life-history and mating-system parameters with F-statistics in order to produce indirect estimates of effective sizes. However, for the same practical reasons that prevent direct genetic estimates, the accuracy of demographic models is difficult to evaluate. Here we use individual-based, genetically explicit computer simulations in order to investigate the accuracy of two such demographic models aimed at investigating the hierarchical structure of populations. We show that, by and large, these models provide good estimates under a wide range of mating systems and dispersal patterns. However, one of the models should be avoided whenever the focal species' breeding system approaches monogamy with no sex bias in dispersal or when a substructure within social groups is suspected because effective sizes may then be strongly overestimated. The timing during the life cycle at which F-statistics are evaluated is also of crucial importance and attention should be paid to it when designing field sampling since different demographic models assume different timings. Our study shows that individual-based, genetically explicit models provide a promising way of evaluating the accuracy of demographic models of effective size and delineate their field of applicability.     

On Multiple Time-step Algorithms and the Ewald Sum

Abstract

We show how standard multiple time-step algorithms devised for systems with short-range potentials can be used successfully in simulations of periodic systems with long-range (Coulombic) potentials. Three strategies for incorporating the Ewald sum into a multiple time-step algorithm are considered. These are (i) evaluation of reciprocal space terms every time-step (ii) evaluating reciprocal space terms once every n time-steps and placing these terms in with the slowly varying forces and energies (iii) a modified form of the second strategy in which primary shell (close) electrostatic interactions are evaluated directly and the more distant interactions handled by the Ewald sum (once every n time-steps). Only the first and third approaches give satisfactory thermodynamic results. The third strategy is much more efficient than the first. With the third strategy substantial savings in cpu time are acheived in both the real space and, most importantly, the reciprocal space terms of the Ewald sum. This is achieved without significant loss of accuracy or stability. Overall execution time is decreased by a factor of between 2 and 3.     

Analysis of a novel offset cone-beam computed mammotomography system geometry for accomodating various breast sizes

We evaluate a newly developed dedicated cone-beam transmission computed mammotomography (CmT) system configuration using an optimized quasi-monochromatic cone beam technique for attenuation correction of SPECT in a planned dual-modality emission and transmission system for pendant, uncompressed breasts. In this study, we perform initial CmT acquisitions using various sized breast phantoms to evaluate an offset cone-beam geometry. This offset geometry provides conjugate projections through a full 360 degree gantry rotation, and thus yields a greatly increased effective field of view, allowing a much wider range of breast sizes to be imaged without truncation in reconstructed images. Using a tungsten X-ray tube and digital flat-panel X-ray detector in a compact geometry, we obtained initial CmT scans without shift and with the offset geometry, using geometrical frequency/resolution phantoms and two different sizes of breast phantoms. Acquired data were reconstructed using an ordered subsets transmission iterative algorithm. Projection images indicate that the larger, 20 cm wide, breast requires use of a half-cone-beam offset scan to eliminate truncation artifacts. Reconstructed image results illustrate elimination of truncation artifacts, and that the novel quasi-monochromatic beam yields reduced beam hardening. The offset geometry CmT system can indeed potentially be used for structural imaging and accurate attenuation correction for the functional dedicated breast SPECT system.     

Combined use of periodic reaction field and coarse-grained molecular dynamics simulations. I. phospholipid monolayer systems

Abstract

A periodic reaction field based on a linear-combination-based isotropic periodic sum (LIPS) method was applied for coarse-grained molecular dynamics simulations of zwitterionic lipid systems. In phospholipid monolayer systems with various number of lipid molecules, the density profile, lipid orientation and surface tension were mainly calculated using the periodic reaction field and Ewald sum. The results from the periodic reaction field were almost equal to that from the Ewald sum. It is concluded that the periodic reaction field method has a great possibility to provide a high accuracy in determining coarse-grained zwitterionic lipid systems.     

Cutoff size does strongly influence molecular dynamics results on solvated polypeptides.

The behavior of a 17-residue model peptide is analyzed by means of molecular dynamics simulations including explicitly more than a thousand water molecules. On the basis of the charge-group concept, Coulomb interactions are truncated for three values of the cutoff radius: 0.6, 1.0, and 1.4 nm. It is found that the stability of an alpha-helix, which acts as a common starting configuration, is a function of the cutoff size. While the overall stability of the helix is conserved in a simulation using a cutoff of 1.0 nm, it is lost within a very short period of 100 ps when the cutoff is increased to 1.4 nm. This demonstrates that the commonly used cutoff size of 1.0 nm is inappropriate because it does not ensure the convergence of Coulomb interactions. In order to permit an independent judgment, we have performed a 225-ps simulation using the Ewald summation technique, which is more elaborate but circumvents the problem to find an appropriate cutoff value. In contrast to the 1.4-nm cutoff trajectory, the Ewald technique simulation conserves the helical character of the peptide conformation. This demonstrates that even 1.4 nm is too short a cutoff. Due to the fundamental uncertainty introduced by the use of a simple cutoff, this truncation scheme seems questionable for molecular dynamics simulations of solvated biomolecules.     

DNA polymorphism: a comparison of force fields for nucleic acids

The improvements of the force fields and the more accurate treatment of long-range interactions are providing more reliable molecular dynamics simulations of nucleic acids. The abilities of certain nucleic acid force fields to represent the structural and conformational properties of nucleic acids in solution are compared. The force fields are AMBER 4.1, BMS, CHARMM22, and CHARMM27; the comparison of the latter two is the primary focus of this paper. The performance of each force field is evaluated first on its ability to reproduce the B-DNA decamer d(CGATTAATCG)(2) in solution with simulations in which the long-range electrostatics were treated by the particle mesh Ewald method; the crystal structure determined by Quintana et al. (1992) is used as the starting point for all simulations. A detailed analysis of the structural and solvation properties shows how well the different force fields can reproduce sequence-specific features. The results are compared with data from experimental and previous theoretical studies.     

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.     

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.     

Contribution of energy values to the analysis of global searching molecular dynamics simulations of transmembrane helical bundles

Molecular interactions between transmembrane alpha-helices can be explored using global searching molecular dynamics simulations (GSMDS), a method that produces a group of probable low energy structures. We have shown previously that the correct model in various homooligomers is always located at the bottom of one of various possible energy basins. Unfortunately, the correct model is not necessarily the one with the lowest energy according to the computational protocol, which has resulted in overlooking of this parameter in favor of experimental data. In an attempt to use energetic considerations in the aforementioned analysis, we used global searching molecular dynamics simulations on three homooligomers of different sizes, the structures of which are known. As expected, our results show that even when the conformational space searched includes the correct structure, taking together simulations using both left and right handedness, the correct model does not necessarily have the lowest energy. However, for the models derived from the simulation that uses the correct handedness, the lowest energy model is always at, or very close to, the correct orientation. We hypothesize that this should also be true when simulations are performed using homologous sequences, and consequently lowest energy models with the right handedness should produce a cluster around a certain orientation. In contrast, using the wrong handedness the lowest energy structures for each sequence should appear at many different orientations. The rationale behind this is that, although more than one energy basin may exist, basins that do not contain the correct model will shift or disappear because they will be destabilized by at least one conservative (i.e. silent) mutation, whereas the basin containing the correct model will remain. This not only allows one to point to the possible handedness of the bundle, but can be used to overcome ambiguities arising from the use of homologous sequences in the analysis of global searching molecular dynamics simulations. In addition, because clustering of lowest energy models arising from homologous sequences only happens when the estimation of the helix tilt is correct, it may provide a validation for the helix tilt estimate.     

A comparison of two indirect methods for estimating average levels of gene flow using microsatellite data

We compare the performance of Nm estimates based on FST and RST obtained from microsatellite data using simulations of the stepwise mutation model with range constraints in allele size classes. The results of the simulations suggest that the use of microsatellite loci can lead to serious overestimations of Nm, particularly when population sizes are large (N > 5000) and range constraints are high (K < 20). The simulations also indicate that, when population sizes are small (N /= 50) and many loci (nl >/= 20), RST performs better than FST for most of the parameter space. However, FST-based estimates are always better than RST when sample sizes are moderate or small (ns 相似文献