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.     

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.     

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.     

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.     

Characterization of displacement forces and image artifacts in the presence of passive medical implants in low-field (<100 mT) permanent magnet-based MRI systems,and comparisons with clinical MRI systems

PurposeTo investigate the displacement forces and image artifacts associated with passive medical implants for recently-developed low-field (<100 mT) MRI systems, and to compare these with values from higher field strengths used for clinical diagnosis.MethodsSetups were constructed to measure displacement forces in a permanent magnet-based Halbach array used for in vivo MRI at 50 mT, and results compared with measurements at 7 T. Image artifacts were assessed using turbo (fast) spin echo imaging sequences for four different passive medical implants: a septal occluder, iliac stent, pedicle screw and (ferromagnetic) endoscopic clip. Comparisons were made with artifacts produced at 1.5, 3 and 7 T. Finally, specific absorption rate (SAR) simulations were performed to determine under what operating conditions the limits might be approached at low-field.ResultsDisplacement forces at 50 mT on all but the ferromagnetic implant were between 1 and 10 mN. Image artifacts at 50 mT were much less than at clinical field strengths for all passive devices, and with the exception of the ferromagnetic clip. SAR simulations show that very long echo train (>128) turbo spin echo sequences can be run with short inter-pulse times (5–10 ms) within SAR limits.ConclusionsThis work presents the first evaluation of the effects of passive implants at field strengths less than 100 mT in terms of displacement forces, image artifacts and SAR. The results support previous claims that such systems can be used safely and usefully in challenging enviroments such as the intensive care unit.     

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     

Cutoff Errors in the Ewald Summation Formulae for Point Charge Systems

Abstract

Closed formulae for both real and reciprocal space parts of cutoff errors in the Ewald summation method in cubic periodic boundary conditions are derived. Such estimates are useful in tuning parameters in molecular simulations. Errors in both the electrostatic energy and forces are considered. The estimates apply to a disordered configuration of point charges and, with some limitations, also to point-charge molecular models. The accuracy of our estimates is tested and confirmed using simulated configurations of two systems (molten salt and diethylether) under a variety of conditions.     

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.     

The extent of representation,the relationships of artifacts and the anthropology of art

This paper provides an account of the potential roles that artifacts can occupy and distinguishes their occurrence as instruments of representation from other types of relationship of artifact use. When artifacts are employed as instruments of representation there is a deliberately constructed causal connection between the artifact and what it represents. This is in contrast to relationships of association in which the artifact takes on features of the context of its occurrence. Anthropological studies of artifact use in the native societies of Africa, America, the Indian Subcontinent and the Pacific are reviewed by comparing “dominant functions” that artifacts can serve.     

Molecular Dynamics Simulations of Calcium-Free Calmodulin in Solution

Abstract

A 4-ns molecular dynamics simulation of calcium-free calmodulin in solution has been performed, using Ewald summation to treat electrostatic interactions. Our simulation results were mostly consistent with solution experimental studies, including NMR, fluorescence and x-ray scattering. The secondary structures within the N- and C-terminal domains were conserved in the simulation, with trajectory structures similar to the NMR-derived model structure 1CFD. However, the relative orientations of the domains, for which there are no NMR restraints, differed in details between the simulation and the 1CFD model. The most interesting information provided by the simulations is that the dynamics of calcium-free calmod- ulin in solution is dominated by slow rigid body reorientations of the domains. The interdomain distance fluctuated between 29 and 39 Å, and interdomain orientation angle, defined as the pseudo-dihedral formed by the four calcium binding sites, varied between ?2° and 108°. Similarly, the domain linker region also exhibited significant fluctuations, with its length varying in the 34–45 Å range and its bend angle in the 10–100° range. The simulations are in accord with fluorescence results suggesting that calcium-free calmodulin is more compact and more flexible than the calcium activated form. Surprisingly, quite similar solvent accessibilities of the hydrophobic patches were seen in the calcium-free trajectory described in this work and previously generated calcium-loaded calmodulin simulations. Thus, our simulations suggest a reexamination of the standard model of the structural change of calmodulin upon calcium binding, involving exposure of the hydrophobic patches to solvent.     

Effect of Coordinated Ions on Structure and Flexibility of Parallel G-quadruplexes: A Molecular Dynamics Study

Abstract

Single tract guanine residues can associate to form stable parallel quadruplex structures in the presence of certain cations. Nanosecond scale molecular dynamics simulations have been performed on fully solvated fibre model of parallel d(G₇) quadruplex structures with Na⁺ or K⁺ ions coordinated in the cavity formed by the O6 atoms of the guanine bases. The AMBER 4.1 force field and Particle Mesh Ewald technique for electrostatic interactions have been used in all simulations. These quadruplex structures are stable during the simulation, with the middle four base tetrads showing root mean square deviation values between 0.5 to 0.8 Å from the initial structure as well the high resolution crystal structure. Even in the absence of any coordinated ion in the initial structure, the G-quadruplex structure remains intact throughout the simulation. During the 1.1 ns MD simulation, one Na⁺ counter ion from the solvent as well as several water molecules enter the central cavity to occupy the empty coordination sites within the parallel quadruplex and help stabilize the structure. Hydrogen bonding pattern depends on the nature of the coordinated ion, with the G-tetrad undergoing local structural variation to accommodate cations of different sizes. In the absence of any coordinated ion, due to strong mutual repulsion, O6 atoms within G-tetrad are forced farther apart from each other, which leads to a considerably different hydrogen bonding scheme within the G-tetrads and very favourable interaction energy between the guanine bases constituting a G-tetrad. However, a coordinated ion between G-tetrads provides extra stacking energy for the G-tetrads and makes the quadruplex structure more rigid. Na⁺ ions, within the quadruplex cavity, are more mobile than coordinated K⁺ ions. A number of hydrogen bonded water molecules are observed within the grooves of all quadruplex structures.     

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.     

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 Implementation of Friedman Boundary Conditions in Liquid Water Simulations

Abstract

We have applied the image approximation to the reaction field as suggested by H.L. Friedman [Mol. Phys., 29, 1533 (1975)] by investigating appropriate cavity sizes and system parameters for use in molecular simulations. The energy of and the structure around a central simple point charge (SPC) water molecule in a dielectric cavity was found to be in good agreement with the properties of a liquid sample. To confine the water molecules within the cavity, we introduced a short-range repulsion between a real charge and its image as the Lennard-Jones repulsive potential between oxygen atoms of the SPC potential. For a system of 65 water molecules a cavity radius of 10.45 Å is appropriate; this radius is altered to 12.00 Å for a cavity surrounding 113 molecules. The effect of the boundary is restricted to the outer-most water layer which is in contact with the dielectric continuum.     

Using beam profile inflection point in process of treatment planning system verification

BackgroundThe comparison between profiles during the commissioning of the treatment planning system is an essential procedure. It is impossible to designate a field size for off-axis, wedged, and FFF beams directly by using the definition of the on-axis symmetric field size. This work proposes the use of different characteristic points as indicators of the field size for commissioning and QA purposes. This work aimed to search for the beam profile’s characteristic points and use them for the TPS commissioning purposes.Materials and methodsThe proposal is to use profile inflection points as the beam profile characteristic points. The usage of dedicated software allowed for comparing distances between inflection points and between points of 50% intensity. For the off-axis, wedged, and FFF fields, comparisons were made to the nominal field sizes.ResultsDistances between inflection points proved to be different by less than 1 mm from nominal field sizes for all kinds of investigated beams.ConclusionsInflection points are convenient for comparing the off-axis, wedged, and FFF field sizes because of their independence from profile normalization. With finite accuracy, the inflection points could be used for the above kind of beam sizes designation.     

Estimation of Solvent Diffusion Coefficients Using Molecular Dynamics Simulations

Abstract

Molecular dynamics simulations have been used to investigate diffusion in two commonly used industrial solvents, toluene and tetrahydrofuran. Several different models for the solvents are compared (flexible vs. rigid, all-atom vs. united atom), and it is found that united atom and all-atom models of the solvents produce very different diffusion coefficients at the experimental density. This disagreement can be explained by the pressure dependence of the diffusion coefficient, which is found to vary in accord with the Chapman-Enskog result for hard spheres. It is recommended that force fields be parametrized carefully to produce reasonable pressures at the experimental densities, or that simulations be carried out at constant pressure, if they are to be used for the purposes of calculating transport coefficients.     

Ewald Summation in the Molecular Dynamics Simulation of Large Ionic Systems

Abstract

The accuracy and efficiency of the direct Ewald summation are discussed in terms of the size of a Molecular Dynamics (MD) ionic system and the ranges of the r-space and q-space summations. The dependence of the convergence parameter α on the size of the system and on the choice of cut-off radius for the short-range potential is given. The possibility of neglecting the q-space term for large ionic systems is discussed in terms of the accuracy and efficiency of the simulation.     

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.     

Kinetic Monte Carlo Predictions of the Conditions Necessary to Grow Helical (Chiral) and Vertical Columnar Structures

Abstract

Rare Event Dynamics Monte Carlo simulations have been used to investigate the possibility of growing porous crystalline material possessing vertical columnar morphology. This is achieved using a deposition process in which the incoming beam of atoms is held at a grazing angle and, importantly, is rotated azimuthally. For incident beams 80° from normal incidence, rotational speeds of around 1 revolution per second to 1 per 10 seconds were found to produce columnar thin film growth with essentially vertical walls. Slower rotational speeds, around 1 revolution per 30 seconds, produced a helical, but still vertical, columnar structure. Such so-called chiral structures are postulated to be potentially important optical materials. The effect of raising the temperature of the substrate is to decrease the density of the columns, but to broaden their size. This suggests that a temperature-rotational speed set of parameters could be found to produce designer pore sizes with relatively little variation in inter-column spacing and height and either with or without helical structure. Data for one such representation are presented. A movie of the evolution of the nanostructural features of a vertical columnar material is included.     

Effect of number of views on cross-sectional Compton imaging: A fundamental study with backprojection

IntroductionWe have been developing a medical imaging technique using a Compton camera, which is expected to reconstruct three-dimensional images. If the number of views is not sufficient, star-shaped artifacts (streak artifacts) could arise in cross-sectional images. Therefore, we estimated the point spread function (PSF) of cross-sectional Compton images and the effect of the number of views by Monte Carlo simulations and experimental studies.Materials and methodsA cross-sectional Compton image was reconstructed using a dataset comprising 719 view directions and PSF was analyzed using a radial distribution. The peak height, full width at half maximum (FWHM), background (BG), and residual sum of squares (RSS) were calculated from the obtained PSF. In addition, RSSs were plotted against the number of views to estimate the required number to suppress star-shaped artifacts.ResultsThere was no correlation found between the number of views and both FWHM (16 mm) and peak/BG ratio (∼1 × 10⁴). RSSs were reduced with the number of views and approached the minimum asymptotically. Correlation was observed between the required number of views and the number of Compton events used for image reconstruction.ConclusionWe determined the PSF of cross-sectional Compton images and the effect of the number of views on the images. The required number of views to suppress the star-shaped artifact is related to the square root of the number of Compton events used to reconstruct the image. From this study, we concluded that 21 or more views are required for clinical purposes.