Performance of fast multipole methods for calculating electrostatic interactions in biomacromolecular simulations

The fast multipole method proposed by Greengard and Rokhlin (GR) is applied to large biomacromolecular systems. In this method, the system is divided into a hierarchy of cells, and electric field exerted on a particle is decomposed into two parts. The first part is a rapidly varying field due to nearby cells, so that it needs rigorous pairwise calculations. The second part is a slowly varying local field due to distant cells; hence, it allows rapid calculations through a multipole expansion technique. In this work, two additional possibilities for improving the performance are numerically examined. The first is an improvement of the convergence of the expansion by increasing the number of nearby cells, without including higher-order multipole moments. The second is an acceleration of the calculations by the particle–particle and particle–mesh/multipole expansion (PPPM/MPE) method, which uses fast Fourier transform instead of the hierarchy. For this purpose, the PPPM/MPE method originally developed by the authors for a periodic system is extended to a nonperiodic isolated system. The advantages and disadvantages of the GR and PPPM/MPE methods are discussed for both periodic and isolated systems. It is numerically shown that these methods with reasonable costs can reduce the error in potential felt by each particle to 0.1–1 kcal/mol, much smaller than the 30-kcal/mol error involved in conventional simple truncations. © 1994 by John Wiley & Sons, Inc.     

Rigorous calculations of linearized Poisson-Boltzmann interaction between dissimilar spherical colloids and osmotic pressure in concentrated dispersions

We present computational results on the static properties of concentrated dispersions of bidisperse colloids. The long-range electrostatic interactions between dissimilar spherical colloids are determined using the singularity method, which provides rigorous solutions to the linearized electrostatic field. The NVT Monte Carlo simulation is applied to the bulk suspension to obtain the radial distribution function for the concentrated system. The increasing trend of osmotic pressure with increasing total particle concentration is reduced as the concentration ratio between large and small particles is increased. The increase of electrostatic interaction between similarly charged particles caused by the Debye screening effect provides an increase in the osmotic pressure. From the estimation of total structure factor, we observe the strong correlations developed between dissimilar spheres, and the small spheres are expected to tend to fit into the spaces between the larger ones. As the particle concentration increases at a given ionic strength, the magnitude of the first peak in structure factors increases and also moves to higher wavenumber values.     

Electrostatic energies and forces computed without explicit interparticle interactions: a linear time complexity formulation

A rapid method for the calculation of the electrostatic energy of a system without a cutoff is described in which the computational time grows linearly with the number of particles or charges. The inverse of the distance is approximated as a polynomial, which is then transformed into a function whose terms involve individual particles, instead of particle pairs, by a partitioning of the double sum. In this way, the electrostatic energy that is determined by the interparticle interactions is obtained without explicit calculation of these interactions. For systems of positive charges positioned on a face-centered cubic lattice, the calculation of the energy by the new method is shown to be faster than the calculation of the exact energy, in many cases by an order of magnitude, and to be accurate to within 1-2%. The application of this method to increase the accuracy of conventional truncation-based calculations in condensed-phase systems is also demonstrated by combining the approximated long-range electrostatic interactions with the exact short-range interactions in a "hybrid" calculation. For a 20-A sphere of water molecules, the forces are shown to be six times as accurate using this hybrid method as those calculated with conventional truncation of the electrostatic energy function at 12 A. This is accomplished with a slight increase in speed, and with a sevenfold increase in speed relative to the exact all-pair calculation. Structures minimized with the hybrid function are shown to be closer to structures minimized with an exact all-pair electrostatic energy function than are those minimized with a conventional 13-A cutoff-based electrostatic energy function. Comparison of the energies and forces calculated with the exact method illustrate that the absolute errors obtained with standard truncation can be very large. The extension of the current method to other pairwise functions as well as to multibody functions, is described.     

Removal of fine powders from film surface. I. Effect of electrostatic force on the removal efficiency

A novel fine particle removal system composed of a corona-discharge neutralizer, a pulse-jet air unit and an image processing system has been developed. First of all, adhesion force between particle and film was directly measured and effect of electrostatic force on the adhesion force was calculated experimentally and theoretically. The electrostatic force was found to be significant, leading to the suggestion that the countermeasure for the electrostatic force was required to effectively remove fine particles. This system was then applied to the removal of fine particles from surface of a gelatin film used for conventional capsule material. The number of particles removed by the system was calculated by an image processing system and number base removal efficiency was computed with and without the elimination of electrostatic charge by the neutralizer. It was found that the difference between the removal efficiency of particles with elimination of electrostatic charge and that of without the elimination showed linear relationship with the electrostatic adhesion force. The data confirmed the necessity of electrostatic charge elimination for the effective removal of fine particles.     

Removal of fine powders from film surface. II. Effect of operating parameters on the removal efficiency

In the previous paper, a novel fine particle removal system composed of a corona-discharge neutralizer, a pulse-jet air unit and an image processing system has been developed and applied to the removal of fine particles from film surface. We have calculated the van der Waals and electrostatic forces between particle and film and then reported that the electrostatic force influenced the adhesion characteristics significantly and thus the elimination of electrostatic charge should be necessary for the effective removal of fine particles. In this paper, we have modified the corona-discharge neutralizer for getting much better removal performance. The effect of operating parameters on the removal efficiency was investigated experimentally. The ratio of fine particle remained on the film surface after removal experiment as a function of particle size was measured. It was found that fine particles smaller than 15 microm, which were impossible to remove by other conventional techniques, could be almost completely removed. This method is anticipated to be used in the capsule filling, film packaging and tabletting processes for prevention of stain on lens of video automatic inspection machines, unpredictable movement of electronic devices, and deteriorates of product quality.     

Extension of adaptive tree code and fast multipole methods to high angular momentum particle charge densities

The development and implementation of a tree code (TC) and fast multipole method (FMM) for the efficient, linear-scaling calculation of long-range electrostatic interactions of particle distributions with variable shape and multipole character are described. The target application of these methods are stochastic boundary molecular simulations with polarizable force fields and/or combined quantum mechanical/molecular mechanical potentials. Linear-scaling is accomplished through the adaptive decomposition of the system into a hierarchy of interacting particle sets. Two methods for effecting this decomposition are evaluated: fluc-splitting and box-splitting, for which the latter is demonstrated to be generally more accurate. In addition, a generalized termination criterion is developed that delivers optimal performance at fixed error tolerance that, in the case of quadrupole-represented Drude water, effects a speed-up by a factor of 2-3 relative to a multipole-independent termination criteria. The FMM is shown to be approximately 2-3 times faster than the TC, independent of the system size and multipole order of the particles. The TC and FMM are tested for a variety of static and polarizable water systems, and for the the 70S ribosome functional complex containing an assembly of transfer and messenger RNAs.     

The midpoint method for parallelization of particle simulations

The evaluation of interactions between nearby particles constitutes the majority of the computational workload involved in classical molecular dynamics (MD) simulations. In this paper, we introduce a new method for the parallelization of range-limited particle interactions that proves particularly suitable to MD applications. Because it applies not only to pairwise interactions but also to interactions involving three or more particles, the method can be used for evaluation of both nonbonded and bonded forces in a MD simulation. It requires less interprocessor data transfer than traditional spatial decomposition methods at all but the lowest levels of parallelism. It gains an additional practical advantage in certain commonly used interprocessor communication networks by distributing the communication burden more evenly across network links and by decreasing the associated latency. When used to parallelize MD, it further reduces communication requirements by allowing the computations associated with short-range nonbonded interactions, long-range electrostatics, bonded interactions, and particle migration to use much of the same communicated data. We also introduce certain variants of this method that can significantly improve the balance of computational load across processors.     

Incremental update of electrostatic interactions in adaptively restrained particle simulations

The computation of long‐range potentials is one of the demanding tasks in Molecular Dynamics. During the last decades, an inventive panoply of methods was developed to reduce the CPU time of this task. In this work, we propose a fast method dedicated to the computation of the electrostatic potential in adaptively restrained systems. We exploit the fact that, in such systems, only some particles are allowed to move at each timestep. We developed an incremental algorithm derived from a multigrid‐based alternative to traditional Fourier‐based methods. Our algorithm was implemented inside LAMMPS, a popular molecular dynamics simulation package. We evaluated the method on different systems. We showed that the new algorithm's computational complexity scales with the number of active particles in the simulated system, and is able to outperform the well‐established Particle Particle Particle Mesh (P3M) for adaptively restrained simulations. © 2018 Wiley Periodicals, Inc.     

凝并和成核机理下颗粒尺度分布的Monte Carlo求解

颗粒的凝并和成核现象影响其尺度分布,现有的MonteCarlo方法描述颗粒尺度分布的时间演变过程存在若干困难.提出了一种新的多重MonteCarlo(MMC)算法,基于时间驱动,利用加权的虚拟颗粒的思想,在模拟过程中保持虚拟颗粒总数不变和计算区域体积不变.利用该算法对“常凝并核,一阶成核”的情况下颗粒尺度分布的时间演变过程进行了数值求解,所得结果与数值解相符,表明MMC算法具有高且稳定的计算精度.另外,MMC算法由于跟踪比实际颗粒数目少得多的虚拟颗粒而具有较低的计算代价.     

FAMUSAMM: An algorithm for rapid evaluation of electrostatic interactions in molecular dynamics simulations

Within molecular dynamics simulations of protein–solvent systems the exact evaluation of long-range Coulomb interactions is computationally demanding and becomes prohibitive for large systems. Conventional truncation methods circumvent that computational problem, but are hampered by serious artifacts concerning structure and dynamics of the simulated systems. To avoid these artifacts we have developed an efficient and yet sufficiently accurate approximation scheme which combines the structure-adapted multipole method (SAMM) [C. Niedermeier and P. Tavan, J. Chem. Phys., 101 , 734 (1994)] with a multiple-time-step method. The computational effort for MD simulations required within our fast multiple-time-step structure-adapted multipole method (FAMUSAMM) scales linearly with the number of particles. For a system with 36,000 atoms we achieve a computational speed-up by a factor of 60 as compared with the exact evaluation of the Coulomb forces. Extended test simulations show that the applied approximations do not seriously affect structural or dynamical properties of the simulated systems. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1729–1749, 1997     

GALAMOST: GPU‐accelerated large‐scale molecular simulation toolkit

GALAMOST [graphics processing unit (GPU)‐accelerated large‐scale molecular simulation toolkit] is a molecular simulation package designed to utilize the computational power of GPUs. Besides the common features of molecular dynamics (MD) packages, it is developed specially for the studies of self‐assembly, phase transition, and other properties of polymeric systems at mesoscopic scale by using some lately developed simulation techniques. To accelerate the simulations, GALAMOST contains a hybrid particle‐field MD technique where particle–particle interactions are replaced by interactions of particles with density fields. Moreover, the numerical potential obtained by bottom‐up coarse‐graining methods can be implemented in simulations with GALAMOST. By combining these force fields and particle‐density coupling method in GALAMOST, the simulations for polymers can be performed with very large system sizes over long simulation time. In addition, GALAMOST encompasses two specific models, that is, a soft anisotropic particle model and a chain‐growth polymerization model, by which the hierarchical self‐assembly of soft anisotropic particles and the problems related to polymerization can be studied, respectively. The optimized algorithms implemented on the GPU, package characteristics, and benchmarks of GALAMOST are reported in detail. © 2013 Wiley Periodicals, Inc.     

Dynamic drag force based on iterative density mapping: A new numerical tool for three‐dimensional analysis of particle trajectories in a dielectrophoretic system

Dielectrophoresis is a widely used means of manipulating suspended particles within microfluidic systems. In order to efficiently design such systems for a desired application, various numerical methods exist that enable particle trajectory plotting in two or three dimensions based on the interplay of hydrodynamic and dielectrophoretic forces. While various models are described in the literature, few are capable of modeling interactions between particles as well as their surrounding environment as these interactions are complex, multifaceted, and computationally expensive to the point of being prohibitive when considering a large number of particles. In this paper, we present a numerical model designed to enable spatial analysis of the physical effects exerted upon particles within microfluidic systems employing dielectrophoresis. The model presents a means of approximating the effects of the presence of large numbers of particles through dynamically adjusting hydrodynamic drag force based on particle density, thereby introducing a measure of emulated particle–particle and particle–liquid interactions. This model is referred to as “dynamic drag force based on iterative density mapping.” The resultant numerical model is used to simulate and predict particle trajectory and velocity profiles within a microfluidic system incorporating curved dielectrophoretic microelectrodes. The simulated data are compared favorably with experimental data gathered using microparticle image velocimetry, and is contrasted against simulated data generated using traditional “effective moment Stokes‐drag method,” showing more accurate particle velocity profiles for areas of high particle density.     

On the behavior of the electrostatic colloidal interaction in the membrane filtration of latex suspensions

In order to investigate effects of the colloidal interaction in the membrane filtrations, the dead-end ultrafiltration of latex colloids was conducted with fully retentive membranes. Experimental results concerning the permeate flux during the filtration indicate that the void fraction of cake layer increased with the decrease of the ionic strength, due to the expanded Debye double layer thickness around the particles. The concentration dependence of the gradient diffusion coefficient of colloidal particles has been examined as a function of solution ionic strength. The NVT Monte Carlo simulation was applied on the bulk suspension so as to determine the thermodynamic coefficient, and the hydrodynamic coefficient was evaluated from the previously developed relation for an ordered system. The long-range electrostatic interactions between the particles are determined by using a singularity method, which provides accurate solutions to the linearized electrostatic field. The predictions on the variation of concentration polarization layer have been presented, from which we found that both the permeate flux and the particle diffusion are related to determine the concentration distribution above the cake layer.     

New 8-step symmetric embedded predictor–corrector (EPCM) method with vanished phase-lag and its first derivative for the numerical integration of the Schrödinger equation

In the present work, a new embedded predictor–corrector phase-fitted method with vanished phase-lag is developed for the first time in literature. It is about a multistep symmetric method built on the multistep method of Quinlan and Tremaine (Astron J 100(5):1694–1700, 1990) with eight steps. It can be used to solve numerically IVPs with oscillatory solutions, orbital problems and the Schrödinger equation. Initially we present a pair of embedded predictor–corrector method upon which the new method is built. We test our method and the numerical results indicate that this method is much more accurate than other well known methods including the radial Schrödinger equation.     

Optical chromatography Size determination by eluting particles

A new method for the determination of particle size was developed using optical chromatography. After separating polystyrene particles, the laser power was gradually reduced, permitting the elution of small to large particles. Particle size was calculated from the laser power when the particle was eluted with a medium flow. This approach is more accurate than the technique previously reported because there is no need to determine the position of the beam waist. Advantages of the new approach are discussed theoretically and experimentally. The precision in size determination was improved by a factor of 3.3, i.e. the standard deviation in the measurement was reduced from 10 to 3% for 1 mum beads by replacing optical chromatography with the present method.     

On the effect of thermophoretic force,gravitational force,and particle–particle interactions in field-flow fractionation

The theoretical calculations confirmed that the gravitational force cannot be neglected in all field-flow fractionation techniques separating nanometer-sized colloidal particles whenever particle diameter is approximately 200?nm and larger. Particle–particle repulsive interactions, mostly electrostatic repulsions, influence substantially concentration distribution established by any effective field acting across the fractionation channel, as confirmed explicitly for thermophoretic force generated by temperature gradient in microthermal field-flow fractionation. The ionic strength of the carrier liquid causes the screening of the electrostatic double layer around the dispersed particles and thus influences the retention. The attractive particle–particle forces occur when the zeta potential of the particles approaches to 0?mV, the electrostatic repulsions are screened, and the aggregation of the particles is observed. The pH influences differently the size and zeta potential of the plain polystyrene latex particles and of the particles modified on the surface by the groups –COOH and –NH₂. The role of a detergent in carrier liquid is non-negligible, as demonstrated by its presence or absence in carrier liquid.     

Surface Forces in Nanodispersions

The stability of nanodispersions are analyzed on the basis of data on interaction forces between nanoparticles calculated using more precise (than Derjaguin's approximation) approaches. When calculating the dispersion attraction between nanoparticles in dispersions, we use Mitchell and Ninham equations for the case of small (compared to particle radii) interlayer thickness. For the calculation of electrostatic interaction in nanodispersions, the approximation of low potentials of particle surfaces developed by McCartney and Levine are employed. Estimates based on more precise approaches demonstrate that the energy of electrostatic repulsion between particles lowers with a decrease in their sizes (other conditions being equal) that can bring a nanodisperse system closer to the coagulation threshold.     

Size-fractionated sampling and chemical analysis by total-reflection X-ray fluorescence spectrometry of PMx in ambient air and emissions

PM 10 and PM 2.5 (PMx) have been recently introduced as new air quality standards in the EU (Council Directive 1999/30/EC) for particulate matter. Different estimates and measurements showed that the limit values for PM 10 will be exceeded at different locations in Europe, and thus measures will have to be taken to reduce PMx mass concentrations. Source apportionment has to be carried out, demanding comparable methods for ambient air and emission sampling and chemical analysis. Therefore, a special ambient-air sampler and a specially designed emission sampler have been developed. Total-reflection X-ray fluorescence analysis (TXRF) was used for multi-element analyses as a fast method with low detection limits. For ambient air measurements, a sampling unit was built, impacting particle size classes 10–2.5 μm and 2.5–1.0 μm directly onto TXRF sample carriers. An electrostatic precipitator (ESP) was used as back-up filter to also collect particles <1 μm directly onto the TXRF sample carriers. Air quality is affected by natural and anthropogenic sources, and the emissions of particles <10 μm and <2.5 μm, respectively, have to be determined to quantify their contributions to the so-called coarse (10–2.5 μm) and fine (<2.5 μm) particle modes in ambient air. For this, an in-stack particle sampling system was developed, according to the new ambient air quality standards and in view of subsequent analysis by TXRF. These newly developed samplers, in combination with TXRF analyses, were employed in field campaigns to prove the feasibility and capabilities of the approach. Ambient air data show the quantification of a wide spectrum of elements. From those concentrations, PMx ratios were calculated as an indicator for different sources of elements. Results useful for source apportionment are also the elemental day/night ratios calculated to determine local contributions to PMx mass concentrations. With regard to the emission measurements, results of mass and elemental concentrations obtained in two different processes (steel industry) show that the new PM 10/PM 2.5 cascade impactor and measurements with TXRF give characteristic fingerprints for different sources. Size-fractionated ambient air and emission sampling, together with multi-element analysis, prove to be a useful approach to derive information for source–receptor modeling, a method necessary to set up effective abatement strategies to reduce PMx mass concentrations.     

A modeling approach to describe the adhesion of rough, asymmetric particles to surfaces

A combined theoretical and experimental study of the adhesion of alumina particles and polystyrene latex spheres to silicon dioxide surfaces was performed. A boundary element technique was used to model electrostatic interactions between micron-scale particles and planar surfaces when the particles and surfaces were in contact. This method allows quantitative evaluation of the effects of particle geometry and surface roughness on the electrostatic interaction. The electrostatic interactions are combined with a previously developed model for van der Waals forces in particle adhesion. The combined model accounts for the effects of particle and substrate geometry, surface roughness and asperity deformation on the adhesion force. Predictions from the combined model are compared with experimental measurements made with an atomic force microscope. Measurements are made in aqueous solutions of varying ionic strength and solution pH. While van der Waals forces are generally dominant when particles are in contact with surfaces, results obtained here indicate that electrostatic interactions contribute to the overall adhesion force in certain cases. Specifically, alumina particles with complex geometries were found to adhere to surfaces due to both electrostatic and van der Waals interactions, while polystyrene latex spheres were not affected by electrostatic forces when in contact with various surfaces.