A fast, scalable method for the parallel evaluation of distance-limited pairwise particle interactions

Classical molecular dynamics simulations of biological macromolecules in explicitly modeled solvent typically require the evaluation of interactions between all pairs of atoms separated by no more than some distance R, with more distant interactions handled using some less expensive method. Performing such simulations for periods on the order of a millisecond is likely to require the use of massive parallelism. The extent to which such simulations can be efficiently parallelized, however, has historically been limited by the time required for interprocessor communication. This article introduces a new method for the parallel evaluation of distance-limited pairwise particle interactions that significantly reduces the amount of data transferred between processors by comparison with traditional methods. Specifically, the amount of data transferred into and out of a given processor scales as O(R(3/2)p(-1/2)), where p is the number of processors, and with constant factors that should yield a substantial performance advantage in practice.     

Structure and Rheology of Simulated Gels Formed from Aggregated Colloidal Particles

Soft, elastic, solvent-rich materials made from networks of aggregated colloidal particles are called particle gels. The networks may be regarded as being permanent or transient depending on whether the short-range attractive forces between the particles arise from strong irreversible bonding or weak reversible interactions. Understanding the relationships between the interparticle forces and the structure and rheology of particle gels is a challenging problem. This article shows how useful insight is being provided by Brownian dynamics simulations involving systems of spherical particles interacting with a combination of bonded and nonbonded interparticle potentials. Copyright 2000 Academic Press.     

Data parallel large-scale molecular dynamics for liquids

An efficient data parallel computational scheme is presented for large-scale molecular dynamics (MD ) simulations of liquids with short-range interactions. The method is based on decomposition of the simulation cell into equally sized subcells, with the shortest side length equal to the cutoff radius. Inter- and intracell interactions are calculated in a coarse-grained manner. A geometric sorting procedure, based on particle distances to subcell boundaries, is used to minimize the overall computations and the nonproductive communications. Using only nearest-neighbor communications, an efficient scheme is developed for periodic updates of the contents of subcells due to the migration of particles. Special “null-particles” are introduced, which act as buffers during the periodic updates and allow for a globally uniform algorithm during the calculations. Communication cost is about 7% of the total CPU time. The method is found to be linearly scalable with the number of particles, performing better as the ratio of virtual to physical processors increases. The MD code is written in Fortran 90 and implemented on a CM-200. The overall speed is approximately 5.9 μs. per MD step and per particle for 1 million particles and 5.5 μs for 5 million particles. The method should be easily transferred to other massively parallel computers of SIMD and MIMD type. © 1993 John Wiley & Sons, Inc.     

Development of a parallel molecular dynamics code on SIMD computers: Algorithm for use of pair list criterion

In recent years several implementations of molecular dynamics (MD) codes have been reported on multiple instruction multiple data (MIMD) machines. However, very few implementations of MD codes on single instruction multiple data (SIMD) machines have been reported. The difficulty in using pair lists of nonbonded interactions is the major problem with MD codes for SIMD machines, such that, generally, the full connectivity computation has been used. We present an algorithm, the global cut-off algorithm (GCA), which permits the use of pair lists on SIMD machines. GCA is based on a probabilistic approach and requires the cut-off condition to be simultaneously verified on all nodes of the machine. The MD code used was taken from the GROMOS package; only the routines involved in the pair lists and in the computation of nonbonded interactions were rewritten for a parallel architecture. The remaining calculations were performed on the host computer. The algorithm has been tested on Quadrics computers for configurations of 32, 128, and 512 processors and for systems of 4000, 8000, 15,000, and 30,000 particles. Quadrics was developed by Istituto Nazionale di Fisica Nucleare (INFN) and marketed by Alenia Spazio. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 685–694, 1998     

Efficient lookup table using a linear function of inverse distance squared

The major bottleneck in molecular dynamics (MD) simulations of biomolecules exist in the calculation of pairwise nonbonded interactions like Lennard‐Jones and long‐range electrostatic interactions. Particle‐mesh Ewald (PME) method is able to evaluate long‐range electrostatic interactions accurately and quickly during MD simulation. However, the evaluation of energy and gradient includes time‐consuming inverse square roots and complementary error functions. To avoid such time‐consuming operations while keeping accuracy, we propose a new lookup table for short‐range interaction in PME by defining energy and gradient as a linear function of inverse distance squared. In our lookup table approach, densities of table points are inversely proportional to squared pair distances, enabling accurate evaluation of energy and gradient at small pair distances. Regardless of the inverse operation here, the new lookup table scheme allows fast pairwise nonbonded calculations owing to efficient usage of cache memory. © 2013 Wiley Periodicals, Inc.     

A coarse-grained model for polyethylene glycol polymer

A coarse-grained (CG) model of polyethylene glycol (PEG) was developed and implemented in CG molecular dynamics (MD) simulations of PEG chains with degree of polymerization (DP) 20 and 40. In the model, two repeat units of PEG are grouped as one CG bead. Atomistic MD simulation of PEG chains with DP = 20 was first conducted to obtain the bonded structural probability distribution functions (PDFs) and nonbonded pair correlation function (PCF) of the CG beads. The bonded CG potentials are obtained by simple inversion of the corresponding PDFs. The CG nonbonded potential is parameterized to the PCF using both an inversion procedure based on the Ornstein-Zernike equation with the Percus-Yevick approximation (OZPY(-1)) and a combination of OZPY(-1) with the iterative Boltzmann inversion (IBI) method (OZPY(-1)+IBI). As a simple one step method, the OZPY(-1) method possesses an advantage in computational efficiency. Using the potential from OZPY(-1) as an initial guess, the IBI method shows fast convergence. The coarse-grained molecular dynamics (CGMD) simulations of PEG chains with DP = 20 using potentials from both methods satisfactorily reproduce the structural properties from atomistic MD simulation of the same systems. The OZPY(-1)+IBI method yields better agreement than the OZPY(-1) method alone. The new CG model and CG potentials from OZPY(-1)+IBI method was further tested through CGMD simulation of PEG with DP = 40 system. No significant changes are observed in the comparison of PCFs from CGMD simulations of PEG with DP = 20 and 40 systems indicating that the potential is independent of chain length.     

An improved method for nonbonded list generation: rapid determination of near-neighbor pairs

Generation of the list of near-neighbor pairs of atoms not bonded to each other is a key feature of many programs for calculating the energy and energy derivatives for large molecules. Because this step can take a significant amount of CPU time, more efficient nonbonded list generation can speed up the energy calculations. In this article, a novel nonbonded list generation algorithm, BYCC, is introduced. It combines certain features of other algorithms and achieves more rapid nonbonded list generation; a factor of approximately 2.5 for a molecule of 5000 atoms with a cutoff in the 10 A range is obtained on Hewlett-Packard (HP) and Alpha processors, without greatly increasing memory requirements.     

Efficient calculations of coulombic interactions in biomolecular simulations with periodic boundary conditions

To make improved treatments of electrostatic interactions in biomacromolecular simulations, two possibilities are considered. The first is the famous particle–particle and particle–mesh (PPPM) method developed by Hockney and Eastwood, and the second is a new one developed here in their spirit but by the use of the multipole expansion technique suggested by Ladd. It is then numerically found that the new PPPM method gives more accurate results for a two-particle system at small separation of particles. Preliminary numerical examination of the various computational methods for a single configuration of a model BPTI–water system containing about 24,000 particles indicates that both of the PPPM methods give far more accurate values with reasonable computational cost than do the conventional truncation methods. It is concluded the two PPPM methods are nearly comparable in overall performance for the many-particle systems, although the first method has the drawback that the accuracy in the total electrostatic energy is not high for configurations of charged particles randomly generated. © 1993 John Wiley & Sons, Inc.     

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.     

Development of hardware accelerator for molecular dynamics simulations: a computation board that calculates nonbonded interactions in cooperation with fast multipole method

Evaluation of long-range Coulombic interactions still represents a bottleneck in the molecular dynamics (MD) simulations of biological macromolecules. Despite the advent of sophisticated fast algorithms, such as the fast multipole method (FMM), accurate simulations still demand a great amount of computation time due to the accuracy/speed trade-off inherently involved in these algorithms. Unless higher order multipole expansions, which are extremely expensive to evaluate, are employed, a large amount of the execution time is still spent in directly calculating particle-particle interactions within the nearby region of each particle. To reduce this execution time for pair interactions, we developed a computation unit (board), called MD-Engine II, that calculates nonbonded pairwise interactions using a specially designed hardware. Four custom arithmetic-processors and a processor for memory manipulation ("particle processor") are mounted on the computation board. The arithmetic processors are responsible for calculation of the pair interactions. The particle processor plays a central role in realizing efficient cooperation with the FMM. The results of a series of 50-ps MD simulations of a protein-water system (50,764 atoms) indicated that a more stringent setting of accuracy in FMM computation, compared with those previously reported, was required for accurate simulations over long time periods. Such a level of accuracy was efficiently achieved using the cooperative calculations of the FMM and MD-Engine II. On an Alpha 21264 PC, the FMM computation at a moderate but tolerable level of accuracy was accelerated by a factor of 16.0 using three boards. At a high level of accuracy, the cooperative calculation achieved a 22.7-fold acceleration over the corresponding conventional FMM calculation. In the cooperative calculations of the FMM and MD-Engine II, it was possible to achieve more accurate computation at a comparable execution time by incorporating larger nearby regions.     

MMP-2和Hydroxamate类抑制剂绝对自由能的计算

采用基于线性响应近似的自由能计算方法计算了一类hydroxamate抑制剂和MMP-2的绝对结合自由能。计算中,催化锌离子和MMP-2以及配体之间采用了非键模型。分子动力学模拟结果显示,采用非键模型时,催化Zn离子采用五配位的形式,但配位键的形式和初始结构比较有很大的差别。通过拟合,分别得到了单参数、双参数以及三参数的自由能预测模型,其中,含有常数校正项的三参数模型具有最佳的预测能力,预测自由能和实际自由能之间平均绝对误差仅为2.38kJ/mol。     

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.     

Midpoint cell method for hybrid (MPI+OpenMP) parallelization of molecular dynamics simulations

We have developed a new hybrid (MPI+OpenMP) parallelization scheme for molecular dynamics (MD) simulations by combining a cell‐wise version of the midpoint method with pair‐wise Verlet lists. In this scheme, which we call the midpoint cell method, simulation space is divided into subdomains, each of which is assigned to a MPI processor. Each subdomain is further divided into small cells. The interaction between two particles existing in different cells is computed in the subdomain containing the midpoint cell of the two cells where the particles reside. In each MPI processor, cell pairs are distributed over OpenMP threads for shared memory parallelization. The midpoint cell method keeps the advantages of the original midpoint method, while filtering out unnecessary calculations of midpoint checking for all the particle pairs by single midpoint cell determination prior to MD simulations. Distributing cell pairs over OpenMP threads allows for more efficient shared memory parallelization compared with distributing atom indices over threads. Furthermore, cell grouping of particle data makes better memory access, reducing the number of cache misses. The parallel performance of the midpoint cell method on the K computer showed scalability up to 512 and 32,768 cores for systems of 20,000 and 1 million atoms, respectively. One MD time step for long‐range interactions could be calculated within 4.5 ms even for a 1 million atoms system with particle‐mesh Ewald electrostatics. © 2014 Wiley Periodicals, Inc.     

Coarse‐grained molecular dynamics simulations of stereoregular poly(methyl methacrylate)/poly(vinyl chloride) blends

The stereoregular poly(methyl methacrylate)/poly(vinyl chloride) blends with a wide formulation range are extensively simulated using the coarse‐grained (CG) molecular dynamics (MD) method. To improve the representability, the bonded CG potentials are re‐parameterized against the atomistic simulated melt systems whereas the nonbonded CG potentials are adopted as developed in our previous work. Based on the CG potentials, the MD simulations reproduce all the local distributions of pure systems and the miscibility of mixed systems. Moreover, the global conformational properties are also closer to the target ones than those obtained using the previous CG potentials. The changes in density and volume upon mixing are computed together with the energies of mixing. They are all negative over the entire composition range and indicate stronger intermolecular interactions between distinct components than those between identical components. In particular, it is found that upon mixing the changes in density are insensible to chain tacticity but the changes in volume and the energies of mixing do, which quantitatively confirms that both inter‐molecular interactions and free‐volumes mainly contribute to the observed phase behaviors. Such models and methods reported herein can be used to quickly optimize formulations of polymer blends. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 203–212     

Molecular Dynamic Simulation of Side-Chain Liquid Crystalline Elastomer

Summary: Molecular dynamic simulation of side chain liquid crystalline elastomer has been carried out. As an initial state a flexible polymer network in a low molecular liquid-crystal (LC) solvent was used. The LC solvent comprises of anisotropic rod-like semiflexible linear molecules (mesogens) composed of particles bonded into the chain by FENE potential. Rigidity of LC molecules was induced by a bending potential. All interactions between nonbonded particles are described by a repulsive Lennard-Jones potential. For the systems with different values of density and order parameter obtained after sufficiently long trajectory the attachment of ends of mesogens to the polymer network was simulated. The kinetic of the process of mesogens attachment to network was studied as well as morphology of attachment. The structural and dynamical behaviour of side chain LC elastomer was studied and compared with systems of polymer network in low molecular LC solvent.     

Phase behavior of self-associating fluids with weaker dispersion interactions between bonded particles

In this study, we explore the global phase behavior of a simple model for self-associating fluids where association reduces the strength of the dispersion interactions between bonded particles. Recent research shows that this type of behavior likely explains the thermodynamic properties of strongly polar fluids and certain micellar solutions. Based on Wertheim's theory of associating liquids [M. S. Wertheim, J. Stat. Phys. 42, 459 (1986); 42, 477 (1986)], our model takes into account the effect that dissimilar particle interactions have on the equilibrium constant for self-association in the system. We find that weaker interactions between bonded molecules tend to favor the dissociation of chains at any temperature and density. This effect stabilizes a monomeric liquid phase at high densities, enriching the global phase behavior of the system. In particular, for systems in which the energy of mixing between bonded and unbonded species is positive, we find a triple point involving a vapor, a dense phase of chain aggregates, and a monomeric liquid. Phase coexistence between the vapor and the monomeric fluid is always more stable at temperatures above the triple point, but a highly associated fluid may exist as a metastable phase under these conditions. The presence of this metastable phase may explain the characteristic nucleation behavior of the liquid phase in strongly dipolar fluids.     

Effective force field for liquid hydrogen fluoride from ab initio molecular dynamics simulation using the force-matching method

A recently developed force-matching method for obtaining effective force fields for condensed matter systems from ab initio molecular dynamics (MD) simulations has been applied to fit a simple nonpolarizable two-site pairwise force field for liquid hydrogen fluoride. The ab initio MD in this case was a Car-Parrinello (CP) MD simulation of 64 HF molecules at nearly ambient conditions within the Becke-Lee-Yang-Parr approximation to the electronic density functional theory. The force-matching procedure included a fit of short-ranged nonbonded forces, bonded forces, and atomic partial charges. The performance of the force-match potential was examined for the gas-phase dimer and for the liquid phase at various temperatures. The model was able to reproduce correctly the bent structure and energetics of the gas-phase dimer, while the results for the structural properties, self-diffusion, vibrational spectra, density, and thermodynamic properties of liquid HF were compared to both experiment and the CP MD simulation. The force-matching model performs well in reproducing nearly all of the liquid properties as well as the aggregation behavior at different temperatures. The model is computationally cheap and compares favorably to many more computationally expensive potential energy functions for liquid HF.     

Fast lookup tables for interatomic interactions

We describe novel lookup tables for the rapid calculation of interatomic interactions. The tables have nonuniform distributions of bin widths tailored to minimize numerical error and maximize computational speed. Since interaction energies are precalculated, computer time requirements are essentially independent of the form of the potential function used. In test calculations using the AMBER force field and an internal coordinate Monte Carlo algorithm, the lookup table runs 15% faster than direct calculation of nonbonded interactions. The method is more advantageous for more complicated energy functions. As an example of a more complicated potential function, we have tested a pairwise approximation to accessible surface area. In this case, the use of the lookup table results in a speedup of a factor of two. The method is straightforward to implement and should be widely applicable. © 1996 by John Wiley & Sons, Inc.