A cell multipole based domain decomposition algorithm for molecular dynamics simulation of systems of arbitrary shape

A domain decomposition algorithm for molecular dynamics simulation of atomic and molecular systems with arbitrary shape and non-periodic boundary conditions is described. The molecular dynamics program uses cell multipole method for efficient calculation of long range electrostatic interactions and a multiple time step method to facilitate bigger time steps. The system is enclosed in a cube and the cube is divided into a hierarchy of cells. The deepest level cells are assigned to processors such that each processor has contiguous cells and static load balancing is achieved by redistributing the cells so that each processor has approximately same number of atoms. The resulting domains have irregular shape and may have more than 26 neighbors. Atoms constituting bond angles and torsion angles may straddle more than two processors. An efficient strategy is devised for initial assignment and subsequent reassignment of such multiple-atom potentials to processors. At each step, computation is overlapped with communication greatly reducing the effect of communication overhead on parallel performance. The algorithm is tested on a spherical cluster of water molecules, a hexasaccharide and an enzyme both solvated by a spherical cluster of water molecules. In each case a spherical boundary containing oxygen atoms with only repulsive interactions is used to prevent evaporation of water molecules. The algorithm shows excellent parallel efficiency even for small number of cells/atoms per processor.     

A fine grained parallel smooth particle mesh Ewald algorithm for biophysical simulation studies: Application to the 6-D torus QCDOC supercomputer

In order to model complex heterogeneous biophysical macrostructures with non-trivial charge distributions such as globular proteins in water, it is important to evaluate the long range forces present in these systems accurately and efficiently. The Smooth Particle Mesh Ewald summation technique (SPME) is commonly used to determine the long range part of electrostatic energy in large scale molecular simulations. While the SPME technique does not give rise to a performance bottleneck on a single processor, current implementations of SPME on massively parallel, supercomputers become problematic at large processor numbers, limiting the time and length scales that can be reached. Here, a synergistic investigation involving method improvement, parallel programming and novel architectures is employed to address this difficulty. A relatively simple modification of the SPME technique is described which gives rise to both improved accuracy and efficiency on both massively parallel and scalar computing platforms. Our fine grained parallel implementation of the modified SPME method for the novel QCDOC supercomputer with its 6D-torus architecture is then given. Numerical tests of algorithm performance on up to 1024 processors of the QCDOC machine at BNL are presented for two systems of interest, a β-hairpin solvated in explicit water, a system which consists of 1142 water molecules and a 20 residue protein for a total of 3579 atoms, and the HIV-1 protease solvated in explicit water, a system which consists of 9331 water molecules and a 198 residue protein for a total of 29508 atoms.     

PLUMED: A portable plugin for free-energy calculations with molecular dynamics

Here we present a program aimed at free-energy calculations in molecular systems. It consists of a series of routines that can be interfaced with the most popular classical molecular dynamics (MD) codes through a simple patching procedure. This leaves the possibility for the user to exploit many different MD engines depending on the system simulated and on the computational resources available. Free-energy calculations can be performed as a function of many collective variables, with a particular focus on biological problems, and using state-of-the-art methods such as metadynamics, umbrella sampling and Jarzynski-equation based steered MD. The present software, written in ANSI-C language, can be easily interfaced with both Fortran and C/C++ codes.

Program summary

Program title: PLUMEDCatalogue identifier: AEEE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEE_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Lesser GPLNo. of lines in distributed program, including test data, etc.: 107 505No. of bytes in distributed program, including test data, etc.: 2 052 759Distribution format: tar.gzProgramming language: ANSI-CComputer: Any computer capable of running an executable produced by GCC compilerOperating system: Linux/UnixRAM: Depending on the number of atoms, the method chosen and the collective variables usedClassification: 23External routines: Must be interfaced with a MD code (such as GROMACS, NAMD, DL_POLY or SANDER).Nature of problem: Calculation of free-energy surfaces for biological and condensed matter systems.Solution method: Implementation of various enhanced sampling techniques.Unusual features: PLUMED is not a stand-alone program but it must be interfaced with a MD code (such as GROMACS, NAMD, DL_POLY or SANDER) that needs to be recompiled. Each interface is provided in a patch form.Running time: Depending on the number of atoms, the method chosen and the collective variables used.     

A method for solving the molecular Schrödinger equation in Cartesian coordinates via angular momentum projection operators

A method for solving the Schrödinger equation of N-atom molecules in 3N−3 Cartesian coordinates usually defined by Jacobi vectors is presented. The separation and conservation of the total angular momentum are obtained not by transforming the Hamiltonian in internal curvilinear coordinates but instead, by keeping the Cartesian formulation of the Hamiltonian operator and projecting the initial wavefunction onto the proper irreducible representation angular momentum subspace. The increased number of degrees of freedom from 3N−6 to 3N−3, compared to previous methods for solving the Schrödinger equation, is compensated by the simplicity of the kinetic energy operator and its finite difference representations which result in sparse Hamiltonian matrices. A parallel code in Fortran 95 has been developed and tested for model potentials of harmonic oscillators. Moreover, we compare data obtained for the three-dimensional hydrogen molecule and the six-dimensional water molecule with results from the literature. The availability of large clusters of computers with hundreds of CPUs and GBytes of memory, as well as the rapid development of distributed (Grid) computing, make the proposed method, which is unequivocally highly demanding in memory and computer time, attractive for studying Quantum Molecular Dynamics.     

A general purpose parallel molecular dynamics simulation program

We present a general purpose parallel molecular dynamics simulation code. The code can handle NVE, NVT, and NPT ensemble molecular dynamics, Langevin dynamics, and dissipative particle dynamics. Long-range interactions are handled by using the smooth particle mesh Ewald method. The implicit solvent model using solvent-accessible surface area was also implemented. Benchmark results using molecular dynamics, Langevin dynamics, and dissipative particle dynamics are given.

Program summary

Title of program:MM_PARCatalogue identifier:ADXP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXP_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer for which the program is designed and others on which it has been tested:any UNIX machine. The code has been tested on Linux cluster and IBM p690Operating systems or monitors under which the program has been tested:Linux, AIXProgramming language used:CMemory required to execute with typical data:∼60 MB for a system of atoms Has the code been vectorized or parallelized? parallelized with MPI using atom decomposition and domain decompositionNo. of lines in distributed program, including test data, etc.:171 427No. of bytes in distributed program, including test data, etc.:4 558 773Distribution format:tar.gzExternal routines/libraries used:FFTW free software (http://www.fftw.org)Nature of physical problem:Structural, thermodynamic, and dynamical properties of fluids and solids from microscopic scales to mesoscopic scales.Method of solution:Molecular dynamics simulation in NVE, NVT, and NPT ensemble, Langevin dynamics simulation, dissipative particle dynamics simulation.Typical running time:Table below shows the typical run times for the four test programs.

Benchmark results. The values in the parenthesis are the number of processors used
System	Method	Timing for 100 steps in seconds
256 TIP3P	MD	23.8 (1)
64 DMPC + 1645 TIP3P	MD	890 (1)	528 (2)	326 (4)	209 (8)
8 Aβ16-22	LD	1.02 (1)
23760 Groot-Warren particles	DPD	22.16 (1)

Full-size table

     

A general-purpose coarse-grained molecular dynamics program

In this article, we describe a general-purpose coarse-grained molecular dynamics program COGNAC (COarse Grained molecular dynamics program by NAgoya Cooperation). COGNAC has been developed for general molecular dynamics simulation, especially for coarse-grained polymer chain models. COGNAC can deal with general molecular models, in which each molecule consists of coarse-grained atomic units connected by chemical bonds. The chemical bonds are specified by bonding potentials for the stretching, bending and twisting of the bonds, each of which are the functions of the position coordinates of the two, three and four atomic units. COGNAC can deal with both isotropic and anisotropic interactions between the non-bonded atomic units. As an example, the Gay-Berne potential is implemented. New potential functions can be added to the list of existing potential functions by users. COGNAC can do simulations for various situations such as under constant temperature, under constant pressure, under shear and elongational deformation, etc. Some new methods are implemented in COGNAC for modeling multiphase structures of polymer blends and block copolymers. A density biased Monte Carlo method and a density biased potential method can generate equilibrium chain configurations from the results of the self-consistent field calculations. Staggered reflective boundary conditions can generate interfacial structures with smaller system size compared with those of periodic boundary conditions.     

An efficient parallel implementation of the smooth particle mesh Ewald method for molecular dynamics simulations

This paper focuses on the implementation and the performance analysis of a smooth particle mesh Ewald method on several parallel computers. We present the details of the algorithms and our implementation that are used to optimize parallel efficiency on such parallel computers.     

TiReX: Replica-exchange molecular dynamics using Tinker

We present a driver program for performing replica-exchange molecular dynamics simulations with the Tinker package. Parallelization is based on the Message Passing Interface, with every replica assigned to a separate process. The algorithm is not communication intensive, which makes the program suitable for running even on loosely coupled cluster systems. Particular attention is paid to the practical aspects of analyzing the program output.

Program summary

Program title: TiReXCatalogue identifier: AEEK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEK_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 43 385No. of bytes in distributed program, including test data, etc.: 502 262Distribution format: tar.gzProgramming language: Fortran 90/95Computer: Most UNIX machinesOperating system: LinuxHas the code been vectorized or parallelized?: parallelized with MPIClassification: 16.13External routines: TINKER version 4.2 or 5.0, built as a libraryNature of problem: Replica-exchange molecular dynamics.Solution method: Each replica is assigned to a separate process; temperatures are swapped between replicas at regular time intervals.Running time: The sample run may take up to a few minutes.     

A handy tool for history keeping of Geant4 tracks - J4HistoryKeeper

The Particle Flow Analysis (PFA) is currently under intense studies as the most promising way to achieve precision jet energy measurements required at the future linear e⁺e⁻ collider. In order to optimize detector configurations and to tune up the PFA it is crucial to identify factors that limit the PFA performance and clarify the fundamental limits on the jet energy resolution that remain even with the perfect PFA and an infinitely granular calorimeter. This necessitates a tool to connect each calorimeter hit in particle showers to its parent charged track, if any, and eventually all the way back to its corresponding primary particle, while identifying possible interactions and decays along the way. In order to realize this with a realistic memory space, we have developed a set of C++ classes that facilitates history keeping of particle tracks within the framework of Geant4. This software tool, hereafter called J4HistoryKeeper, comes in handy in particular when one needs to stop this history keeping for memory space economy at multiple geometrical boundaries beyond which a particle shower is expected to start. In this paper this software tool is described and applied to a generic detector model to demonstrate its functionality.     

Numerical solving of the vibrational time-independent Schrödinger equation in one and two dimensions using the variational method

A program package for variational solving of the time-independent Schrödinger equation (SE) in one and two dimensions is described. The first part of the the program package includes the fitting program (FIT) with which the ab initio or DFT calculated points are fitted to a computationally inexpensive functional form. Proper fitting of the potential energy surface is crucial for the quality of the results. The second part of the package consists of a program for variational solving of the SE (2DSCHRODINGER) using either a shifted Gaussian basis set or the rectangular basis set proposed by Balint-Kurti and coworkers [J. Chem. Phys. 91 (1989) 3571]. The third part of the program package consists of the calculation of the expectation values, IR and Raman spectra XPECT), and the visualization of results (PLOT). The program package is applied to study a quantum harmonic oscillator and an intramolecular, strong hydrogen bond in picolinic acid N-oxide. For the former system analytical solutions exist, while for the latter system a comparison with the experimental data is made. The advantages and disadvantages of the applied methods are discussed.     

A new class of hybrid global optimization algorithms for peptide structure prediction: integrated hybrids

A novel class of hybrid global optimization methods for application to the structure prediction in protein-folding problem is introduced. These optimization methods take the form of a hybrid between a deterministic global optimization algorithm, the αBB, and a stochastically based method, conformational space annealing (CSA), and attempt to combine the beneficial features of these two algorithms. The αBB method as previously extant exhibits consistency, as it guarantees convergence to the global minimum for twice-continuously differentiable constrained nonlinear programming problems, but can benefit from improvements in the computational front. Computational studies for met-enkephalin demonstrate the promise for the proposed hybrid global optimization method.     

A hybrid multi-loop genetic-algorithm/simplex/spatial-grid method for locating the optimum orientation of an adsorbed protein on a solid surface

Atomistic simulation of protein adsorption on a solid surface in aqueous environment is computationally demanding, therefore the determination of preferred protein orientations on the solid surface usually serves as an initial step in simulation studies. We have developed a hybrid multi-loop genetic-algorithm/simplex/spatial-grid method to search for low adsorption-energy orientations of a protein molecule on a solid surface. In this method, the surface and the protein molecule are treated as rigid bodies, whereas the bulk fluid is represented by spatial grids. For each grid point, an effective interaction region in the surface is defined by a cutoff distance, and the possible interaction energy between an atom at the grid point and the surface is calculated and recorded in a database. In searching for the optimum position and orientation, the protein molecule is translated and rotated as a rigid body with the configuration obtained from a previous Molecular Dynamic simulation. The orientation-dependent protein-surface interaction energy is obtained using the generated database of grid energies. The hybrid search procedure consists of two interlinked loops. In the first loop A, a genetic algorithm (GA) is applied to identify promising regions for the global energy minimum and a local optimizer with the derivative-free Nelder-Mead simplex method is used to search for the lowest-energy orientation within the identified regions. In the second loop B, a new population for GA is generated and competitive solution from loop A is improved. Switching between the two loops is adaptively controlled by the use of similarity analysis. We test the method for lysozyme adsorption on a hydrophobic hydrogen-terminated silicon (110) surface in implicit water (i.e., a continuum distance-dependent dielectric constant). The results show that the hybrid search method has faster convergence and better solution accuracy compared with the conventional genetic algorithm.     

g_permute: Permutation-reduced phase space density compaction

Biomolecular processes are governed by free energy changes and thus depend on a fine-tuned interplay between entropy and enthalpy. To calculate accurate values for entropies from simulations is particularly challenging for the solvation shell of proteins, which contributes crucially to the total entropy of solvated proteins, due to the diffusive motion of the solvent molecules. Accordingly, for each frame of a Molecular dynamics (MD) trajectory, our software relabels the solvent molecules, such that the resulting configuration space volume is reduced by a factor of N! with N being the number of solvent molecules. The combinatorial explosion of a naive implementation is here overcome by transforming the task into a linear assignment problem, for which algorithms with complexity O(N³) exist. We have shown in previous research that the solvent entropy can be estimated from such a compacted trajectory by established entropy estimation methods. In this paper, we describe the software implementation which also allows applications beyond entropy estimation, such as the permutation of lipids in membrane bilayers.

Program summary

Program title: g_permuteCatalogue identifier: AECJ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECJ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GPLNo. of lines in distributed program, including test data, etc.: 45 173No. of bytes in distributed program, including test data, etc.: 2 730 678Distribution format: tar.gzProgramming language: CComputer: PC-compatible running LinuxOperating system: LinuxRAM: Dependent on the number of solvent molecules, min 12 582 912 bytesClassification: 3, 4.8, 4.9External routines: liblap (included); From GROMACS-3.3.1: libgmx (not included)Nature of problem: Estimating the entropy of solvent molecules from a molecular dynamics simulation trajectory cannot be performed on ordinary trajectories.Solution method: Compacting the configuration space of molecules by exploiting their permutation symmetry. Applies to trajectories either compatible to those obtained with the GROMACS simulation package [1] or multi-model pdb (Protein Data Bank) files.Restrictions: In rare cases the time to find a solution for the linear assignment problem can be very long.Running time: Dependent on trajectory length and number of molecules to be permuted.References:[1] D. van der Spoel, et al., J. Comput. Chem. 26 (2005) 1701.     

REACH: A program for coarse-grained biomolecular simulation

REACH (Realistic Extension Algorithm viaCovariance Hessian) is a program package for residue-scale coarse-grained biomolecular simulation. The program calculates the force constants of a residue-scale elastic network model in single-domain proteins using the variance-covariance matrix obtained from atomistic molecular dynamics simulation. Secondary-structure dependence of the force constants is integrated. The method involves self-consistent, direct mapping of atomistic simulation results onto a coarse-grained force field in an efficient automated procedure without requiring iterative fits and avoiding system dependence.

Program summary

Program title: REACHCatalogue identifier: AEDA_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDA_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 42 244No. of bytes in distributed program, including test data, etc.: 3 682 118Distribution format: tar.gzProgramming language: FORTRAN 77Computer: x86 PCOperating system: GNU/Linux, SUSE and Red HatRAM: Depends on the system size to be calculatedWord size: 32 or 64 bitsClassification: 3External routines: LAPACK, BLASNature of problem: A direct calculation of force field for residue-scale coarse-grained biomolecular simulation derived from atomistic molecular dynamics trajectory.Solution method: A variance-covariance matrix and the associated Hessian (second-derivative) matrix are calculated from an atomistic molecular dynamics trajectory of single-domain protein internal motion and the off-diagonal Hessian matrix is fitted to that of a residue-scale elastic network model. The resulting force constants for the residue pair interactions are expressed as model functions as a function of pairwise distance.Running time: Depends on the system size and the number of MD trajectory frames used. The test run provided with the distribution takes only a few seconds to execute.     

A scalable parallel algorithm for large-scale reactive force-field molecular dynamics simulations

A scalable parallel algorithm has been designed to perform multimillion-atom molecular dynamics (MD) simulations, in which first principles-based reactive force fields (ReaxFF) describe chemical reactions. Environment-dependent bond orders associated with atomic pairs and their derivatives are reused extensively with the aid of linked-list cells to minimize the computation associated with atomic n-tuple interactions (n?4 explicitly and ?6 due to chain-rule differentiation). These n-tuple computations are made modular, so that they can be reconfigured effectively with a multiple time-step integrator to further reduce the computation time. Atomic charges are updated dynamically with an electronegativity equalization method, by iteratively minimizing the electrostatic energy with the charge-neutrality constraint. The ReaxFF-MD simulation algorithm has been implemented on parallel computers based on a spatial decomposition scheme combined with distributed n-tuple data structures. The measured parallel efficiency of the parallel ReaxFF-MD algorithm is 0.998 on 131,072 IBM BlueGene/L processors for a 1.01 billion-atom RDX system.     

A space-time-ensemble parallel nudged elastic band algorithm for molecular kinetics simulation

A scalable parallel algorithm has been designed to study long-time dynamics of many-atom systems based on the nudged elastic band method, which performs mutually constrained molecular dynamics simulations for a sequence of atomic configurations (or states) to obtain a minimum energy path between initial and final local minimum-energy states. A directionally heated nudged elastic band method is introduced to search for thermally activated events without the knowledge of final states, which is then applied to an ensemble of bands in a path ensemble method for long-time simulation in the framework of the transition state theory. The resulting molecular kinetics (MK) simulation method is parallelized with a space-time-ensemble parallel nudged elastic band (STEP-NEB) algorithm, which employs spatial decomposition within each state, while temporal parallelism across the states within each band and band-ensemble parallelism are implemented using a hierarchy of communicator constructs in the Message Passing Interface library. The STEP-NEB algorithm exhibits good scalability with respect to spatial, temporal and ensemble decompositions on massively parallel computers. The MK simulation method is used to study low strain-rate deformation of amorphous silica.     

A new treecode for long-range force calculation

We propose a new hierarchical tree algorithm with high adaptivity to various particle distributions for long-range force calculations. This algorithm divides parent cells into k daughter cells using the k-means algorithm. The tree structure provided by this algorithm is independent of the coordinate system used. This method also includes a unique procedure for determining cell sizes adjusted to particle distributions.We investigated the characteristics of the tree structure and the effect on the long-range force calculation performance of various branching ratios k. The results of numerical experiments using various particle distributions showed that the number of interactions between particles and cells grows with k, but the number of distance evaluations between particles and cells decreased when k is around 5. We can therefore select an optimized value of k according to the characteristics of the problem to be analyzed. Comparing the algorithm to Barnes-Hut treecode using gravitational calculations at the same error level, we found that the calculation cost could be decreased remarkably.