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678
NAMD2: Greater Scalability for Parallel Molecular Dynamics
 JOURNAL OF COMPUTATIONAL PHYSICS
, 1998
"... Molecular dynamics programs simulate the behavior of biomolecular systems, leading to insights and understanding of their functions. However, the computational complexity of such simulations is enormous. Parallel machines provide the potential to meet this computational challenge. To harness this ..."
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Cited by 317 (45 self)
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Molecular dynamics programs simulate the behavior of biomolecular systems, leading to insights and understanding of their functions. However, the computational complexity of such simulations is enormous. Parallel machines provide the potential to meet this computational challenge. To harness this potential, it is necessary to develop a scalable program. It is also necessary that the program be easily modified by applicationdomain programmers. The
Mechanical Integrators Derived from a Discrete Variational Principle
"... Many numerical integrators for mechanical system simulation are created by using discrete algorithms to approximate the continuous equations of motion. In this paper, we present a procedure to construct timestepping algorithms that approximate the flow of continuous ODE's for mechanical system ..."
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Cited by 86 (12 self)
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Many numerical integrators for mechanical system simulation are created by using discrete algorithms to approximate the continuous equations of motion. In this paper, we present a procedure to construct timestepping algorithms that approximate the flow of continuous ODE's for mechanical systems by discretizing Hamilton's principle rather than the equations of motion. The discrete equations share similarities to the continuous equations by preserving invariants, including the symplectic form and the momentum map. We girst present a formulation of discrete mechanics along with a discrete variational principle. We then show that the resulting equations of motion preserve the symplectic form and that this formulation of mechanics leads to conservation laws from a discrete version of Noether's theorem. We then use the discrete mechanics formulation to develop a procedure for constructing mechanical integrators for continuous Lagrangian systems. We apply the construction procedure to the rigid body and the double spherical pendulum to demonstrate numerical properties of the integrators.
Geometric numerical integration illustrated by the StörmerVerlet method
, 2003
"... The subject of geometric numerical integration deals with numerical integrators that preserve geometric properties of the flow of a differential equation, and it explains how structure preservation leads to improved longtime behaviour. This article illustrates concepts and results of geometric nume ..."
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Cited by 65 (6 self)
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The subject of geometric numerical integration deals with numerical integrators that preserve geometric properties of the flow of a differential equation, and it explains how structure preservation leads to improved longtime behaviour. This article illustrates concepts and results of geometric numerical integration on the important example of the Störmer–Verlet method. It thus presents a crosssection of the recent monograph by the authors, enriched by some additional material. After an introduction to the Newton–Störmer–Verlet–leapfrog method and its various interpretations, there follows a discussion of geometric properties: reversibility, symplecticity, volume preservation, and conservation of first integrals. The extension to Hamiltonian systems on manifolds is also described. The theoretical foundation relies on a backward error analysis, which translates the geometric properties of the method into the structure of a modified differential equation, whose flow is nearly identical to the numerical method. Combined with results from perturbation theory, this explains the excellent longtime behaviour of the method: longtime energy conservation, linear error growth and preservation of invariant tori in nearintegrable systems, a discrete virial theorem, and preservation of adiabatic invariants.
Symplectic Numerical Integrators in Constrained Hamiltonian Systems
, 1994
"... : Recent work reported in the literature suggests that for the longtime integration of Hamiltonian dynamical systems one should use methods that preserve the symplectic (or canonical) structure of the flow. Here we investigate the symplecticness of numerical integrators for constrained dynamics, su ..."
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Cited by 62 (8 self)
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: Recent work reported in the literature suggests that for the longtime integration of Hamiltonian dynamical systems one should use methods that preserve the symplectic (or canonical) structure of the flow. Here we investigate the symplecticness of numerical integrators for constrained dynamics, such as occur in molecular dynamics when bond lengths are made rigid in order to overcome stepsize limitations due to the highest frequencies. This leads to a constrained Hamiltonian system of smaller dimension. Previous work has shown that it is possible to have methods which are symplectic on the constraint manifold in phase space. Here it is shown that the very popular Verlet method with SHAKEtype constraints is equivalent to the same method with RATTLEtype constraints and that the latter is symplectic and time reversible. (This assumes that the iteration is carried to convergence.) We also demonstrate the global convergence of the Verlet scheme in the presence of SHAKEtype and RATTLE...
Molecular Modeling Of Proteins And Mathematical Prediction Of Protein Structure
 SIAM Review
, 1997
"... . This paper discusses the mathematical formulation of and solution attempts for the socalled protein folding problem. The static aspect is concerned with how to predict the folded (native, tertiary) structure of a protein, given its sequence of amino acids. The dynamic aspect asks about the possib ..."
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Cited by 59 (5 self)
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. This paper discusses the mathematical formulation of and solution attempts for the socalled protein folding problem. The static aspect is concerned with how to predict the folded (native, tertiary) structure of a protein, given its sequence of amino acids. The dynamic aspect asks about the possible pathways to folding and unfolding, including the stability of the folded protein. From a mathematical point of view, there are several main sides to the static problem:  the selection of an appropriate potential energy function;  the parameter identification by fitting to experimental data; and  the global optimization of the potential. The dynamic problem entails, in addition, the solution of (because of multiple time scales very stiff) ordinary or stochastic differential equations (molecular dynamics simulation), or (in case of constrained molecular dynamics) of differentialalgebraic equations. A theme connecting the static and dynamic aspect is the determination and formation of...
Molecular dynamics simulations of the 136 unique tetranucleotide sequences of DNA oligonucleotides. I. Research design and results on d(CpG) steps
 Biophys. J
, 2004
"... ABSTRACT We describe herein a computationally intensive project aimed at carrying out molecular dynamics (MD) simulations including water and counterions on BDNA oligomers containing all 136 unique tetranucleotide base sequences. This initiative was undertaken by an international collaborative effo ..."
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Cited by 55 (14 self)
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ABSTRACT We describe herein a computationally intensive project aimed at carrying out molecular dynamics (MD) simulations including water and counterions on BDNA oligomers containing all 136 unique tetranucleotide base sequences. This initiative was undertaken by an international collaborative effort involving nine research groups, the ‘‘Ascona BDNA Consortium’ ’ (ABC). Calculations were carried out on the 136 cases imbedded in 39 DNA oligomers with repeating tetranucleotide sequences, capped on both ends by GC pairs and each having a total length of 15 nucleotide pairs. All MD simulations were carried out using a welldefined protocol, the AMBER suite of programs, and the parm94 force field. Phase I of the ABC project involves a total of;0.6 msof simulation for systems containing;24,000 atoms. The resulting trajectories involve 600,000 coordinate sets and represent;400
Variational time integrators
 Int. J. Numer. Methods Eng
"... The purpose of this paper is to review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest. In particular, the conservation properties of both synchronous and asynchronous variational integrators (AVIs) are discussed in de ..."
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Cited by 53 (11 self)
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The purpose of this paper is to review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest. In particular, the conservation properties of both synchronous and asynchronous variational integrators (AVIs) are discussed in detail. We present selected numerical examples which demonstrate the excellent accuracy, conservation and convergence characteristics of AVIs. In these tests, AVIs are found to result in substantial speedups, at equal accuracy, relative to explicit Newmark. A mathematical proof of convergence of the AVIs is also presented in this paper. Finally, we develop the subject of horizontal variations and configurational forces in discrete dynamics. This theory leads to exact pathindependent characterizations of the configurational forces acting on discrete systems. Notable examples are the configurational forces acting on material nodes in a finite element discretisation; and the Jintegral at the tip of a crack in
DNA and its counterions: a molecular dynamics study
 Nucleic Acids Res
, 2004
"... The behaviour of mobile counterions, Na+ and K+, was analysed around a BDNA double helix with the sequence CCATGCGCTGAC in aqueous solution during two 50 ns long molecular dynamics trajectories. The movement of both monovalent ions remains diffusive in the presence of DNA. Ions sample the comple ..."
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Cited by 48 (10 self)
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The behaviour of mobile counterions, Na+ and K+, was analysed around a BDNA double helix with the sequence CCATGCGCTGAC in aqueous solution during two 50 ns long molecular dynamics trajectories. The movement of both monovalent ions remains diffusive in the presence of DNA. Ions sample the complete space available during the simulation time, although individual ions sample only about onethird of the simulation box. Ions preferentially sample electronegative sites around DNA, but direct binding to DNA bases remains a rather rare event, with highest site occupancy values of <13%. The location of direct binding sites depends greatly on the nature of the counterion. While Na+ binding in both grooves is strongly sequencedependent with the preferred binding site in the minor groove, K+ mainly visits the major groove and binds close to the centre of the oligomer. The electrostatic potential of an average DNA structure therefore cannot account for the ability of a site to bind a given cation; other factors must also play a role. An extensive analysis of the influence of counterions on DNA conformation showed no evidence of minor groove narrowing upon ion binding. A significant difference between the conformations of the double helix in the different simulations can be attributed to extensive a/g transitions in the phosphate backbone during the simulation with Na+. These transitions, with lifetimes over tens of nanoseconds, however, appear to be correlated with ion binding to phosphates. The ionspecific conformational properties of DNA, hitherto largely overlooked, may play an important role in DNA recognition and binding.
A New Parallel Method for Molecular Dynamics Simulation of Macromolecular Systems
, 1994
"... Shortrange molecular dynamics simulations of molecular systems are commonly parallelized by replicateddata methods, where each processor stores a copy of all atom positions. This enables computation of bonded 2, 3, and 4body forces within the molecular topology to be partitioned among p ..."
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Cited by 39 (3 self)
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Shortrange molecular dynamics simulations of molecular systems are commonly parallelized by replicateddata methods, where each processor stores a copy of all atom positions. This enables computation of bonded 2, 3, and 4body forces within the molecular topology to be partitioned among processors straightforwardly. A drawback to such methods is that the interprocessor communication scales as N , the number of atoms, independent of P , the number of processors. Thus, their parallel efficiency falls off rapidly when large numbers of processors are used. In this article a new parallel method for simulating macromolecular or smallmolecule systems is presented, called forcedecomposition. Its memory and communication costs scale as N= p P , allowing larger problems to be run faster on greater numbers of processors. Like replicateddata techniques, and in contrast to spatialdecomposition approaches, the new method can be simply loadbalanced and performs well eve...
Algorithmic challenges in computational molecular biophysics
 Journal of Computational Physics
, 1999
"... A perspective of biomolecular simulations today is given, with illustrative applications and an emphasis on algorithmic challenges, as reflected by the work of a multidisciplinary team of investigators from five institutions. Included are overviews and recent descriptions of algorithmic work in long ..."
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Cited by 37 (3 self)
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A perspective of biomolecular simulations today is given, with illustrative applications and an emphasis on algorithmic challenges, as reflected by the work of a multidisciplinary team of investigators from five institutions. Included are overviews and recent descriptions of algorithmic work in longtime integration for molecular dynamics; fast electrostatic evaluation; crystallographic refinement approaches; and implementation of large, computationintensive programs on modern architectures. Expected future developments of the field are also discussed. c ○ 1999 Academic Press Key Words: biomolecular simulations; molecular dynamics; longtime integration; fast electrostatics; crystallographic refinement; highperformance platforms.