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 application-domain programmers. The

For decades, researchers have been applying computer simulation to address problems in biology. However, many of these grand challenges in computational biology, such as simulating how proteins fold, remained unsolved due to their great complexity. Indeed, even to simulate the fastest folding protein would require decades on the fastest modern CPUs. Here, we review novel methods to fundamentally speed such previously intractable problems using a new computational paradigm: distributed computing. By efficiently harnessing tens of thousands of computers throughout the world, we have been able to break previous computational barriers. However, distributed computing brings new challenges, such as how to efficiently divide a complex calculation of many PCs that are connected by relatively slow networking. Moreover, even if the challenge of accurately reproducing reality can be conquered, a new challenge emerges: how can we take the results of these simulations (typically tens to hundreds of gigabytes of raw data) and gain some insight into the questions at hand. This challenge of the analysis of the sea of data resulting from large-scale simulation will likely remain for decades to come.

: Recent work reported in the literature suggests that for the long-time 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 SHAKE-type constraints is equivalent to the same method with RATTLE-type 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 SHAKE--type and RATTLE-...

Short--range molecular dynamics simulations of molecular systems are commonly parallelized by replicated--data methods, where each processor stores a copy of all atom positions. This enables computation of bonded 2--, 3--, and 4--body forces within the molecular topology to be partitioned among processors straightforwardly. A drawback to such methods is that the inter--processor 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 small--molecule systems is presented, called force--decomposition. Its memory and communication costs scale as N= p P , allowing larger problems to be run faster on greater numbers of processors. Like replicated--data techniques, and in contrast to spatial--decomposition approaches, the new method can be simply load--balanced and performs well eve...

We use recent results on symplectic integration of Hamiltonian systems with constraints to construct symplectic integrators on cotangent bundles of manifolds by embedding the manifold in a linear space. We also prove that these methods are equivariant under cotangent lifts of a symmetry group acting linearly on the ambient space and consequently preserve the corresponding momentum. These results provide an elementary construction of symplectic integrators for Lie-Poisson systems and other Hamiltonian systems with symmetry. The methods are illustrated on the free rigid body, the heavy top, and the double spherical pendulum. 1.

Factory [Gamma et al. 1995, pp. 87-95] and the Prototype [Gamma et al. 1995, pp. 117-126] patterns. The Abstract Factory pattern delegates the object creation, and the Prototype pattern allows dynamic configuration. The factory is in charge of converting the user-specified force into an object that has been properly setup to do computation. The factory creates replicas of "prototypes" that have been registered by the developer. This restricts the factory to create only supported objects, since not all combinations of R1-R5 make sense or are supported at a given stage of development.

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 long-time behaviour. This article illustrates concepts and results of geometric numerical integration on the important example of the Störmer–Verlet method. It thus presents a cross-section 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 long-time behaviour of the method: long-time energy conservation, linear error growth and preservation of invariant tori in near-integrable systems, a discrete virial theorem, and preservation of adiabatic invariants.

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-time integration for molecular dynamics; fast electrostatic evaluation; crystallographic refinement approaches; and implementation of large, computation-intensive programs on modern architectures. Expected future developments of the field are also discussed. c ○ 1999 Academic Press Key Words: biomolecular simulations; molecular dynamics; long-time integration; fast electrostatics; crystallographic refinement; high-performance platforms.

Innovative algorithms have been developed during the past decade for simulating Newtonian physics for macromolecules. A major goal is alleviation of the severe requirement that the integration timestep be small enough to resolve the fastest components of the motion and thus guarantee numerical stability. This timestep problem is challenging if strictly faster methods with the same all-atom resolution at small timesteps are sought. Mathematical techniques that have worked well in other multiple-timescale contexts—where the fast motions are rapidly decaying or largely decoupled from others—have not been as successful for biomolecules, where vibrational coupling is strong. This review examines general issues that limit the timestep and describes available methods (constrained, reduced-variable, implicit, symplectic, multipletimestep, and normal-mode-based schemes). A section compares results of selected integrators for a model dipeptide, assessing physical and numerical performance. Included is our dual timestep method LN, which relies on an approximate linearization of the equations of motion every �t interval (5 fs or less), the solution of which is obtained by explicit integration at the inner timestep �τ (e.g., 0.5 fs). LN is computationally competitive, providing 4–5 speedup factors, and results are in good agreement, in comparison to 0.5 fs trajectories. These collective algorithmic efforts help fill the gap between the time range that can be simulated and the timespans of major biological interest (milliseconds and longer). Still, only a hierarchy of models and methods, along with

ABSTRACT Simulating protein folding thermodynamics starting purely from a protein sequence is a grand challenge of computational biology. Here, we present an algorithm to calculate a canonical distribution from molecular dynamics simulation of protein folding. This algorithm is based on the replica exchange method where the kinetic trapping problem is overcome by exchanging noninteracting replicas simulated at different temperatures. Our algorithm uses multiplexed-replicas with a number of independent molecular dynamics runs at each temperature. Exchanges of configurations between these multiplexed-replicas are also tried, rendering the algorithm applicable to large-scale distributed computing (i.e., highly heterogeneous parallel computers with processors having different computational power). We demonstrate the enhanced sampling of this algorithm by simulating the folding thermodynamics of a 23 amino acid miniprotein. We show that better convergence is achieved compared to constant temperature molecular dynamics simulation, with an efficient scaling to large number of computer processors. Indeed, this enhanced sampling results in (to our knowledge) the first example of a replica exchange algorithm that samples a folded structure starting from a completely unfolded state.