Molecular dynamics (MD) simulation involves simulating the interactions of particles. MD has many applications in basic biological sciences, drug discovery, materials science, and other fields. Simulating$1\mu \mathrm{s}$of a 100K-atom system can take hours or days11https://www.bdr.riken.jp/en/research/labs/taiji-mlmdgrape4.html, where the compute-heavy aspect of MD is calculating the long-range forces between pairs of particles. In this paper, we explore the application of approximate computing in MD as a means to improve compute density. Specifically, we employ approximate memoization, where previously computed forces (and more) are stored in a table, and are retrieved in subsequent force calculations, provided the inputs to the force calculation are the same or similar. If the prior-computed table values can be used, significant computational work is avoided. In an experimental study, we apply software simulation to understand the degree to which approximation is feasible. We then propose a hardware implementation of memoization to be used within an ASIC MD simulator, MDGRAPE-4A [18]. We show that compute density, measured as$\text{pair-interactions}/(s\cdot\mu m^{2})$is improved substantially, between 40 % and 70 % for the studied cases. This is contingent on the particular system being simulated, the table size, and permitted level of approximation.

We developed MDGRAPE-4A, a special-purpose computer system for molecular dynamics simulations, consisting of 512 nodes of custom system-on-a-chip LSIs with dedicated processor cores and interconnects designed to achieve strong scalability for biomolecular simulations. To reduce the global communications required for the evaluation of Coulomb interactions, we conducted a co-design of the MDGRAPE-4A and the novel algorithm, tensor-structured multilevel Ewald summation method (TME), which produced hardware modules on the custom LSI circuit for particle-grid operations and for grid-grid separable convolutions on a 3D torus network. We implemented the convolution for the top-level grid potentials by using 3D FFTs on an FPGA, along with an FPGA-based octree network to gather grid charges. The elapsed time for the long-range part of Coulomb is 50 μs, which can mostly overlap with those for the short-range part, and the additional cost is approximately 10 μs/step, which is only a 5% performance loss.

Networks-on-Chip has become the de facto design paradigm for many-core systems. This poster presents a general purpose Networks-on-Chip (NoC) generator with optimal configurations, named EAGEN. The NoC producer module of EAGEN is written in Chisel3 language which generates both Verilog and C++ model for hardware implementation and software simulation, respectively. Once the application specification and design constrains are fed to EAGEN, the synthesizable RTL code with optimal configuration will be output.

Electrostatic potentials (ESPs) are frequently used in structural biology for the characterization of biomolecules. Here we study the potential employment of hardware accelerators like the graphics processing unit or the application-specific integrated circuit MD-GRAPE-3 for the purpose of efficient computation of ESPs. An algorithm closely coupled to the general description of molecular surfaces is ported to both specialized architectures. The high-level interface library MR1/3 is used, which greatly simplifies the porting process. Hardware-accelerated versions show significant Speed-Up factors reaching values of up to 27×. Once ESP computations have become a matter of seconds, the underlying application can be offered in the form of a web service. © The Author 2009. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved.

As an entry for the 2009 Gordon Bell price/performance prize, we present the results of two different hierarchical N-body simulations on a cluster of 256 graphics processing units (GPUs). Unlike many previous N-body simulations on GPUs that scale as O(N2), the present method calculates the O(N log N) treecode and O(N) fast multipole method (FMM) on the GPUs with unprecedented efficiency. We demonstrate the performance of our method by choosing one standard application --a gravitational N-body simulation-- and one non-standard application --simulation of turbulence using vortex particles. The gravitational simulation using the treecode with 1,608,044,129 particles showed a sustained performance of 42.15 TFlops. The vortex particle simulation of homogeneous isotropic turbulence using the periodic FMM with 16,777,216 particles showed a sustained performance of 20.2 TFlops. The overall cost of the hardware was 228,912 dollars. The maximum corrected performance is 28.1TFlops for the gravitational simulation, which results in a cost performance of 124 MFlops/$. This correction is performed by counting the Flops based on the most efficient CPU algorithm. Any extra Flops that arise from the GPU implementation and parameter differences are not included in the 124 MFlops/$.

Virtual compound screening using molecular docking is widely used in the discovery of new lead compounds for drug design. However, this method is not completely reliable and therefore unsatisfactory. In this study, we used massive molecular dynamics simulations of protein-ligand conformations obtained by molecular docking in order to improve the enrichment performance of molecular docking. Our screening approach employed the molecular mechanics/Poisson-Boltzmann and surface area method to estimate the binding free energies. For the top-ranking 1,000 compounds obtained by docking to a target protein, approximately 6,000 molecular dynamics simulations were performed using multiple docking poses in about a week. As a result, the enrichment performance of the top 100 compounds by our approach was improved by 1.6-4.0 times that of the enrichment performance of molecular dockings. This result indicates that the application of molecular dynamics simulations to virtual screening for lead discovery is both effective and practical. However, further optimization of the computational protocols is required for screening various target proteins.

We have achieved a sustained calculation speed of 281 Tflops for the optimization of the 3-D structures of proteins from the X-ray experimental data by the Genetic Algorithm - Direct Space (GA-DS) method. In this calculation we used MDGRAPE-3, special-purpose computer for molecular simulations, with the peak performance of 752 Tflops. In the GA-DS method, a set of selected parameters which define the crystal structures of proteins is optimized by the Genetic Algorithm. As a criterion to estimate the model parameters, we used the reliability factor R1 which indicates the statistical difference between the calculated and the measured diffraction data. To evaluate this factor it is necessary to reconstruct the diffraction patterns of the model structures every time the model is updated. Therefore, in this method the nonequispaced Discrete Fourier Transformation (DFT) used to calculate the diffraction patterns dominates most of the computation time. To accelerate DFT calculations, we used the special-purpose computer, MDGRAPE-3. A molecule, Carbamoyl-Phosphate Synthetase was investigated. The final reliability factors were much smaller than the typical values obtained in other methods such as the Molecular Replacement (MR) method. Our results successfully demonstrate that high-performance computing with GA-DS method on special-purpose computers is effective for the structure determination of biological molecules and the method has a potential to be widely used in near future.

We have achieved a sustained performance of 55 TFLOPS for molecular dynamics simulations of the amyloid fibril formation of peptides from the yeast Sup35 in an aqueous solution. For performing the calculations, we used the MDGRAPE-3 system---a special-purpose computer system for molecular dynamics simulations. Its nominal peak performance was 415 TFLOPS for Coulomb force calculations; this is the highest-ever performance reported for classical molecular dynamics simulations. Amyloid fibril formation is known to be related to the occurrence of severe diseases such as Alzheimer's, Parkinson's, and Creutzfeldt-Jakob diseases. The Sup35 protein is a "yeast prion protein," which forms mini-crystals due to aggregation; it forms an effective platform for studying the formation process of amyloid fibrils. In these simulations, we first elucidate that the amyloid-forming peptides GNNQQNY aggregate at a higher frequency than non-amyloid-forming peptides SQNGNQQRG; further, the GNNQQNY peptides tend to form parallel two-stranded ß-sheets that would grow into a cross-ß amyloid nucleus. The results are consistent with those obtained experimentally. Furthermore, we could observe an early elongation of the amyloid nucleus. This result is expected to contribute toward a deeper understanding of the amyloid growth mechanism.

We are developing the 'Protein Explorer' system, a petaflops special-purpose computer system for molecular dynamics simulations. The Protein Explorer is a PC cluster equipped with special-purpose engines that calculate nonbonded interactions between atoms, which is the most time-consuming part of the simulations. A dedicated LSI 'MDGRAPE-3 chip' performs these force calculations at a speed of 165 gigaflops or higher. The system will have 6,144 MDGRAPE-3 chips to achieve a nominal peak performance of one petaflop. The system will be completed in 2006. In this paper, we describe the project plans and the architecture of the Protein Explorer.

We report on resent astrophysical N-body simulations performed on the GRAPE-4 (GRAvity PipE 4) system, a special-purpose computer for astrophysical N-body simulations. We first review the astrophysical motivation, the algorithm, the structure of the GRAPE system, and the actual performance. The GRAPE-4 system consists of 1692 pipeline processors. The peak speed of one pipeline processor is 523 Mflops and that of the total system is 884 Gflops. The performance obtained is 529 Gflops for the simulation of two massive black holes in the core of a galaxy with 700,000 stars.

We describe the GRAPE-4 (Gravity Pipe 4) system, a special-purpose computer for astrophysical N-body simulations. In N-body simulations, most of the computing time is spent to calculate the force between particles, since the number of interactions is proportional to the square of the number of particles. For many problems the accuracy of fast algorithms such as the particle-mesh scheme is not sufficient and we have to use the straightforward direct summation. In order to accelerate the force calculation, we have developed a series of hardware, the GRAPE (Gravity Pipe) systems. The basic idea of our GRAPE systems is to develop a hardware specialized for the force calculation. The rest of the calculation is performed on the general-purpose computer connected to GRAPE. The GRAPE-4 system is our newest hardware, scheduled to be completed in early 1995. Planned peak speed is 1.15 Tflops. This speed is achieved by running 1920 pipeline LSIs, each provides 600 Mflops, in parallel. A prototype system has been completed July 1994, and the full system is now under manufacturing.>