Efficient nonbonded interactions for molecular dynamics on a graphics processing unit

We describe an algorithm for computing nonbonded interactions with cutoffs on a graphics processing unit. We have incorporated it into OpenMM, a library for performing molecular simulations on high‐performance computer architectures. We benchmark it on a variety of systems including boxes of water molecules, proteins in explicit solvent, a lipid bilayer, and proteins with implicit solvent. The results demonstrate that its performance scales linearly with the number of atoms over a wide range of system sizes, while being significantly faster than other published algorithms. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Accelerating molecular modeling applications with graphics processors

Molecular mechanics simulations offer a computational approach to study the behavior of biomolecules at atomic detail, but such simulations are limited in size and timescale by the available computing resources. State-of-the-art graphics processing units (GPUs) can perform over 500 billion arithmetic operations per second, a tremendous computational resource that can now be utilized for general purpose computing as a result of recent advances in GPU hardware and software architecture. In this article, an overview of recent advances in programmable GPUs is presented, with an emphasis on their application to molecular mechanics simulations and the programming techniques required to obtain optimal performance in these cases. We demonstrate the use of GPUs for the calculation of long-range electrostatics and nonbonded forces for molecular dynamics simulations, where GPU-based calculations are typically 10-100 times faster than heavily optimized CPU-based implementations. The application of GPU acceleration to biomolecular simulation is also demonstrated through the use of GPU-accelerated Coulomb-based ion placement and calculation of time-averaged potentials from molecular dynamics trajectories. A novel approximation to Coulomb potential calculation, the multilevel summation method, is introduced and compared with direct Coulomb summation. In light of the performance obtained for this set of calculations, future applications of graphics processors to molecular dynamics simulations are discussed.     

Accelerating molecular docking calculations using graphics processing units

The generation of molecular conformations and the evaluation of interaction potentials are common tasks in molecular modeling applications, particularly in protein-ligand or protein-protein docking programs. In this work, we present a GPU-accelerated approach capable of speeding up these tasks considerably. For the evaluation of interaction potentials in the context of rigid protein-protein docking, the GPU-accelerated approach reached speedup factors of up to over 50 compared to an optimized CPU-based implementation. Treating the ligand and donor groups in the protein binding site as flexible, speedup factors of up to 16 can be observed in the evaluation of protein-ligand interaction potentials. Additionally, we introduce a parallel version of our protein-ligand docking algorithm PLANTS that can take advantage of this GPU-accelerated scoring function evaluation. We compared the GPU-accelerated parallel version to the same algorithm running on the CPU and also to the highly optimized sequential CPU-based version. In terms of dependence of the ligand size and the number of rotatable bonds, speedup factors of up to 10 and 7, respectively, can be observed. Finally, a fitness landscape analysis in the context of rigid protein-protein docking was performed. Using a systematic grid-based search methodology, the GPU-accelerated version outperformed the CPU-based version with speedup factors of up to 60.     

Accelerating molecular dynamic simulation on the cell processor and Playstation 3

Implementation of molecular dynamics (MD) calculations on novel architectures will vastly increase its power to calculate the physical properties of complex systems. Herein, we detail algorithmic advances developed to accelerate MD simulations on the Cell processor, a commodity processor found in PlayStation 3 (PS3). In particular, we discuss issues regarding memory access versus computation and the types of calculations which are best suited for streaming processors such as the Cell, focusing on implicit solvation models. We conclude with a comparison of improved performance on the PS3's Cell processor over more traditional processors.     

Accelerating chemical database searching using graphics processing units

The utility of chemoinformatics systems depends on the accurate computer representation and efficient manipulation of chemical compounds. In such systems, a small molecule is often digitized as a large fingerprint vector, where each element indicates the presence/absence or the number of occurrences of a particular structural feature. Since in theory the number of unique features can be exceedingly large, these fingerprint vectors are usually folded into much shorter ones using hashing and modulo operations, allowing fast "in-memory" manipulation and comparison of molecules. There is increasing evidence that lossless fingerprints can substantially improve retrieval performance in chemical database searching (substructure or similarity), which have led to the development of several lossless fingerprint compression algorithms. However, any gains in storage and retrieval afforded by compression need to be weighed against the extra computational burden required for decompression before these fingerprints can be compared. Here we demonstrate that graphics processing units (GPU) can greatly alleviate this problem, enabling the practical application of lossless fingerprints on large databases. More specifically, we show that, with the help of a ~$500 ordinary video card, the entire PubChem database of ~32 million compounds can be searched in ~0.2-2 s on average, which is 2 orders of magnitude faster than a conventional CPU. If multiple query patterns are processed in batch, the speedup is even more dramatic (less than 0.02-0.2 s/query for 1000 queries). In the present study, we use the Elias gamma compression algorithm, which results in a compression ratio as high as 0.097.     

Implementation and testing of stable, fast implicit solvation in molecular dynamics using the smooth-permittivity finite difference Poisson-Boltzmann method

A fast stable finite difference Poisson-Boltzmann (FDPB) model for implicit solvation in molecular dynamics simulations was developed using the smooth permittivity FDPB method implemented in the OpenEye ZAP libraries. This was interfaced with two widely used molecular dynamics packages, AMBER and CHARMM. Using the CHARMM-ZAP software combination, the implicit solvent model was tested on eight proteins differing in size, structure, and cofactors: calmodulin, horseradish peroxidase (with and without substrate analogue bound), lipid carrier protein, flavodoxin, ubiquitin, cytochrome c, and a de novo designed 3-helix bundle. The stability and accuracy of the implicit solvent simulations was assessed by examining root-mean-squared deviations from crystal structure. This measure was compared with that of a standard explicit water solvent model. In addition we compared experimental and calculated NMR order parameters to obtain a residue level assessment of the accuracy of MD-ZAP for simulating dynamic quantities. Overall, the agreement of the implicit solvent model with experiment was as good as that of explicit water simulations. The implicit solvent method was up to eight times faster than the explicit water simulations, and approximately four times slower than a vacuum simulation (i.e., with no solvent treatment).     

Efficient implementation of constant pH molecular dynamics on modern graphics processors

The treatment of pH sensitive ionization states for titratable residues in proteins is often omitted from molecular dynamics (MD) simulations. While static charge models can answer many questions regarding protein conformational equilibrium and protein–ligand interactions, pH‐sensitive phenomena such as acid‐activated chaperones and amyloidogenic protein aggregation are inaccessible to such models. Constant pH molecular dynamics (CPHMD) coupled with the Generalized Born with a Simple sWitching function (GBSW) implicit solvent model provide an accurate framework for simulating pH sensitive processes in biological systems. Although this combination has demonstrated success in predicting pK_a values of protein structures, and in exploring dynamics of ionizable side‐chains, its speed has been an impediment to routine application. The recent availability of low‐cost graphics processing unit (GPU) chipsets with thousands of processing cores, together with the implementation of the accurate GBSW implicit solvent model on those chipsets (Arthur and Brooks, J. Comput. Chem. 2016, 37, 927), provide an opportunity to improve the speed of CPHMD and ionization modeling greatly. Here, we present a first implementation of GPU‐enabled CPHMD within the CHARMM‐OpenMM simulation package interface. Depending on the system size and nonbonded force cutoff parameters, we find speed increases of between one and three orders of magnitude. Additionally, the algorithm scales better with system size than the CPU‐based algorithm, thus allowing for larger systems to be modeled in a cost effective manner. We anticipate that the improved performance of this methodology will open the door for broad‐spread application of CPHMD in its modeling pH‐mediated biological processes. © 2016 Wiley Periodicals, Inc.     

Comparison of various implicit solvent models in molecular dynamics simulations of immunoglobulin G light chain dimer

The present study tests performance of different solvation models applied to molecular dynamics simulation of a large, dimeric protein molecule. Analytical Continuum Electrostatics (ACE) with two different parameter sets, older V98 and new V01, and Effective Energy Function (EEF) are employed in molecular dynamics simulation of immunoglobulin G (IgG) light chain dimer and variable domain of IgG light chain. Results are compared with explicit solvent and distance dependent dielectric constant (DDE) calculations. The overall analysis shows that the EEF method yields results comparable to explicit solvent simulations; however, the stability of simulations is lower. On the other hand, the ACE_V98 model does not seem to achieve the accuracy or stability expected in nanosecond timescale MD simulation for the studied systems. The ACE_V01 model greatly improves stability of the calculation; nonetheless, changes in radius of gyration and solvent accessible surface of the studied systems may indicate that the parameter set still needs to be improved if the method is supposed to be used for simulations of large, polymeric proteins. Additionally, electrostatic contribution to the solvation free energy calculated in the ACE model is compared with a numerical treatment of the dielectric continuum model. Wall clock time of all simulations is compared. It shows that EEF calculation is six times faster than corresponding ACE and 50 times faster than explicit solvent simulations.     

Potential of mean force of water–proton bath and molecular dynamic simulation of proteins at constant pH

An advanced implicit solvent model of water–proton bath for protein simulations at constant pH is presented. The implicit water–proton bath model approximates the potential of mean force of a protein in water solvent in a presence of hydrogen ions. Accurate and fast computational implementation of the implicit water–proton bath model is developed using the continuum electrostatic Poisson equation model for calculation of ionization equilibrium and the corrected MSR6 generalized Born model for calculation of the electrostatic atom–atom interactions and forces. Molecular dynamics (MD) method for protein simulation in the potential of mean force of water–proton bath is developed and tested on three proteins. The model allows to run MD simulations of proteins at constant pH, to calculate pH‐dependent properties and free energies of protein conformations. The obtained results indicate that the developed implicit model of water–proton bath provides an efficient way to study thermodynamics of biomolecular systems as a function of pH, pH‐dependent ionization‐conformation coupling, and proton transfer events. © 2012 Wiley Periodicals, Inc.     

An N log N approximation based on the natural organization of biomolecules for speeding up the computation of long range interactions

Presented here is a method, the hierarchical charge partitioning (HCP) approximation, for speeding up computation of pairwise electrostatic interactions in biomolecular systems. The approximation is based on multiple levels of natural partitioning of biomolecular structures into a hierarchical set of its constituent structural components. The charge distribution in each component is systematically approximated by a small number of point charges, which, for the highest level component, are much fewer than the number of atoms in the component. For short distances from the point of interest, the HCP uses the full set of atomic charges available. For long‐distance interactions, the approximate charge distributions with smaller sets of charges are used instead. For a structure consisting of N charges, the computational cost of computing the pairwise interactions via the HCP scales as O(N log N), under assumptions about the structural organization of biomolecular structures generally consistent with reality. A proof‐of‐concept implementation of the HCP shows that for large structures it can lead to speed‐up factors of up to several orders of magnitude relative to the exact pairwise O(N²) all‐atom computation used as a reference. For structures with more than 2000–3000 atoms the relative accuracy of the HCP (relative root‐mean‐square force error per atom), approaches the accuracy of the particle mesh Ewald (PME) method with parameter settings typical for biomolecular simulations. When averaged over a set of 600 representative biomolecular structures, the relative accuracies of the two methods are roughly equal. The HCP is also significantly more accurate than the spherical cutoff method. The HCP has been implemented in the freely available nucleic acids builder (NAB) molecular dynamics (MD) package in Amber tools. A 10 ns simulation of a small protein indicates that the HCP based MD simulation is stable, and that it can be faster than the spherical cutoff method. A critical benefit of the HCP approximation is that it is algorithmically very simple, and unlike the PME, the HCP is straightforward to use with implicit solvent models. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

基于分子模拟技术煤焦分子模型构建

煤、焦是过程工业的重要原料。因此,有必要深入了解煤、焦分子结构以揭示其反应性。采用Materials Studio 7.0软件,从分子层次研究煤、焦的分子结构。根据已报道的文献,构建煤、焦的初始结构;基于分子力学原理对这些结构进行优化,使得模型物性与煤、焦物性相符;基于退火模拟算法对模型进行优化,从而使得模型密度、元素分析数据与真实值吻合;基于能量最小化原理,对煤、焦模型再次优化,从而获得其稳定、真实的分子构型。由计算结果发现,模型的估算密度、元素组成与已报道一致,说明构建的模型是有效、合理的;在模型优化过程中,相对于其他能量而言,库伦能和范德华能起着重要的作用。因此可以推断在煤、焦热加工过程中,弱键占据主要地位。另外,本文采用分子模拟技术构建煤、焦模型的方法对于构建其他复杂大分子结构有着重要的借鉴作用。     

A fast parallel clustering algorithm for molecular simulation trajectories

We implemented a GPU‐powered parallel k‐centers algorithm to perform clustering on the conformations of molecular dynamics (MD) simulations. The algorithm is up to two orders of magnitude faster than the CPU implementation. We tested our algorithm on four protein MD simulation datasets ranging from the small Alanine Dipeptide to a 370‐residue Maltose Binding Protein (MBP). It is capable of grouping 250,000 conformations of the MBP into 4000 clusters within 40 seconds. To achieve this, we effectively parallelized the code on the GPU and utilize the triangle inequality of metric spaces. Furthermore, the algorithm's running time is linear with respect to the number of cluster centers. In addition, we found the triangle inequality to be less effective in higher dimensions and provide a mathematical rationale. Finally, using Alanine Dipeptide as an example, we show a strong correlation between cluster populations resulting from the k‐centers algorithm and the underlying density. © 2012 Wiley Periodicals, Inc.     

Explicit ion, implicit water solvation for molecular dynamics of nucleic acids and highly charged molecules

An explicit ion, implicit water solvent model for molecular dynamics was developed and tested with DNA and RNA simulations. The implicit water model uses the finite difference Poisson (FDP) model with the smooth permittivity method implemented in the OpenEye ZAP libraries. Explicit counter-ions, co-ions, and nucleic acid were treated with a Langevin dynamics molecular dynamics algorithm. Ion electrostatics is treated within the FDP model when close to the solute, and by the Coulombic model when far from the solute. The two zone model reduces computation time, but retains an accurate treatment of the ion atmosphere electrostatics near the solute. Ion compositions can be set to reproduce specific ionic strengths. The entire ion/water treatment is interfaced with the molecular dynamics package CHARMM. Using the CHARMM-ZAPI software combination, the implicit solvent model was tested on A and B form duplex DNA, and tetraloop RNA, producing stable simulations with structures remaining close to experiment. The model also reproduced the A to B duplex DNA transition. The effect of ionic strength, and the structure of the counterion atmosphere around B form duplex DNA were also examined.     

Strategies to model the near-solute solvent molecular density/polarization

The solvent molecular distribution significantly affects the behavior of the solute molecules and is thus important in studying many biological phenomena. It can be described by the solvent molecular density distribution, g, and the solvent electric dipole distribution, p. The g and p can be computed directly by counting the number of solvent molecules/dipoles in a microscopic volume centered at r during a simulation or indirectly from the mean force F and electrostatic field E acting on the solvent molecule at r, respectively. However, it is not clear how the g and p derived from simulations depend on the solvent molecular center or the solute charge and if the g(F) and p(E) computed from the mean force and electric field acting on the solvent molecule, respectively, could reproduce the corresponding g and p obtained by direct counting. Hence, we have computed g, p, g(F), and p(E) using different water centers from simulations of a solute atom of varying charge solvated in TIP3P water. The results show that g(F) and p(E) can reproduce the g and p obtained using a given count center. This implies that rather than solving the coordinates of each water molecule by MD simulations, the distribution of water molecules could be indirectly obtained from analytical formulas for the mean force F and electrostatic field E acting on the solvent molecule at r. Furthermore, the dependence of the g and p distributions on the solute charge revealed provides an estimate of the change in g and p surrounding a biomolecule upon a change in its conformation.     

Derivatives of molecular surface area and volume: simple and exact analytical formulas

The computational effort of biomolecular simulations can be significantly reduced by means of implicit solvent models in which the energy generally contains a correction depending on the surface area and/or the volume of the molecule. In this article, we present simple derivation of exact, easy-to-use analytical formulas for these quantities and their derivatives with respect to atomic coordinates. In addition, we provide an efficient, linear-scaling algorithm for the construction of the power diagram required for practical implementation of these formulas. Our approach is implemented in a C++ header-only template library.     

麋鹿朊蛋白结构稳定性的分子动力学研究

朊蛋白病是一种致命且具有高度传染性的神经退行性疾病.糜鹿是目前已经报道的哺乳类动物中较易发生朊蛋白病的物种之一.作者使用分子动力学和操控式分子动力学模拟相结合的方法对糜鹿正常朊蛋白的结构稳定性进行了研究.发现了麋鹿朊蛋白结构中的不稳定结构域分布以及热动力学性质,揭示了糜鹿朊蛋白稳定性的分子结构基础以及力学特征.     

IMiCMO: a new integrated ab initio multicenter molecular orbitals method for molecular dynamics calculations in solvent cluster systems

A new computational scheme integrating ab initio multicenter molecular orbitals for determining forces of individual atoms in large cluster systems is presented. This method can be used to treat systems of many molecules, such as solvents by quantum mechanics. The geometry parameters obtained for three models of water clusters by the present method are compared with those obtained by the full ab initio MO method. The results agree very well. The scheme proposed in this article also intended for use in modeling cluster systems using parallel algorithms. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1107–1112, 2001     

Acceleration of coarse grain molecular dynamics on GPU architectures

Coarse grain (CG) molecular models have been proposed to simulate complex systems with lower computational overheads and longer timescales with respect to atomistic level models. However, their acceleration on parallel architectures such as graphic processing units (GPUs) presents original challenges that must be carefully evaluated. The objective of this work is to characterize the impact of CG model features on parallel simulation performance. To achieve this, we implemented a GPU‐accelerated version of a CG molecular dynamics simulator, to which we applied specific optimizations for CG models, such as dedicated data structures to handle different bead type interactions, obtaining a maximum speed‐up of $14$ on the NVIDIA GTX480 GPU with Fermi architecture. We provide a complete characterization and evaluation of algorithmic and simulated system features of CG models impacting the achievable speed‐up and accuracy of results, using three different GPU architectures as case studies. © 2012 Wiley Periodicals, Inc.     

Molecular dynamics simulation of complex multiphase flow on a computer cluster with GPUs

Compute Unified Device Architecture (CUDA) was used to design and implement molecular dynamics (MD) simulations on graphics processing units (GPU). With an NVIDIA Tesla C870, a 20–60 fold speedup over that of one core of the Intel Xeon 5430 CPU was achieved, reaching up to 150 Gflops. MD simulation of cavity flow and particle-bubble interaction in liquid was implemented on multiple GPUs using a message passing interface (MPI). Up to 200 GPUs were tested on a special network topology, which achieves good scalability. The capability of GPU clusters for large-scale molecular dynamics simulation of meso-scale flow behavior was, therefore, uncovered. Supported by the National Natural Science Foundation of China (Grant Nos. 20336040, 20221603 and 20490201), and the Chinese Academy of Sciences (Grant No. Kgcxz-yw-124)