Potential Force Field Research Articles

Algorithms of GPU-enabled reactive force field (ReaxFF) molecular dynamics

Reactive force field (ReaxFF), a recent and novel bond order potential, allows for reactive molecular dynamics (ReaxFF MD) simulations for modeling larger and more complex molecular systems involving chemical reactions when compared with computation intensive quantum mechanical methods. However, ReaxFF MD can be approximately 10–50 times slower than classical MD due to its explicit modeling of bond forming and breaking, the dynamic charge equilibration at each time-step, and its one order smaller time-step than the classical MD, all of which pose significant computational challenges in simulation capability to reach spatio-temporal scales of nanometers and nanoseconds. The very recent advances of graphics processing unit (GPU) provide not only highly favorable performance for GPU enabled MD programs compared with CPU implementations but also an opportunity to manage with the computing power and memory demanding nature imposed on computer hardware by ReaxFF MD. In this paper, we present the algorithms of GMD-Reax, the first GPU enabled ReaxFF MD program with significantly improved performance surpassing CPU implementations on desktop workstations. The performance of GMD-Reax has been benchmarked on a PC equipped with a NVIDIA C2050 GPU for coal pyrolysis simulation systems with atoms ranging from 1378 to 27,283. GMD-Reax achieved speedups as high as 12 times faster than Duin et al.’s FORTRAN codes in Lammps on 8 CPU cores and 6 times faster than the Lammps’ C codes based on PuReMD in terms of the simulation time per time-step averaged over 100 steps. GMD-Reax could be used as a new and efficient computational tool for exploiting very complex molecular reactions via ReaxFF MD simulation on desktop workstations.

Polynomial in momenta invariants of Hamilton's equations, divergent series and generalized functions

We consider the problem of the motion of two identical interacting particles on a circle in a potential force field. We study conditions for the existence of an additional first integral in the form of a polynomial of degree 4 in momenta with periodic coefficients. These conditions are reduced to the solvability of a certain nonlinear functional-differential equation for the potential of the external force and the interaction potential. If the potentials are smooth, this equation has only trivial solutions: at least one of the potentials is a constant function. We classify generalized solutions of this equation when the interaction potential is a distribution while the external potential is a smooth function. Formal Fourier series for the interaction potential can be summed up by the (C, 2)-Cesaro method to periodic functions with singularities.

On the brachistochronic motion of a variable-mass mechanical system in general force fields

The problem of the brachistochronic motion of a mechanical system composed of rigid bodies and variable-mass particles is solved. The laws of the time-rate of mass variation of the particles as well as relative velocities of the expelled (or gained) masses are assumed to be known. The system moves in an arbitrary field of known potential and nonpotential forces. Applying Pontryagin’s minimum principle along with singular optimal control theory, a corresponding two-point boundary value problem is obtained. The appropriate numerical procedure based on the shooting method to solve the obtained two-point boundary value problem is presented. The considerations in the paper are illustrated by an example of determining the brachistochronic motion of a system composed of a rigid rod and two variable-mass particles attached to the rod.

Reactive force field potential for carbon deposition on silicon surfaces

In this paper a new interatomic potential based on the Kieffer force field and designed to perform molecular dynamics (MD) simulations of carbon deposition on silicon surfaces is implemented. This potential is a third-order reactive force field that includes a dynamic charge transfer and allows for the formation and breaking of bonds. The parameters for Si–C and C–C interactions are optimized using a genetic algorithm. The quality of the potential is tested on its ability to model silicon carbide and diamond physical properties as well as the formation energies of point defects. Furthermore, MD simulations of carbon deposition on reconstructed (100) silicon surfaces are carried out and compared to similar simulations using a Tersoff-like bond order potential. Simulations with both potentials produce similar results showing the ability to extend the use of the Kieffer potential to deposition studies. The investigation reveals the presence of a channelling effect when depositing the carbon at 45° incidence angle. This effect is due to channels running in directions symmetrically equivalent to the (110) direction. The channelling is observed to a lesser extent for carbon atoms with 30° and 60° incidence angles relative to the surface normal. On a pristine silicon surface, sticking coefficients were found to vary between 100 and 73%, depending on deposition conditions.

Enhanced Van der Waals calculations in genetic algorithms for protein structure prediction

SUMMARYSeveral ab initio computational methods for protein structure prediction have been designed using full‐atom models and force field potentials to describe interactions among atoms. Those methods involve the solution of a combinatorial problem with a huge search space. Genetic algorithms (GAs) have shown significant performance increases for such methods. However, even a small protein may require hundreds of thousands of energy function evaluations making GAs suitable only for the prediction of very small proteins. We propose an efficient technique to compute the van der Waals energy (the greatest contributor to protein stability) speeding up the whole GA. First, we developed a Cell‐List Reconstruction procedure that divides the tridimensional space into a cell grid for each new structure that the GA generates. The cells restrict the calculations of van der Waals potentials to ranges in which they are significant, reducing the complexity of such calculations from quadratic to linear. Moreover, the proposal also uses the structure of the cell grid to parallelize the computation of the van der Waals energy, achieving additional speedup. The results have shown a significant reduction in the run time required by a GA. For example, the run time for the prediction of a protein with 147,980 atoms can be reduced from 217 days to 7 h. Copyright © 2012 John Wiley & Sons, Ltd.

Concept of the effective potential in describing the motion of ions in a quadrupole mass filter

We propose a generalization of the effective potential theory for the motion of particles in a rapidly oscillating electric field for the stability parameters lying near the boundary of the diagram where the standard effective potential theory is inapplicable. We derive the dynamic equations describing the variation of the envelope of ion oscillations for the motion of ions near the stability vertex of the first zone of the quadrupole mass filter. We reduce them to the form of the Hamilton equations for oscillations of a material particle in the field of potential forces. We obtain expressions for the effective potential well. It is shown that in spite of the high kinetic energy of oscillations, the depth of the effective potential well for ions in the quadrupole is less than 1 eV in the case of filtration with a mass resolution exceeding 200 units. The acceptance of the mass filter is calculated as a function of the stability parameters and the resolving power.

Molecular dynamics re-refinement of two different small RNA loop structures using the original NMR data suggest a common structure.

Restrained molecular dynamics simulations are a robust, though perhaps underused, tool for the end-stage refinement of biomolecular structures. We demonstrate their utility—using modern simulation protocols, optimized force fields, and inclusion of explicit solvent and mobile counterions—by re-investigating the solution structures of two RNA hairpins that had previously been refined using conventional techniques. The structures, both domain 5 group II intron ribozymes from yeast ai5γ and Pylaiella littoralis, share a nearly identical primary sequence yet the published 3D structures appear quite different. Relatively long restrained MD simulations using the original NMR restraint data identified the presence of a small set of violated distance restraints in one structure and a possibly incorrect trapped bulge nucleotide conformation in the other structure. The removal of problematic distance restraints and the addition of a heating step yielded representative ensembles with very similar 3D structures and much lower pairwise RMSD values. Analysis of ion density during the restrained simulations helped to explain chemical shift perturbation data published previously. These results suggest that restrained MD simulations, with proper caution, can be used to “update” older structures or aid in the refinement of new structures that lack sufficient experimental data to produce a high quality result. Notable cautions include the need for sufficient sampling, awareness of potential force field bias (such as small angle deviations with the current AMBER force fields), and a proper balance between the various restraint weights.Electronic supplementary materialThe online version of this article (doi:10.1007/s10858-012-9642-5) contains supplementary material, which is available to authorized users.

A Phylogenetic Analysis of Normal Modes Evolution in Enzymes and Its Relationship to Enzyme Function

Since the dynamic nature of protein structures is essential for enzymatic function, it is expected that functional evolution can be inferred from the changes in protein dynamics. However, dynamics can also diverge neutrally with sequence substitution between enzymes without changes of function. In this study, a phylogenetic approach is implemented to explore the relationship between enzyme dynamics and function through evolutionary history. Protein dynamics are described by normal mode analysis based on a simplified harmonic potential force field applied to the reduced C(α) representation of the protein structure while enzymatic function is described by Enzyme Commission numbers. Similarity of the binding pocket dynamics at each branch of the protein family's phylogeny was analyzed in two ways: (1) explicitly by quantifying the normal mode overlap calculated for the reconstructed ancestral proteins at each end and (2) implicitly using a diffusion model to obtain the reconstructed lineage-specific changes in the normal modes. Both explicit and implicit ancestral reconstruction identified generally faster rates of change in dynamics compared with the expected change from neutral evolution at the branches of potential functional divergences for the α-amylase, D-isomer-specific 2-hydroxyacid dehydrogenase, and copper-containing amine oxidase protein families. Normal mode analysis added additional information over just comparing the RMSD of static structures. However, the branch-specific changes were not statistically significant compared to background function-independent neutral rates of change of dynamic properties and blind application of the analysis would not enable prediction of changes in enzyme specificity.

Infrared Spectra at a Conical Intersection: Vibrations of Methoxy

The J = 0 infrared spectrum of methoxy is theoretically calculated for the ground X̃(2)E state using a quartic potential energy force field, and the quadratic dipole moment expansion is calculated ab initio at the CCSD(T) level of theory and cc-pVTZ basis. Writing these expansions with vibronic operators whose symmetry properties are defined with respect to C(3v) rotation greatly simplifies these calculations. With minor adjustments to the force field, excellent agreement with experiment is found for both the transition energies of CH(3)O and those of CD(3)O. The role of Jahn-Teller and Fermi coupling is illustrated by scaling these terms by a parameter δ that varies from 0 to 1. Plotting the eigenvalues as a function of δ yields a correlation diagram connecting the harmonic eigenvalues to those of the fully coupled problem. The spectrum for CH(3)O is determined using a combination of Davidson and Lanczos iteration schemes. The spectral features are found to be dominated by Jahn-Teller effects, but direct Fermi coupling and indirect potential couplings have important roles. The origin of the complexities in the CH stretch region are discussed.

Chirality-Dependent Anisotropic Elastic Properties of a Monolayer Graphene Nanosheet

An analytical approach is presented to predict the elastic properties of a monolayer graphene nanosheet based on interatomic potential energy and continuum mechanics. The elastic extension and torsional springs are utilized to simulate the stretching and angle variation of carbon-carbon bond, respectively. The constitutive equation of the graphene nanosheet is derived by using the strain energy density, and the analytical formulations for nonzero elastic constants are obtained. The in-plane elastic properties of the monolayer graphene nanosheet are proved to be anisotropic. In addition, Young's moduli, Poisson's ratios and shear modulus of the monolayer graphene nanosheet are calculated according to the force constants derived from Morse potential and AMBER force field, respectively, and they were proved to be chirality-dependent. The comparison with experimental results shows a very agreement.

OS1-2-4 酸化物形燃料電池材料の原子モデリングのためのポテンシャル作成(OS1 マルチスケール現象のシミュレーション技術(2))

To reveal the mechanism of degradation of solid-oxide fuel cell (SOFC), which one of the most promising energy source in the near future due to high energy-conversion efficiency, atomic-scale simulations for change in microstructures are urged. It is therefore essential to build interatomic potential (force field) with high efficiency and transferability. We develop a dipole-model potential for YSZ (yttria stabilized zirconia), which mimics charge polarization around each atom by a dipole moment, by real-coded genetic algorithm. Potential parameters are fitted so that the potential reproduces reference data calculated by ab initio density functional theory (DFT) calculations, including cohesive energy, forces exerted on atoms and stresses, with a good accuracy. Structural stability of cubic crystal is held, which is confirmed by molecular dynamics simulation with finite temperatures. Energy barrier for oxygen migration via vacancy, which is closely linked with ionic conductivity of YSZ, is examined. Barrier energies for some migration paths show good agreement with ab initio DFT calculations.

A Phylogenetic Analysis of Normal Modes Evolution in Enzymes and its Relationship to Enzyme Function

Enzyme function and catalysis is often dictated by the vibrational dynamics and flexibility of the protein. Since the catalytic functions of enzymes are necessary in nearly all biochemical pathways essential for life, evolutionary conservation of the dynamics that aid enzymatic function is an expected outcome. In this study, a novel phylogenetic approach is implemented to explore the relationship between enzyme dynamics and function as it relates to evolutionary history. Protein dynamics and flexibility are described by normal mode analysis based on a simplified harmonic potential force field applied to the Cα backbone while enzymatic function is described by the Enzyme Commission (EC) numbers in the ENZYME database. Analyzing the comparative normal mode analysis of a catalytic domain family with respects to its phylogenetic tree revealed a negative correlation in dynamic conservation as evolutionary distance increases, which has not been accounted for in prior studies. By correcting the overlap scores of the normal modes for the natural negative relationship, a new score dependent on evolution can be obtained. This novel approach exhibited potential for predicting functional divergence in a protein family's phylogeny and adds a new layer of insight in regards to the role of protein dynamics in enzyme evolution.

2B1400 単一アミノ酸ポテンシャル力場の改良と短鎖ペプチドの構造予測への応用(蛋白質-構造機能相関II:理論,凝集,口頭発表,日本生物物理学会第50回年会(2012年度))

2B1400 単一アミノ酸ポテンシャル力場の改良と短鎖ペプチドの構造予測への応用(蛋白質-構造機能相関II:理論,凝集,口頭発表,日本生物物理学会第50回年会(2012年度))

Electric Field-Shaping Microdevices for Manipulation of Collections of Microscale Objects

This paper analyzes and develops new approaches for handling and shaping collections of microscale objects such as particles or cells. While traditional dielectrophoretic manipulation approaches are based on creating an energy trap, this work employs a distributed manipulation philosophy: shaping the energy field to model the point-wise forces and hence the characteristics of the field. This method offers a better perspective on the behavior, exact shape, position, and orientation of the collection of objects under manipulation. Furthermore, this research showcases devices that artificially generate planar quadratic and squeezing force fields by setting the potential at each point in space. These devices enable the positioning of particles and collections of particles to a predefined shape and orientation. Finally, we demonstrate a novel approach to distributed manipulation. We construct a 3-D potential force field by setting the boundary conditions of the differential equation describing the dynamics of a natural medium (the voltage profile in our case). This approach is illustrated by constructing cylindrical and ellipsoidal potential force fields for use in particle and cell manipulation.

Poisson Theory and Inverse Problem in a Controllable Mechanical System

The Poisson theory and inverse problem are studied in a controllable mechanical system. Equations of motion of the controllable mechanical system in phase space are given. Poisson's integral theory of the system is established. The potential force field is constructed by solving the inverse problem in a controllable mechanical system. Finally, an example is given to illustrate the application of the results.

Stress-Induced Wurtzite to Hexagonal Phase Transformation in Zinc Oxide Nanowires

The stress-induced wurtzite to hexagonal phase transformation in [0110] oriented zinc oxide nanowires were investigated using a molecular dynamics simulation and reactive force field potentials. The yield strength of the 2.13 x 1.93 nm wurtzite nanowires is 12 GPa at 50 K. The wurtzite to hexagonal phase transformation was successfully observed at stress plateaus (5-5.5 GPa at 50 K) located after the yield point of the wurtzite phase. The wurtzite to hexagonal phase transformation was a result of the propagation of {0111} twinning boundaries. During the phase transformation, the wurtzite and hexagonal phases were clearly separated by the {0111} twinning boundaries. To analyze the difference between ceramic and metallic systems, all the calculation data of wurtzite to hexagonal transformation were compared with stress-induced phase transformation in metallic nanowires such as CuZr and NiA1. As the result of the [0110] tensile loading of the ZnO nanowires, the hexagonal phase was obtained.

Large time behavior of solutions to 3D compressible Navier-Stokes-Poisson system

We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation. If the Fourier modes of the initial data are degenerate at the low frequency or the initial data decay fast at spatial infinity, we show that the density converges to its equilibrium state at the L 2-rate $$(1 + t)^{ - \tfrac{7} {4}}$$ or L ∞-rate $$(1 + t)^{ - \tfrac{5} {2}}$$ , and the momentum decays at the L 2-rate $$(1 + t)^{ - \tfrac{5} {4}}$$ or L ∞-rate (1 + t)−2. These convergence rates are shown to be optimal for the compressible Navier-Stokes-Poisson system.

Dosimetry of cosmic radiation in the troposphere based on the measurements at the summit of Mt. Fuji

Abstract Dose rate of cosmic-ray origin neutrons (abbreviated to “cosmic neutrons”) at aviation altitude was estimated based on the measurements at Mt. Fuji. Cosmic neutrons were measured in a facility of the Mt. Fuji Weather Station located at the summit of Mt. Fuji, the highest mountain in Japan (3776 m in altitude), in the summer of 2008 and 2009. The average of 1 cm ambient dose equivalent H*(10) for two measurements was verified by numerical model simulation and then used to empirically estimate the solar force field potential (FFP). The H*(10) rates at aviation altitude estimated from the measurements at Mt. Fuji were compared to those obtained in in-flight measurements onboard a civilian aircraft flying near Mt. Fuji at the time between the two measurements at the mountain. According to the results obtained, we expect that the empirical estimation based on the measurements at Mt. Fuji will work effectively for dosimetry of cosmic radiation in troposphere.

SDOCK: A global protein‐protein docking program using stepwise force‐field potentials

Fast Fourier transform (FFT) method limits the forms of scoring functions in global protein-protein docking. On the other hand, force field potentials can effectively describe the energy hyper surface of biological macromolecules. In this study, we developed a new protein-protein docking program, SDOCK, that incorporates van der Waals attractive potential, geometric collision, screened electrostatic potential, and Lazaridis-Karplus desolvation energy into the scoring function in the global searching process. Stepwise potentials were generated from the corresponding continuous forms to treat the structure flexibility. After optimization of the atom solvation parameters and the weights of different potential terms based on a new docking test set that contains 142 cases with small or moderate conformational changes upon binding, SDOCK slightly outperformed the well-known FFT based global docking program ZDOCK3.0. Among the 142 cases tested, 52.8% gave at least one near-native solutions in the top 100 solutions. SDOCK was also tested on six blind testing cases in Critical Assessment of Predicted Interactions rounds 13 to 18. In all six cases, the near-native solutions could be found within the top 350 solutions. Because the SDOCK approach performs global docking based on force-field potentials, one of its advantages is that it provides global binding free energy surface profiles for further analysis. The efficiency of the program is also comparable with that of other FFT based protein-protein docking programs. SDOCK is available for noncommercial applications at http://mdl.ipc.pku.edu.cn/cgi-bin/down.cgi.

Transverse vibration of single-layer graphene sheets

We investigate the vibrational properties of zigzag and armchair single-layer graphene sheets (SLGSs) using the molecular mechanics (MM) approach. The natural frequencies of vibration and their associated intrinsic vibration modes are obtained. Vibrational analysis is performed with different chirality and boundary conditions. The simulations are carried out for three types of zigzag and armchair SLGS. The universal force field potential is used for the MM approach. The first four natural frequencies are obtained for increasing lengths. The results indicate that the natural frequencies decrease as the length increases. The results follow similar trends with results of previous studies for SLGS using a continuum structural mechanics approach. These results have shown the applicability of SLGSs as electromechanical resonators.