Application of MDGRAPE-3, a special purpose board for molecular dynamics simulations, to periodic biomolecular systems

We describe the application of a special purpose board for molecular dynamics simulations, named MDGRAPE-3, to the problem of simulating periodic bio-molecular systems. MDGRAPE-3 is the latest board in a series of hardware accelerators designed to calculate the nonbonding long-range interactions much more rapidly than normal processors. So far, MDGRAPEs were mainly applied to isolated systems, where very many nonbonded interactions were calculated without any distance cutoff. However, in order to regulate the density and pressure during simulations of membrane embedded protein systems, one has to evaluate interactions under periodic boundary conditions. For this purpose, we implemented the Particle-Mesh Ewald (PME) method, and its approximation with distance cutoffs and charge neutrality as proposed by Wolf et al., using MDGRAPE-3. When the two methods were applied to simulations of two periodic biomolecular systems, a single MDGRAPE-3 achieved 30-40 times faster computation times than a single conventional processor did in the both cases. Both methods are shown to have the same molecular structures and dynamics of the systems.     

Cutoff radius effect of the isotropic periodic sum and Wolf method in liquid-vapor interfaces of water

As a more economical but similarly accurate computation method than the Ewald sum, the isotropic periodic sum (IPS) method for nonpolar molecules (IPSn) and polar molecules (IPSp), along with the Wolf method are of interest, but the cutoff radius dependence is an important issue. To evaluate the cutoff radius effect of the three methods, a water-vapor interfacial system has been studied by molecular dynamics. The Wolf method can produce adequate results for surface tension compared to that of the Ewald sum (within 2.9%) at a long enough cutoff radius, r(c). However, the estimation of the electrostatic potential profile and dipole orientational function is poor. The Wolf method cannot estimate electrostatic configuration at r(c) ≤ L(z)∕2 (L(z) is the longest lattice of the system). We have found that the convergence of the surface tension and the electrostatic configuration of the IPSn method is faster than that of the IPSp method. Moreover, the IPSn method is most accurate among the three methods for the same cutoff radius. Furthermore, the behavior of the surface tension against the cutoff radius shows a greater difference for the IPSn and IPSp method. The surface tension of the IPSp method fluctuates and presents a similar result to that of the Ewald sum, but the surface tension for the IPSn method greatly deviates near r(c) = L(z)∕3. The cause of this deviation is the difference between the interfacial configuration of the water surface and the cutoff treatment of the IPS method. The deviation becomes insignificant far from r(c) = L(z)∕3. In spite of this shortcoming, the IPSn method gives the most accurate result in estimating the surface tension at r(c) = L(z)∕2. From all the results in this work, the IPSn and IPSp method have been found to be more accurate than the Wolf method. In conclusion, the surface tension and structure of water-vapor interface can be calculated by the IPSn method when r(c) is greater than or equal to the longest lattice of the system. The IPSp method and the Wolf method require a longer cutoff radius than the longest lattice of the system to estimate interfacial properties.     

Computer simulation of charged hard spherocylinders

In this work we present a computer simulation study of charged hard spherocylinders of aspect ratio L/sigma=5, using NVT and NPT Monte Carlo methods. Coulombic interactions are handled using the Wolf method [D. Wolf, P. Keblinski, S. R. Phillpot, and J. Eggebrecht, J. Chem. Phys. 110, 8254 (1999)]. Thermodynamic and structural properties are in excellent agreement with the results obtained with the standard Ewald summation method. A partial prediction of the corresponding phase diagram is obtained by studying two isotherms of this system. The stability of the liquid crystalline phases is examined and compared with the phase diagrams of neutral hard spherocylinders and dipolar hard spherocylinders.     

A long-range electrostatic potential based on the Wolf method charge-neutral condition

Molecular simulations rely heavily on a long range electrostatic Coulomb interaction. The Coulomb potential decays inversely with distance, indicating infinite effective range. In practice, molecular simulations do not directly take into account such an infinite interaction. Therefore, the Ewald, fast multipole, and cutoff methods are frequently used. Although cutoff methods are implemented easily and the calculations are fast, it has been pointed out that they produce serious artifacts. Wolf and coworkers recently discovered one source of the artifacts. They found that when the total charge in a cutoff sphere disappeared, the cutoff error is dramatically suppressed. The Wolf method uses the charge-neutral principle combined with a potential damping that is realized using a complementary error function. To date, many molecular simulation studies have demonstrated the accuracy and reliability of the Wolf method. We propose a novel long-range potential that is constructed only from the charge-neutral condition of the Wolf method without potential damping. We also show that three simulation systems, in which involve liquid sodium-chloride, TIP3P water, and a charged protein in explicit waters with neutralized ions using the new potential, provide accurate statistical and dielectric properties when compared with the particle mesh Ewald method.     

The Wolf method applied to the liquid-vapor interface of water

The Wolf method for the calculation of electrostatic interactions is applied in a liquid phase and at the liquid-vapor interface of water and its results are compared with those from the Ewald sums method. Molecular dynamics simulations are performed to calculate the radial distribution functions at room temperature. The interface simulations are used to obtain the coexisting densities and surface tension along the coexistence curve. The water model is a flexible version of the extended simple point charge model. The Wolf method gives good structural results, fair coexistence densities, and poor surface tensions as compared with those obtained using the Ewald sums method.     

Is the Ewald summation still necessary? Pairwise alternatives to the accepted standard for long-range electrostatics

We investigate pairwise electrostatic interaction methods and show that there are viable computationally efficient (O(N)) alternatives to the Ewald summation for typical modern molecular simulations. These methods are extended from the damped and cutoff-neutralized Coulombic sum originally proposed by Wolf et al. [J. Chem. Phys. 110, 8255 (1999)]. One of these, the damped shifted force method, shows a remarkable ability to reproduce the energetic and dynamic characteristics exhibited by simulations employing lattice summation techniques. Comparisons were performed with this and other pairwise methods against the smooth particle-mesh Ewald summation to see how well they reproduce the energetics and dynamics of a variety of molecular simulations.     

Gaussian split Ewald: A fast Ewald mesh method for molecular simulation

Gaussian split Ewald (GSE) is a versatile Ewald mesh method that is fast and accurate when used with both real-space and k-space Poisson solvers. While real-space methods are known to be asymptotically superior to k-space methods in terms of both computational cost and parallelization efficiency, k-space methods such as smooth particle-mesh Ewald (SPME) have thus far remained dominant because they have been more efficient than existing real-space methods for simulations of typical systems in the size range of current practical interest. Real-space GSE, however, is approximately a factor of 2 faster than previously described real-space Ewald methods for the level of force accuracy typically required in biomolecular simulations, and is competitive with leading k-space methods even for systems of moderate size. Alternatively, GSE may be combined with a k-space Poisson solver, providing a conveniently tunable k-space method that performs comparably to SPME. The GSE method follows naturally from a uniform framework that we introduce to concisely describe the differences between existing Ewald mesh methods.     

Affecting an Ultra-High Work Function of Silver

An ultra-high increase in the WF of silver, from 4.26 to 7.42 eV, that is, an increase of up to circa 3.1 eV is reported. This is the highest WF increase on record for metals and is supported by recent computational studies which predict the potential ability to affect an increase of the WF of metals by more than 4 eV. We achieved the ultra-high increase by a new approach: Rather than using the common method of 2D adsorption of polar molecules layers on the metal surface, WF modifying components, l -cysteine and Zn(OH)₂, were incorporated within the metal, resulting in a 3D architecture. Detailed material characterization by a large array of analytical methods was carried out, the combination of which points to a WF enhancement mechanism which is based on directly affecting the charge transfer ability of the metal separately by cysteine and hydrolyzed zinc(II), and synergistically by the combination of the two through the known Zn-cysteine finger redox trap effect.     

Amorphous silica modeled with truncated and screened Coulomb interactions: a molecular dynamics simulation study

We show that finite-range alternatives to the standard long-range pair potential for silica by van Beest et al. [Phys. Rev. Lett. 64, 1955 (1990)] might be used in molecular dynamics simulations. We study two such models that can be efficiently simulated since no Ewald summation is required. We first consider the Wolf method, where the Coulomb interactions are truncated at a cutoff distance rc such that the requirement of charge neutrality holds. Various static and dynamic quantities are computed and compared to results from simulations using Ewald summations. We find very good agreement for rc approximately 10 A. For lower values of rc, the long-range structure is affected which is accompanied by a slight acceleration of dynamic properties. In a second approach, the Coulomb interaction is replaced by an effective Yukawa interaction with two new parameters determined by a force fitting procedure. The same trend as for the Wolf method is seen. However, slightly larger cutoffs have to be used in order to obtain the same accuracy with respect to static and dynamic quantities as for the Wolf method.     

Affecting an Ultra‐High Work Function of Silver

An ultra‐high increase in the WF of silver, from 4.26 to 7.42 eV, that is, an increase of up to circa 3.1 eV is reported. This is the highest WF increase on record for metals and is supported by recent computational studies which predict the potential ability to affect an increase of the WF of metals by more than 4 eV. We achieved the ultra‐high increase by a new approach: Rather than using the common method of 2D adsorption of polar molecules layers on the metal surface, WF modifying components, l ‐cysteine and Zn(OH)₂, were incorporated within the metal, resulting in a 3D architecture. Detailed material characterization by a large array of analytical methods was carried out, the combination of which points to a WF enhancement mechanism which is based on directly affecting the charge transfer ability of the metal separately by cysteine and hydrolyzed zinc(II), and synergistically by the combination of the two through the known Zn‐cysteine finger redox trap effect.     

Non-Fickian water vapor sorption dynamics by Nafion membranes

Dynamics of water absorption from a saturated vapor and water desorption into dry air for Nafion 1100 EW ionomers have been measured for film thicknesses between 51 and 606 microm and at temperatures ranging from 30 to 90 degrees C. Water absorption and desorption exhibit two distinct non-Fickian characteristics: (1) desorption is 10 times faster than absorption and (2) the normalized mass change does not collapse to a single master curve when plotted against time normalized by membrane thickness squared, t/l2, for either absorption or desorption. Water desorption data were fit well by a model in which diffusion is rapid and interfacial mass transport resistance is the rate-limiting process for water loss. Water absorption is described by a two-stage process. At early times, interfacial mass transport controls water absorption, and at longer times, water absorption is controlled by the dynamics of polymer swelling and relaxation.     

Rapid QM/MM approach for biomolecular systems under periodic boundary conditions: Combination of the density‐functional tight‐binding theory and particle mesh Ewald method

A quantum mechanical/molecular mechanical (QM/MM) approach based on the density‐functional tight‐binding (DFTB) theory is a useful tool for analyzing chemical reaction systems in detail. In this study, an efficient QM/MM method is developed by the combination of the DFTB/MM and particle mesh Ewald (PME) methods. Because the Fock matrix, which is required in the DFTB calculation, is analytically obtained by the PME method, the Coulomb energy is accurately and rapidly computed. For assessing the performance of this method, DFTB/MM calculations and molecular dynamics simulation are conducted for a system consisting of two amyloid‐β(1‐16) peptides and a zinc ion in explicit water under periodic boundary conditions. As compared with that of the conventional Ewald summation method, the computational cost of the Coulomb energy by utilizing the present approach is drastically reduced, i.e., 166.5 times faster. Furthermore, the deviation of the electronic energy is less than . © 2016 Wiley Periodicals, Inc.     

Fast and spectrally accurate Ewald summation for 2-periodic electrostatic systems

A new method for Ewald summation in planar/slablike geometry, i.e., systems where periodicity applies in two dimensions and the last dimension is "free" (2P), is presented. We employ a spectral representation in terms of both Fourier series and integrals. This allows us to concisely derive both the 2P Ewald sum and a fast particle mesh Ewald (PME)-type method suitable for large-scale computations. The primary results are: (i) close and illuminating connections between the 2P problem and the standard Ewald sum and associated fast methods for full periodicity; (ii) a fast, O(N log N), and spectrally accurate PME-type method for the 2P k-space Ewald sum that uses vastly less memory than traditional PME methods; (iii) errors that decouple, such that parameter selection is simplified. We give analytical and numerical results to support this.     

MDSIMAID: automatic parameter optimization in fast electrostatic algorithms

MDSIMAID is a recommender system that optimizes parallel Particle Mesh Ewald (PME) and both sequential and parallel multigrid (MG) summation fast electrostatic solvers. MDSIMAID optimizes the running time or parallel scalability of these methods within a given error tolerance. MDSIMAID performs a run time constrained search on the parameter space of each method starting from semiempirical performance models. Recommended parameters are presented to the user. MDSIMAID's optimization of MG leads to configurations that are up to 14 times faster or 17 times more accurate than published recommendations. Optimization of PME can improve its parallel scalability, making it run twice as fast in parallel in our tests. MDSIMAID and its Python source code are accessible through a Web portal located at http://mdsimaid.cse.nd.edu.     

计算机分子模拟中静电相互作用能的计算及参数优化

Molecular simulation is a powerful tool in studying properties of complex fluids composed of charged particles such as electrolyte solutions, room temperature ionic liquids and colloid solutions, where the long-range interactions play a determinative role. Several methods have been available for treating the long-range interactions between charged particles and point dipole. These include the Ewald sum (ES), the reaction field and particle-particle particle-mesh methods. Among these approaches, the ES is most commonly used. However, several ES versions have been occurred in the literatures of molecular simulation, and some times it is difficult for one to choose the right formula to use in molecular simulation study. The coulombic interaction energy between charged particles is divided into the sum of real space, reciprocal space and self energy, and theircal culation equations are obtained respectively using electrostatics theory and Fourier transformation method. The Ewald sum formulate have been derived and the clear physical picture involved has been depicted. A Monte Carlo computer simulation for electrostatic interaction energy of charged hard sphere system has been conducted at varying conditions, and a good agreement with MSA is obtained. On this basis the effects on the simulation accuracy and efficiency of real space cut distance r(cut), convergence parameter 1 and reciprocal maximum vector K(max) have been analyzed. From the theoretical and computer simulation presented here, the optimization parameters for rcut, 1 and K(max) are obtained as 0.5 L (i.e. half box length), 5.8 and 3～5, respectively.     

Theoretical study on selectivity trends in (N‐heterocyclic carbene)‐Pd catalyzed mizoroki–heck reactions: Exploring density functionals methods and molecular models

The regioselectivity of the NHC‐Pd catalyzed Heck coupling reaction between phenyl bromide and styrene has been investigated using the density functional theory, wave‐function (WF)‐based methods and two different sizes of model ligands. In addition to the WF methods, the TPSS‐D3, B97X‐D, BP86‐D3, and M06‐L density functionals were reliable approaches to be applied, independently of the basis set. Moreover, the NCI analysis showed that weak interactions are important forces to be taken into account when exploring the regioselectivity of this reaction, mainly when a crowded NHC ligand is present. © 2017 Wiley Periodicals, Inc.     

Searching for conical intersections of potential energy surfaces with the ONIOM method: application to previtamin D

We demonstrate that the ONIOM method can be used to optimize a conical intersection between the ground and first excited-state potential energy surfaces of previtamin D (precalciferol), with excitation localized in a small part of the molecule: the hexatriene chromophore. These calculations were up to 100 times faster with little loss of accuracy compared to a full non-ONIOM Target calculation. The most accurate ONIOM method combination was CASSCF/4-31G//ROHF/STO-3G(Triplet): in comparison to the Target (CASSCF/4-31G), bond lengths and angles in the hexatriene model region were calculated to within 0.02 A and 0.7 degrees , respectively, and the energy difference between the conical intersection and nearest associated S 1 minimum to within 0.5 kcal x mol (-1). All of the low-level methods selected produced accurate geometries, including the UFF molecular mechanics and AM1 semiempirical methods, suggesting a cheap and efficient way of initially optimizing conical intersections geometries. Furthermore, ONIOM allows for an assessment of the localization of excited states, providing some fundamental insight into the physical processes involved.     

A comparison of Coulombic interaction methods in non-equilibrium studies of heat transfer in water

We investigate the impact of the treatment of electrostatic interactions on the heat conduction of liquid water. With this purpose, we report a series of non-equilibrium molecular dynamics computer simulations of the Modified Central Force Model of water. We consider both the Ewald summation approach, which includes the full range of the electrostatic interactions, and the Wolf method, which uses a cutoff to truncate the long range contributions. It is shown that the relaxation of the temperature profiles towards the stationary state solution and the equation of state of the liquid are not affected by the treatment of the electrostatic interactions. However, the truncation of the interactions results in lower internal energy fluxes as well as lower thermal conductivities. We also find that the anomalous increase of the thermal conductivity of water with temperature is reproduced by the different methods considered in this work, showing that this physical behavior is independent of the treatment of the long range electrostatic interactions.     

Tungsten fluorides: syntheses and electrochemical characterization in the FLINAK molten salt eutectic

The following tungsten fluorides have been synthesized by simple addition reactions or by reduction with tungsten metal at elevated temperature: KWF7, K2WF8, MWF6 (M = K, Na, Rb, Cs), K2WF7, M3WF8 (M = K, Na, Rb), and K3WF6. The compounds were characterized by their Raman spectra and by cyclic voltammetry in the molten FLINAK eutectic melt (46.5, 11.5, and 42.0 mol % of LiF, NaF, and KF, respectively) at 475-800 degrees C. X-ray crystal structures are reported for two new compounds K2WF7 and K3WF6. The crystals of K2WF7 were orthorhombic, space group Pnma (No. 62) with a = 9.800(2) A, b = 5.7360(11) A, c = 11.723(2) A, and Z = 4. Crystals of K3WF6 were cubic, space group Fm3 (No. 225) with a = b = c = 8.9160(10) A, Z = 4. Electrodeposition of tungsten metal on Pt from FLINAK, prepared by the addition of WF6 gas and metallic tungsten to the melt, is suggested to result from reduction of an equilibrium mixture of WF8(3-) and WF6(3-).     

Theoretical prediction of fast 3D AC electro-osmotic pumps

AC electro-osmotic (ACEO) pumps in microfluidics currently involve planar electrode arrays, but recent work on the underlying phenomenon of induced-charge electro-osmosis (ICEO) suggests that three-dimensional (3D) geometries may be exploited to achieve faster flows. In this paper, we present some new design principles for periodic 3D ACEO pumps, such as the "fluid conveyor belt" of ICEO flow over a stepped electrode array. Numerical simulations of these designs (using the standard low-voltage model) predict flow rates almost twenty times faster than existing planar ACEO pumps, for the same applied voltage and minimum feature size. These pumps may enable new portable or implantable lab-on-a-chip devices, since rather fast (mm s(-1)), tuneable flows should be attainable with battery voltages (<10 V).