Simple and accurate scheme to compute electrostatic interaction: Zero-dipole summation technique for molecular system and application to bulk water

The zero-dipole summation method was extended to general molecular systems, and then applied to molecular dynamics simulations of an isotropic water system. In our previous paper [I. Fukuda, Y. Yonezawa, and H. Nakamura, J. Chem. Phys. 134, 164107 (2011)], for evaluating the electrostatic energy of a classical particle system, we proposed the zero-dipole summation method, which conceptually prevents the nonzero-charge and nonzero-dipole states artificially generated by a simple cutoff truncation. Here, we consider the application of this scheme to molecular systems, as well as some fundamental aspects of general cutoff truncation protocols. Introducing an idea to harmonize the bonding interactions and the electrostatic interactions in the scheme, we develop a specific algorithm. As in the previous study, the resulting energy formula is represented by a simple pairwise function sum, enabling facile applications to high-performance computation. The accuracy of the electrostatic energies calculated by the zero-dipole summation method with the atom-based cutoff was numerically investigated, by comparison with those generated by the Ewald method. We obtained an electrostatic energy error of less than 0.01% at a cutoff length longer than 13 A for a TIP3P isotropic water system, and the errors were quite small, as compared to those obtained by conventional truncation methods. The static property and the stability in an MD simulation were also satisfactory. In addition, the dielectric constants and the distance-dependent Kirkwood factors were measured, and their coincidences with those calculated by the particle mesh Ewald method were confirmed, although such coincidences are not easily attained by truncation methods. We found that the zero damping-factor gave the best results in a practical cutoff distance region. In fact, in contrast to the zero-charge scheme, the damping effect was insensitive in the zero-charge and zero-dipole scheme, in the molecular system we treated. We discussed the origin of this difference between the two schemes and the dependence of this fact on the physical system. The use of the zero damping-factor will enhance the efficiency of practical computations, since the complementary error function is not employed. In addition, utilizing the zero damping-factor provides freedom from the parameter choice, which is not trivial in the zero-charge scheme, and eliminates the error function term, which corresponds to the time-consuming Fourier part under the periodic boundary conditions.     

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.     

General methodology to optimize damping functions to account for charge penetration effects in electrostatic calculations using multicentered multipolar expansions

We developed a methodology to optimize exponential damping functions to account for charge penetration effects when computing molecular electrostatic properties using the multicentered multipolar expansion method (MME). This methodology is based in the optimization of a damping parameter set using a two-step fast local fitting procedure and the ab initio (Hartree-Fock/6-31G** and 6-31G**+) electrostatic potential calculated in a set of concentric grid of points as reference. The principal aspect of the methodology is a first local fitting step which generates a focused initial guess to improve the performance of a simplex method avoiding the use of multiple runs and the choice of initial guesses. Three different strategies for the determination of optimized damping parameters were tested in the following studies: (1) investigation of the error in the calculation of the electrostatic interaction energy for five hydrogen-bonded dimers at standard and nonstandard hydrogen-bonded geometries and at nonequilibrium geometries; (2) calculation of the electrostatic molecular properties (potential and electric field) for eight small molecular systems (methanol, ammonia, water, formamide, dichloromethane, acetone, dimethyl sulfoxide, and acetonitrile) and for the 20 amino acids. Our results show that the methodology performs well not only for small molecules but also for relatively larger molecular systems. The analysis of the distinct parameter sets associated with different optimization strategies show that (i) a specific parameter set is more suitable and more general for electrostatic interaction energy calculations, with an average absolute error of 0.46 kcal/mol at hydrogen-bond geometries; (ii) a second parameter set is more suitable for electrostatic potential and electric field calculations at and outside the van der Waals (vdW) envelope, with an average error decrease >72% at the vdW surface. A more general amino acid damping parameter set was constructed from the original damping parameters derived for the small fragments and for the amino acids. This damping set is more insensitive to protein backbone and residue side-chain conformational changes and can be very useful for future docking and molecular dynamics protein simulations using ab initio based polarizable classical methods.     

Fragment-based quantum mechanical methods for periodic systems with Ewald summation and mean image charge convention for long-range electrostatic interactions

We describe an Ewald-summation method to incorporate long-range electrostatic interactions into fragment-based electronic structure methods for periodic systems. The present method is an extension of the particle-mesh Ewald technique for combined quantum mechanical and molecular mechanical (QM/MM) calculations, and it has been implemented into the explicit polarization (X-Pol) potential to illustrate the computational details. As in the QM/MM-Ewald method, the X-Pol-Ewald approach is a linear-scaling electrostatic method, in which the short-range electrostatic interactions are determined explicitly in real space and the long-range Ewald pair potential is incorporated into the Fock matrix as a correction. To avoid the time-consuming Fock matrix update during the self-consistent field procedure, a mean image charge (MIC) approximation is introduced, in which the running average with a user-chosen correlation time is used to represent the long-range electrostatic correction as an average effect. Test simulations on liquid water show that the present X-Pol-Ewald method takes about 25% more CPU time than the usual X-Pol method using spherical cutoff, whereas the use of the MIC approximation reduces the extra costs for long-range electrostatic interactions by 15%. The present X-Pol-Ewald method provides a general procedure for incorporating long-range electrostatic effects into fragment-based electronic structure methods for treating biomolecular and condensed-phase systems under periodic boundary conditions.     

ORAC: A Molecular dynamics program to simulate complex molecular systems with realistic electrostatic interactions

In this study, we present a new molecular dynamics program for simulation of complex molecular systems. The program, named ORAC, combines state-of-the-art molecular dynamics (MD) algorithms with flexibility in handling different types and sizes of molecules. ORAC is intended for simulations of molecular systems and is specifically designed to treat biomolecules efficiently and effectively in solution or in a crystalline environment. Among its unique features are: (i) implementation of reversible and symplectic multiple time step algorithms (or r-RESPA, reversible reference system propagation algorithm) specifically designed and tuned for biological systems with periodic boundary conditions; (ii) availability for simulations with multiple or single time steps of standard Ewald or smooth particle mesh Ewald (SPME) for computation of electrostatic interactions; and (iii) possibility of simulating molecular systems in a variety of thermodynamic ensembles. We believe that the combination of these algorithms makes ORAC more advanced than other MD programs using standard simulation algorithms. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1848–1862, 1997     

The effect of different cutoff schemes in molecular simulations of proteins

Molecular simulations of nanoscale systems invariably involve assumptions and approximations to describe the electrostatic interactions, which are long-ranged in nature. One approach is the use of cutoff schemes with a reaction-field contribution to account for the medium outside the cutoff scheme. Recent reports show that macroscopic properties may depend on the exact choice of cutoff schemes in modern day simulations. In this work, a systematic analysis of the effects of different cutoff schemes was performed using a set of 52 proteins. We find no statistically significant differences between using a twin-range or a single-range cutoff scheme. Applying the cutoff based on charge groups or based on atomic positions, does lead to significant differences, which is traced to the cutoff noise for energies and forces. While group-based cutoff schemes show increased cutoff noise in the potential energy, applying an atomistic cutoff leads to artificial structure in the solvent at the cutoff distance. Carefully setting the temperature control, or using an atomistic cutoff for the solute and a group-based cutoff for the solvent significantly reduces the effects of the cutoff noise, without introducing structure in the solvent. This study aims to deepen the understanding of the implications different cutoffs have on molecular dynamics simulations.     

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.     

New spherical-cutoff methods for long-range forces in macromolecular simulation

New atom- and group-based spherical-cutoff methods have been developed for the treatment of nonbonded interactions in molecular dynamics (MD) simulation. A new atom-based method, force switching, leaves short-range forces unaltered by adding a constant to the potential energy, switching forces smoothly to zero over a specified range. A simple improvement to group-based cutoffs is presented: Switched group-shifting shifts the group–group potential energy by a constant before being switched smoothly to zero. Also introduced are generalizations of atom-based force shifting, which adds a constant to the Coulomb force between two charges. These new approaches are compared to existing methods by evaluating the energy of a model hydrogen-bonding system consisting of two N-methyl acetamide molecules and by full MD simulation. Thirty-five 150 ps simulations of carboxymyoglobin (MbCO) hydrated by 350 water molecules indicate that the new methods and atom-based shifting are each able to approximate no-cutoff results when a cutoff at or beyond 12 Å is used. However, atom-based potential-energy switching and truncation unacceptably contaminate group–group electrostatic interactions. Group-based potential truncation should not be used in the presence of explicit water or other mobile electrostatic dipoles because energy is not a state function with this method, resulting in severe heating (about 4 K/ps in the simulations of hydrated MbCO). The distance-dependent dielectric (? ∝? r) is found to alter the temperature dependence of protein dynamics, suppressing anharmonic motion at high temperatures. Force switching and force shifting are the best atom-based spherical cutoffs, whereas switched group-shifting is the preferred group-based method. To achieve realistic simulations, increasing the cutoff distance from 7.5 to 12 Å or beyond is much more important than the differences among the three best cutoff methods. © 1994 by John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

Scalable improvement of SPME multipolar electrostatics in anisotropic polarizable molecular mechanics using a general short‐range penetration correction up to quadrupoles

We propose a general coupling of the Smooth Particle Mesh Ewald SPME approach for distributed multipoles to a short‐range charge penetration correction modifying the charge‐charge, charge‐dipole and charge‐quadrupole energies. Such an approach significantly improves electrostatics when compared to ab initio values and has been calibrated on Symmetry‐Adapted Perturbation Theory reference data. Various neutral molecular dimers have been tested and results on the complexes of mono‐ and divalent cations with a water ligand are also provided. Transferability of the correction is adressed in the context of the implementation of the AMOEBA and SIBFA polarizable force fields in the TINKER‐HP software. As the choices of the multipolar distribution are discussed, conclusions are drawn for the future penetration‐corrected polarizable force fields highlighting the mandatory need of non‐spurious procedures for the obtention of well balanced and physically meaningful distributed moments. Finally, scalability and parallelism of the short‐range corrected SPME approach are addressed, demonstrating that the damping function is computationally affordable and accurate for molecular dynamics simulations of complex bio‐ or bioinorganic systems in periodic boundary conditions. © 2016 Wiley Periodicals, Inc.     

Net charge changes in the calculation of relative ligand‐binding free energies via classical atomistic molecular dynamics simulation

The calculation of binding free energies of charged species to a target molecule is a frequently encountered problem in molecular dynamics studies of (bio‐)chemical thermodynamics. Many important endogenous receptor‐binding molecules, enzyme substrates, or drug molecules have a nonzero net charge. Absolute binding free energies, as well as binding free energies relative to another molecule with a different net charge will be affected by artifacts due to the used effective electrostatic interaction function and associated parameters (e.g., size of the computational box). In the present study, charging contributions to binding free energies of small oligoatomic ions to a series of model host cavities functionalized with different chemical groups are calculated with classical atomistic molecular dynamics simulation. Electrostatic interactions are treated using a lattice‐summation scheme or a cutoff‐truncation scheme with Barker–Watts reaction‐field correction, and the simulations are conducted in boxes of different edge lengths. It is illustrated that the charging free energies of the guest molecules in water and in the host strongly depend on the applied methodology and that neglect of correction terms for the artifacts introduced by the finite size of the simulated system and the use of an effective electrostatic interaction function considerably impairs the thermodynamic interpretation of guest‐host interactions. Application of correction terms for the various artifacts yields consistent results for the charging contribution to binding free energies and is thus a prerequisite for the valid interpretation or prediction of experimental data via molecular dynamics simulation. Analysis and correction of electrostatic artifacts according to the scheme proposed in the present study should therefore be considered an integral part of careful free‐energy calculation studies if changes in the net charge are involved. © 2013 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

How polarization damping affects ion solvation dynamics

In a recent paper (Sala et al. in J Chem Phys 133:234101, 2010), static properties of chloride in water have been addressed using a polarizable force field and by adding screening functions to damp short-range electrostatic interactions. In this contribution, we further explore the impact of damping polarizable interactions on system dynamics. To this end, results from Car–Parrinello molecular dynamics simulations have been used as benchmark for assessing the impact of damping schemes on the ion solvation dynamics of chloride in water. The results are of general validity, and the methodology could be easily implemented in all methods used to include polarization.     

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.     

Accelerated Poisson-Boltzmann calculations for static and dynamic systems

We report here an efficient implementation of the finite difference Poisson-Boltzmann solvent model based on the Modified Incomplete Cholsky Conjugate Gradient algorithm, which gives rather impressive performance for both static and dynamic systems. This is achieved by implementing the algorithm with Eisenstat's two optimizations, utilizing the electrostatic update in simulations, and applying prudent approximations, including: relaxing the convergence criterion, not updating Poisson-Boltzmann-related forces every step, and using electrostatic focusing. It is also possible to markedly accelerate the supporting routines that are used to set up the calculations and to obtain energies and forces. The resulting finite difference Poisson-Boltzmann method delivers efficiency comparable to the distance-dependent dielectric model for a system tested, HIV Protease, making it a strong candidate for solution-phase molecular dynamics simulations. Further, the finite difference method includes all intrasolute electrostatic interactions, whereas the distance dependent dielectric calculations use a 15-A cutoff. The speed of our numerical finite difference method is comparable to that of the pair-wise Generalized Born approximation to the Poisson-Boltzmann method.     

Design of a reaction field using a linear‐combination‐based isotropic periodic sum method

In our previous study (Takahashi et al., J. Chem. Theory Comput. 2012, 8, 4503), we developed the linear‐combination‐based isotropic periodic sum (LIPS) method. The LIPS method is based on the extended isotropic periodic sum theory that produces a ubiquitous interaction potential function to estimate homogeneous and heterogeneous systems. The LIPS theory also provides the procedure to design a periodic reaction field. To demonstrate this, in the present work, a novel reaction field of the LIPS method was developed. The novel reaction field was labeled LIPS‐SW, because it provides an interaction potential function with a shape that resembles that of the switch function method. To evaluate the ability of the LIPS‐SW method to describe in homogeneous and heterogeneous systems, we carried out molecular dynamics (MD) simulations of bulk water and water–vapor interfacial systems using the LIPS‐SW method. The results of these simulations show that the LIPS‐SW method gives higher accuracy than the conventional interaction potential function of the LIPS method. The accuracy of simulating water–vapor interfacial systems was greatly improved, while that of bulk water systems was maintained using the LIPS‐SW method. We conclude that the LIPS‐SW method shows great potential for high‐accuracy, high‐performance computing to allow large scale MD simulations. © 2014 Wiley Periodicals, Inc.     

Methodological problems in pressure profile calculations for lipid bilayers

From molecular dynamics simulations of a dipalmitoyl-phosphatidyl-choline (DPPC) lipid bilayer in the liquid crystalline phase, pressure profiles through the bilayer are calculated by different methods. These profiles allow us to address two central and unresolved problems in pressure profile calculations: The first problem is that the pressure profile is not uniquely defined since the expression for the local pressure involves an arbitrary choice of an integration contour. We have investigated two different choices leading to the Irving-Kirkwood (IK) and Harasima (H) expressions for the local pressure tensor. For these choices we find that the pressure profile is almost independent of the contour used, which indicates that the local pressure is well defined for a DPPC bilayer in the liquid crystalline phase. This may not be the case for other systems and we therefore suggest that both the IK and H profiles are calculated in order to test the uniqueness of the profile. The second problem is how to include electrostatic interactions in pressure profile calculations when the simulations are conducted without truncating the electrostatic potential, i.e., using the Ewald summation technique. Based on the H expression for the local pressure, we present a method for calculating the contribution to the lateral components of the local pressure tensor from electrostatic interactions evaluated by the Ewald summation technique. Pressure profiles calculated with an electrostatic potential truncation (cutoff) from simulations conducted with Ewald summation are shown to depend on the cutoff in a subtle manner which is attributed to the existence of long-ranged charge ordering in the system. However, the pressure profiles calculated with relatively long cutoffs are qualitatively similar to the Ewald profile for the DPPC bilayer studied here.     

Enzyme‐Compatible Dynamic Nanoreactors from Electrostatically Bridged Like‐Charged Surfactants and Polyelectrolytes

Reported is an unanticipated mechanism of attractive electrostatic interactions of fully neutralized polyacrylic acid (PAA) with like‐charged surfactants. Amphiphilic polymer‐surfactant complexes with high interfacial activity and a solubilization capacity exceeding that of conventional micelles are formed by bridging with Ca²⁺ ions. Incorporation of a protease into such dynamic nanoreactors results in a synergistically enhanced cleaning performance because of the improved solubilization of poorly water‐soluble immobilized proteins. Competitive interfacial and intermolecular interactions on different time‐ and length‐scales have been resolved using colorimetric analysis, dynamic tensiometry, light scattering, and molecular dynamic simulations. The discovered bridging association mechanism suggests reengineering of surfactant/polymer/enzyme formulations of modern detergents and opens new opportunities in advancing labile delivery systems.     

An efficient parallelization scheme for molecular dynamics simulations with many-body, flexible, polarizable empirical potentials: application to water

An efficient parallelization scheme for classical molecular dynamics simulations with flexible, polarizable empirical potentials is presented. It is based on the standard Ewald summation technique to handle the long-range electrostatic and induction interactions. The algorithm for this parallelization scheme is designed for systems containing several thousands of polarizable sites in the simulation box. Its performance is evaluated during molecular dynamics simulations under periodic boundary conditions with unit cell sizes ranging from 128 to 512 molecules employing two flexible polarizable water models [DC(F) and TTM2.1-F] containing 1 and 3 polarizable sites, respectively. The time-to-solution for these two polarizable models is compared with the one for a flexible, pairwise-additive water model (TIP4F). The benchmarks were performed on both shared and distributed memory platforms. As a result of the efficient calculation of the induced dipole moments, a superlinear scaling as a function of the number of the processors is observed. To the best of our knowledge, this is the first reported results of parallel scaling and performance for simulations of liquid water with a polarizable potential under periodic boundary conditions.     

Lattice dynamics of solid α-carbon monoxide

The lattice dynamics of α-CO is studied assuming a fully-ordered antiferro P2₁3 structure, using a potential model which includes electrostatic, dispersion and exchange interactions. The coupling of translational and librational motions leads to mixed modes at finite wave vectors and to anomalous acoustic dispersion. Anharmonic frequency shifts and the damping due to phonon—phonon interactions are evaluated for the zero wave vector modes. The single-particle potential wells for the high-frequency librational modes are investigated and suggest that translation—rotation coupling plays a primary role in the molecular reorientations.     

Multiple time scale behaviors and network dynamics in liquid methanol

Canonical ensemble molecular dynamics simulations of liquid methanol, modeled using a rigid-body, pair-additive potential, are used to compute static distributions and temporal correlations of tagged molecule potential energies as a means of characterizing the liquid state dynamics. The static distribution of tagged molecule potential energies shows a clear multimodal structure with three distinct peaks, similar to those observed previously in water and liquid silica. The multimodality is shown to originate from electrostatic effects, but not from local, hydrogen bond interactions. An interesting outcome of this study is the remarkable similarity in the tagged potential energy power spectra of methanol, water, and silica, despite the differences in the underlying interactions and the dimensionality of the network. All three liquids show a distinct multiple time scale (MTS) regime with a 1/ f (alpha) dependence with a clear positive correlation between the scaling exponent alpha and the diffusivity. The low-frequency limit of the MTS regime is determined by the frequency of crossover to white noise behavior which occurs at approximately 0.1 cm (-1) in the case of methanol under standard temperature and pressure conditions. The power spectral regime above 200 cm (-1) in all three systems is dominated by resonances due to localized vibrations, such as librations. The correlation between alpha and the diffusivity in all three liquids appears to be related to the strength of the coupling between the localized motions and the larger length/time scale network reorganizations. Thus, the time scales associated with network reorganization dynamics appear to be qualitatively similar in these systems, despite the fact that water and silica both display diffusional anomalies but methanol does not.     

Effects of the cutoff center on the mean potential and pair distribution functions in liquid water

Molecular dynamics simulations of extended simple point charge (SPC/E) water have been performed to study the effects of the truncation of long-range interactions on some calculated bulk properties of the liquid. The mean potential calculated in liquid water is sensitive to the choice of the cutoff center in the water molecule. The pair distribution function is also dependent on this choice, although not as strongly as the mean potential. An analysis is carried out to understand the origin of these effects. A common cutoff center is at the oxygen atom in the water molecule, but our study shows that this choice does not yield a mean potential value consistent with a more accurate estimate when no cutoff is applied. © 1995 John Wiley & Sons, Inc.