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.     

Multiscale fast summation of long‐range charge and dipolar interactions

Here we present a linear order multiscale method for the fast summation of long range forces in a system consisting of a large number of charge and dipolar particles. For a N‐body system, our algorithm requires an order of work that is proportional to O(N), in comparison to order O(N²) of the direct pairwise computation. Our method is demonstrated on two‐dimensional homogeneous point‐charge and dipolar systems, and a combined heterogeneous particle system, for the calculation of the induced electrostatic potential and energy. The electrostatic interaction is decomposed into a local part and a smooth part. The method thus, has several potential advantages over other O(N log N) or O(N) techniques, especially for calculation with moving particles or implicit charges locations. This approach is beneficial to large‐scale problems such as molecular statics, molecular dynamics, equilibrium statistics (Monte‐Carlo simulations), molecular docking, and in areas such as magnetism and astrophysics. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 717–731, 2001     

Efficient lookup table using a linear function of inverse distance squared

The major bottleneck in molecular dynamics (MD) simulations of biomolecules exist in the calculation of pairwise nonbonded interactions like Lennard‐Jones and long‐range electrostatic interactions. Particle‐mesh Ewald (PME) method is able to evaluate long‐range electrostatic interactions accurately and quickly during MD simulation. However, the evaluation of energy and gradient includes time‐consuming inverse square roots and complementary error functions. To avoid such time‐consuming operations while keeping accuracy, we propose a new lookup table for short‐range interaction in PME by defining energy and gradient as a linear function of inverse distance squared. In our lookup table approach, densities of table points are inversely proportional to squared pair distances, enabling accurate evaluation of energy and gradient at small pair distances. Regardless of the inverse operation here, the new lookup table scheme allows fast pairwise nonbonded calculations owing to efficient usage of cache memory. © 2013 Wiley Periodicals, Inc.     

Binding structures of tri‐N‐acetyl‐β‐glucosamine in hen egg white lysozyme using molecular dynamics with a polarizable force field

Lysozyme is a well‐studied enzyme that hydrolyzes the β‐(1,4)‐glycosidic linkage of N‐acetyl‐β‐glucosamine (NAG)_n oligomers. The active site of hen egg‐white lysozyme (HEWL) is believed to consist of six subsites, A‐F that can accommodate six sugar residues. We present studies exploring the use of polarizable force fields in conjunction with all‐atom molecular dynamics (MD) simulations to analyze binding structures of complexes of lysozyme and NAG trisaccharide, (NAG)₃. MD trajectories are applied to analyze structures and conformation of the complex as well as protein–ligand interactions, including the hydrogen‐bonding network in the binding pocket. Two binding modes (ABC and BCD) of (NAG)₃ are investigated independently based on a fixed‐charge model and a polarizable model. We also apply molecular mechanics with generalized born and surface area (MM‐GBSA) methods based on MD using both nonpolarizable and polarizable force fields to compute binding free energies. We also study the correlation between root‐mean‐squared deviation and binding free energies of the wildtype and W62Y mutant; we find that for this prototypical system, approaches using the MD trajectories coupled with implicit solvent models are equivalent for polarizable and fixed‐charge models. © 2012 Wiley Periodicals, Inc.     

Various atomic charge calculation schemes of CoMFA on HIF‐1 inhibitors of moracin analogs

Selection of appropriate partial charges in a molecule is crucial to derive good quantitative structure–activity relationship models. In this work, several partial atomic charges were assigned and tested in a comparative molecular field analysis (CoMFA) models. Many CoMFA models were generated for a series of hypoxia inducible factor 1 (HIF‐1) inhibitors using various partial atomic charges including charge equalization, Mülliken population analysis (MPA), natural population analysis, and electrostatic potential (ESP)‐derived charges. These atomic charges were investigated at various theoretical levels such as empirical, semiempirical, Hartree–Fock (HF), and density functional theory (DFT). Among them, Merz‐Singh‐Kollman (MK) ESP‐derived charges at the level of HF/6‐31G* gave the highest predictive q² with experimental pIC₅₀ values. With this charge scheme, a detailed analysis of CoMFA model was performed to understand the electrostatic interactions between ligand and receptor. More elaborate charge calculation schemes such as HF and DFT correlated more strongly with activity than empirical or semiempirical schemes. The choice of optimization methods was important. As geometries were fully optimized at the given levels of theory, the aligned structures were different. They differed considerably, especially for the flexible parts. This was likely the source of the substantial variation of q² values, even when the same steric factor was considered without electrostatic parameters. ESP‐derived charges were most appropriate to describe CoMFA electrostatic interactions among MPA, NBA, and ESP charges. Overall q² values vary considerably (0.8–0.5) depending on the charge schemes applied. The results demonstrate the need to consider more appropriate atomic charges rather than default CoMFA charges. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Creation of Ternary Multicomponent Crystals by Exploitation of Charge‐Transfer Interactions

Four new ternary crystalline molecular complexes have been synthesised from a common 3,5‐dinitrobenzoic acid (3,5‐dnda) and 4,4′‐bipyridine (bipy) pairing with a series of amino‐substituted aromatic compounds (4‐aminobenzoic acid (4‐aba), 4‐(N,N‐dimethylamino)benzoic acid (4‐dmaba), 4‐aminosalicylic acid (4‐asa) and sulfanilamide (saa)). The ternary crystals were created through the application of complementary charge transfer and hydrogen‐bonding interactions. For these systems a dimer was created through a charge‐transfer interaction between two of the components, while hydrogen bonding between the third molecule and this dimer completed the construction of the ternary co‐crystal. All resulting structures display the same acid ??? pyridine interaction between 3,5‐dnba and bipy. However, changing the third component causes the proton of this bond to shift from neutral OH ??? N to a salt form, O^? ??? HN⁺, as the nature of the group hydrogen bonding to the carboxylic acid was changed. This highlights the role of the crystal environment on the level of proton transfer and the utility of ternary systems for the study of this process.     

A study of the additivity of interactions in cation-water systems

The mono- to tetra-hydrates and hexahydrates of Na⁺, Mg²⁺ and Al³⁺ have been taken as examples to investigate to what extend the interactions in water-metal complexes can be replaced by sums of water-water and water-ion two-body interactions. It is found that the quality of the approximation of pairwise additivity of the interaction energies decreases with increasing charge of the ion and also with the number of water molecules in the hydrates. For cations with a charge of more than two the pair approximation can be expected to significantly influence the results of computer simulations of electrolyte solutions.     

Atomic multipoles: Electrostatic potential fit,local reference axis systems,and conformational dependence

Currently, all standard force fields for biomolecular simulations use point charges to model intermolecular electrostatic interactions. This is a fast and simple approach but has deficiencies when the electrostatic potential (ESP) is compared to that from ab initio methods. Here, we show how atomic multipoles can be rigorously implemented into common biomolecular force fields. For this, a comprehensive set of local reference axis systems is introduced, which represents a universal solution for treating atom‐centered multipoles for all small organic molecules and proteins. Furthermore, we introduce a new method for fitting atomic multipole moments to the quantum mechanically derived ESP. This methods yields a 50–90% error reduction compared to both point charges fit to the ESP and multipoles directly calculated from the ab initio electron density. It is shown that it is necessary to directly fit the multipole moments of conformational ensembles to the ESP. Ignoring the conformational dependence or averaging over parameters from different conformations dramatically deteriorates the results obtained with atomic multipole moments, rendering multipoles worse than partial charges. © 2012 Wiley Periodicals, Inc.     

Intrinsic Surface Reaction Constant in 1-pK Model of Mg-Fe Hydrotalcite-like Compounds

The relationship among intrinsic surface reaction constant (K) in 1-pK model, point of zero net charge (PZNC) and structural charge density (σst) for amphoteric solid with structural charges was established in order to investigate the effect of σst on pK. The theoretical analysis based on 1-pK model indicates that the independent PZNC of electrolyte concentration (c) exists for amphoteric solid with structural charges. A common intersection point (CIP) should appear on the acid-base titration curves at different c, and the pH at the CIP is pHPZNC. The pK can be expressed as pK=-pHPZNC log[(1 2αPZNC)/(1-2αPZNC)], where αPZNC≡σst/eNANs, in which e is the elementary charge, NA the Avogadro‘s constant and Ns the total density of surface sites. For solids without structural charges, pK=-pHPZNC. The pK values of hydrotalcite-like compounds (HTlc) with general formula of [Mg1-xFex(OH)2](Cl,OH)x were evaluated. With increasing x, the pK increases, which can be explained based on the affinity of metal cations for H^- or OH^- and the electrostatic interaction between charging surface and H^- or OH^-.     

Synthesis and Structural Analysis of Aspergillus fumigatus Galactosaminogalactans Featuring α‐Galactose, α‐Galactosamine and α‐N‐Acetyl Galactosamine Linkages

Galactosaminogalactan (GAG) is a prominent cell wall component of the opportunistic fungal pathogen Aspergillus fumigatus. GAG is a heteropolysaccharide composed of α‐1,4‐linked galactose, galactosamine and N‐acetylgalactosamine residues. To enable biochemical studies, a library of GAG‐fragments was constructed featuring specimens containing α‐galactose‐, α‐galactosamine and α‐N‐acetyl galactosamine linkages. Key features of the synthetic strategy include the use of di‐tert‐butylsilylidene directed α‐galactosylation methodology and regioselective benzoylation reactions using benzoyl‐hydroxybenzotriazole (Bz‐OBt). Structural analysis of the Gal, GalN and GalNAc oligomers by a combination of NMR and MD approaches revealed that the oligomers adopt an elongated, almost straight, structure, stabilized by inter‐residue H‐bonds, one of which is a non‐conventional C?H???O hydrogen bond between H5 of the residue (i+1) and O3 of the residue (i). The structures position the C‐2 substituents almost perpendicular to the oligosaccharide main chain axis, pointing to the bulk solvent and available for interactions with antibodies or other binding partners.     

N2O in small para‐hydrogen clusters: Structures and energetics

We present the minimum‐energy structures and energetics of clusters of the linear N₂O molecule with small numbers of para‐hydrogen molecules with pairwise additive potentials. Interaction energies of (p‐H₂)–N₂O and (p‐H₂)–(p‐H₂) complexes were calculated by averaging the corresponding full‐dimensional potentials over the H₂ angular coordinates. The averaged (p‐H₂)–N₂O potential has three minima corresponding to the T‐shaped and the linear (p‐H₂)–ONN and (p‐H₂)–NNO structures. Optimization of the minimum‐energy structures was performed using a Genetic Algorithm. It was found that p‐H₂ molecules fill three solvation rings around the N₂O axis, each of them containing up to five p‐H₂ molecules, followed by accumulation of two p‐H₂ molecules at the oxygen and nitrogen ends. The first solvation shell is completed at N = 17. The calculated chemical potential oscillates with cluster size up to the completed first solvation shell. These results are consistent with the available experimental measurements. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Control of the Optical Properties of a Star Copolymer with a Hyperbranched Conjugated Polymer Core and Poly(ethylene glycol) Arms by Self‐Assembly

A self‐assembly approach to tuning the optical properties of a star copolymer is reported herein. The star copolymer HCP‐star‐PEG with a hyperbranched conjugated polymer (HCP) core and many linear poly(ethylene glycol) (PEG) arms has been prepared successfully. The HCP core was synthesized by Wittig coupling of N‐(n‐hexyl)‐3,6‐diformylcarbazole and 1,3,5‐bis[(triphenylphosphonio)methyl]benzene tribromide. Subsequently, the linear PEG arms were grafted onto the HCP core by acylhydrazone connection. It was found that the optical properties of HCP‐star‐PEG in chloroform solution changed on addition of acid. Both ¹H NMR and UV/Vis spectroscopic investigations confirmed that the variation of the optical properties was related to the complexation of the acid and the imine bond in the acylhydrazone group. HCP‐star‐PEG self‐assembled into core–shell micelles in the mixed solvent of chloroform and acetonitrile, which affected the protonation of the imine bond. Therefore the optical properties of HCP‐star‐PEG can be readily controlled by self‐assembly.     

Subsystem‐Based Theoretical Spectroscopy of Biomolecules and Biomolecular Assemblies

The absorption properties of chromophores in biomolecular systems are subject to several fine‐tuning mechanisms. Specific interactions with the surrounding protein environment often lead to significant changes in the excitation energies, but bulk dielectric effects can also play an important role. Moreover, strong excitonic interactions can occur in systems with several chromophores at close distances. For interpretation purposes, it is often desirable to distinguish different types of environmental effects, such as geometrical, electrostatic, polarization, and response (or differential polarization) effects. Methods that can be applied for theoretical analyses of such effects are reviewed herein, ranging from continuum and point‐charge models to explicit quantum chemical subsystem methods for environmental effects. Connections to physical model theories are also outlined. Prototypical applications to optical spectra and excited states of fluorescent proteins, biomolecular photoreceptors, and photosynthetic protein complexes are discussed.     

Polymorphism of 3‐(5‐phenyl‐1,3,4‐oxadiazol‐2‐yl)‐ and 3‐[5‐(pyridin‐4‐yl)‐1,3,4‐oxadiazol‐2‐yl]‐2H‐chromen‐2‐ones

This study of 3‐(5‐phenyl‐1,3,4‐oxadiazol‐2‐yl)‐2H‐chromen‐2‐one, C₁₇H₁₀N₂O₃, 1 , and 3‐[5‐(pyridin‐4‐yl)‐1,3,4‐oxadiazol‐2‐yl]‐2H‐chromen‐2‐one, C₁₆H₉N₃O₃, 2 , was performed on the assumption of the potential anticancer activity of the compounds. Three polymorphic structures for 1 and two polymorphic structures for 2 have been studied thoroughly. The strongest intermolecular interaction is stacking of the `head‐to‐head' type in all the studied crystals. The polymorphic structures of 1 differ with respect to the intermolecular interactions between stacked columns. Two of the polymorphs have a columnar or double columnar type of crystal organization, while the third polymorphic structure can be classified as columnar‐layered. The difference between the two structures of 2 is less pronounced. Both crystals can be considered as having very similar arrangements of neighbouring columns. The formation of polymorphic modifications is caused by a subtle balance of very weak intermolecular interactions and packing differences can be identified only using an analysis based on a study of the pairwise interaction energies.     

Charge redistribution effect on the properties of charge transfer complexes HnR⋅XY and HnR⋅X2 (X,Y = F,Cl, Br,I; R = O,S, N,P)

Systematic studies on structures, energies, charge transfer, dipole moments, and ionic character of a series of weakly bonded charge transfer (CT) complexes (D⋅AB, D = H₂O, H₂S, NH₃, PH₃, AB = F₂, Cl₂, Br₂, I₂, BrCl, IBr, ClF, ICl, BrF, IF) have been carried out by the hybrid Hartree–Fock density functional theory (HF‐DFT) method, where those results are validated by available experimental and theoretical investigations. Employing the Hohenberg–Kohn theorem, the property of a multicomponent system is formulated with contributions from both component properties and the charge redistribution (CR) effect, which describes the electronic coupling between components. For any property of a multicomponent system, provided that the intercomponent coupling is weak enough, the first‐order approximation can be applied, which yields a linear correlation of the component contribution to the CR effect. In fact, this kind of linear relationship can be evidenced by all the studied properties including the geometry, energy, charge transfer, dipole moment, and ionic character of all 40 complexes. This approximation quantitatively describes the relative contribution of the components to a given property, which shows the same tendency in a series of complexes. Based on the investigations of the CT effect on the intermolecular bond energy and the total dipole moment, it has been found that the principal bonding character of the title complexes was ascertained to be ionic with the exception of the F₂ complexes, which agrees well with the calculated ionic character. The CT effect, though small in a quantitative aspect, is directly connected to various kinds of system properties. The effectiveness and consistency of the present type of calculations in multicomponent systems may allow their wider applications in the study of intermolecular interactions. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 327–338, 2001     

Comparison of the accuracy of periodic reaction field methods in molecular dynamics simulations of a model liquid crystal system

A periodic reaction field (PRF) method is a technique to estimate long‐range interactions. The method has the potential to effectively reduce the computational cost while maintaining adequate accuracy. We performed molecular dynamics (MD) simulations of a model liquid‐crystal system to assess the accuracy of some variations of the PRF method in low‐charge‐density systems. All the methods had adequate accuracy compared with the results of the particle mesh Ewald (PME) method, except for a few simulation conditions. Furthermore, in all of the simulation conditions, one of the PRF methods had the same accuracy as the PME method. © 2015 Wiley Periodicals, Inc.     

Influence of N‐Alkyl Substituents and Counterions on the Structural and Mesomorphic Properties of Guanidinium Salts: Experiment and Quantum Chemical Calculations

A series of N‐4‐(4′‐alkoxybiphenyl)‐N′,N′,N”,N“‐tetramethylguanidinium salts was synthesized with varying alkoxy chain lengths and additional N‐alkyl substituents, each with a number of different counterions. X‐ray crystal‐structure analyses of 1b I , 1b PF₆ , 2a I , and 4a I reveal bilayer structures in the solid state and, for the 1b and 1b PF₆ salts, a hydrogen‐bond‐type connectivity between the guanidinium N‐H group and the anion is found. For the N‐alkyl homologues 2a I and 4a I the anion is still oriented close to the head group, although at a larger distance. Ion pairs are present also in solution, as demonstrated by ¹H NMR: the N‐H chemical shift shows a good linear correlation with the radius, and hence the hardness, of the anion. The intramolecular conformational flexibility of 1b I , 2b I , 3b I, and 4b I was studied by temperature‐dependent ¹H NMR spectroscopy and discrete activation barriers were determined for rotations about each of the three C? N partial double bonds of the guanidinium core. The relative heights of the individual barriers change between the N‐H and the N‐alkylguanidinium salts. A fourth barrier is observed for the rotation about the N? biphenyl bond. DFT calculations of charge densities show that the positive charge resides primarily on the central carbon atom. Rotational barriers were calculated for N′‐substituted 2‐amino‐1,3‐dimethylimidazolidinium cations as models, and are in qualitatively good agreement with the NMR data. Mesomorphic properties were studied by differential‐scanning calorimetry, polarizing optical microscopy, and X‐ray diffraction (WAXS/SAXS). All liquid‐crystalline guanidinium salts exhibit smectic A mesophases. Clearing temperatures show a linear correlation with the anionic radius. Substitution of the N‐H group with methyl, ethyl, or propyl results in decreasing mesophase widths and a concomitant shrinkage of the layer spacings.