Electrostatic Energy Terms Research Articles

Theory of electrosorption of water from ionic liquids

We propose and develop a classical density functional theory for the description of a minor amount of water dissolved in ionic liquid in the vicinity of an electrode. In addition to the electrostatic energy and lattice-gas mixing entropy terms, the utilised grand canonical potential contains several phenomenological terms/parameters that describe short-range interactions between ions, water molecules and the electrode. Here we investigate: (i) specific interaction of ions and molecules with the electrode, which are responsible for their specific adsorption; (ii) hydrophilicity/hydrophobicity of ions. We obtain water electrosorption isotherms as a function of the potential drop across the electrical double layer, investigate its asymmetry with respect to the sign of electrode potential, and establish the relationship between the sign of this asymmetry and hydrophobicity/hydrophilicity of cations and anions. We also calculate the effect of water electrosorption on the double layer differential capacitance which brings clear new features to its voltage dependence, some of which have been already experimentally observed.

MM-PBSA and per-residue decomposition energy studies on 7-Phenyl-imidazoquinolin-4(5H)-one derivatives: Identification of crucial site points at microsomal prostaglandin E synthase-1 (mPGES-1) active site

The huge therapeutic potential and the market share of painkillers are well-known. Due to the side effects associated with traditional NSAIDs and selective cyclooxygenase (COX-2) inhibitors, a new generation of painkillers is the need of the hour. In this regard, microsomal prostaglandin E synthase-1 (mPGES-1) offers great potential as an alternative drug target against inflammatory disorders. The present study is aimed at identifying the amino acids crucial in effective inhibitor binding at the mPGES-1 active site by performing molecular dynamics based studies on a series of 7-Phenyl-imidazoquinolin-4(5H)-one derivatives. Molecular dynamics (MD) simulations, MM-PBSA, per-residue energy decomposition and Dimensionality Reduction through Covariance matrix Transformation for Identification of Differences in dynamics (DIRECT-ID) analysis were performed to get insights into the structural details that can aid in novel drug design against mPGES-1. The high correlations of electrostatic and polar energy terms with biological activity highlight their importance and applicability in in silico screening studies. Further, per-residue energy decomposition studies revealed that Lys42, Arg52, Arg122, Pro124, Ser127, Val128 and Thr131 were contributing more towards inhibitor binding energy. The results clearly show that MM-PBSA can act as a filter in virtual screening experiments and can play major role in facilitating various mPGES-1 drug discovery studies.

Influence of the protein and DFT method on the broken‐symmetry and spin states in nitrogenase

AbstractThe enzyme nitrogenase contains a complicated MoFe7CS9 cofactor with 35 possible broken‐symmetry (BS) states. We have studied how the energies of these states depend on the geometry, the surrounding protein, the DFT functional and the basis set, studying the resting state, a one‐electron reduced state and a protonated state. We find that the effect of the basis set is small, up to 11 kJ/mol. Likewise, the effect of the surrounding protein is restricted, up to 10 and 7 kJ/mol for the electrostatic and van der Waals energy terms. Single‐point energies calculated on a single geometry give a good correlation (R2 = 0.92‐0.98) to energies calculated after geometry optimization, but some BS states may be disfavored by up to 37 kJ/mol. A change from the pure TPSS functional to the hybrid B3LYP functional may change the relative energies by up to 58 kJ/mol and the correlation between the two results is only 0.57‐0.72. Both functionals agree that BS7 is the most stable BS state and that the ground spin state is the quartet for the resting state and the quintet for the reduced state. With the TPSS functional, the BS6 state is the second most stable state, always at least 21 kJ/mol less stable than the BS7 state. However, with the B3LYP functional, BS10 is the second most stable state and for the protonated state it comes close in energy. Based on these results, we suggest a procedure how to consider the 35 BS states in future investigations of the nitrogenase reaction mechanism.

The effect of deformation dependent permittivity on the elastic response of a finitely deformed dielectric tube

In this paper, the influence of a radial electric field generated by compliant electrodes on the curved surfaces of a tube of dielectric electroelastic material subject to radially symmetric finite deformations is analyzed within the framework of the general theory of nonlinear electroelasticity. The analysis is illustrated for two constitutive equations based on the neo-Hookean and Gent elasticity models supplemented by an electrostatic energy term with a deformation dependent permittivity.

Application of a simple quantum chemical approach to ligand fragment scoring for Trypanosoma brucei pteridine reductase\xa01 inhibition

There is a need for improved and generally applicable scoring functions for fragment-based approaches to ligand design. Here, we evaluate the performance of a computationally efficient model for inhibitory activity estimation, which is composed only of multipole electrostatic energy and dispersion energy terms that approximate long-range ab initio quantum mechanical interaction energies. We find that computed energies correlate well with inhibitory activity for a compound series with varying substituents targeting two subpockets of the binding site of Trypanosoma brucei pteridine reductase 1. For one subpocket, we find that the model is more predictive for inhibitory activity than the ab initio interaction energy calculated at the MP2 level. Furthermore, the model is found to outperform a commonly used empirical scoring method. Finally, we show that the results for the two subpockets can be combined, which suggests that this simple nonempirical scoring function could be applied in fragment–based drug design.

Theoretical insights into the π-hole interactions in the complexes containing triphosphorus hydride (P3H3) and its derivatives.

The π-hole of triphosphorus hydride (P3H3) and its derivatives Z3X3 (Z = P, As; X = H, F, Cl, Br) was discovered and analyzed. MP2/aug-cc-pVDZ calculations were performed on the π-hole interactions in the HCN...Z3X3 complexes and the mutual influence between π-hole interactions and the hydrogen bond in the HCN...HCN...Z3X3 and HCN...Z3X3...HCN complexes studied. The π-hole interaction belongs to the typical closed-shell noncovalent interaction. The linear relationship was found between the most positive electrostatic potential of the π-hole (VS,max) and the interaction energy. Moreover, the VS,max of the π-hole was also found to be linearly correlated to the electrostatic energy term, indicating the important contribution of the electrostatic energy term to the π-hole interaction. There is positive cooperativity between the π-hole interaction and the hydrogen bond in the termolecular complexes. The π-hole interaction has a greater influence on the hydrogen bond than vice versa. The mutual enhancing effect between the π-hole interaction and the hydrogen bond in the HCN...HCN...Z3X3 complexes is greater than that in the HCN...Z3X3...HCN complexes.

Protein Frustratometer 2: a tool to localize energetic frustration in protein molecules, now with electrostatics.

The protein frustratometer is an energy landscape theory-inspired algorithm that aims at localizing and quantifying the energetic frustration present in protein molecules. Frustration is a useful concept for analyzing proteins’ biological behavior. It compares the energy distributions of the native state with respect to structural decoys. The network of minimally frustrated interactions encompasses the folding core of the molecule. Sites of high local frustration often correlate with functional regions such as binding sites and regions involved in allosteric transitions. We present here an upgraded version of a webserver that measures local frustration. The new implementation that allows the inclusion of electrostatic energy terms, important to the interactions with nucleic acids, is significantly faster than the previous version enabling the analysis of large macromolecular complexes within a user-friendly interface. The webserver is freely available at URL: http://frustratometer.qb.fcen.uba.ar.

A molecular analysis provides novel insights into androgen receptor signalling in breast cancer.

BackgroundAndrogen Receptor (AR) is an essential transcription factor for the development of secondary sex characteristics, spermatogenesis and carcinogenesis. Recently AR has been implicated in the development and progression of breast and prostate cancers. Although some of the functions of the AR are known but the mechanistic details of these divergent processes are still not clear. Therefore understanding the regulatory mechanisms of the functioning of the AR in ER-/AR+ breast cancer will provide many novel targets for the purpose of therapeutic intervention.Methods/ResultsUsing bioinformatics tools, we have identified 75 AR targets having prominent roles in cell cycle, apoptosis and metabolism. Herein, we validated 10 genes as AR targets by studying the regulation of these genes in MDA-MB-453 cell line on stimulation by androgens like 5α-dihydrotestosterone (DHT), using RT-qPCR and ChIP assay. It was observed that all the identified genes involved in cell cycle except MAD1L1 were found to be up regulated whereas expression of apoptosis related genes was decreased in response to DHT treatment. We performed an exhaustive, rigid-body docking between individual ARE and DNA binding domain (DBD) of the AR protein and it was found that novel residues K567, K588, K591 and R592 are involved in the process of DNA binding. To verify these specific DNA-protein interactions electrostatic energy term calculations for each residue was determined using the linearized Poisson–Boltzmann equation. Our experimental data showed that treatment of breast cancer cells with DHT promotes cell proliferation and decreases apoptosis. It was observed that bicalutamide treatment was able to reverse the effect of DHT.ConclusionTaken together, our results provide new insights into the mechanism by which AR promotes breast cancer progression. Moreover our work proposes to use bicalutamide along with taxanes as novel therapy for the treatment of TNBCs, which are positive for downstream AR signalling.

Efficient Maintenance and Update of Nonbonded Lists in Macromolecular Simulations.

Molecular mechanics and dynamics simulations use distance based cutoff approximations for faster computation of pairwise van der Waals and electrostatic energy terms. These approximations traditionally use a precalculated and periodically updated list of interacting atom pairs, known as the “nonbonded neighborhood lists” or nblists, in order to reduce the overhead of finding atom pairs that are within distance cutoff. The size of nblists grows linearly with the number of atoms in the system and superlinearly with the distance cutoff, and as a result, they require significant amount of memory for large molecular systems. The high space usage leads to poor cache performance, which slows computation for large distance cutoffs. Also, the high cost of updates means that one cannot afford to keep the data structure always synchronized with the configuration of the molecules when efficiency is at stake. We propose a dynamic octree data structure for implicit maintenance of nblists using space linear in the number of atoms but independent of the distance cutoff. The list can be updated very efficiently as the coordinates of atoms change during the simulation. Unlike explicit nblists, a single octree works for all distance cutoffs. In addition, octree is a cache-friendly data structure, and hence, it is less prone to cache miss slowdowns on modern memory hierarchies than nblists. Octrees use almost 2 orders of magnitude less memory, which is crucial for simulation of large systems, and while they are comparable in performance to nblists when the distance cutoff is small, they outperform nblists for larger systems and large cutoffs. Our tests show that octree implementation is approximately 1.5 times faster in practical use case scenarios as compared to nblists.

Microscopic mechanism for asymmetric charge distribution in Rashba-type surface states and the origin of the energy splitting scale

Microscopic mechanism for the Rashba-type band splitting is examined in detail. We show how asymmetric charge distribution is formed when local orbital angular momentum (OAM) and crystal momentum get interlocked due to surface effects. An electrostatic energy term in the Hamiltonian appears when such OAM and crystal momentum dependent asymmetric charge distribution is placed in an electric field produced from an inversion symmetry breaking (ISB). Analysis by using an effective Hamiltonian shows that, as the atomic spin-orbit coupling (SOC) strength increases from weak to strong, originally OAM-quenched states evolve into well-defined chiral OAM states and then to total angular momentum J-states. In addition, the energy scale of the band splitting changes from atomic SOC energy to electrostatic energy. To confirm the validity of the model, we study OAM and spin structures of Au(111) system by using an effective Hamiltonian for the d-orbitals case. As for strong SOC regime, we choose Bi2Te2Se as a prototype system. We performed circular dichroism angle resolved photoemission spectroscopy experiments as well as first-principles calculations. We find that the effective model can explain various aspects of spin and OAM structures of the system.

Quantum polarized ligand docking investigation to understand the significance of protonation states in histone deacetylase inhibitors

The effects of different protonation states of the hydroxamic acid (HA) inhibitors against the class I histone deacetylase enzymes (HDACs) have been studied using the state of the art quantum polarized ligand docking (QPLD) and molecular mechanics-generalized Born surface area (MM-GBSA) approaches. The binding modes of the inhibitors and their inter-molecular interactions with class I HDACs, in response to the protonation states of the inhibitors, are explored. Our results indicate that the different protonation states of the inhibitors exhibit significant differences in their interactions with the catalytic zinc metal ion and the other active site residues in the HDAC enzymes, which in turn affect the ‘Histidine-Aspartate’ charge relay mechanism. The QPLD calculations show that the protonated states of the inhibitors display higher scores in all the class I HDACs in this study, while the deprotonated forms present lower scores. The molecular electrostatic potentials and the other physico-chemical descriptors support the results. The MM-GBSA approach employed in the present work has been able to accurately calculate the relative binding free energies of the neutral and the protonated HA inhibitors; those were close to the experimental values. However, the MM-GBSA approach breaks down while calculating the binding free energies of the deprotonated inhibitors, which resulted in unrealistic values. Large energetic differences were found in the polar electrostatic solvation energy terms and the coulombic contributions in the deprotonated inhibitors. Thus improvements in the present solvation models and force fields become inevitable for the inclusions of charged states of inhibitors in computational drug discovery.

Exploring PHD Fingers and H3K4me0 Interactions with Molecular Dynamics Simulations and Binding Free Energy Calculations: AIRE-PHD1, a Comparative Study

PHD fingers represent one of the largest families of epigenetic readers capable of decoding post-translationally modified or unmodified histone H3 tails. Because of their direct involvement in human pathologies they are increasingly considered as a potential therapeutic target. Several PHD/histone-peptide structures have been determined, however relatively little information is available on their dynamics. Studies aiming to characterize the dynamic and energetic determinants driving histone peptide recognition by epigenetic readers would strongly benefit from computational studies. Herein we focus on the dynamic and energetic characterization of the PHD finger subclass specialized in the recognition of histone H3 peptides unmodified in position K4 (H3K4me0). As a case study we focused on the first PHD finger of autoimmune regulator protein (AIRE-PHD1) in complex with H3K4me0. PCA analysis of the covariance matrix of free AIRE-PHD1 highlights the presence of a “flapping” movement, which is blocked in an open conformation upon binding to H3K4me0. Moreover, binding free energy calculations obtained through Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) methodology are in good qualitative agreement with experiments and allow dissection of the energetic terms associated with native and alanine mutants of AIRE-PHD1/H3K4me0 complexes. MM/PBSA calculations have also been applied to the energetic analysis of other PHD fingers recognizing H3K4me0. In this case we observe excellent correlation between computed and experimental binding free energies. Overall calculations show that H3K4me0 recognition by PHD fingers relies on compensation of the electrostatic and polar solvation energy terms and is stabilized by non-polar interactions.

Physical nature of interactions in charge-inverted hydrogen bonds

Based on the hybrid variational-perturbation decomposition scheme we show that the electrostatic and delocalization energy terms are the most stabilizing components of the interaction energy of the charge-inverted hydrogen-bond (CIHB). It is shown that the electrostatic multipole term is the only one that closely reproduces the MP2 minimum conformation thus indicating that the bent structure results from a peculiar distribution of charge that can be described by atomic multipole moments of interacting monomers. To isolate the origin of observed bending of CIHB idealized linear structures have been analyzed as well. In this case the delocalization energy term outweighs all other stabilizing terms.

Assessment of Atomic Charge Models for Gas-Phase Computations on Polypeptides.

The concept of the atomic charge is extensively used to model the electrostatic properties of proteins. Atomic charges are not only the basis for the electrostatic energy term in biomolecular force fields but are also derived from quantum mechanical computations on protein fragments to get more insight into their electronic structure. Unfortunately there are many atomic charge schemes which lead to significantly different results, and it is not trivial to determine which scheme is most suitable for biomolecular studies. Therefore, we present an extensive methodological benchmark using a selection of atomic charge schemes [Mulliken, natural, restrained electrostatic potential, Hirshfeld-I, electronegativity equalization method (EEM), and split-charge equilibration (SQE)] applied to two sets of penta-alanine conformers. Our analysis clearly shows that Hirshfeld-I charges offer the best compromise between transferability (robustness with respect to conformational changes) and the ability to reproduce electrostatic properties of the penta-alanine. The benchmark also considers two charge equilibration models (EEM and SQE), which both clearly fail to describe the locally charged moieties in the zwitterionic form of penta-alanine. This issue is analyzed in detail because charge equilibration models are computationally much more attractive than the Hirshfeld-I scheme. Based on the latter analysis, a straightforward extension of the SQE model is proposed, SQE+Q(0), that is suitable to describe biological systems bearing many locally charged functional groups.

ChemInform Abstract: Phenylacetylene: A Hydrogen Bonding Chameleon

AbstractReview: 117 refs.

Large-Scale Computational Analysis of Protein Arrangement in the Lipid Bilayer

Spatial arrangements in the lipid bilayer of more than 1500 integral and peripheral membrane proteins with known 3D structures were calculated using a new continuum anisotopic solvent model of the lipid bilayer. The new model accounts for hydrophobic, hydrogen bonding, and long-range electrostatic solute-solvent interactions and includes the preferential solvation of protein groups by water. The model implements empirical dependencies of atomic solvation parameters and electrostatic energy terms on the bulk solvent properties including its dielectric constant (ε), hydrogen bonding acidity and basicity (α, β) and dipolarity/polarizability parameter (π∗). The dependencies were determined from 1269 partition coefficients of neutral molecules and ions from water to 19 solvents. The transmembrane profiles of polarity parameters (ε, α, β, π∗) in DOPC and DOPS bilayers were calculated based on published distributions of lipid fragments and water along the bilayer normal obtained in X-ray diffraction, neutron scattering and ESR studies. The obtained profiles indicate the existence of a “mid-polar” region (9 to 16 Å from the membrane center) that provides a significant energy gain from the hydrophobic interactions of nonpolar groups, but only a small electrostatic energy penalty associated with transfer of polar hydrogen-bonding groups and dipoles from water to this region. This explains the preferential accumulation of protein “hydrophobic dipoles” (aromatic rings of Trp and Tyr residues) in the “mid-polar” region. The results of the calculations have been included in the second version of the OPM database at opm.phar.umich.edu. The developed method and the database were applied for identification and functional assignment of potential membrane-associated proteins, planning mutagenesis experiments to verify the predicted membrane binding mode of peripheral proteins, prediction and interpretation of experimental membrane binding data.

Computational analysis of aspartic protease plasmepsin II complexed with EH58 inhibitor: a QM/MM MD study

Plasmepsin (PM) II is one of four enzymes in the food vacuole of Plasmodium falciparum. It has become an attractive target for combating malaria through research regarding its importance in the P. falciparum metabolism and life cycle, making it the target of choice for structure-based drug design. This paper reports the results of hybrid quantum mechanics / molecular mechanics (QM/MM) molecular dynamics (MD) simulations employed to study the details of the interactions established between PM II and N-(3-{(2-benzo[1, 3]dioxol-5-yl-ethyl)[3-(1-methyl-3-oxo-1,3-dihydro-isoindol-2-yl) propionyl]-amino}-1-benzyl-2-(hydroxyl-propyl)-4-benzyloxy-3,5dimethoxy-benzamide (EH58), a well-known potent inhibitor for this enzyme. Electrostatic binding free energy and energy terms decomposition have been computed for PM II complexed with the EH58 inhibitor. The results reveal that there is a strong interaction between Asp34, Val78, Ser79, Tyr192 and Asp214 residues and the EH58 inhibitor. In addition, we have computed the potential of the mean force (PMF) profile in order to assign the protonation state of the two catalytic aspartates in PM II-EH58 complex. The results indicate that the protonation of Asp214 favors a stable active site structure, which is consistent with our electrostatic binding free energy calculation and with previous published works.

Density Functional Steric Analysis of Linear and Branched Alkanes

Branched alkane hydrocarbons are thermodynamically more stable than straight-chain linear alkanes. This thermodynamic stability is also manifest in alkane bond separation energies. To understand the physical differences between branched and linear alkanes, we have utilized a novel density functional theory (DFT) definition of steric energy based on the Weizäcker kinetic energy. Using the M06-2X functional, the total DFT energy was partitioned into a steric energy term (E(s)[ρ]), an electrostatic energy term (E(e)[ρ]), and a fermionic quantum energy term (E(q)[ρ]). This analysis revealed that branched alkanes have less (destabilizing) DFT steric energy than linear alkanes. The lower steric energy of branched alkanes is mitigated by an equal and opposite quantum energy term that contains the Pauli component of the kinetic energy and exchange-correlation energy. Because the steric and quantum energy terms cancel, this leaves the electrostatic energy term that favors alkane branching. Electrostatic effects, combined with correlation energy, explains why branched alkanes are more stable than linear alkanes.

Computational Mapping of Anchoring Spots on Protein Surfaces

Protein–protein and protein–peptide interactions are often controlled by few strong contacts that involve hot spot residues. Computational detection of such contacts, termed here anchoring spots, is important for understanding recognition processes and for predicting interactions; it is an essential step in designing interaction interfaces and therapeutic agents. We describe ANCHORS MAP, an algorithm for computational mapping of amino acid side chains on protein surfaces. The algorithm consists of two stages: A geometry based stage (LSMdet), in which sub-pockets adequate for binding single side chains are detected and amino acid probes are scattered near them, and an energy based stage in which optimal positions of the probes are determined through repeated energy minimization and clustering of nearby poses and their Δ G are calculated. ANCHORS MAP employs a new function for Δ G calculations, which is specifically designed for the context of protein-protein recognition by introducing a correction in the electrostatic energy term that compensates for the dielectric shielding exerted by a hypothetical protein bound to the probe. The algorithm successfully detects known anchoring sites and accurately positions the probes. The calculated ΔG rank high the correct anchoring spots in maps produced for unbound proteins. We find that Arg, Trp, Glu and Tyr, which are favorite hot spot residues, are also more selective of their binding environment. The usefulness of anchoring spots mapping is demonstrated by detecting the binding surfaces in the protein-protein complex barnase/barstar and the protein-peptide complex kinase/PKI, and by identifying phenylalanine anchoring sites on the surface of the nuclear transporter NTF2, C-terminus anchors on PDZ domains and phenol anchors on thermolysin. Finally, we discuss the role of anchoring spots in molecular recognition processes.

Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulation of Wild-Type and Seven Mutants of CpNagJ in Complex with PUGNAc

The enzyme O-glycoprotein 2-acetamino-2-deoxy-beta-d-glucopyranosidase (O-GlcNAcase) is responsible for the removal of N-acetylglucosamine moieties from 2-acetamido-2-deoxy-beta-D-glucopyranose (O-GlcNAc) residues of serine/threonine residues of modified proteins. We herein present results of hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations applied to the study of the interactions established between a bacterial Clostridium perfringens homologue (CpNagJ) and PUGNAc, a potent known inhibitor of this enzyme. Electrostatic binding free energy and energy term decomposition have been computed for the wild-type CpNagJ and several mutants: D297N, D298N, Y335F, N390A, N396A, D401A, and W490A. The theoretical results have been compared with recently experimental data based on crystallographic and mutation studies on the same system. Our results reveal that, first, there is a strong interaction between Asp401, Asp298, and Asp297 residues and the PUGNAc inhibitor; and, second, the electrostatic substrate binding free energy is higher in wild-type, N390A and W490A mutants than in D297N, D298N, Y335F, N396A, and D401A ones, in accordance with the experimental results. Finally, both our theoretical predictions and the experimental data are compatible with a substrate-assisted reaction mechanism, involving two conserved aspartate residues.