Electrostatic Interaction Energy Research Articles

Physicochemical origin of high correlation between thermal stability of a protein and its packing efficiency: a theoretical study for staphylococcal nuclease mutants.

There is an empirical rule that the thermal stability of a protein is related to the packing efficiency or core volume of the folded state and the protein tends to exhibit higher stability as the backbone and side chains are more closely packed. Previously, the wild type and its nine mutants of staphylococcal nuclease were compared by examining their folded structures. The results obtained were as follows: The stability was not correlated with the number of intramolecular hydrogen bonds, intramolecular electrostatic interaction energy, or degree of burial of the hydrophobic surface; though the empirical rule mentioned above held, it was not the proximate cause of higher stability; and the number of van der Waals contacts NvdW, or equivalently, the intramolecular van der Waals interaction energy was an important factor governing the stability. Here we revisit the wild type and its nine mutants of staphylococcal nuclease using our statistical-mechanical theory for hydration of a protein. A molecular model is employed for water. We show that the pivotal factor is the magnitude of the water-entropy gain upon folding. The gain originates from an increase in the total volume available to the translational displacement of water molecules coexisting with the protein in the system. The magnitude is highly correlated with the denaturation temperature Tm. Moreover, the apparent correlation between NvdW and Tm as well as the empirical rule is interpretable (i.e., their physicochemical meanings can be clarified) on the basis of the water-entropy effect.

BPE toolkit: toolkit for computational protein engineering.

We present a computational toolkit consisting of five utility tools, for performing basic operations on a protein structure file in PDB format. The toolkit consists of five different programs which can be integrated as part of a pipeline for computational protein structure characterization or as a standalone analysis package. The programs include tools for chirality check for amino acids (ProChiral), contact map generation (CoMa), data redundancy (DaRe), hydrogen bond potential energy (HyPE) and electrostatic interaction energy (EsInE). All programs in the toolkit can be accessed and downloaded through the following link: http://www.iitg.ac.in/bpetoolkit/.

Mathematical expressions for a system of two identical uniformly charged rods

Uniformly charged bodies with various symmetries are of great interest to many models in several disciplines. In particular, there are numerous physical and biological systems that contain rod-like charged particles. In this work, we consider a system of two identical uniformly charged rods and calculate their electrostatic interaction energy for a special case of orientation between them. A first approach that relies on standard integration methods allows us to obtain an exact analytic expression for such an interaction in this case. Application of a second different method to the same problem leads to mathematical expressions involving hypergeometric functions, a class of special functions not frequently encountered in the field. Comparison of the two results leads to interesting mathematical identities that might be of interest to a broad audience of researchers working in mathematical and physical sciences.

Ionic strength independence of charge distributions in solvation of biomolecules

Electrostatic forces enormously impact the structure, interactions, and function of biomolecules. We perform all-atom molecular dynamics simulations for 5 proteins and 5 RNAs to determine the dependence on ionic strength of the ion and water charge distributions surrounding the biomolecules, as well as the contributions of ions to the electrostatic free energy of interaction between the biomolecule and the surrounding salt solution (for a total of 40 different biomolecule/solvent combinations). Although water provides the dominant contribution to the charge density distribution and to the electrostatic potential even in 1M NaCl solutions, the contributions of water molecules and of ions to the total electrostatic interaction free energy with the solvated biomolecule are comparable. The electrostatic biomolecule/solvent interaction energies and the total charge distribution exhibit a remarkable insensitivity to salt concentrations over a huge range of salt concentrations (20 mM to 1M NaCl). The electrostatic potentials near the biomolecule's surface obtained from the MD simulations differ markedly, as expected, from the potentials predicted by continuum dielectric models, even though the total electrostatic interaction free energies are within 11% of each other.

A mechanistic growth model for inorganic crystals: Solid‐state interactions

Growth shapes of inorganic crystalline solids govern material properties such as catalytic activity and selectivity, solar cell efficiency, and so forth. A systematic understanding of the crystal growth process and the solid‐state interactions within inorganic crystals should help to engineer crystal shapes. A general model that identifies periodic bond chains in inorganic crystals while accounting for the long‐range electrostatic interactions is presented. The variation in the electronic structure and the partial charges of growth units on the inorganic crystal surfaces has been captured using the bond valence model. The electrostatic interaction energies in the kink sites of inorganic crystals were calculated using a space partitioning method that is computationally efficient. This model provides a quantitative explanation for the asymmetric growth spirals formed on the surface of calcite. This methodology for studying solid‐state interactions can be used with a mechanistic growth model to predict the morphology of a wide variety of inorganic crystals. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3707–3719, 2014

Ultrafast molecular rotor based DNA sensor: An insight into the mode of interaction

Abstract Benzothiazole based ultrafast molecular rotor, Thioflavin T (ThT), is a well known fluorescence sensor for nucleic acids. Thus, the knowledge of mode of interaction between ThT and DNA is very important for efficient utilization of such fluorescence sensors. In the present article, we have reported detail studies on the mode of interaction between ThT and a natural DNA using steady-state and femtosecond time-resolved transient emission techniques. Detail steady-state studies show that ThT binds strongly with natural DNA and causes a large change in its spectroscopic properties. Femtosecond transient emission studies show a substantial decrease in the torsional motion in the excited state of ThT bound to DNA molecules, indicating a strong interaction between them. It is observed that ThT binds to DNA through two modes of interaction. Studies with salt indicate that large fraction of ThT binds to DNA by electrostatic interaction, whereas, viscosity and resonance energy transfer studies indicate the intercalation of ThT with DNA molecules.

Unravelling nanoconfined films of ionic liquids.

The confinement of an ionic liquid between charged solid surfaces is treated using an exactly solvable 1D Coulomb gas model. The theory highlights the importance of two dimensionless parameters: the fugacity of the ionic liquid, and the electrostatic interaction energy of ions at closest approach, in determining how the disjoining pressure exerted on the walls depends on the geometrical confinement. Our theory reveals that thermodynamic fluctuations play a vital role in the "squeezing out" of charged layers as the confinement is increased. The model shows good qualitative agreement with previous experimental data, with all parameters independently estimated without fitting.

New Ligands and New Insights for Vitamin D Receptor from Charge Density

Vitamin D protective effects result from its role as a nuclear transcription factor that regulates cell growth, differentiation, and a wide range of cellular mechanisms crucial to the development and progression of cancer.[1] Many academic investigators and pharmaceutical companies try to develop calcitriol analogs that exhibit equal or even increased anti-proliferative activity while exhibiting a reduced tendency to cause hypercalcemia. Analysis of 24 Vitamin D analogs bearing similar molecular structures with a complex of a Vitamin D Receptor (VDR) enabled the design of new agonists (TB1, TB2, TB3 and TB4). Undertaken approach was to minimize the electrostatic interaction energies available after the reconstruction of charge density with the aid of the pseudoatom databank (UBDB[2]). Comprehensive studies revealed 29 residues crucial for agonist binding. Trp286, which is specific to VDR among the representatives of the Nuclear Receptor Family, plays the crucial role of positioning the ligand forming dispersive interactions, mostly C-H...π, with an average strength of -4 kcal mol-1. The ligand binding pocket is primarily composed of hydrophobic residues, however there are 6 hydrogen bonds characteristic for all the ligands. They electrostatic interaction energies strongly contribute to the total interaction energy, with an average strength of -8, -19, -11 and -12 kcal mol-1 for hydrogen bonds to Ser237, Arg274, Ser278 and Tyr143. The aliphatic chain of the Vitamin D analogs adopt an extended conformation and the 25-hydroxyl group is hydrogen bonded to His305 and His397 with electrostatic interaction energies of -13 and -11 kcal mol-1. The geometries of complexes of the proposed ligand with VDR were obtained by the docking procedure implemented in Autodock4.3[3]. New agonsits form all mentioned before interactions with VDR. The final results of electrostatic interaction energy for TB1 and TB2 are -153 and -120 kcal mol-1, and this results are the smallest among all studied Vitamin D analogs.

Charge density studies of interactions in macromolecules – the case of sunitinib

Electron density is a key factor in determining properties of molecules. Knowledge of the electron density distribution allows to determine not only the 3D structure of molecules, but also various one-electron properties (electric moments, electrostatic potential, electrostatic interaction energy, etc.). X-ray diffraction is a great tool for obtaining this kind of information. For macromolecules, however, quantitative determination of charge density from experiment is possible on rare occasions only. We will present that with the University at Buffalo pseudoatom database (UBDB) approach [1,2] it is now possible to reconstruct electron density of any macromolecular system for which atomic coordinates are available. The approach is fast and opens an excellent opportunity to investigate macromolecular complexes by means of topological analysis of electron density (and derivatives thereof), electrostatic interaction energy analysis, and many others. The results of our studies on sunitinib (SU) will illustrate the possibilities of the approach. SU is an inhibitor of tyrosine kinases and was approved as a drug in 2006. Comprehensive analysis of the SU malate crystal and SU complexes with a series of protein kinases was carried out. The high resolution single crystal X-ray measurement and UBDB approach served as the basis for the reconstruction of the charge density of SU and the protein complexes. Hirshfeld surface and topological analyses revealed a similar interaction pattern in the SU malate crystal to that in the protein binding pockets. SU forms nine preserved bond paths corresponding to hydrogen bonds and also to the C-H...O and C-H...π contacts common for all analyzed kinases. It interacts typically with similar electrostatic interaction energy with the studied proteins and can adjust its conformation to fit the binding pocket in a way to enhance the electrostatic interactions. Such behavior can be responsible for a broad spectrum of action of SU as kinase inhibitor.

Rationalising molecular crystal structures using Hirshfeld surfaces

Hirshfeld surface analysis [1] has very quickly become a routine tool for rationalising and visualising intermolecular interactions in crystals. The serendipitous discovery of an intriguing and novel way to identify the space `belonging' to a molecule in a crystal has led to the development of a suite of computational tools that facilitate a deeper understanding of how molecules pack in crystals and why it makes sense that a particular crystal packing occurs [2]. We have previously used the Hirshfeld surface as a vehicle for mapping inherent shape and curvature, surface-mediated distances between closest atoms, as well as quantum mechanical properties such as molecular orbital density, electron density and electrostatic potential. Combining visualisation tools like these with quantum mechanical wavefunctions – and hence properties derived from these wavefunctions – offers a powerful and unique opportunity to investigate intuitive concepts like `electrostatic complementarity' [3]. With this in mind we have been investigating ways to subdivide Hirshfeld surfaces into discrete patches that can be identified with specific pairs of molecules in close contact in crystals, and testing different expressions to quantify our ideas on electrostatic complementarity. Coupled with this appealing visual approach we also compute the electrostatic energy of interaction between the respective molecular wavefunctions. This combination of approaches within an easy to use software package will be powerful enough to not only routinely explore and visualise the patterns of interaction exhibited by molecules in crystals, but also provide meaningful energies of interaction between relevant pairs of molecules. In this way we can readily attach some real significance – energetics – to what are more usually classified as close contacts of various kinds.

Binding site preorganization and ligand discrimination in the purine riboswitch.

The progress of RNA research has suggested a wide variety of RNA molecules as possible targets for pharmaceutical drug molecules. Structure-based computational methods for predicting binding modes and affinities are now important tools in drug discovery, but these methods have mainly been focused on protein targets. Here we employ molecular dynamics free-energy perturbation calculations and the linear interaction energy method to analyze the energetics of ligand binding to purine riboswitches. Calculations are carried out for 14 different purine complexes with the guanine and adenine riboswitches in order to examine their ligand recognition principles. The simulations yield binding affinities in good agreement with experimental data and rationalize the selectivity of the riboswitches for different ligands. In particular, it is found that these receptors have an unusually high degree of electrostatic preorganization for their cognate ligands, and this effect is further quantified by explicit free-energy calculations, which show that the standard electrostatic linear interaction energy parametrization is suboptimal in this case. The adenine riboswitch specifically uses the electrostatic preorganization to discriminate against guanine by preventing the formation of a G-U wobble base pair.

Temperature dependent surface tension estimation using COSMO-RS sigma moments

In this work, a nonlinear multivariate QSPR model based on the COSMO-RS sigma moments was presented for the estimation of the temperature dependent surface tension of various organic compounds in wide surface tension (0.07–45.08mNm−1) and temperature (283–373K) range. 1500 data points were used to establish, validate and test the model. An artificial neural network was developed, optimized and used as regression model. The prediction power of the new model was validated with an external data set, with a squared correlation coefficient of R2=0.963 and a mean absolute error of MAE=0.81mNm−1. The factor sensitivity and importance analyses show that all of the proposed five COSMO-RS sigma moments and the temperature are significant input variables of the ANN model and the kind of skewness of the σ-profile, the electrostatic interaction energy and the hydrogen bonding acceptor function are the most sensitive and important molecular descriptors used in the new nonlinear multivariate QSPR model.

Quantum-Chemical Investigations on the Structural Variability of Anion–π Interactions

The structural versatility of anion-p interactions was investigated computationally. Employing quantum-chemically optimized structures of a series of C6H6-nF n /Br- complexes and the Coulomb law together with the London formula to calculate the electrostatic and the dispersion energy of the interaction between the anion and the π-system led to the result that up to the number of n = 2 due to a significantly repulsive electrostatic energy of interaction the dispersion energy is not sufficient to stabilize such structures in the gas phase where the anion is located above the plane defined by the aromatic ring. The energy surfaces resulting from the interaction of bromide anions with isolated arenes bearing varying numbers of fluorine atoms in different positions of the aromatic ring also show a pronounced dependency on the subsitution pattern of the aromatic system. Depending on the nature of the electron withdrawing group and its position, the energy surface can have a sharply defined energetically low minimum, in which the anion is ‘fixed’. Other substitution patterns result in very flat energy surfaces, and even a surface with more than two local minima within the scanned area was found. Thus, our study reveals the reason for the experimentally observed structural versatility depending on the substitution pattern in the solid state.

PH modulates the TGF‐β ligands binding to the receptors: a computational analysis

In spite of showing high sequence similarity and forming structurally similar ternary complex in vitro, the in vivo role of TGF-β1 and TGF-β3 ligands suggests against their functional redundancy and necessitates the importance for the study of the specificity of these ligands. A comparative computational analysis of binary and ternary complexes of these two ligands shows that anchor residues of ligand and receptor at TGF-β:TβR2 interface are similar in both complexes. However, the potential anchor residues of TGF-β at TGF-β:TβR1 interface are different, Tyr50 and Lys51 in TGF-β3 complex and Lys60 and Tyr6 in TGF-β1 complex. Pro55 and Asp57 of TβRI may act as anchor residues in complexes of both ligands along with Ile54 for TGF-β3 complex and Val61 for TGF-β1 complex. Arg58 of TβR1 acts as a potential hot residue for TGF-β3 ternary complex but not for TGF-β1 ternary complex formation whereas Pro55 and Phe60 may act as hot residues for both complexes. The Delphi analysis of the pH dependence of the binding energy indicates that pH has a remarkable effect on the binding energy of TβR2 to the open form of TGF-β3. Lowering of pH from 7 to 4 favors binding of the open form of TGF-β3 to TβR2. Now, apart from the residues at pH 7, residues Arg25, Lys31 and Arg94 of TGF-β3 and Asp118 and Glu119 of TβR2 also contribute significantly to the binding energy. Contrary to the binding energy of TβR2 to TGF-β3/TGF-β1, TβR1 shows appreciable pH dependence for its binding in ternary complex of TGF-β3/TGF-β1. In TGF-β3 ternary complex, the TβR1 electrostatic interaction energy disfavors complex formation at pH 7 while it is favored at pH 4.

Assessing the effect of surface modification of polyamide RO membrane by l-DOPA on the short range physiochemical interactions with biopolymer fouling on the membrane

Theoretical predictions of interaction energies for membrane–biopolymer foulant pairs were used to compare the fouling tendencies of a virgin commercial polyamide reverse osmosis (RO) membrane with a amino acid 3-(3,4-dihydroxyphenyl)-l-alanine (l-DOPA) coated RO membrane. Lifshitz–van der Waals (LW) and Lewis acid–base (AB) surface tension components of the membranes were determined based on contact angle results using the van Oss approach. From these values, the LW and AB components of the free energy of adhesion between membrane and foulants were calculated. Electrostatic (EL) double layer interaction energies between the membrane and foulants were also estimated using the measured surface charge data of the membranes and fouling agents. Bovine serum albumin (BSA) and alginic acid sodium salt (alginate) were used as model biopolymers causing membrane fouling. Based on the calculated adhesion free energies, acid–base interactions were found to have the strongest impact on the adhesion of both BSA and alginate to the either membranes surfaces. It was found that l-DOPA modification has significantly lowered acid–base interaction affinity toward the adhesion of both foulants studied. On the basis of calculated free energies of adhesion, lower fouling tendency of the l-DOPA modified membrane was expected. The accelerated fouling tests indicated a lower flux decline rate for the modified membrane and confirmed the results obtained from theory.

Sunitinib: from charge-density studies to interaction with proteins.

Protein kinases are targets for the treatment of a number of diseases. Sunitinib malate is a type I inhibitor of tyrosine kinases and was approved as a drug in 2006. This contribution constitutes the first comprehensive analysis of the crystal structures of sunitinib malate and of complexes of sunitinib with a series of protein kinases. The high-resolution single-crystal X-ray measurement and aspherical atom databank approach served as a basis for reconstruction of the charge-density distribution of sunitinib and its protein complexes. Hirshfeld surface and topological analyses revealed a similar interaction pattern in the sunitinib malate crystal structure to that in the protein binding pockets. Sunitinib forms nine preserved bond paths corresponding to hydrogen bonds and also to the C-H···O and C-H···π contacts common to the VEGRF2, CDK2, G2, KIT and IT kinases. In general, sunitinib interacts with the studied proteins with a similar electrostatic interaction energy and can adjust its conformation to fit the binding pocket in such a way as to enhance the electrostatic interactions, e.g. hydrogen bonds in ligand-kinase complexes. Such behaviour may be responsible for the broad spectrum of action of sunitinib as a kinase inhibitor.

Multipolar electrostatics based on the Kriging machine learning method: an application to serine

A multipolar, polarizable electrostatic method for future use in a novel force field is described. Quantum Chemical Topology (QCT) is used to partition the electron density of a chemical system into atoms, then the machine learning method Kriging is used to build models that relate the multipole moments of the atoms to the positions of their surrounding nuclei. The pilot system serine is used to study both the influence of the level of theory and the set of data generator methods used. The latter consists of: (i) sampling of protein structures deposited in the Protein Data Bank (PDB), or (ii) normal mode distortion along either (a) Cartesian coordinates, or (b) redundant internal coordinates. Wavefunctions for the sampled geometries were obtained at the HF/6-31G(d,p), B3LYP/apc-1, and MP2/cc-pVDZ levels of theory, prior to calculation of the atomic multipole moments by volume integration. The average absolute error (over an independent test set of conformations) in the total atom-atom electrostatic interaction energy of serine, using Kriging models built with the three data generator methods is 11.3 kJ mol⁻¹ (PDB), 8.2 kJ mol⁻¹ (Cartesian distortion), and 10.1 kJ mol⁻¹ (redundant internal distortion) at the HF/6-31G(d,p) level. At the B3LYP/apc-1 level, the respective errors are 7.7 kJ mol⁻¹, 6.7 kJ mol⁻¹, and 4.9 kJ mol⁻¹, while at the MP2/cc-pVDZ level they are 6.5 kJ mol⁻¹, 5.3 kJ mol⁻¹, and 4.0 kJ mol⁻¹. The ranges of geometries generated by the redundant internal coordinate distortion and by extraction from the PDB are much wider than the range generated by Cartesian distortion. The atomic multipole moment and electrostatic interaction energy predictions for the B3LYP/apc-1 and MP2/cc-pVDZ levels are similar, and both are better than the corresponding predictions at the HF/6-31G(d,p) level.

A Comparative Study of Transferable Aspherical Pseudoatom Databank and Classical Force Fields for Predicting Electrostatic Interactions in Molecular Dimers.

Accurate and fast evaluation of electrostatic interactions in molecular systems is one of the most challenging tasks in the rapidly advancing field of macromolecular chemistry and drug design. Electrostatic interactions are of crucial importance in biological systems. They are well represented by quantum mechanical methods; however, such calculations are computationally expensive. In this study, we have evaluated the University of Buffalo Pseudoatom Databank (UBDB)1,2 approach for approximation of electrostatic properties of macromolecules and their complexes. We selected the S663 and JSCH-20054 data sets (208 molecular complexes in total) for this study. These complexes represent a wide range of chemical and biological systems for which hydrogen bonding, electrostatic, and van der Waals interactions play important roles. Reference electrostatic energies were obtained directly from wave functions at the B3LYP/aug-cc-pVTZ level of theory using the SAPT (Symmetry-Adapted Perturbation Theory) scheme for calculation of electrostatic contributions to total intermolecular interaction energies. Electrostatic energies calculated on the basis of the UBDB were compared with corresponding reference results. Results were also compared with energies computed using a point charge model from popular force fields (AM1-BCC and RESP used in AMBER and CGenFF from CHARMM family). The energy trends are quite consistent (R2 ≈ 0.98) for the UBDB method as compared to the AMBER5 and CHARMM force field methods6(R2 ≈ 0.93 on average). The RSMEs do not exceed 3.2 kcal mol–1 for the UBDB and are in the range of 3.7–7.6 kcal mol–1 for the point charge models. We also investigated the discrepancies in electrostatic potentials and magnitudes of dipole moments among the tested methods. This study shows that estimation of electrostatic interaction energies using the UBDB databank is accurate and reasonably fast when compared to other known methods, which opens potential new applications to macromolecules.

Charge-density analysis using multipolar atom and spherical charge models: 2-methyl-1,3-cyclopentanedione, a compound displaying a resonance-assisted hydrogen bond

The experimental charge-density distribution in 2-methyl-1,3-cyclopentanedione in the crystal state was analyzed by synchrotron X-ray diffraction data collection at 0.33 Å resolution. The molecule in the crystal is in the enol form. The experimental electron density was refined using the Hansen-Coppens multipolar model and an alternative modeling, based on spherical atoms and additional charges on the covalent bonds and electron lone-pair sites. The crystallographic refinements, charge-density distributions, molecular electrostatic potentials, dipole moments and intermolecular interaction energies obtained from the different charge-density models were compared. The experimental results are also compared with the theoretical charge densities using theoretical structure factors obtained from periodic quantum calculations at the B3LYP/6-31G** level. A strong intermolecular O-H···O hydrogen bond connects molecules along the [001] direction. The deformation density maps show the resonance within the O=C-C=C-OH fragment and merged lone pair lobes on the hydroxyl O atom. This resonance is further confirmed by the analysis of charges and topology of the electron density.

Interaction of Various Gas Molecules with Paddle-Wheel-Type Open Metal Sites of Porous Coordination Polymers: Theoretical Investigation

We theoretically evaluated binding energies (Eb's) between various gas molecules and the Cu center open metal site (Cu-OMS) of Cu paddle-wheel units, [Cu2(O2CR)4] (R = H, Me, or Ph) using density functional theory (DFT) and MP2-MP4. The optimized geometry of the model system [Cu2(O2CPh)4] agrees with the experimental structure. The Eb of CO with [Cu2(O2CH)4] is only slightly different between the open-shell singlet and triplet states. The calculated Eb decreases in the order MeNC > H2O > MeCN > C2H4 > C2H2 > CO > CO2 > N2 > CH4 > H2. The trend is discussed in terms of the electrostatic interaction energy (ES), exchange repulsion energy (EX), and charge-transfer (CT) + polarization (Pol) interaction energy at the Hartree-Fock level and the electron correlation effect. The ES increases linearly with an increase in Eb, while the EX decreases linearly with an increase in Eb. These relationships indicate that the ES compensates for the EX. In other words, the Eb does not depend on the sum of ES and EX, which corresponds to the static energy. The electron correlation effect contributes little to the above-mentioned decreasing order of Eb. The total Eb roughly increases with an increase in the CT+Pol term, suggesting that the CT+Pol term plays important roles in determining the trend of Eb. The shift of the stretching frequency of adsorbed gas molecules on the Cu-OMS is reproduced well by the DFT calculation with the model system [Cu2(O2CH)4(L)2] (L = gas molecule). We found that the positive charge on the Cu significantly contributes to the shift in the end-on coordination gas molecules such as CO, MeNC, MeCN, and N2. Although the shift has been generally discussed in terms of donation and back-donation, the present result indicates that the electrostatic potential field in the porous coordination polymer should be considered in the discussion of the frequency shift.