静电和疏水效应对TGEV主蛋白酶二聚体稳定性的影响

从TGEV 3CL蛋白酶二聚体结构出发,研究了TGEV 3CL蛋白酶二聚体单体之间的静电和疏水相互作用.蛋白质的静电相互作用通过有限差分方法求解Poisson-Boltzmann方程得到,疏水相互作用通过分析溶剂可及性表面模型得到.考察了不同pH值对TGEV 3CL蛋白酶二聚体静电和疏水相互作用的影响,在pH值为5.5～8.5时,二聚体静电相互作用能、静电去溶剂化能和疏水自由能都较小,表明在该条件下静电和疏水相互作用有利于二聚体的稳定存在,这符合实验结晶所需条件.pH值对静电去溶剂化能的影响大于疏水自由能,表明静电作用是造成强酸或强碱条件下二聚体不能稳定存在的主要原因.     

静电和疏水效应对SARS冠状病毒3CL蛋白酶二聚体稳定性的影响

从TGEV3CL蛋白酶二聚体结构出发,研究了TGEV3CL蛋白酶二聚体单体之间的静电和疏水相互作用.蛋白质的静电相互作用通过有限差分方法求解Poisson-Boltzmann方程得到,疏水相互作用通过分析溶剂可及性表面模型得到.考察了不同pH值对SARS3CL蛋白酶二聚体静电和疏水相互作用的影响,在pH=5.5～8.5时,二聚体静电相互作用能、静电去溶剂化能和疏水自由能都具有较小的数值,表明在该条件下静电和疏水相互作用有利于二聚体的稳定存在.由于SARS3CL蛋白酶活性模式为二聚体,因此,在该pH值范围内,有利于蛋白酶保持活性.在pH=7.0条件下,蛋白酶单体之间具有最强的静电和疏水相互作用,从而使蛋白酶具有最强的活性,这与实验结果相一致.pH值对静电去溶剂化能的影响大于疏水自由能,表明静电作用是造成强酸或强碱条件下二聚体不能稳定存在的主要原因.     

On the relationship between the chemical bond energy and the electron energy levels of strongly ionic compounds

The analysis of experimental data suggests that the energy levels of ions in a crystal shift rigidly by an amount equal to the Madelung energy (electrostatic bond energy) maintaining the same separation as in the free ion. This leads to the conclusion that the electrostatic bonding energies of ions in a crystal is taken up partly by the orbital electrons and partly by the nuclear charge.     

Accurate modeling of the intramolecular electrostatic energy of proteins

The (?, ψ) energy surface of blocked alanine (N-acetyl–N′-methyl alanineamide) was calculated at the Hartree-Fock (HF)/6-31G* level using ab initio molecular orbital theory. A collection of six electrostatic models was constructed, and the term electrostatic model was used to refer to (1) a set of atomic charge densities, each unable to deform with conformation; and (2) a rule for estimating the electrostatic interaction energy between a pair of atomic charge densities. In addition to two partial charge and three multipole electrostatic models, this collection includes one extremely detailed model, which we refer to as nonspherical CPK. For each of these six electrostatic models, parameters—in the form of partial charges, atomic multipoles, or generalized atomic densities—were calculated from the HF/6-31G* wave functions whose energies define the ab initio energy surface. This calculation of parameters was complicated by a problem that was found to originate from the locking in of a set of atomic charge densities, each of which contains a small polarization-induced deformation from its idealized unpolarized state. It was observed that the collective contribution of these small polarization-induced deformations to electrostatic energy differences between conformations can become large relative to ab initio energy differences between conformations. For each of the six electrostatic models, this contribution was reduced by an averaging of atomic charge densities (or electrostatic energy surfaces) over a large collection of conformations. The ab initio energy surface was used as a target with respect to which relative accuracies were determined for the six electrostatic models. A collection of 42 more complete molecular mechanics models was created by combining each of our six electrostatic models with a collection of seven models of repulsion + dispersion + intrinsic torsional energy, chosen to provide a representative sample of functional forms and parameter sets. A measure of distance was defined between model and ab initio energy surfaces; and distances were calculated for each of our 42 molecular mechanics models. For most of our 12 standard molecular mechanics models, the average error between model and ab initio energy surfaces is greater than 1.5 kcal/mol. This error is decreased by (1) careful treatment of the nonspherical nature of atomic charge densities, and (2) accurate representation of electrostatic interaction energies of types 1—2 and 1—3. This result suggests an electrostatic origin for at least part of the error between standard model and ab initio energy surfaces. Given the range of functional forms that is used by the current generation of protein potential functions, these errors cannot be corrected by compensating for errors in other energy components. © 1995 by John Wiley & Sons, Inc.     

Effective polarization energy of the naphthalene molecular crystal: a study on the polarizable force field

polarization energy of the localized charge in organic solids consists of electronic polarization energy, permanent electrostatic interactions, and inter/intra molecular relaxation energies. The effective electronic polarization energies for an electron/hole carrier were successfully estimated by AMOEBA polarizable force field in naphthalene molecular crystals. Both electronic polarization energy and permanent electrostatic interaction were in agreement with the preview experimental values. In addition, the influence of the multipoles from different distributed mutipole analysis (DMA) fitting options on the electrostatic interactions are discussed in this paper. We found that the multipoles obtained from Gauss-Hermite quadrature without diffuse function or grid-based quadrature with 0.325 Å H atomic radius will give reasonable electronic polarization energies and permanent interactions for electron and hole carriers.     

Evaluation of the charge penetration energy between non-orthogonal molecular orbitals using the Spherical Gaussian Overlap approximation

An overlap dependent formula for evaluating the charge penetration energy between non-orthogonal molecular orbitals is derived using the Spherical Gaussian Overlap approximation. When combined with an accurate multipole representation of the electrostatic energy, such as in the effective fragment potential method, ab initio electrostatic energies are generally reproduced to within 0.2 kcal/mol for a variety of molecular dimers and basis sets. The only larger error is for the DMSO dimer, where the electrostatic energy is overestimated by 0.7 kcal/mol.     

Electrostatic energy of vacancy formation in crystals of polar molecules

An exact expression is derived for the electrostatic energy of a crystal of polar polarizable molecules containing an unrelaxed vacancy. The energy exceeds twice the electrostatic binding energy per molecule L by a polarization energy term, when changes in dielectric response due to the vacancy are ignored. The electrostatic energy of a molecule at a crystal surface is estimated from surface and bulk polarization energy measurements. It can be as high as 1.5 L. making the electrostatic energy of vacancy formation significantly less than L. the value for non-polarizable molecules. This may help to explain anomalous results for certain plastic crystals.     

Substituent effects on the edge-to-face aromatic interactions

The edge-to-face interactions for either axially or facially substituted benzenes are investigated by using ab initio calculations. The predicted maximum energy difference between substituted and unsubstituted systems is approximately 0.7 kcal/mol (approximately 1.2 kcal/mol if substituents are on both axially and facially substituted positions). In the case of axially substituted aromatic systems, the electron density at the para position is an important stabilizing factor, and thus the stabilization/destabilization by substitution is highly correlated to the electrostatic energy. This results in its subsequent correlation with the polarization and charge transfer. Thus, the stabilization/destabilization by substitution is represented by the sum of electrostatic energy and induction energy. On the other hand, the facially substituted aromatic system depends on not only the electron-donating ability responsible for the electrostatic energy but also the dispersion interaction and exchange repulsion. Although the dispersion energy is the most dominating interaction in both axial and facial substitutions, it is almost canceled by the exchange repulsion in the axial substitution, whereas in the facial substitution, together with the exchange repulsion it augments the electrostatic energy. The systems with electron-accepting substituents (NO2, CN, Br, Cl, F) favor the axial substituent conformation, while those with electron-donating substituents (NH2, CH3, OH) favor the facial substituent conformation. The interactions for the T-shape complex systems of an aromatic ring with other counterpart such as H2, H2O, HCl, and HF are also studied.     

Molecular simulation of the hydration Gibbs energy of barbiturates

In the present work, molecular dynamics calculations of the Gibbs energy of hydration of 10 different substituted barbiturates in SPC/E water were performed using thermodynamic integration. Given that experimental determination of the Gibbs hydration energy for this class of compounds is currently unfeasible, computer simulations appear as the only alternative for the estimation of this important quantity. Several simulation parameters are discussed and optimized based on calculations for barbituric acid. It is concluded that accounting for electrostatic interactions with the Reaction-Field method can be up to two times faster than with Particle-Mesh-Ewald method, without loss of accuracy. Different number of solvent molecules and simulation lengths were also tested. Lennard-Jones and electrostatic contributions were scaled down to zero in an independent way. It is shown that the electrostatic contribution is dominant (representing approximately 90% of the total Gibbs energy of hydration) and that barbiturate intra-molecular interactions cannot be neglected. The importance of the electrostatic contribution is attributed to the formation of hydrogen bonds between the barbiturates and water, which play an important role in the solvation process. The influence of the different substituents and their contribution to the Gibbs energy of hydration was assessed. Finally, the Lennard-Jones contributions and the total hydration Gibbs energy can both be correlated against molecular weight or partition coefficient data for mono- and di-substituted barbiturates.     

Molecular orientations at interfaces by extended polarizable continuum model

This study presents an investigation into orientation of molecular solutes at the interface of liquid water and other media. The calculation of electrostatic free energy of molecular solute is based on an extension of the polarizable continuum model (PCM) to interfacial system. The extended PCM computational scheme is incorporated with the self‐consistent field procedure which is necessary to obtain more accurate electrostatic free energy and charge density distribution. The computation of non‐electrostatic energy for interfacial system is also realized. Applying the numerical procedure to molecular systems, N,N′‐diethyl‐p‐nitroaniline (DEPNA) at air/water interface and p‐nitrophenol (PNP) at cyclohexane/water interface, the average orientational angles are in reasonable agreement with the experimental results. Taking both the electrostatic and the non‐electrostatic energies into account, the analysis on the energy profiles shows that the electrostatic solvation energy is the dominant factor in determining the orientation angle for PNP, whereas for DEPNA, the orientation angle mainly depends on the cavitation energy. This suggests that, in addition to the electrostatic energy, taking the cavitation energy into account may provide a more complete view when we survey the molecular orientation at interface. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Study on the nature of interaction of furan with various hydrides

The nature of interactions of furan with various hydrides (Y) (Y=HF,HCl,H2O,H2S,NH3,PH3) is investigated using ab initio calculations. The contribution of attractive (electrostatic, inductive, and dispersive) and repulsive (exchange) components to the interactions energy is analyzed. HF, H2O, and NH3 favor sigma o-type H bonding, while HCl, H2S, and PH3 favor pi-type H bonding. Interaction energy decomposition reveals that sigma o-type complexes interactions are predominantly electrostatic in nature, while the dispersion and electrostatic interactions dominate the pi-type complexes.     

An analysis of the electrostatic interaction between nucleic acid bases

Results from several commonly used approximate methods of evaluating electrostatic interactions have been compared to the rigorous, nonexpanded electrostatic energies at both uncorrelated and correlated levels of theory. We examined a number of energy profiles for both hydrogen bonded and stacked configurations of the nucleic acid base pairs. We found that the penetration effects play an extremely important role and the expanded electrostatic energies are significantly underestimated with respect to the ab initio values. Apart from the inability to reproduce the magnitudes of the ab initio electrostatic energy, there are other problems with the available approximate electrostatic models. For example, the distributed multipole analysis, one of the most advanced methods, is extremely sensitive to the basis set and level of theory used to evaluate the multipole moments. Detailed ab initio results are provided that other researchers could use to test their approximate models.     

Electric quadrupole model on the formation of molecular chirality dependent domain shapes of lipid monolayers at the air-water interface

Shapes and orientational deformation of a lipid monolayer domain have been analyzed taking into account the surface pressure, line tension, and electrostatic energy due to the spontaneous polarization and electric quadrupole density generated from the domain. The electrostatic energy due to the generation of spontaneous polarization and electric quadrupole density contributes to the formation of orientational deformation as the Frank elastic energy and spontaneous splay, respectively. Since the orientational configuration of the electric quadrupole density and in-plane spontaneous polarization is dependent on the molecular chirality, and the positive splay deformation of electric quadrupole density is induced by the spontaneous splay, the bending direction of in-plane spontaneous polarization depends on the chirality of constituent lipids. The electrostatic energy due to the in-plane spontaneous polarization is dependent on the orientational deformation of in-plane spontaneous polarization, and bends the domain shape towards the bending direction of the in-plane spontaneous polarization. It has been demonstrated that the chiral dependence of the domain shapes of lipid monolayers originated from the chiral dependence of orientational structure due to the electric quadrupole density.     

Extended Debye–Hückel Theory for Studying the Electrostatic Solvation Energy

The electrostatic part of the solvation energy has been studied by using extended Debye–Hückel (DH) theories. Specifically, our molecular Debye–Hückel theory [J. Chem. Phys. 2011 , 135, 104104] and its simplified version, an energy‐scaled Debye–Hückel theory, were applied to electrolytes with strong electrostatic coupling. Our theories provide a practical methodology for calculating the electrostatic solvation free energies, and the accuracy was verified for atomic and diatomic charged solutes.     

Free energy partitioning analysis of the driving forces that determine ion density profiles near the water liquid-vapor interface

Free energy partitioning analysis is employed to explore the driving forces for ions interacting with the water liquid-vapor interface using recently optimized point charge models for the ions and SPC/E water. The Na(+) and I(-) ions are examined as an example kosmotrope/chaotrope pair. The absolute hydration free energy is partitioned into cavity formation, attractive van der Waals, local electrostatic, and far-field electrostatic contributions. We first compute the bulk hydration free energy of the ions, followed by the free energy to insert the ions at the center of a water slab. Shifts of the ion free energies occur in the slab geometry consistent with the SPC/E surface potential of the water liquid-vapor interface. Then the free energy profiles are examined for ion passage from the slab center to the dividing surface. The profiles show that, for the large chaotropic I(-) ion, the relatively flat total free energy profile results from the near cancellation of several large contributions. The far-field electrostatic part of the free energy, largely due to the water liquid-vapor interface potential, has an important effect on ion distributions near the surface in the classical model. We conclude, however, that the individual forms of the local and far-field electrostatic contributions are expected to be model dependent when comparing classical and quantum results. The substantial attractive cavity free energy contribution for the larger I(-) ion suggests that there is a hydrophobic component important for chaotropic ion interactions with the interface.     

Effect of spatial irregularities on the temperature and field dependence of the mobility in liquid-crystalline conjugated polymer films

We have performed simulations of time-of-flight measurements via the Monte Carlo approach for films made of conjugated polymers in the liquid-crystalline phase. In spatially regular films with a distribution of on-site energies the mobility is affected by the interplay between electrostatic and thermal energy. When the width of the on-site energy distribution is comparable to the thermal energy, the mobility increases with temperature at low fields, but shows the opposite behaviour at larger fields. However, when spatial irregularities in the arrangement of the film are introduced, the mobility is enhanced at all temperatures, as the electrostatic energy plays less of a role in charge transport than thermal activation over energy barriers.     

Orientation and structure-building role of the water molecules bound at the contact surface of the dihydrofolate reductase-methotrexate complex

Summary Orientation of ten water molecules bound strongly at the contact surface of the dihydrofolate reductase-methotrexate enzyme-inhibitor complex was determined theoretically. To optimize the orientation of the water molecules, a recent method based on a simple electrostatic model was applied. The electrostatic complementarity in the binary complex was investigated using the lock-and-key model, considering the effect of the water molecules as well. The strongly bound water molecules improve the electrostatic fit in the pteridine region of methotrexate. Their role in the benzoic amide and-glutamate region is to decrease the internal energy by creating water bridges among remote polar sites making it possible to form H-bonds. Some modifications in the inhibitor structure were proposed for achieving greater inhibitor potency. The presumably enhanced effect is ascribed to the free energy gain in repelling the water molecules from the contact surface to the bulk of the solvent, and, in other cases, to internal energy decreases due to better electrostatic fit in the enzyme-inhibitor complex.     

Study on the Cation-π Interactions between Ammonium Ion and Aromatic π Systems

The nature and strength of the cation-π interactions between NH4^＋ and toluene, p-cresol, or Me-indole were studied in terms of the topological properties of molecular charge density and binding energy decomposition. The results display that the diversity in the distribution pattern of bond and cage critical points reflects the profound influence of the number and nature of substituent on the electron density of the aromatic rings. On the other hand, the energy decomposition shows that dispersion and repulsive exchange forces play an important role in the organic cation （NH4^＋）-π interaction, although the electrostatic and induction forces dominate the interaction. In addition, it is intriguing that there is an excellent correlation between the electrostatic energy and ellipticity at the bond critical point of the aromatic π systems, which would be helpful to further understand the electrostatic interaction in the cation-π complexes.     

Electrostatic Maxwell stress model of the shapes of condensed phase domains in monolayers at the air-water interface

The formation mechanism of the shapes of condensed phase domains in monolayers at the air-water interface was investigated taking into account the surface pressure, line tension, and electrostatic energy due to the spontaneous polarization generated in normal and in-plane direction. By deriving the shape equation of monolayer domains as the mechanical balance at the domain boundary, we found that the electrostatic energy contributes to the shape equation as electrostatic Maxwell stress. Development of a cusp from condensed phase domains of fatty acid monolayers, which has been experimentally observed, was analyzed by the shape equation. It was found that the development of a cusp originated from the strong Maxwell stress, which was induced by the non-uniform orientational distribution in the fatty acid domain, and that cusped shapes gave a minimum of the free energy of the domain. It demonstrates that the shape equation with Maxwell stress, which is derived in the present study, is useful to study the formation mechanism of the shapes of condensed phase domains in monolayers.     

Calculations of the electrostatic free energy contributions to the binding free energy of sulfonamides to carbonic anhydrase

The interactions between biologically important enzymes and drugs are of great interest. In order to address some aspects of these interactions we have initiated a program to investigate enzymedrug interactions. Specifically, the interactions between one of the isozymes of carbonic anhydrase and a family of drugs known as sulfonamides have been studied using computational methods. In particular the electrostatic free energy of binding of carbonic anhydrase II with acetazolamide, methazolamide,p-chlorobenzenesulfonamide,p-aminobenzenesulfonamide and three new compounds (MK1, MK2, and MK3) has been computed using finite-difference Poisson-Boltzmann (FDPB) [1] method and the semimacroscopic version [2, 3] of the protein dipole Langevin dipole (PDLD) method [4]. Both methods, FDPB and PDLD, give similar results for the electrostatic free energy of binding even though different charges and different treatments were used for the protein. The calculated electrostatic binding free energies are in reasonable agreement with the experimental data. The potential and the limitation of electrostatic models for studies of binding energies are discussed.