Conformational sensitivity of polyether macrocycles to electrostatic potential: Partial atomic charges,molecular mechanics,and conformational prediction

Molecular recognition (whether by enzymes, the immune system, or chelating ligands) depends critically on molecular conformation. Molecular mechanics predicts energetically favorable molecular conformations by locating low energy conformations using an empirical fit of molecular potential energy as a function of internal coordinates. Molecular mechanics analysis of 18-crown-6 demonstrates that the nonbonded term (primarily the electrostatic part) is the largest contributor to the conformational energy. Nevertheless, common methods of treating the electrostatic interaction for 18-crown-6 yield inconsistent values for conformational energies partly because partial charges assigned to each atom can change with conformation due to through-space inductive effects which are not considered in most molecular mechanics programs. Similar findings from several other groups are reviewed to support our conclusions. We argue for care and caution in predicting conformational preferences of molecules with two or more highly polar atoms. We also discuss the desirability of using an empirical method of partial charge determination such as the charge equilibration algorithm of Rappé and Goddard (or a suitable generalization which includes polarization) as a method of including these effects in molecular mechanics and molecular dynamics calculations.     

Long-range electrostatic interactions in hybrid quantum and molecular mechanical dynamics using a lattice summation approach

A method based on a lattice summation technique for treating long-range electrostatic interactions in hybrid quantum mechanics/molecular mechanics simulations is presented in this article. The quantum subsystem is studied at the semiempirical level, whereas the solvent is described by a two-body potential of molecular mechanics. Molecular dynamics simulations of a (quantum) chloride ion in (classical) water have been performed to test this technique. It is observed that the application of the lattice summations to solvent-solvent interactions as well as on solute-solvent ones has a significant effect on solvation energy and diffusion coefficient. Moreover, two schemes for the computation of the long-range contribution to the electrostatic interaction energy are investigated. The first one replaces the exact charge distribution of the quantum solute by a Mulliken charge distribution. The long-range electrostatic interactions are then calculated for this charge distribution that interacts with the solvent molecule charges. The second one is more accurate and involves a modified Fock operator containing long-range electron-charge interactions. It is shown here that both schemes lead to similar results, the method using Mulliken charges for the evaluation of long-range interactions being, however, much more computationally efficient.     

Electrostatic Energies in the 1,4‐Dichlorobenzene Polymorph Crystals: the Role of Charge Density Overlap Effects in Crystal Packing Analysis

Electrostatic and polarization energies for the three known polymorphic crystal structures of 1,4‐dichlorobenzene, as well as for one particularly stable virtual crystal structure generated by computer search, were calculated by a new accurate numerical integration method over static molecular charge densities obtained from high level ab initio molecular‐orbital calculations. Results are compared with those from standard empirical atom‐atom force fields. The new electrostatic energies, which include charge density overlap (penetration) effects, are seen to be much larger than and sometimes of opposite sign to those derived from point‐charge models. None of the four polymorphs is substantially more stable than the others on electrostatic‐energy grounds. Molecule‐molecule electrostatic energies have been calculated for the more important molecular pairs in each of the four structures; trends are found to be very different from those indicated by point‐charge energies or by total energies estimated with a parametric atom‐atom force field. Conclusions based exclusively on analysis of intermolecular atom contacts and point‐charge electrostatics may need to be modified in the light of the new kind of calculation.     

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements.     

The nature of halogen...halogen synthons: crystallographic and theoretical studies

A study of the halogen...halogen contacts in organic compounds using ab initio calculations and the results of previously reported crystallographic studies show that these interactions are controlled by electrostatics. These contacts can be represented by the geometric parameters of the C--X1...X2--C moieties (where theta1=C--X1...X2 and theta2=X1...X2--C; ri=X1...X2 distance). The distributions of the contacts within the sum of van der Waals radii (rvdW) versus thetai (theta1=theta2) show a maximum at theta approximately 150 degrees for X=Cl, Br, and I. This maximum is not seen in the distribution of F...F contacts. These results are in good agreement with our ab initio calculations. The theoretical results show that the position of the maximum depends on three factors: 1) The type of halogen atom, 2) the hybridization of the ipso carbon atom, and 3) the nature of the other atoms that are bonded to the ipso carbon atom apart from the halogen atom. Calculations show that the strength of these contacts decreases in the following order: I...I>Br...Br>Cl...Cl. Their relative strengths decrease as a function of the hybridization of the ipso carbon atom in the following order: sp2>sp>sp3. Attaching an electronegative atom to the carbon atom strengthens the halogen...halogen contacts. An electrostatic model is proposed based on two assumptions: 1) The presence of a positive electrostatic end cap on the halogen atom (except for fluorine) and 2) the electronic charge is anisotropically distributed around the halogen atom.     

Solvent reorganization in electron and ion transfer reactions near a smooth electrified surface: a molecular dynamics study

Molecular dynamics simulations of electron and ion transfer reactions near a smooth surface are presented, analyzing the effect of the geometrical constraint of the surface and the interfacial electric field on the relevant solvation properties of both a monovalent negative ion and a neutral atom. The simulations show that, from the solvation point of view, ion adsorption is an uphill process due to the need to shed off the ion's solvation shell and displace water from the surface. Atom adsorption, on the other hand, has only a small barrier, related to the molecularity of the solvent. Both the electrostatic interaction of the ion with the solvent and the ion's solvent reorganization energy (the relevant parameter in the Marcus electron transfer theory) decrease as the surface is approached, whereas these parameters are not sensitive to the distance from the surface for the atom. This is a consequence of the importance of long-range electrostatic interactions for ion solvation and the importance of short-range interactions for atom solvation. The electric field either attracts or repels an ion to or from the surface, but the field has no influence on the solvent reorganization energy. By including the quantum-mechanical electron transfer between the metal surface and the ion/atom in solution in the MD simulation by using a model Hamiltonian, we calculated two-dimensional free energy surfaces for ion adsorption allowing for partial charge transfer, based on a fully molecular picture of ion solvation near the surface.     

Electrostatics of DNA complexes with cationic lipid membranes

We present the exact solutions of the linear Poisson-Boltzmann equation for several problems relevant to electrostatics of DNA complexes with cationic lipids. We calculate the electrostatic potential and electrostatic energy for lamellar and inverted hexagonal phases, concentrating on the effects of dielectric boundaries. We compare our results for the complex energy with the known results of numerical solution of the nonlinear Poisson-Boltzmann equation. Using the solution for the lamellar phase, we calculate the compressibility modulus and compare our findings with the experimental data available. Also, we treat charge-charge interactions across, along, and between two low-dielectric membranes. We obtain an estimate for the strength of electrostatic interactions of one-dimensional DNA smectic layers across the lipid membrane. We discuss in the end some aspects of two-dimensional DNA condensation and DNA-DNA attraction in the DNA-lipid lamellar phase in the presence of di- and trivalent cations. We analyze the equilibrium DNA-DNA separations in lamellar complexes using the recently developed theory of electrostatic interactions of DNA helical charge motifs.     

Accurate conformation‐dependent molecular electrostatic potentials for high‐throughput in silico drug discovery

The atom‐centered partial charges‐approximation is commonly used in current molecular modeling tools as a computationally inexpensive alternative to quantum mechanics for modeling electrostatics. Even today, the use of partial charges remains useful despite significant advances in improving the efficiency of ab initio methods. Here, we report on new parameters for the EEM and SFKEEM electronegativity equalization‐based methods for rapidly determining partial charges that will accurately model the electrostatic potential of flexible molecules. The developed parameters cover most pharmaceutically relevant chemistries, and charges obtained using these parameters reproduce the B3LYP/cc‐pVTZ reference electrostatic potential of a set of FDA‐approved drug molecules at best to an average accuracy of 13 ± 4 kJ mol^?1; thus, equipped with these parameters electronegativity equalization‐based methods rival the current best non‐quantum mechanical methods, such as AM1‐BCC, in accuracy, yet incur a lower computational cost. Software implementations of EEM and SFKEEM, including the developed parameters, are included in the conformer‐generation tool BALLOON , available free of charge at http://web.abo.fi/fak/mnf/bkf/research/johnson/software.php . © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

甲硫氨酸-脑啡肽的活性位点

用ＡＭ１方法中计算静电势的ＰＭＥＰ子程序了甲硫氨酸－脑啡肽的活性位点。通过计算得到了整个分子的三维空间静电势分布和由静电势导出的各原子的电荷分布。进一步分析,确定模型分子活性位点为酪氨酸残在的叔氨原子和苯酚基、苯丙氨酸残基的苯基及部分氧原子。     

pKa calculations in solution and proteins with QM/MM free energy perturbation simulations: a quantitative test of QM/MM protocols

The accuracy of biological simulations depends, in large part, on the treatment of electrostatics. Due to the availability of accurate experimental values, calculation of pKa provides stringent evaluation of computational methods. The generalized solvent boundary potential (GSBP) and Ewald summation electrostatic treatments were recently implemented for combined quantum mechanical and molecular mechanics (QM/MM) simulations by our group. These approaches were tested by calculating pKa shifts due to differences in electronic structure and electrostatic environment; the shifts were determined for a series of small molecules in solution, using various electrostatic treatments, and two residues (His 31, Lys 102) in the M102K T4-lysozyme mutant with large pKa shifts, using the GSBP approach. The calculations utilized a free energy perturbation scheme with the QM/MM potential function involving the self-consistent charge density functional tight binding (SCC-DFTB) and CHARMM as the QM and MM methods, respectively. The study of small molecules demonstrated that inconsistent electrostatic models produced results that were difficult to correct in a robust manner; by contrast, extended electrostatics, GSBP, and Ewald simulations produced consistent results once a bulk solvation contribution was carefully chosen. In addition to the electrostatic treatment, the pKa shifts were also sensitive to the level of the QM method and the scheme of treating QM/MM Coulombic interactions; however, simple perturbative corrections based on SCC-DFTB/CHARMM trajectories and higher level single point energy calculations were found to give satisfactory results. Combining all factors gave a root-mean-square difference of 0.7 pKa units for the relative pKa values of the small molecules compared to experiment. For the residues in the lysozyme, an accurate pKa shift was obtained for His 31 with multiple nanosecond simulations. For Lys 102, however, the pKa shift was estimated to be too large, even after more than 10 nanosecond simulations for each lambda window; the difficulty was due to the significant, but slow, reorganization of the protein and water structure when Lys 102 was protonated. The simulations support that Lys 102 is deprotonated in the X-ray structure and the protein is highly destabilized when this residue is protonated.     

Electrostatics and aggregation: how charge can turn a crystal into a gel

The crystallization of proteins or colloids is often hindered by the appearance of aggregates of low fractal dimension called gels. Here we study the effect of electrostatics upon crystal and gel formation using an analytic model of hard spheres bearing point charges and short range attractive interactions. We find that the chief electrostatic free energy cost of forming assemblies comes from the entropic loss of counterions that render assemblies charge-neutral. Because there exists more accessible volume for these counterions around an open gel than a dense crystal, there exists an electrostatic entropic driving force favoring the gel over the crystal. This driving force increases with increasing sphere charge, but can be counteracted by increasing counterion concentration. We show that these effects cannot be fully captured by pairwise-additive macroion interactions of the kind often used in simulations, and we show where on the phase diagram to go in order to suppress gel formation.     

Reliable treatment of electrostatics in combined QM/MM simulation of macromolecules

A robust approach for dealing with electrostatic interactions for spherical boundary conditions has been implemented in the QM/MM framework. The development was based on the generalized solvent boundary potential (GSBP) method proposed by Im et al. [J. Chem. Phys. 114, 2924 (2001)], and the specific implementation was applied to the self-consistent-charge density-functional tight-binding approach as the quantum mechanics (QM) level, although extension to other QM methods is straightforward. Compared to the popular stochastic boundary-condition scheme, the new protocol offers a balanced treatment between quantum mechanics/molecular mechanics (QM/MM) and MM/MM interactions; it also includes the effect of the bulk solvent and macromolecule atoms outside of the microscopic region at the Poisson-Boltzmann level. The new method was illustrated with application to the enzyme human carbonic anhydrase II and compared to stochastic boundary-condition simulations using different electrostatic treatments. The GSBP-based QM/MM simulations were most consistent with available experimental data, while conventional stochastic boundary simulations yielded various artifacts depending on different electrostatic models. The results highlight the importance of carefully treating electrostatics in QM/MM simulations of biomolecules and suggest that the commonly used truncation schemes should be avoided in QM/MM simulations, especially in simulations that involve extensive conformational samplings. The development of the GSBP-based QM/MM protocol has opened up the exciting possibility of studying chemical events in very complex biomolecular systems in a multiscale framework.     

A critical evaluation of different QM/MM frontier treatments with SCC-DFTB as the QM method

The performance of different link atom based frontier treatments in QM/MM simulations was evaluated critically with SCC-DFTB as the QM method. In addition to the analysis of gas-phase molecules as in previous studies, an important element of the present work is that chemical reactions in realistic enzyme systems were also examined. The schemes tested include all options available in the program CHARMM for SCC-DFTB/MM simulation, which treat electrostatic interactions due to the MM atoms close to the QM/MM boundary in different ways. In addition, a new approach, the divided frontier charge (DIV), has been implemented in which the partial charge associated with the frontier MM atom ("link host") is evenly distributed to the other MM atoms in the same group. The performance of these schemes was evaluated based on properties including proton affinities, deprotonation energies, dipole moments, and energetics of proton transfer reactions. Similar to previous work, it was found that calculated proton affinities and deprotonation energies of alcohols, carbonic acids, amino acids, and model DNA bases are very sensitive to the link atom scheme; the commonly used single link atom approach often gives error on the order of 15 to 20 kcal/mol. Other schemes give better and, on average, mutually comparable results. For proton transfer reactions, encouragingly, both activation barriers and reaction energies are fairly insensitive (within a typical range of 2-4 kcal/mol) to the link atom scheme due to error cancellation, and this was observed for both gas-phase and enzyme systems. Therefore, the effect of using different link atom schemes in QM/MM simulations is rather small for chemical reactions that conserve the total charge. Although the current study used an approximate DFT method as the QM level, the observed trends are expected to be applicable to QM/MM methods with use of other QM approaches. This observation does not mean to encourage QM/MM simulations without careful benchmark in the study of specific systems, rather it emphasizes that other technical details, such as the treatment of long-range electrostatics, tend to play a more important role and need to be handled carefully.     

Force related atomic multipoles in planar molecules. Derivation of atomic quadrupole and octupole moments

Atomic multipoles as defined by current methods generally do not account for forces in molecules that arise from external electrostatic fields. It is pointed out that such forces and the electrostatic potential that the molecule itself generates are both determined by the molecular multipolar tensors. The latter constitute therefore the fundamental molecular constants that determine the molecular electrostatics apart from polarization. In general the multipolar tensors include contributions from the atomic multipoles and their fluxes. In planar molecules, however, the perpendicular charge flux is zero by symmetry. This gives rise to a (previously introduced) formalism that extracts analytical, force-related, atomic multipoles from the molecular multipolar tensors. This formalism is extended in this work to include force-related (FR) atomic quadrupoles and octupoles in planar molecules. The properties of the FR atomic multipoles, including their perpendicular fluxes, are discussed and some formal theoretical and computational advantages that characterize them are indicated. As an example, the electrostatics of OCS, including the molecular electrostatic potential and the forces on the nuclei due to an external point charge, is discussed.     

Dimethyl selenide complexes with compounds of Group IIIA elements: electron density redistribution and interaction energy partitioning

Molecular structures of dimethyl selenide complexes with AX₃ (A = B, Al, Ga, In; X = H, Me) compounds of Group IIIA elements were calculated by the PBE1PBE/Sapporo-TZ method. A complex approach to study the nature of interactions is proposed, which involves analysis of electron localization/delocalization characteristics and their influence on charge transfer and energy effects of complexation. It is shown that electron sharing is more important for stabilization of the complexes under study than electrostatic interaction between their fragments. It is demonstrated that analysis of local (topological) characteristics of the electron density distribution is insufficient to discover similarity/dissimilarity in the nature of some complexes. The energies of interaction in the complexes under study are mainly composed of the contributions of Se atom as active center of the donor molecule and the entire acceptor molecule. Energy characteristics of local interaction between Se atom and Group IIIA element atom are not representative.     

Classical molecular electrostatics: recognition of ligands in proteins and the vibrational Stark effect

It is shown that classical electrostatics quantitatively describes both the binding of the diatomic ligands XO (X = C, N, O) to the heme group in myoglobin and the dependence of their vibrational frequencies upon an external field, the vibrational Stark effect. The key is a proper treatment of induced dipoles. The results suggest that ligand binding occurs via an "electrostatic bond", a generalization of the standard ionic bond to include induction, and, more generally, that classical electrostatics can replace quantum mechanics for a considerable simplification of some complex problems.     

Electrostatic attraction between cationic-anionic assemblies with surface compositional heterogeneities

Electrostatics play a key role in biomolecular assembly. Oppositely charged biomolecules, for instance, can be coassembled into functional units, such as DNA and histone proteins into nucleosomes and actin-binding protein complexes into cytoskeleton components, at appropriate ionic conditions. These cationic-anionic coassemblies often have surface charge heterogeneities that result from the delicate balance between electrostatics and packing constraints. Despite their importance, the precise role of surface charge heterogeneities in the organization of cationic-anionic coassemblies is not well understood. We show here that coassemblies with charge heterogeneities strongly interact through polarization of the domains. We find that this leads to symmetry breaking, which is important for functional capabilities, and structural changes, which is crucial in the organization of coassemblies. We determine the range and strength of the attraction as a function of the competition between the steric and hydrophobic constraints and electrostatic interactions.     

Electrostatics in protein binding and function

Protein electrostatic properties stem from the proportion and distribution of polar and charged residues. Polar and charged residues regulate the electrostatic properties by forming short-range interactions, like salt-bridges and hydrogen-bonds, and by defining the over-all electrostatic environment in the protein. Electrostatics play a major role in defining the mechanisms of protein-protein complex formation, molecular recognitions, thermal stabilities, conformational adaptabilities and protein movements. For example:- Functional hinges, or flexible regions of the protein, lack short-range electrostatic interactions; Thermophilic proteins have higher electrostatic interactions than their mesophilic counter parts; Increase in binding specificity and affinity involve optimization of electrostatics; High affinity antibodies have higher, and stronger, electrostatic interactions with their antigens; Rigid parts of proteins have higher and stronger electrostatic interactions. In this review we address the significance of electrostatics in protein folding, binding and function. We discuss that the electrostatic properties are evolutionally selected by a protein to perform an specific function. We also provide bona fide examples to illustrate this. Additionally, using continuum electrostatic and molecular dynamics approaches we show that the "hot-spot" inter-molecular interactions in a very specific antibody-antigen binding are mainly established through charged residues. These "hot-spot" molecular interactions stay intact even during high temperature molecular dynamics simulations, while the other inter-molecular interactions, of lesser functional significance, disappear. This further corroborates the significance of charge-charge interactions in defining binding mechanisms. High affinity binding frequently involves "electrostatic steering". The forces emerge from over-all electrostatic complementarities and by the formation of charged and polar interactions. We demonstrate that although the high affinity binding of barnase-barstar and anti-hen egg white lysozyme (HEL) antibody-HEL complexes involve different molecular mechanisms, it is electrostatically regulated in both the cases. These observations, and several other studies, suggest that a fine tuning of local and global electrostatic properties are essential for protein binding and function.