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PubMed1999

Charge optimization leads to favorable electrostatic binding free energy.

Variational optimization of molecular electrostatic charge distributions is a tool for the study of association reactions of molecules in solution. In principle, this method can be used in drug design and protein folding to analyze and improve molecular interactions and to provide electrostatic templates for molecular design. This optimization problem reduces to an inverse source problem in classical electrostatics, where the sources are determined by a combination of external and self-polarization potentials. In this paper, we show that the electrostatic portion of the free energy of association for electrostatically optimized molecules has an upper bound of zero in many situations of physical interest. That is, variational optimization provides a ligand-charge distribution that contributes favorably to the energetics of binding, even in a strongly polar medium. This stabilizing effect on association reactions is contrary to the usual role of electrostatics in aqueous complexes, in which desolvation effects generally dominate. We also show the existence and nonuniqueness of the variational solution and make a connection to the electrostatic image charge problem.

Biophysical Phenomena↗
PubMed2002

Removal of fine powders from film surface. I. Effect of electrostatic force on the removal efficiency.

A novel fine particle removal system composed of a corona-discharge neutralizer, a pulse-jet air unit and an image processing system has been developed. First of all, adhesion force between particle and film was directly measured and effect of electrostatic force on the adhesion force was calculated experimentally and theoretically. The electrostatic force was found to be significant, leading to the suggestion that the countermeasure for the electrostatic force was required to effectively remove fine particles. This system was then applied to the removal of fine particles from surface of a gelatin film used for conventional capsule material. The number of particles removed by the system was calculated by an image processing system and number base removal efficiency was computed with and without the elimination of electrostatic charge by the neutralizer. It was found that the difference between the removal efficiency of particles with elimination of electrostatic charge and that of without the elimination showed linear relationship with the electrostatic adhesion force. The data confirmed the necessity of electrostatic charge elimination for the effective removal of fine particles.

Chemistry, Pharmaceutical↗
PubMed2001

Modeling salt-mediated electrostatics of macromolecules: the discrete surface charge optimization algorithm and its application to the nucleosome.

Much progress has been achieved on quantitative assessment of electrostatic interactions on the all-atom level by molecular mechanics and dynamics, as well as on the macroscopic level by models of continuum solvation. Bridging of the two representations-an area of active research-is necessary for studying integrated functions of large systems of biological importance. Following perspectives of both discrete (N-body) interaction and continuum solvation, we present a new algorithm, DiSCO (Discrete Surface Charge Optimization), for economically describing the electrostatic field predicted by Poisson-Boltzmann theory using a discrete set of Debye-Hückel charges distributed on a virtual surface enclosing the macromolecule. The procedure in DiSCO relies on the linear behavior of the Poisson-Boltzmann equation in the far zone; thus contributions from a number of molecules may be superimposed, and the electrostatic potential, or equivalently the electrostatic field, may be quickly and efficiently approximated by the summation of contributions from the set of charges. The desired accuracy of this approximation is achieved by minimizing the difference between the Poisson-Boltzmann electrostatic field and that produced by the linearized Debye-Hückel approximation using our truncated Newton optimization package. DiSCO is applied here to describe the salt-dependent electrostatic environment of the nucleosome core particle in terms of several hundred surface charges. This representation forms the basis for modeling-by dynamic simulations (or Monte Carlo)-the folding of chromatin. DiSCO can be applied more generally to many macromolecular systems whose size and complexity warrant a model resolution between the all-atom and macroscopic levels.

Algorithms↗
PubMed2004

Different roles of electrostatics in heat and in cold: adaptation by citrate synthase.

Electrostatics plays a major role in heat adaptation by thermophilic proteins. Here we ask whether electrostatics similarly contributes to cold adaptation in psychrophilic proteins. We compare the sequences and structures of citrate synthases from the psychrophile Arthobacter Ds2-3R, from chicken, and from the hyperthermophile Pyrococcus furiosus. The three enzymes share similar packing, burial of nonpolar surface area, and main-chain hydrogen bonding. However, both psychrophilic and hyperthermophilic citrate synthases contain more charged residues, salt bridges, and salt-bridge networks than the mesophile. The electrostatic free-energy contributions toward protein stability by individual charged residues show greater variabilities in the psychrophilic citrate synthase than in the hyperthermophilic enzyme. The charged residues in the active-site regions of the psychrophile are more destabilizing than those in the active-site regions of the hyperthermophile. In the hyperthermophilic enzyme, salt bridges and their networks largely cluster in the active-site regions and at the dimer interface. In contrast, in the psychrophile, they are more dispersed throughout the structure. On average, salt bridges and their networks provide greater electrostatic stabilization to the thermophilic citrate synthase at 100 degrees C than to the psychrophilic enzyme at 0 degrees C. Electrostatics appears to play an important role in both heat and cold adaptation of citrate synthase. However, remarkably, the role may be different in the two types of enzyme: In the hyperthermophile, it may contribute to the integrity of both the protein dimer and the active site by possibly countering conformational disorder at high temperatures. On the other hand, in the psychrophile at low temperatures, electrostatics may contribute to enhance protein solvation and to ensure active-site flexibility.

Adaptation, Physiological↗
PubMed2006

Protonmotive force: development of electrostatic drivers for synthetic molecular motors.

Ferrocene has been investigated as a platform for developing protonmotive electrostatic drivers for molecular motors. When two 3-pyridine groups are substituted to the (rapidly rotating) cyclopentadienyl (Cp) rings of ferrocene, one on each Cp, it is shown that the (Cp) eclipsed, pi-stacked rotameric conformation is preferred both in solution and in the solid state. Upon quaternization of both of the pyridines substituents, either by protonation or by alkylation, it is shown that the preferred rotameric conformation is one where the pyridinium groups are rotated away from the fully pi-stacked conformation. Electrostatic calculations indicate that the rotation is caused by the electrostatic repulsion between the charges. Consistently, when the pi-stacking energy is increased pi-stacked population increases, and conversely when the electrostatic repulsion is increased pi-stacked population is decreased. This work serves to provide an approximate estimate of the amount of torque that the electrostatically driven ferrocene platform can generate when incorporated into a molecular motor. The overall conclusion is that the electrostatic interaction energy between dicationic ferrocene dipyridyl systems is similar to the pi-stacking interaction energy and, consequently, at least tricationic systems are required to fully uncouple the pi-stacked pyridine substituents.

Adenosine Triphosphate↗
PubMed1994

Electrostatic attraction by surface charge does not contribute to the catalytic efficiency of acetylcholinesterase.

Acetylcholinesterases (AChEs) are characterized by a high net negative charge and by an uneven surface charge distribution, giving rise to a negative electrostatic potential extending over most of the molecular surface. To evaluate the contribution of these electrostatic properties to the catalytic efficiency, 20 single- and multiple-site mutants of human AChE were generated by replacing up to seven acidic residues, vicinal to the rim of the active-center gorge (Glu84, Glu285, Glu292, Asp349, Glu358, Glu389 and Asp390), by neutral amino acids. Progressive simulated replacement of these charged residues results in a gradual decrease of the negative electrostatic potential which is essentially eliminated by neutralizing six or seven charges. In marked contrast to the shrinking of the electrostatic potential, the corresponding mutations had no significant effect on the apparent bimolecular rate constants of hydrolysis for charged and non-charged substrates, or on the Ki value for a charged active center inhibitor. Moreover, the kcat values for all 20 mutants are essentially identical to that of the wild type enzyme, and the apparent bimolecular rate constants show a moderate dependence on the ionic strength, which is invariant for all the enzymes examined. These findings suggest that the surface electrostatic properties of AChE do not contribute to the catalytic rate, that this rate is probably not diffusion-controlled and that long-range electrostatic interactions play no role in stabilization of the transition states of the catalytic process.

Acetylcholinesterase↗
PubMed2005

Electrostatic energies and forces computed without explicit interparticle interactions: a linear time complexity formulation.

A rapid method for the calculation of the electrostatic energy of a system without a cutoff is described in which the computational time grows linearly with the number of particles or charges. The inverse of the distance is approximated as a polynomial, which is then transformed into a function whose terms involve individual particles, instead of particle pairs, by a partitioning of the double sum. In this way, the electrostatic energy that is determined by the interparticle interactions is obtained without explicit calculation of these interactions. For systems of positive charges positioned on a face-centered cubic lattice, the calculation of the energy by the new method is shown to be faster than the calculation of the exact energy, in many cases by an order of magnitude, and to be accurate to within 1-2%. The application of this method to increase the accuracy of conventional truncation-based calculations in condensed-phase systems is also demonstrated by combining the approximated long-range electrostatic interactions with the exact short-range interactions in a "hybrid" calculation. For a 20-A sphere of water molecules, the forces are shown to be six times as accurate using this hybrid method as those calculated with conventional truncation of the electrostatic energy function at 12 A. This is accomplished with a slight increase in speed, and with a sevenfold increase in speed relative to the exact all-pair calculation. Structures minimized with the hybrid function are shown to be closer to structures minimized with an exact all-pair electrostatic energy function than are those minimized with a conventional 13-A cutoff-based electrostatic energy function. Comparison of the energies and forces calculated with the exact method illustrate that the absolute errors obtained with standard truncation can be very large. The extension of the current method to other pairwise functions as well as to multibody functions, is described.

Algorithms↗
PubMed1992

Electrostatic interactions in the association of proteins: an analysis of the thrombin-hirudin complex.

The role of electrostatic interactions in stabilization of the thrombin-hirudin complex has been investigated by means of two macroscopic approaches: the modified Tanford-Kirkwood model and the finite-difference method for numerical solution of the Poisson-Boltzmann equations. The electrostatic potentials around the thrombin and hirudin molecules were asymmetric and complementary, and it is suggested that these fields influence the initial orientation in the process of the complex formation. The change of the electrostatic binding energy due to mutation of acidic residues in hirudin has been calculated and compared with experimentally determined changes in binding energy. In general, the change in electrostatic binding energy for a particular mutation calculated by the modified Tanford-Kirkwood approach agreed well with the experimentally observed change. The finite-difference approach tended to overestimate changes in binding energy when the mutated residues were involved in short-range electrostatic interactions. Decreases in binding energy caused by mutations of amino acids that do not make any direct ionic interactions (e.g., Glu 61 and Glu 62 of hirudin) can be explained in terms of the interaction of these charges with the positive electrostatic potential of thrombin. Differences between the calculated and observed changes in binding energy are discussed in terms of the crystal structure of the thrombin-hirudin complex.

Amino Acid Sequence↗
PubMed2005

Design of improved protein inhibitors of HIV-1 cell entry: Optimization of electrostatic interactions at the binding interface.

Continuum electrostatic methods are a powerful tool for the analysis and design of biomolecular complexes, with methodologies that allow for the detailed analysis of the electrostatic contributions to binding affinities and procedures for computing the properties of electrostatically optimal ligands. We have applied these methods to the design of improved inhibitors of HIV-1 cell entry. HIV infection of a cell requires viral-cell membrane fusion, an event partially driven by a large-scale conformational change in the viral membrane glycoprotein gp41. This transformation involves the docking of a helix from the C-terminal region of three gp41 chains against a pre-formed trimeric-coiled coil; several protein constructs that inhibit membrane fusion act by binding to an isolated C-terminal helix and blocking the formation of the fusogenic structure. A detailed analysis of the electrostatic contributions to the binding of one such inhibitor (5-Helix) to a C-terminal helix was performed using the X-ray crystal structure of the core of the HIV-1 gp41 ectodomain as a structural model, and several residues on 5-Helix that make substantial contributions to binding, both favorable and unfavorable, were identified. An electrostatic affinity optimization methodology was applied to the side chains of 5-Helix, with the results showing that significant improvements in binding affinity are possible if the electrostatic contributions to the binding free energy are optimized. Several mutations accessible by experimental methods are suggested, with calculated improvements in binding affinity of as much as 500-fold and greater.

Amino Acid Sequence↗
PubMed1994

Electrostatic complementarity between proteins and ligands. 3. Structural basis.

Electrostatic potential complementarity between ligands and their receptor sites is evaluated by the superposition of the electrostatic potential, generated by the receptor, onto the ligand potential over the ligand van der Waals surface. We would like to examine which structural factors generate this pattern of superposition. Example studies suggest that in many ligand-protein pairs, there exist principal formal charges on each molecule, largely responsible for the electrostatic potential complementarity observed. Electrostatic potential complementarity depends on the relative disposition of these principal charges and the ligand van der Waals surface. Simple mathematical models were constructed to predict the complementarity solely from structural considerations. The essential conditions for electrostatic potential complementarity were elucidated. These can be used in ligand design strategies to obtain an electrostatically optimal ligand.

Amino Acid Sequence↗
PubMed1992

Ligand atom partial charges assignment for complementary electrostatic potentials.

The design of molecules to fit into the active site of receptors is a rapidly developing area of pharmacology and medicinal chemistry. A good ligand needs a suitable geometry and also appropriate electrostatic properties. The electrostatic properties of the ligand should complement those of the receptor. We present a method for the assignment of atom-centred point charges for a ligand, based on the electrostatic potential of the receptor. These point charges are chosen to give the best possible complementarity to the receptor electrostatic potential over the van der Waals surface of the ligand. We demonstrate that point charges can be chosen to give good electrostatic complementarity, and suggest that a molecule with similar electrostatic properties should bind well to the receptor.

Binding Sites↗
PubMed1991

On the representation of electrostatic fields around ab initio charge distributions.

We compare two methods (Mulliken charges and a distributed multipole analysis, DMA) of representing an ab initio charge distribution for calculating the electrostatic field and potential outside the molecule, using pyrimidine and the RNA base uracil as examples. This is done using a 3-D graphical display of the electrostatic fields, which, when used with real-time rotation, zooming and clipping, has many advantages for qualitatively assessing the electrostatic interactions of a molecule. The errors involved in using Mulliken point charges may be of similar magnitude to the total electrostatic field in regions which are important in recognition processes. The DMA representation automatically includes the anisotropic electrostatic effects of non-spherical features in the charge distribution of each atom, and yet the displayed electrostatic fields around the atoms which have lone-pair density do not show marked anisotropy.

Chemical Phenomena↗
PubMed1998

Investigating the dielectric effects of channel pore water on the electrostatic barriers of the permeation ion by the finite difference Poisson-Boltzmann method.

In this paper, the finite difference Poisson-Boltzmann (FDPB) method with four dielectric constants is developed to study the effect of dielectric saturation on the electrostatic barriers of the permeation ion. In this method, the inner shape of the channel pore is explicitly represented, and the fact that the dielectric constant inside the channel pore is different from that of bulk water is taken into account. A model channel system which is a righthanded twist bundle with four alpha-helical segments is provided for this study. From the FDPB calculations, it is found that the difference of the ionic electrostatic solvation energy for wider domains depends strongly on the pore radius in the vicinity of the ion when the pore dielectric constant is changed from 78 to 5. However, the electrostatic solvation energy of the permeation ion can not be significantly affected by the dielectric constant in regions with small pore radii. Our results indicate that the local electrostatic interactions inside the ion channel are of major importance for ion electrostatic solvation energies, and the effect of dielectric saturation on the electrostatic barriers is coupled to the interior channel dimensions.

Amino Acid Sequence↗
PubMed1990

Visualization of molecular flexibility and its effects on electrostatic recognition.

To study the effect of protein flexibility on electrostatic recognition, we have devised two novel computer graphic representations of the changes in the electrostatic field of a protein resulting from its internal motions. The atomic structure of Cu, Zn superoxide dismutase was minimized, and the 200 lowest frequency normal modes of the enzyme were determined. Individual and combined normal-mode vibrations were visualized interactively with the program Flex. Normal-mode motions are fast enough (approximately 10(-11) s cycle-1) to evade solvent damping, thus allowing long-range electrostatic interactions to dominate. The changing electrostatic environment of the protein was examined by animating precalculated frames of electrostatic field vectors with GRAMPS. With Vu, changes in electrostatic potential were displayed as variations in the color-coding of dots lying on a consensus surface that maintains the protein's shape. The consensus surface was calculated with the program Sphinx, and was derived from spherical harmonic approximations of expanded molecular surfaces. The ability to view the effects of molecular motions interactively should be useful in understanding the relationships of protein structure to function.

Computer Graphics↗
PubMed1988

Is the activity-linked electrostatic gradient of bovine Cu, Zn superoxide dismutases conserved in homologous enzymes irrespective of the number and distribution of charges?

Electrostatic potential calculations have been performed on three different Cu, Zn superoxide dismutases (superoxide: superoxide oxidoreductase, EC 1.15. 1.1), in order to evaluate the degree of conservation of the pattern of electrostatic interactions between O2- and the active site recently pointed out in bovine Cu Zn SOD. The three Cu, Zn SODs that have been selected for this study, namely the bovine, ovine, and porcine enzymes, are highly homologous as to reasonably assume identical three-dimensional structure but display large differences in their net charge, as shown by their pI's, which span over a wide pH range: 8.0 (sheep), 6.5 (pig), 5.2 (ox). Despite such a large difference in the net protein charge and in the spatial arrangement of electrostatic charges, electrostatic potential calculations show that the electrostatic channel directing the negatively charged substrate toward the positive catalytic site is strictly preserved with the same features for the three proteins. This suggests that the electrostatic funnel for conducting small anions into the active site is a highly conservative property in the evolution of Cu, Zn SOD.

Animals↗
PubMed2002

Relationship between ion pair geometries and electrostatic strengths in proteins.

The electrostatic free energy contribution of an ion pair in a protein depends on two factors, geometrical orientation of the side-chain charged groups with respect to each other and the structural context of the ion pair in the protein. Conformers in NMR ensembles enable studies of the relationship between geometry and electrostatic strengths of ion pairs, because the protein structural contexts are highly similar across different conformers. We have studied this relationship using a dataset of 22 unique ion pairs in 14 NMR conformer ensembles for 11 nonhomologous proteins. In different NMR conformers, the ion pairs are classified as salt bridges, nitrogen-oxygen (N-O) bridges and longer-range ion pairs on the basis of geometrical criteria. In salt bridges, centroids of the side-chain charged groups and at least a pair of side-chain nitrogen and oxygen atoms of the ion-pairing residues are within a 4 A distance. In N-O bridges, at least a pair of the side-chain nitrogen and oxygen atoms of the ion-pairing residues are within 4 A distance, but the distance between the side-chain charged group centroids is greater than 4 A. In the longer-range ion pairs, the side-chain charged group centroids as well as the side-chain nitrogen and oxygen atoms are more than 4 A apart. Continuum electrostatic calculations indicate that most of the ion pairs have stabilizing electrostatic contributions when their side-chain charged group centroids are within 5 A distance. Hence, most (approximately 92%) of the salt bridges and a majority (68%) of the N-O bridges are stabilizing. Most (approximately 89%) of the destabilizing ion pairs are the longer-range ion pairs. In the NMR conformer ensembles, the electrostatic interaction between side-chain charged groups of the ion-pairing residues is the strongest for salt bridges, considerably weaker for N-O bridges, and the weakest for longer-range ion pairs. These results suggest empirical rules for stabilizing electrostatic interactions in proteins.

Biophysical Phenomena↗
PubMed2003

Electrostatic tuning of permeation and selectivity in aquaporin water channels.

Water permeation and electrostatic interactions between water and channel are investigated in the Escherichia coli glycerol uptake facilitator GlpF, a member of the aquaporin water channel family, by molecular dynamics simulations. A tetrameric model of the channel embedded in a 16:0/18:1c9-palmitoyloleylphosphatidylethanolamine membrane was used for the simulations. During the simulations, water molecules pass through the channel in single file. The movement of the single file water molecules through the channel is concerted, and we show that it can be described by a continuous-time random-walk model. The integrity of the single file remains intact during the permeation, indicating that a disrupted water chain is unlikely to be the mechanism of proton exclusion in aquaporins. Specific hydrogen bonds between permeating water and protein at the channel center (at two conserved Asp-Pro-Ala "NPA" motifs), together with the protein electrostatic fields enforce a bipolar water configuration inside the channel with dipole inversion at the NPA motifs. At the NPA motifs water-protein electrostatic interactions facilitate this inversion. Furthermore, water-water electrostatic interactions are in all regions inside the channel stronger than water-protein interactions, except near a conserved, positively charged Arg residue. We find that variations of the protein electrostatic field through the channel, owing to preserved structural features, completely explain the bipolar orientation of water. This orientation persists despite water translocation in single file and blocks proton transport. Furthermore, we find that for permeation of a cation, ion-protein electrostatic interactions are more unfavorable at the conserved NPA motifs than at the conserved Arg, suggesting that the major barrier against proton transport in aquaporins is faced at the NPA motifs.

Aquaporins↗
PubMed2004

Anion pathway and potential energy profiles along curvilinear bacterial ClC Cl- pores: electrostatic effects of charged residues.

X-ray structures permit theoretical study of Cl(-) permeation along bacterial ClC Cl(-) pores. We determined the lowest energy curvilinear pathway, identified anion-coordinating amino acids, and calculated the electrostatic potential energy profiles. We find that all four bacterial ClC Cl(-) crystal structures correspond to closed states. E148 and S107 side chains form steric barriers on both sides of the crystal binding site in the StClC wild-type and EcClC wild-type crystals; both the EcClC(E148A) and EcClC(E148Q) mutants are blocked at the S107 site. We studied the effect that mutating the charge of some strongly conserved pore-lining amino acids has on the electrostatic potential energy profiles. When E148 is neutralized, it creates an electrostatic trap, binding the ion near midmembrane. This suggests a possible electrostatic mechanism for controlling anion flow: neutralize E148, displace the side chain of E148 from the pore pathway to relieve the steric barrier, then trap the anion at midmembrane, and finally either deprotonate E148 and block the pore (pore closure) or bring a second Cl(-) into the pore to promote anion flow (pore conductance). Side-chain displacement may arise by competition for the binding site between the oxygens of E148 and the anion moving down the electrostatic energy gradient. We also find that the charge state of E111 and E113 may electrostatically control anion conductance and occupancy of the binding site within the cytoplasmic pore.

Amino Acid Substitution↗