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Conserved enzyme-substrate electrostatic attraction in prokaryotic Cu,Zn superoxide dismutases.

The catalytic activity of wild type Escherichia coli Cu,Zn superoxide dismutases and of two mutants in which two lysine residues conserved in most bacterial Cu,Zn superoxide dismutases have been replaced by serine was investigated by pulse radiolysis and Brownian dynamics simulations. Experimental and computational data show that neutralization of Lys60 strongly reduces the catalytic activity of the enzyme (approximately 50%), indicating that this residue has a primary role in the electrostatic attraction of the substrate towards the catalytic copper. Neutralization of Lys63 does not significantly influence the catalytic rate constant. The results suggest that prokaryotic Cu,Zn superoxide dismutases have evolved an electrostatic mechanism to facilitate the enzyme-substrate encounter that is functionally equivalent to that already found in the eukaryotic enzymes.

Amino Acid Sequence↗

Mechanistic basis for site-site interactions in inhibitor and substrate binding to band 3 (AE1): evidence distinguishing allosteric from electrostatic effects.

Kinetic studies suggest that stilbenedisulfonates inhibit erythrocyte anion exchange by competing with substrate anions for binding to band 3 (AE1). Such competition seems to involve site-site interactions between distinct inhibitor and substrate binding sites. The molecular basis for site-site interactions could be allosteric or electrostatic. In this paper, inhibitor binding kinetic studies are reviewed, and 35Cl(-) NMR line-broadening experiments are presented, both of which seem to rule out an electrostatic hypothesis. The results are consistent with an allosteric site-site interaction mechanism in the binding of stilbenedisulfonate and substrate anions to band 3.

4,4'-Diisothiocyanostilbene-2,2'-Disulfonic Acid↗

Apolar, Polar, and Electrostatic Interactions of Spherical Particles in Cylindrical Pores

A new Surface Element Integration (SEI) technique is developed for determination of the interaction energy of a spherical particle in a cylindrical pore based on the knowledge of the corresponding interaction energy per unit area between plane-parallel half spaces. Like the celebrated Deryaguin's approximation, the SEI can be used for any component of the interaction energy (e.g., apolar Lifshitz-van der Waals, electrostatic, polar) whenever interaction between corresponding half-spaces is known theoretically or experimentally. Accuracy of the SEI is assessed based on its comparison with the exact results for the van der Waals interaction energy. Results of the SEI are also compared with the approximate series solution for the electrostatic interaction in the Debye-Huckel approximation. While Deryaguin's approximation fails for the particle-pore geometry for small pores (<10 nm), the SEI is accurate for all realistic combinations of particle and pore radii, radial position of the particle, and decay length of interactions. Based on the SEI, the role of polar repulsion (hydration pressure) on the partitioning behavior of macromolecules across small pores is also studied. The hydration force in aqueous hydrophilic systems can lead to a significant lowering of the distribution coefficient in small pores characteristic of ultrafiltration.

Journal Article↗

Adsorption Kinetics of Ionic Surfactants with Detailed Account for the Electrostatic Interactions

The problem of diffusion-controlled adsorption from a non-micellar solution of an ionic surfactant in the absence of added electrolyte is solved analytically for the case of small deviations from equilibrium. For that purpose the electro-diffusion equations of the transport of surfactant ions and counterions are combined with the Poisson-Boltzmann equation for the electrical field. The resulting set of equations is linearized and Laplace transform is applied. Analytical expression for the Laplace image of the adsorption is obtained in terms of elementary functions. Simple formulae for the short-time and long-time asymptotics of adsorption and surface tension relaxation are derived. To illustrate the effect of the electrostatic interactions we calculated the theoretical dependence of the characteristic relaxation time on the bulk surfactant concentration and surface potential for aqueous surfactant solutions in contact with various non-aqueous phases (air, heptane, decane, petroleum ether) and two surfactants: SDS and DTAB. The general trend is that the electrostatic effects decelerate the process of adsorption, as it could be expected. The derived exact analytical expressions quantifying these effects can be directly applied for the interpretation of experimental data for the kinetics of ionic surfactant adsorption. The reliability of our approach is verified through a comparison with other available theories.

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Effect of Interparticle Electrostatic Double Layer Interactions on Permeate Flux Decline in Crossflow Membrane Filtration of Colloidal Suspensions: An Experimental Investigation.

A systematic study on the effect of electrostatic double layer interaction on permeate flux decline and deposit cake formation in crossflow membrane filtration of colloidal suspensions is reported. Three monodisperse silica suspensions with diameters of 47, 110, and 310 nm were used as model colloids, and a tubular zirconia membrane with an average pore diameter of 20 nm was used as a model membrane. The magnitude and range of the electrostatic double layer interactions were controlled via changes in solution ionic strength and pH. The coupling between colloidal interactions and hydrodynamic forces was investigated by changing the transmembrane pressure and particle size. The results indicate that the rate of flux decline is strongly dependent on solution ionic strength and, to a much lesser degree, on solution pH (for the investigated pH range 6.1-10.0). Variations in flux decline rate with solution ionic strength are especially significant as the particle size decreases. Particle cake thickness, permeability, and porosity generally increased with a decrease in solution ionic strength for a given particle size. For given physical and chemical conditions, the cake layer porosity increased with decreasing particle size, while cake permeability decreased with decreasing particle size. These trends are consistent with the increased importance of double layer repulsive forces in controlling the cake layer structure as the solution ionic strength and particle size decrease. Pressure relaxation experiments indicated that the particle cake layer is reversible, implying no irreversible deposition (attachment) of silica colloids onto the zirconia membrane surface. Copyright 1998 Academic Press.

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Electrostatic and Hydrophobic Effects of Oligopeptide Insertions on Protein Adsorption.

The effects of oligopeptide insertions on the adsorption of the protein ZZ, where Z is the IgG binding domain of staphylococcal Protein A, was investigated by in situ ellipsometry. In particular, the interplay between hydrophobic and electrostatic interactions as driving force for adsorption was investigated by studying the effects of oligopeptide insertions of the type Tn((AlaTrpTrpPro)n), Nn((AlaTrpTrpAspPro)n), and Pn((AlaTrpTrpLysPro)n) on the adsorption at silica, methylated silica, and diaminocyclohexane (DACH) plasma polymer surfaces. For comparison, the adsorption of the inserted peptide stretches was also investigated. It was found that the adsorption of all the peptides increases with the molecular weight at methylated silica. At silica, only the Pn peptides were found to adsorb. The net negatively charged proteins modified through peptide insertions did not adsorb at the hydrophilic and negatively charged silica, irrespective of the peptide insertion, whereas an extensive adsorption was found for the positively charged DACH surface for all the proteins investigated. For hydrophobic and negatively charged methylated silica, on the other hand, the peptide insertions were found to have a major influence on the protein interfacial behavior, and the adsorption followed the peptide stretch charge, thus increasing in the order ZZNn < ZZTn < ZZPn. These effects are discussed in terms of the relative importance of hydrophobic and electrostatic interactions as driving force for the adsorption. Copyright 1998 Academic Press.

Journal Article↗

Comparing Electrostatic and Nonelectrostatic Surface Complexation Modeling of the Sorption of Lanthanum on Hematite.

The sorption of lanthanum on hematite is studied in experiments for three different surface loading ratios. The experiments consist of following the evolution of the amount of cation sorbed on surface with pH, and as well as measuring the number of protons released during sorption for the three different surface loading conditions. The sorption edge shifts to high pH, and the number of protons released during sorption increases, when the surface loading increases. Three different surface complexation models (SCMs), with three different electrostatic descriptions of the interface, are used to fit the experimental sorption curves. The stoichiometries proposed by the models are compared with the measurement of the protons released. Descriptions of the interface are given by the diffuse layer model (DLM), the constant capacitance model (CCM), and a nonelectrostatic model (NEM). If the fit quality is comparable for the three models, only the electrostatic models are able to account for the dependence of stoichiometry on surface loading. On the other hand, the NEM gives the same stoichiometry, with the same number of protons released, when surface loading conditions change. This is not in agreement with experiment observations. The stoichiometries, confirmed by an independent experiment, and the value of the surface constants obtained are the same, error aside, for DLM and CCM for the three different surface loading ratios. The NEM gives different values, even if the fit quality is comparable. Copyright 1999 Academic Press.

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Role of Electrostatic Repulsion on the Viscosity of Bidisperse Silica Suspensions.

The flow behavior of bidisperse aqueous silica suspensions has been studied at different electrolyte concentrations as a function of shear rate, total volume fraction of the particles, and volume ratio of small to large particles. It is shown that the range of the electrostatic repulsion plays an important role in determining the viscosity of the suspension. Binary mixtures of particles of longer range repulsive forces showed higher viscosities than the suspensions of shorter range electrostatic interactions. Bimodal suspensions of long-range interactions showed non-Newtonian behavior over wider ranges of shear due to the deformation of the ionic cloud around the particles, which is larger in these systems. The viscosity of bimodal suspensions used in this study was scaled with respect to the viscosity of the related monosized systems and the viscosity of one bimodal suspension at a fixed total volume fraction of the particles, employing our earlier scaling method. The model normalizes the effect of colloidal forces by introducing a scaling factor that collapses the data into a single curve for bimodal suspensions of a particular size ratio, and it is shown that the model is valid for systems with both short-range and long-range repulsive forces. Copyright 1999 Academic Press.

Journal Article↗

Long-Range Electrostatic Interaction between a Charged Wall and Two Similarly Charged Colloidal Spheres at Low Surface Potentials.

The long-range electrostatic interaction between a pair of similarly charged colloidal spheres and a charged planar wall at low surface potentials is theoretically investigated. The linear Poisson-Boltzmann equation (PBE) and the point charge approximation of the charged sphere are used. The electrical potential distribution in the electrolyte solution is found from the PBE at the constant surface potentials using the image charge method. The electrostatic forces acting on the spheres are then calculated. The results show that the repulsive interaction between a pair of similarly charged colloidal spheres clearly decreases when a charged wall appears nearby, but it is impossible for an attractive force to emerge at the scaled surface potentials less than 1. There is, however, an attractive force between the charged wall and the similarly charged colloidal spheres, when the surface potential zetap on the wall is sufficiently higher than the surface potential zetas on the spheres to make zetap > zetasexp(kappah) (h is the distance from the wall to the sphere center). In this case, there are negative surface charges on the spheres at positive surface potential zetas. It is these negative charges that produce the above attraction. Copyright 1999 Academic Press.

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The Electrostatic Interactions between Two Corrugated Charged Planes.

The surfaces of association colloids often undergo undulating motion due to thermal fluctuations. The electrostatic interactions between two charged planes of arbitrary corrugation are investigated on the basis of the Poisson-Boltzmann equation under the Debye-Hückle approximation. The surfaces are parallel and subject to the spatial periodicity of the amplitude A and wavelength q(-1). When the amplitude is small compared to the wavelength, i.e., (qA)(2) << 1, the electric field can be calculated by using the perturbation method. The interaction free energy is then obtained for surfaces associated with the condition of either constant surface potential or constant surface charge density during interactions. The effects of the amplitude and phase angle on the interaction energy are discussed and asymptotic expressions are obtained when the mean separation is large compared to the amplitude. At the same mean separation, the interaction energy for the corrugated surfaces is always higher than that for the planar surfaces. In other words, undulation enhances the electrostatic repulsion. The repulsive energy is minimum when the two surfaces are in-phase and maximum for the out-of-phase mode. Copyright 1999 Academic Press.

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An Exact Solution to the Electrostatic Interaction between an Ion-Penetrable Sphere and an Ion-Penetrable Rod.

No exact solution for the free energy of electrostatic interaction for a charged sphere and rod geometry in an electrolyte solution has yet been proposed. This geometry is interesting because it can be applied to describe macromolecules interacting with a random fiber-matrix for modeling of hindered transport in diffusional systems. Here we present an analytical approach that yields an exact solution to the problem for ion-penetrable-also called "soft"-sphere and infinitely long rod. This solution is compared to a published finite-element analysis of the same system with nonpenetrable-also called "hard"-sphere and infinitely long rod maintaining a constant surface charge density restriction. For any ionic strength or ratio of rod radius to sphere radius the ion-penetrable method yields an electrostatic free energy of interaction which is lower than that given by the analysis for hard bodies. This free energy is significantly lower for most parameter value combinations and therefore suggests that one should carefully examine the system being modeled to determine if it is approximated better by a hard body or ion-penetrable body approach. Copyright 2000 Academic Press.

Journal Article↗

Electrostatic Repulsion in Concentrated Disperse Systems.

Electrostatic interactions are considered in the framework of the cell model to predict the osmotic pressure in concentrated disperse systems. A procedure was developed to represent the osmotic pressure as a function of two parameters, namely, the dispersed phase volume fraction and the electric potential attributed to the interface between the continuous and dispersed phases. The procedure is based on a general formula which was derived to express the electrostatic contribution to the osmotic pressure through the electric potential at the cell boundary. The potential of the cell boundary is predicted from the solution of the Poisson-Boltzmann problem which was specified for the cell model approach. The Poisson-Boltzmann problem is solved by a perturbation technique using a normalized interface potential as the perturbation parameter. Three leading terms were obtained in the expansion of the osmotic pressure in terms of the normalized interface potential. Two options for the formation of the interface electric potential are discussed in the analysis of the interface potential dependency on the volume fraction of the dispersed phase. The first one is associated with the difference between the individual ionic distribution coefficients characterizing the equilibrium ratio between the concentrations in the bulk of the constituent phases. The second one deals with preferential adsorption of the carriers having a given electric charge sign. The dependency of the osmotic pressure on the system parameters is discussed and interrelated with other relevant theories. Special discussion is presented concerning the theory's application for the study of hydrocarbon disperse systems, e.g., water-in-oil emulsions. Copyright 2001 Academic Press.

Journal Article↗

A Model for Calculating Electrostatic Interactions between Colloidal Particles of Arbitrary Surface Topology.

A numerical model for calculating the electrostatic interaction between two particles of arbitrary shape and topology is described. A key feature of the model is a generalized discretization program, capable of simulating any desired analytical shape as a set of flat, triangular elements. The relative sizes of the elements are adjusted using a density function to better match the desired shape and the spatial variation of the electrical surface properties on each particle. The distribution of either surface potential or surface charge density is then calculated using a boundary element approach to solve the linearized Poisson-Boltzmann equation. Example interaction energy profiles are calculated for three different types of roughness-bumps, pits, and surface waves. It is found that the interaction energy between rough particles remains different from that between two equivalent smooth spheres at all separations, even for gap widths much larger than either the solution Debye length or the characteristic roughness size. This behavior at large gap widths arises from the nature of the decay of the electric potential away from each particle. In addition, the magnitude of the roughness effect is found to depend greatly on the size and shape of the nonuniformity as well as the electrostatic boundary conditions. For example, for a sphere containing asperities of height equal to 0.2 times the particle radius, the interaction energy can be as much as 50% greater than that between two equivalent spheres under the condition of constant surface potential. At constant surface charge density, the ratio of the interaction energies between rough and smooth spheres was found to either diverge or become zero as contact between the two particles is approached, depending on the nature of the roughness. Changes of this magnitude could clearly have a substantial impact on the stability behavior of a dispersion of such particles. Copyright 2001 Academic Press.

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Simplifications of the Poisson-Boltzmann Equation for the Electrostatic Interaction of Close Hydrophilic Surfaces in Water.

Simple solutions of the Poisson-Boltzmann (PB) equation for the electrostatic double-layer interaction of close, planar hydrophilic surfaces in water are evaluated. Four routes, being the weak overlap approximation, the Debye-Hückel linearization based on low electrostatic potentials, the Ettelaie-Buscall linearization based on small variations in the potential, and a new approach based on the fact that concentrations are virtually constant in the gap between close surfaces, are discussed. The Ettelaie-Buscall and constant-concentration approach become increasingly accurate for closer surfaces and are exact for touching surfaces, while the weak overlap approximation is exact for an isolated surface. The Debye-Hückel linearization is valid as long as potentials remain low, independent of separation. In contrast to the Ettelaie-Buscall approach and the weak overlap approximation, the Debye-Hückel linearization and constant-concentration approach can also be used for systems containing multivalent ions. Simulations in which the four approaches are compared with the PB equation for the constant-charge model, the constant-potential model, as being used in the DLVO theory, and the charge-regulation model are presented. Copyright 2001 Academic Press.

Journal Article↗

Improved continuum electrostatic modelling in proteins, with comparison to experiment.

Electrostatic interactions in macromolecules can be calculated with the method of finite differences applied to a continuum model. The accuracy of dielectric and counterion continuum modelling has been tested for long-range interactions by comparison with available experimental data over a range of ionic strengths. Various model parameters have been adjusted. Some have little effect, such as protein dielectric and the selection of Van der Waals radii. It is shown that the reduction in interaction due to dielectric effects is overestimated when a dielectric constant of 80 is assigned to all solvent accessible regions. Improved agreement is seen when the effects of the Kirkwood correlation sphere and dielectric saturation are included. Further support for the use of dielectric saturation arises from a correlation of solvent polarization saturation with crystallographic ordered water structure. Calculations over the medium ionic strength range indicate that requiring counterions to maintain a solvent layer places too great a restriction on their approach to the protein-solvent interface. However, counterion accessibility that coincides with the solvent accessible region gives too much interaction damping. Modelling of observed ion binding sites suggests that a counterion response which includes an ion desolvation term, obtained by difference calculation, will improve the computation of ionic strength effects. This study demonstrates that there is scope for improvement in continuum electrostatics calculations, and shows that progress is possible with the inclusion of physically realistic solvent and counterion properties at the protein surface.

Amino Acid Sequence↗

The activity of porcine pancreatic phospholipase A2 in 20% alcohol/aqueous solvent, by experiment and electrostatics calculations.

The activity of porcine pancreatic phospholipase A2 (pla2), measured at pH 8, is reduced when methanol or ethanol is added to the aqueous solution. Finite difference electrostatics calculations were used to study the effect of modelling mixed solvents on the pKas of histidine 48 and the amino-terminal group, both of which influence the pH-dependence of catalysis. Calculations and experiment indicate that these pKa values cannot account for the activity reduction. Charge separation in the transition state is destabilized in 20% alcohol solvent relative to 100% aqueous solvent. The calculated values, which are combinations of stabilizing and destabilizing contributions, are in qualitative agreement with experiment. Saturating dielectric theory is used to model solvent water ordering in a high electric field, and water dielectric structure is assumed to dominate at the 20% alcohol level. The observed agreement demonstrates the utility of transition state stabilization theory and continuum solvent modelling. It is further suggested that electrostatic effects on kcat contribute to the pH-dependence of activity around pH 7, and to previously reported activity changes for charge mutants.

Amino Acid Sequence↗

Electrostatic mechanism of nucleosome spacing.

Native bulk chromatin is characterized by regular arrays of nucleosomes with defined internucleosomal distances. The nucleosome repeat length is not a constant but varies between species and cell-types, during differentiation and during gene activation. Previous studies have highlighted the importance of linker histones as a major determinant of nucleosome repeat length in vivo. We used a physiological reconstitution system derived from Drosophila embryos to study nucleosome spacing. In these extracts, histone H1 incorporation increases the apparent linker length in a gradual way. Manipulation of the chromatin assembly conditions in vitro allowed us to define additional parameters that modulate nucleosomal distances, such as protein phosphorylation events and the precise ionic conditions during the reconstitution. Interestingly, moderate changes in the concentrations of mono-, di-, and multivalent cations affect the precise distances between nucleosome cores remarkably. These changes in the ionic environment are unlikely to affect the association of linker proteins but are known to influence the folding of the nucleosomal fiber by modulation of electrostatic forces. Our results suggest electrostatic interactions in chromatin units as major determinants of nucleosome spacing. Nucleosome spacing and the folding of the nucleosomal fiber can therefore be explained by common principles, most notably the neutralization of charges in linker DNA.

Animals↗

Electrostatics and hydration at the homeodomain-DNA interface: chemical probes of an interfacial water cavity.

Electrostatics and hydration of a homeodomain-DNA complex are dissected by chemical modification. Selective neutralization of phosphate charges by methylphosphonate substitution demonstrates the differential importance of short- and long-range electrostatic interactions. Whereas the footprint of direct contacts is in accord with crystal structures, interference is also observed at non-contacted sites. Such sites adjoin a novel interfacial water cavity in the major groove. Non-contacted phosphodiester groups in the cavity are proposed to contribute to long-range ordering of an extended protein-water-DNA interface. Use of isolated S(p) and R(p) methylphosphonate diastereomers demonstrates that interference at this extended interface is stereoselective and charge-independent. Attenuation of protein binding presumably reflects groove-specific reorganization of bound water. Surprisingly, such attenuation can exceed that due to neutralization of a direct phosphate-side-chain salt bridge. These results support the hypothesis that hydration of an interfacial cavity functions as a non-covalent extension of the DNA surface. Stereo-specific interrogation of bound water by chemical synthesis provides a general method to assess the coupling between solvation and DNA recognition.

Bacterial Proteins↗