Electrostatics of a simple membrane model using Green''s functions formalism.

The electrostatics of a simple membrane model picturing a lipid bilayer as a low dielectric constant slab immersed in a homogeneous medium of high dielectric constant (water) can be accurately computed using the exact Green's functions obtainable for this geometry. We present an extensive discussion of the analysis and numerical aspects of the problem and apply the formalism and algorithms developed to the computation of the energy profiles of a test charge (e.g., ion) across the bilayer and a molecular model of the acetylcholine receptor channel embedded in it. The Green's function approach is a very convenient tool for the computer simulation of ionic transport across membrane channels and other membrane problems where a good and computationally efficient first-order treatment of dielectric polarization effects is crucial.     

Photogating of ionic currents across lipid bilayers. Electrostatics of ions and dipoles inside the membrane.

The conductances of the lipophilic ions tetraphenylboride and tetraphenylphosphonium across a lipid bilayer can be increased or decreased, i.e., gated, by the photoformation of closed-shell metalloporphyrin cations within the bilayer. The gating can be effected by pulsed or continuous light or by chemical oxidants. At high concentrations of lipophilic anions where the dark conductance is saturated due to space charge in the bilayer, the photogated conductance can increase 15-fold. The formation of porphyrin cations allows the conductance to increase to its nonspace charge limited value. Conversely, the decrease of conductance in the light of phosphonium cations diminishes toward zero as the dark conductance becomes space charge limited. We present electrostatic models of the space charge limited conductance that accurately fit the data. One model includes an exponentially varying dielectric constant for the polar regions of the bilayer that allows an analytical solution to the electrostatic problem. The exponential variation of the dielectric constant effectively screens the potential and implies that the inside and outside of real dielectric interfaces can be electrically isolated from one another. The charge density, the distance into the membrane of the ions, about one-quarter of its thickness, and the dielectric constant at that position are determined by these models. These calculations indicate that there is insufficient porphyrin charge density to cancel the boride ion space charge and the following article proposes a novel ion chain mechanism to explain these effects. These models indicate that the positive potential arising from oriented carbonyl ester groups, previously used to explain the 10(3)-fold larger conductance of hydrophobic anions over cations, is smaller than previously estimated. However, the synergistic movement of the positive choline group into the membrane can account for the large positive potential.     

Electrostatics and electrodynamics of bacteriorhodopsin.

The stationary electric dichroism of bacteriorhodopsin is in qualitative, but not quantitative, agreement with the orientation function for disks having a permanent dipole directed perpendicular to the plane and an induced dipole in the plane. Fits of the orientation function to data measured at low field strengths demonstrate: an increase of the permanent dipole moment mu with the square of the disk radius r2, whereas the polarizability alpha increases with r4; the ionic strength dependence is small for mu and clearly stronger for alpha; the permanent dipole moment is 4x10(6) D at r = 0.5 micron. According to the risetime constants, the induced dipole does not saturate and increases to 4x10(8) D at 40 kV/cm and r = 0.5 micron. The data indicate that the permanent dipole is not of some interfacial character but is due to a real assymetry of the charge distribution. The experimental dipole moment per protein monomer is approximately 55 D, whereas calculations based on the structure of Grigorieff et al. (Grigorieff, N., T.A. Ceska, K.H. Downing, J.M. Baldwin, and R. Henderson. 1996. Electron-crystallographic refinement of the structure of bacteriorhodopsin. J. Mol. Biol. 259:393-421) provide a dipole moment of approximately 570 D. The difference is probably due to a nonsymmetric distribution of charged lipid residues. It is concluded that experimental dipole moments reflect the mu-potential at the plane of shear for rotational diffusion, in analogy to the sigma-potential used for translational diffusion. It is suggested that the permanent dipole of bacteriorhodopsin supports proton transport by attraction of protons inside and repulsion of protons outside of the cell. Dichroism rise curves at field strengths between E = 150 and 800 V/cm reveal an exponential component with time constants tau 3r in the range between 1 and 40 ms, which is not found in Brownian dynamics simulations on a disk structure using hydrodynamic and electric parameters characteristic of bacteriorhodopsin disks. The experimental data suggest that this process reflects a cooperative change of the bacteriorhodopsin structure, which is induced already at a remarkably low field strength of approximately 150 V/cm.     

Electrostatics of lipid bilayer bending.

The electrostatic contribution to spontaneous membrane curvature is calculated within Poisson-Boltzmann theory under a variety of assumptions and emphasizing parameters in the physiological range. Asymmetrical surface charges can be fixed with respect to bilayer midplane area or with respect to the lipid-water area, but induce curvatures of opposite signs. Unequal screening layers on the two sides of a vesicle (e.g., multivalent cationic proteins on one side and monovalent salt on the other) also induce bending. For reasonable parameters, tubules formed by electrostatically induced bending can have radii in the 50-100-nm range, often seen in many intracellular organelles. Thus membrane associated proteins may induce curvature and subsequent budding, without themselves being intrinsically curved. Furthermore, we derive the previously unexplored effects of respecting the strict conservation of charge within the interior of a vesicle. The electrostatic component of the bending modulus is small under most of our conditions and is left as an experimental parameter. The large parameter space of conditions is surveyed in an array of graphs.     

Glycolipid modulation of membrane adhesion

A novel test of carbohydrate-mediated adhesion has been developed. At the tips of two syringes, large spherical model membranes have been made from phosphatidylcholine and varying amounts of mixed brain gangliosides dissolved inn-decane. The apposition of two such membranes resulted in adhesion, not fusion, as judged by the absence of fluorescence mixing in the junction with NBD-phosphatidylethanolamine in one membrane and perylene in the other. Adhesion was observed without gangliosides. The rate of formation of the adhesion area (rate of adhesion) was unchanged from 0 to 0.8 mol% gangliosides. A slightly lower but constant rate was observed within the physiological range from 2 to 10 mol%. Adhesion was frequently blocked at 11 to 15 mol% gangliosides. The rate of adhesion with pure gangliosides increased with the number of sialic acid residues: G_T1>G_D1a>G_M1. These results are interpreted in terms of a sialic acid-dependent segregation of gangliosides into the adhesion zone.     

ERM proteins in cell adhesion and membrane dynamics.

Ezrin, radixin and moesin, collectively known as the ERM proteins, are a group of closely related membrane-cytoskeleton linkers that regulate cell adhesion and cortical morphogenesis. ERM proteins can self-associate through intra- and inter-molecular interactions, and these interactions mask several binding sites on the proteins. ERM activation involves unfolding of the molecule, and allows the protein to bind to plasma membrane components either directly, or indirectly through linker proteins. The discovery that the tumour-suppressor NF2, also known as merlin/schwannomin, is related to ERM proteins has added a new impetus to investigations of their roles. This review discusses current understanding of the structure and function of members of the ERM family of proteins.     

Electrostatics of Polymorphic DNA

Abstract

The molecular electrostatic potential (MEP) and the molecular electrostatic field (MEF) are associated with significantly different patterns of distribution in the nucleic acids and their constituents. In particular, a) while the values of the minimal potentials at the reactive sites of the bases or at the phosphates increase manyfold when going from the subunits to the double helix, the values of the field undergo only very small changes under the same circumstances and b) while the deepest potentials are located in the grooves of the double helix, the greatest fields are concentrated on the phosphates of the backbone. They are also influenced differently by such environmental factors as counterion screening: while the absolute values of the potentials are profoundly reduced, the fields are increased with respect to those of the unscreened acids. MEP and MEF also govern the electrostatics of interaction of DNA with different types of species. The MEP being of particular significance in this respect for interaction with cations and the MEF for the association with neutral dipolar molecules. A number of examples are given to illustrate the significance of this situation for different conformers of DNA.     

Electrostatics of Cytochrome-c assemblies

Electrostatic potentials along with computational mutagenesis are used to obtain atomic level insights into Cytochrome-c in order to design efficient bionanosensors. The electrostatic properties of wild type and mutant Cytochrome-c are examined in the context of their assembly, i.e. are examined in the absence and presence of neighboring molecules from the assembly. An intense increase in the positive potential ensues when the neighboring molecules are taken into account. This suggests that in the extrapolation of electric field effects upon the design of assemblies, considering the properties of only the central molecule may not be sufficient. Additionally, the influence of the uncharged residues becomes quite diminished when the molecule is considered in an assembly. This could pave the way for making mutants that might be more soluble in different media used in the construction of devices.FigureThe electrostatic potential, calculated using the program DELPHI [20] mapped on to the surface of Cytochrome-c when it is considered by itself (in the left column) and in the presence of the electrostatic field generated by the presence of the surrounding 4 molecules on the right (see Fig. 3). The potentials range from –10kT in red to +10kT in blue. The central figure shows the regions that have been mutated to positively charged residues by placing a unit positive charge at the terminal atom of the respective side chain. The figures range from the wild type in the first row, followed by the Gln12, Asn70, Asp50, Glu90 and Ala83 mutants.     

Electrostatics of moving plasma

The stability of charge distribution over the surface of a conducting body in moving plasma is analyzed. Using a finite-width plate streamlined by a cold neutralized electron flow as an example, it is shown that an electrically neutral body can be unstable against the development of spontaneous polarization. The plasma parameters at which such instability takes place, as well as the frequency and growth rate of the fundamental mode of instability, are determined.     

Integrin-mediated adhesion regulates membrane order

The properties of cholesterol-dependent domains (lipid rafts) in cell membranes have been controversial. Because integrin-mediated cell adhesion and caveolin both regulate trafficking of raft components, we investigated the effects of adhesion and caveolin on membrane order. The fluorescent probe Laurdan and two-photon microscopy revealed that focal adhesions are highly ordered; in fact, they are more ordered than caveolae or domains that stain with cholera toxin subunit B (CtxB). Membrane order at focal adhesion depends partly on phosphorylation of caveolin1 at Tyr14, which localizes to focal adhesions. Detachment of cells from the substratum triggers a rapid, caveolin-independent decrease in membrane order, followed by a slower, caveolin-dependent decrease that correlates with internalization of CtxB-stained domains. Endocytosed CtxB domains also become more fluid. Thus, membrane order is highly dependent on caveolae and focal adhesions. These results show that lipid raft properties are conferred by assembly of specific protein complexes. The ordered state within focal adhesions may have important consequences for signaling at these sites.     

Isolation and partial characterization of membrane vesicles carrying markers of the membrane adhesion sites.

At areas of adhesion between outer membrane (OM) and inner membrane (IM) in gram-negative bacteria, newly synthesized membrane constituents are inserted, and bacteriophage infection occurs. We describe here the isolation of these sites from cell membrane fractions of Salmonella anatum. Sucrose density gradients yielded membrane vesicles of the OM and IM; their mutual cross-contamination was low, as measured by 2-keto-3-deoxyoctonate and beta-NADH-oxidase activities. To mark the areas of lipopolysaccharide synthesis in the envelope (the adhesion sites), we infected S. anatum with phage epsilon 15, which causes a rapid change (conversion) in the cell's O-antigenic composition from serogroup E1 to E2; lipopolysaccharide of type E2 also serves as receptor for phage epsilon 34. We found that the fractions of intermediate density (Int. M) from briefly converted cells bound both phage epsilon 34 and E2-specific antibody. In the electron microscope, epsilon 34 was seen to have absorbed with a high degree of significance to the Int. M fraction of briefly converted cells, but not to the Int. M fraction of unconverted cells. Furthermore, the Int. M fractions of briefly converted cells coagglutinated anti-E2-coated Staphylococcus aureus, whereas the OM and IM fractions showed comparatively little agglutination. In addition, Int. M material exhibited elevated phospholipase A1 and A2 activities comparable to those of the OM fraction; the IM was essentially phospholipase free. Our data indicate that this membrane fractionation allows one to isolate from Int. M regions a variety of activities associated with adhesion sites.     

Electrostatics of Polymorphic DNA

The molecular electrostatic potential (MEP) and the molecular electrostatic field (MEF) are associated with significantly different patterns of distribution in the nucleic acids and their constituents. In particular, a) while the values of the minimal potentials at the reactive sites of the bases or at the phosphates increase manyfold when going from the subunits to the double helix, the values of the field undergo only very small changes under the same circumstances and b) while the deepest potentials are located in the grooves of the double helix, the greatest fields are concentrated on the phosphates of the backbone. They are also influenced differently by such environmental factors as counterion screening: while the absolute values of the potentials are profoundly reduced, the fields are increased with respect to those of the unscreened acids. MEP and MEF also govern the electrostatics of interaction of DNA with different types of species. The MEP being of particular significance in this respect for interaction with cations and the MEF for the association with neutral dipolar molecules. A number of examples are given to illustrate the significance of this situation for different conformers of DNA.     

Electrostatics and the ion selectivity of ligand-gated channels.

The nicotinic acetylcholine receptor (nAChR) is a cation-selective ion channel that opens in response to acetylcholine binding. The related glycine receptor (GlyR) is anion selective. The pore-lining domain of each protein may be modeled as a bundle of five parallel M2 helices. Models of the pore-lining domains of homopentameric nAChR and GlyR have been used in continuum electrostatics calculations to probe the origins of ion selectivity. Calculated pKA values suggest that "rings" of acidic or basic side chains at the mouths of the nAChR or GlyR M2 helix bundles, respectively, may not be fully ionized. In particular, for the nAChR the ring of glutamate side chains at the extracellular mouth of the pore is predicted to be largely protonated at neutral pH, whereas those glutamate side chains in the intracellular and intermediate rings (at the opposite mouth of the pore) are predicted to be fully ionized. Inclusion of the other domains of each protein represented as an irregular cylindrical tube in which the M2 bundles are embedded suggests that both the M2 helices and the extramembrane domains play significant roles in determining ion selectivity.     

Electrostatics in the active site of an alpha-amylase.

The importance of electrostatics in catalysis has been emphasized in the literature for a large number of enzymes. We examined this hypothesis for the Bacillus licheniformis alpha-amylase by constructing site-directed mutants that were predicted to change the pKa values of the catalytic residues and thus change the pH-activity profile of the enzyme. To change the pKa of the catalytic residues in the active site, we constructed mutations that altered the hydrogen bonding network, mutations that changed the solvent accessibility, and mutations that altered the net charge of the molecule. The results show that changing the hydrogen bonding network near an active site residue or changing the solvent accessibility of an active site residue will very likely result in an enzyme with drastically reduced activity. The differences in the pH-activity profiles for these mutants were modest. pH-activity profiles of mutants which change the net charge on the molecule were significantly different from the wild-type pH-activity profile. The differences were, however, difficult to correlate with the electrostatic field changes calculated. In several cases we observed that pH-activity profiles shifted in the opposite direction compared to the shift predicted from electrostatic calculations. This strongly suggests that electrostatic effects cannot be solely responsible for the pH-activity profile of the B. licheniformis alpha-amylase.     

Electrostatics of a peptide at a membrane/water interface. The pH dependence of melittin association with lipid vesicles

The association of the peptide melittin with small unilamellar DMPC vesicles was studied as a function of pH. The results are discussed quantitatively assuming a water-membrane partition equilibrium. Electrostatic surface charging is taken into account as more and more of the strongly basic peptide accumulates at the bilayer/water interface. The data could be well described in terms of a Gouy-Chapman approach involving an effective interfacial charge well below the actual physical charge carried by the individual peptide molecules. The partition coefficient turned out to be pH invariant, so that one can exclude deprotonation reactions upon insertion of the peptide into the bilayer. The effective interfacial charge per associated melittin molecule decreased over a broad range of pH (pH 7 to pH above 10). Contributions of the free amino terminus and of the arginine residues could be determined by comparing with results obtained using modified melittin (N-terminally formylated and fully acetylated). The data suggest approximately equal fractional contributions of the amino terminus and the three lysines to the effective interfacial charge. The two arginines contribute less. Thus, they may be located farther away from the interface or be closely associated with counter-ions. The analysis is extended to the effect of different ionic strengths.     

Electrostatics of phosphoinositide bilayer membranes. Theoretical and experimental results.

We made fluorescence, electron paramagnetic resonance (EPR), electrophoretic mobility, and ionizing electrode measurements to study the effect of the monovalent lipid phosphatidylinositol (PI) and the trivalent lipid phosphatidylinositol 4,5-bisphosphate (PIP2) on the electrostatic potential adjacent to bilayer membranes. When the membranes were formed from mixtures of PI and the zwitterionic lipid phosphatidylcholine (PC), the Gouy-Chapman-Stern (GCS) theory described adequately the dependence of potential on distance (0, 1, 2 nm) from the membrane, mole % negative lipid, and [KCI]. Furthermore, all EPR and fluorescence probes reported identical surface potentials with a PC/PI membrane. With PC/PIP2 membranes, however, the anionic (coion) probes reported less negative potentials than the cationic (counterion) probes; the deviations from the GCS theory were greater for the coions than the counterions. Discreteness-of-charge theories based on the Poisson-Boltzmann equation incorrectly predict that deviations from the GCS theory should be greater for counterions than for coions. We discuss a consistent statistical mechanical theory that takes into account three effects ignored in the GCS theory: the finite size of the ions in the double layer, the electrical interaction between pairs of ions (correlation effects), and the mobile discrete nature of the surface charges. This theory correctly predicts that deviations from GCS theory should be negligible for monovalent lipids, significant for trivalent lipids, and greater for coions than for counterions.     

Electrostatics dominate quadruplex stability

Stabilization of nucleic acid structures results from a balance of multiple interactions, including electrostatics, base stacking, hydrophobic interactions, hydrogen bonding, van der Waals forces, etc. Nucleic acid quadruplexes are unusual structures in that their formation is driven by specific binding of metal ions. This unique mode of metal binding, which is tightly coupled to oligonucleotide folding, can engender correspondingly unique solution behavior. In particular, we show that addition of many cosolvents, such as primary aliphatic alcohols, increases the thermal stability of quadruplexes, as determined by melting temperature, Tm, in direct contrast to the response of duplexes to the same admixture of solvents. Thermal stability is observed to increase as the dielectric constant of the composite solvent decreases. This behavior suggests a dominant role for electrostatics in quadruplex formation and stability. Additional studies done with other cosolvents and solutes suggest that, in some cases, other forces may come into play, including the possibility of direct interaction with the quadruplex structure. Nonetheless, many cosolvents and small molecules, such as ethanol, dimethylformamide, and betaine, stabilize the quadruplex conformation in sharp distinction to their destabilization of DNA duplexes.     

Electrostatics in computational protein design

Catalytic activity and protein-protein recognition have proven to be significant challenges for computational protein design. Electrostatic interactions are crucial for these and other protein functions, and therefore accurate modeling of electrostatics is necessary for successfully advancing protein design into the realm of protein function. This review focuses on recent progress in modeling electrostatic interactions in computational protein design, with particular emphasis on continuum models.