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Electrostatic model of S4 motion in voltage-gated ion channels.

The S4 transmembrane domain of the family of voltage-gated ion channels is generally thought to be the voltage sensor, whose translocation by an applied electric field produces the gating current. Experiments on hSkMI Na(+) channels and both Shaker and EAG K(+) channels indicate which S4 residues cross the membrane-solution interface during activation gating. Using this structural information, we derive the steady-state properties of gating-charge transfer for wild-type and mutant Shaker K(+) channels. Assuming that the energetics of gating is dominated by electrostatic forces between S4 charges and countercharges on neighboring transmembrane domains, we calculate the total energy as a function of transmembrane displacement and twist of the S4 domain. The resulting electrostatic energy surface exhibits a series of deep energy minima, corresponding to the transition states of the gating process. The steady-state gating-charge distribution is then given by a Boltzmann distribution among the transition states. The resulting gating-charge distributions are compared to experimental results on wild-type and charge-neutralized mutants of the Shaker K(+) channel.

Amino Acid Sequence↗

Molecular dynamics simulations of lipid bilayers: major artifacts due to truncating electrostatic interactions.

We study the influence of truncating the electrostatic interactions in a fully hydrated pure dipalmitoylphosphatidylcholine (DPPC) bilayer through 20 ns molecular dynamics simulations. The computations in which the electrostatic interactions were truncated are compared to similar simulations using the particle-mesh Ewald (PME) technique. All examined truncation distances (1.8-2.5 nm) lead to major effects on the bilayer properties, such as enhanced order of acyl chains together with decreased areas per lipid. The results obtained using PME, on the other hand, are consistent with experiments. These artifacts are interpreted in terms of radial distribution functions g(r) of molecules and molecular groups in the bilayer plane. Pronounced maxima or minima in g(r) appear exactly at the cutoff distance indicating that the truncation gives rise to artificial ordering between the polar phosphatidyl and choline groups of the DPPC molecules. In systems described using PME, such artificial ordering is not present.

1,2-Dipalmitoylphosphatidylcholine↗

Electrostatic sequestration of PIP2 on phospholipid membranes by basic/aromatic regions of proteins.

The basic effector domain of myristoylated alanine-rich C kinase substrate (MARCKS), a major protein kinase C substrate, binds electrostatically to acidic lipids on the inner leaflet of the plasma membrane; interaction with Ca2+/calmodulin or protein kinase C phosphorylation reverses this binding. Our working hypothesis is that the effector domain of MARCKS reversibly sequesters a significant fraction of the L-alpha-phosphatidyl-D-myo-inositol 4,5-bisphosphate (PIP2) on the plasma membrane. To test this, we utilize three techniques that measure the ability of a peptide corresponding to its effector domain, MARCKS(151-175), to sequester PIP2 in model membranes containing physiologically relevant fractions (15-30%) of the monovalent acidic lipid phosphatidylserine. First, we measure fluorescence resonance energy transfer from Bodipy-TMR-PIP2 to Texas Red MARCKS(151-175) adsorbed to large unilamellar vesicles. Second, we detect quenching of Bodipy-TMR-PIP2 in large unilamellar vesicles when unlabeled MARCKS(151-175) binds to vesicles. Third, we identify line broadening in the electron paramagnetic resonance spectra of spin-labeled PIP2 as unlabeled MARCKS(151-175) adsorbs to vesicles. Theoretical calculations (applying the Poisson-Boltzmann relation to atomic models of the peptide and bilayer) and experimental results (fluorescence resonance energy transfer and quenching at different salt concentrations) suggest that nonspecific electrostatic interactions produce this sequestration. Finally, we show that the PLC-delta1-catalyzed hydrolysis of PIP2, but not binding of its PH domain to PIP2, decreases markedly as MARCKS(151-175) sequesters most of the PIP2.

Amino Acid Sequence↗

A physical method for deriving the electrostatic interaction between rod-like polyions at all mutual angles.

The screened Coulomb interaction between polyelectrolyte cylinders immersed in an ionic bath is examined. The electrostatic force and torque acting between a pair of unlike rods is formulated for all separations in which the electrostatic potential on some dividing surface between rods can be written as a linear superposition of isolated cylinder potentials. (The surface potential on the rods themselves may be much higher than that permitted by a superposition approximation.) The mutual energy in the case of skewed rods is found to be exponential in separation and proportional to 1/sin theta where theta is the twist angle of one rod relative to the other. Rods with similar charge repel each other with a torque acting to make the rods perpendicular while rods of opposite charge attract with the parallel arrangement preferred.

Binding Sites↗

Electrostatic stabilization in sperm whale and harbor seal myoglobins. Identification of groups primarily responsible for changes in anchoring of the A helix.

The compact, largely helical structure of sperm whale and harbor seal myoglobins undergoes an abrupt one-step transition between pH 4.5 and 3.5 as monitored by changes in either the heme Soret band absorbance or circular dichroism probes of secondary structure, for which a modified Tanford-Kirkwood theory provides identification of certain dominant electrostatic interactions responsible for the loss of stability. A similar treatment permits identification of the electrostatic interactions primarily responsible for a process in which the anchoring of the A helix to other parts of the molecule is weakened. This process is detected with both myoglobins, in a pH range approximately 1 unit higher than the onset of the overall unfolding process, through changes in the circular dichroic spectra near 295 nm which correspond to the L1 O-O band of the only two tryptophan residues in these proteins, residues 7 and 14. In each case protonation of certain sites in neighboring parts of the molecule can be identified as producing destabilizing interactions with components of the A helix, particularly with lysine 6.

Animals↗

Effects of monovalent ion binding and screening on measured electrostatic forces between charged phospholipid bilayers.

In an effort to determine the role that monovalent ions play in the modification of intermembrane forces, we have measured these forces between charged phospholipid bilayers in monovalent ionic solutions. The osmotic stress technique allowed the net electrostatic pressure between the bilayers to be measured while their separation was concurrently determined by x-ray diffraction. Taken together, these measurements yielded electrostatic pressure as a function of bilayer separation. We have related measured pressures to the bilayer surface charge density and surface potential through an exact solution of the full nonlinear Poisson-Boltzmann equation for this system. Quantitative differences in bilayer separation amongst monovalent alkali metal cations indicated differential binding of these to phosphatidylglycerol (PG), phosphatidylserine (PS), and phosphatidic acid (PA); binding affinity series were determined for Li+, Na+, K+, Cs+, and TMA+ ions to these lipids. The anions Cl-, Br-, I-, and CH3COO- were found to have no differential effect on the repulsive forces between PS bilayers. Debye lengths for the electric double layer estimated from the slopes of the experimental pressure curves were consistently longer than predicted on the basis of classic Gouy-Chapman theory. Estimates of the van der Waals Hamaker coefficient between bilayers of PS and PG in salt solution were found to be weaker than between phosphatidylcholine bilayers in pure water, a difference possibly due to electromagnetic retardation and ionic screening.

Animals↗

Electrostatic free energy of lysozyme.

The electrostatic free energies of native and acetylated lysozymes were computed by the fixed charge model (Tanford, C., and J. G. Kirkwood, 1957, J. Am. Chem. Soc., 79:5333-5339). For each computation, the charges were transformed into a sphere of fixed radius without changing their depths or the distance between charges. The depths of charges were assumed proportional to one minus accessibility. When the conversion factor was set to 1.62 A, the computed titration curve fitted best to the experimental data. The calculated electrostatic free energies for native and acetylated lysozymes were consistent with our earlier finding that acetylated lysozyme is less stable than native around neutral pH (Imoto, T., K. Fukuda, and K. Yagishita, 1976, J. Biochem. [Tokyo], 80:1313-1318; Imoto, T., S. Moriyama, and K. Yagishita, 1976, J. Biochem. [Tokyo], 80:1319-1325). The contribution of each charge to the stabilization of the protein and the apparent pK's of ionizable groups were computed by this method.

Animals↗

Red blood cells experience electrostatic repulsion but make molecular adhesions with glass.

We have studied the detachment of unfixed red cells from glass coverslips under unit gravity and by centrifugation in buffered isotonic solutions over a range of ionic strengths. Cell-glass contact areas and separation distances were measured by quantitative interference reflection microscopy. Detachment under unit gravity is highly dependent on ionic strength: dilution increases electrostatic repulsion and greatly reduces the proportion of adherent cells. However, even at 1.5 mM some cells stick. Over the range 3-110 mM such adherent cells are progressively removed by increasing centrifugal forces, but in a manner virtually independent of ionic strength. This fact, together with the irreversibility of pre-adherent cells as ionic strength is progressively reduced, as well as the resistance of cells to lateral shearing forces, provide evidence sufficient to reject the notion of secondary minimum adhesion for unfixed cells at any ionic strength down to 1.5 mM. We conclude that all unfixed cells that stick at ionic strengths from 157 to 1.5 mM make molecular contacts with glass. Comparison with long range force calculations suggests that to penetrate the electrostatic repulsion barrier the contact regions are unlikely to have average surface properties. A new method that compares frequency distributions of contact areas with responses to detachment forces shows that detachment forces are not linearly related to contact areas. This lack of relationship is less clearly evident for rigid glutaraldehyde-fixed cells and may therefore depend on the degree of cellular deformability.

Cell Adhesion↗

Electrostatic radius of the gramicidin channel determined from voltage dependence of H+ ion conductance.

The results of Decker and Levitt (1987) suggest that the conductance of H+ ion through the gramicidin channel is limited primarily by diffusion in the bulk solution at the channel mouth. It is assumed in this paper that the H+ conductance is 100% diffusion limited. This means that all the factors that influence the H+ flux are external to the channel and are presumed to be known. In particular, the diffusion coefficient of H+ in this region is assumed to be equal to the bulk solution value and the only force acting on the ion is that due to the applied voltage. A model of the H+ flux is derived, based on the Nernst-Planck equation. It has three adjustable parameters: the electrostatic radius, the capture distance, and the radius of the H+ ion. The acceptable range of the parameters was determined by comparing the predictions of the model with the experimental measurements of the H+ conductance at pH 3.75. The best fit was obtained for an electrostatic radius in the range 2.3-2.7 A. This is in good agreement with earlier predictions (2.5 A) based on the assumption that the dielectric constant of the channel water is equal to that of bulk water. The addition of 1 M choline Cl- (an impermeant) increases the H+ current at low voltage and decreases it at high voltage. The increase can be explained by the small surface charge that results from the separation of charge produced by exclusion of the large choline cation (relative to Cl-) from the membrane surface. The decrease at high voltages can be accounted for by the change in the profile of the applied potential produced by the increase in ionic strength.

Diffusion↗

Asymmetric electrostatic effects on the gating of rat brain sodium channels in planar lipid membranes.

The effects of ionic strength (10-1,000 mM) on the gating of batrachotoxin-activated rat brain sodium channels were studied in neutral and in negatively charged lipid bilayers. In neutral bilayers, increasing the ionic strength of the extracellular solution, shifted the voltage dependence of the open probability (gating curve) of the sodium channel to more positive membrane potentials. On the other hand, increasing the intracellular ionic strength shifted the gating curve to more negative membrane potentials. Ionic strength shifted the voltage dependence of both opening and closing rate constants of the channel in analogous ways to its effects on gating curves. The voltage sensitivities of the rate constants were not affected by ionic strength. The effects of ionic strength on the gating of sodium channels reconstituted in negatively charged bilayers were qualitatively the same as in neutral bilayers. However, important quantitative differences were noticed: in low ionic strength conditions (10-150 mM), the presence of negative charges on the membrane surface induced an extra voltage shift on the gating curve of sodium channels in relation to neutral bilayers. It is concluded that: (a) asymmetric negative surface charge densities in the extracellular (1e-/533A2) and intracellular (1e-/1,231A2) sides of the sodium channel could explain the voltage shifts caused by ionic strength on the gating curve of the channel in neutral bilayers. These surface charges create negative electric fields in both the extracellular and intracellular sides of the channel. Said electric fields interfere with gating charge movements that occur during the opening and closing of sodium channels; (b) the voltage shifts caused by ionic strength on the gating curve of sodium channels can be accounted by voltage shifts in both the opening and closing rate constants; (c) net negative surface charges on the channel's molecule do not affect the intrinsic gating properties of sodium channels but are essential in determining the relative position of the channel's gating curve; (d) provided the ionic strength is below 150 mM, the gating machinery of the sodium channel molecule is able to sense the electric field created by surface changes on the lipid membrane. I propose that during the opening and closing of sodium channels, the gating charges involved in this process are asymmetrically displaced in relation to the plane of the bilayer. Simple electrostatic calculations suggest that gating charge movements are influenced by membrane electrostatic potentials at distances of 48 and 28 A away from the plane of the membrane in the extracellular sides of the channel, respectively.

Animals↗

Effective pore radius of the gramicidin channel. Electrostatic energies of ions calculated by a three-dielectric model.

Electrostatic calculation of the gramicidin channel is performed on the basis of a three-dielectric model in which the peptide backbone of the channel is added as a third dielectric region to the conventional two-dielectric channel model (whose pore radius is often referred to as the effective pore radius reff). A basic principle for calculating electrostatic fields in three-dielectric models is introduced. It is shown that the gramicidin channel has no unique value of reff. The reff with respect to the "self-image energy" (i.e., the image energy in the presence of a single ion) is 2.6-2.7 A, slightly depending upon the position of the ion (the least-square value over the whole length of the pore is 2.6 A). In contrast, the reff with respect to the electric potential due to an ion (and hence the reff with respect to the interaction energy between two ions) is dependent upon the distance s of separation; it ranges from 2.6 to greater than 5 A, increasing with an increase in s. However, for the purpose of rough estimation, the reff with respect to the self-image energy can also be used in calculating the electric potential and the interaction energy, because the error introduced by this approximation is an overestimation of the order of 30% at most. It is also shown that the apparent dielectric constant for the interaction between two charges depends markedly upon the positions of the charges. In the course of this study, the dielectric constant and polarizability of the peptide backbone in the beta-sheet structure is estimated to be 10 and 8.22 A3.

Electrochemistry↗

Structural investigation of the covalent and electrostatic binding of yeast cytochrome c to the surface of various ultrathin lipid multilayers using x-ray diffraction.

X-Ray diffraction was used to characterize the profile structures of ultrathin lipid multilayers having a bound surface layer of cytochrome c. The lipid multilayers were formed on an alkylated glass surface, using the Langmuir-Blodgett method. The ultrathin lipid multilayers of this study were: five monolayers of arachidic acid, four monolayers of arachidic acid with a surface monolayer of dimyristoyl phosphatidylserine, and four monolayers of arachidic acid acid with a surface monolayer of thioethyl stearate. Both the phosphatidylserine and the thioethyl stearate surfaces were found previously to covalently bind yeast cytochrome c, while the arachidic acid surface electrostatically binds yeast cytochrome c. Meridional x-ray diffraction data were collected from these lipid multilayer films with and without a bound yeast cytochrome c surface layer. A box refinement technique, previously shown to be effective in deriving the profile structures of ultrathin multilayer lipid films with and without electrostatically bound cytochrome c, was used to determine the multilayer electron density profiles. The surface monolayer of bound cytochrome c was readily apparent upon comparison of the multilayer electron density profiles for the various pairs of ultrathin multilayer films plus/minus cytochrome c for all cases. In addition, cytochrome c binding to the multilayer surface significantly perturbs the underlying lipid monolayers.

Cytochrome c Group↗

Strong electrostatic loop-helix interactions in bundle motif protein structures.

Based on CHARMM potential (Brooks et al., 1983) an energetic analysis has been carried out for four typical 4-alpha-helix bundle proteins, i.e., methemerythrin, cytochrome b-562, cytochrome c', and bovine somatotropin. The bovine somatotropin possesses long loops, but all the other three proteins have short loops. It was found that in all these four 4-alpha-helix bundle motif structures the interaction between loops and helices was much stronger than the interaction among the four helices themselves. Particularly for the electrostatic interaction energy, the loop-helix interaction is overwhelmingly stronger than the interhelix interaction although the latter involves the favorable helix dipole interaction due to the antiparallel arrangement of neighboring alpha-helices. The present study indicates that such a conclusion holds true regardless of what loops, long or short, are in the 4-alpha-helix bundle protein, and also regardless of which empirical potential, ECEPP or CHARMM, is used for calculations although in CHARMM the electrostatic energy is much more heavily emphasized than in ECEPP. Therefore, no appropriate conclusion can be drawn in arguing whether the dipole interaction among the four alpha-helices play a stabilizing role or destabilizing role for a 4-alpha-helix bundle protein without taking into consideration the effect of interaction between helices and loops. The calculated results reported here provide, from a different point of view, insights that might be useful for revealing the essence of the driving forces during the folding of proteins.

Animals↗

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.

Biophysical Phenomena↗

Determination of electrostatic potentials at biological interfaces using electron-electron double resonance.

A new general method for the determination of electrostatic potentials at biological surfaces is presented. The approach is based on measurement of the collision frequency of a charged nitroxide in solution with a nitroxide fixed to the surface at the point of interest. The collision frequency is determined with 14N:15N double label electron-electron double resonance (ELDOR). As a test, the method is shown to give values for phospholipid bilayer surface potentials consistent with the Gouy-Chapman theory, a simple model shown by many independent tests to accurately describe charged, planar surfaces. In addition, the method is applied to determine the electrostatic potential near the surface of DNA. The results indicate that the potential is significantly smaller than that predicted from Poisson-Boltzmann analysis, but is in qualitative agreement with that predicted by Manning's theory of counter ion condensation. The method is readily extended to measurement of surface potentials of proteins.

Aminacrine↗

Internal electrostatic potentials in bilayers: measuring and controlling dipole potentials in lipid vesicles.

The binding and translocation rates of hydrophobic cation and anion spin labels were measured in unilamellar vesicle systems formed from phosphatidylcholine. As a result of the membrane dipole potential, the binding and translocation rates for oppositely charged hydrophobic ions are dramatically different. These differences were analyzed using a simple electrostatic model and are consistent with the presence of a dipole potential of approximately 280 mV in phosphatidylcholine. Phloretin, a molecule that reduces the magnitude of the dipole potential, increases the translocation rate of hydrophobic cations, while decreasing the rate for anions. In addition, phloretin decreases the free energy of binding of the cation, while increasing the free energy of binding for the anion. The incorporation of 6-ketocholestanol also produces differential changes in the binding and translocation rates of hydrophobic ions, but in an opposite direction to those produced by phloretin. This is consistent with the view that 6-ketocholestanol increases the magnitude of the membrane dipole potential. A quantitative analysis of the binding and translocation rate changes produced by ketocholestanol and phloretin is well accounted for by a point dipole model that includes a dipole layer due to phloretin or 6-ketocholestanol in the membrane-solution interface. This approach allows dipole potentials to be estimated in membrane vesicle systems and permits predictable, quantitative changes in the magnitude of the internal electrostatic field in membranes. Using phloretin and 6-ketocholestanol, the dipole potential can be altered by over 200 mV in phosphatidylcholine vesicles.

Anions↗

Boundary element solution of macromolecular electrostatics: interaction energy between two proteins.

The boundary element technique is implemented to solve for the electrostatic potential of macromolecules in an ionic solution. This technique entails solving surface integral equations that are equivalent to the Poisson and the Poisson-Boltzmann equations governing the electrostatic potential inside the macromolecules and and in the solvent. A simple but robust method is described for discretizing the macromolecular surfaces in order to approximate the integral equations by linear algebraic equations. Particular attention is paid to the interaction energy between two macromolecules, and an iterative procedure is devised to make the calculation more efficient. This iterative procedure is illustrated in the electron transfer system of cytochrome c and cytochrome c peroxidase.

Cytochrome c Group↗

Molecular electrostatic potentials from crystal diffraction: the neurotransmitter gamma-aminobutyric acid.

Given the electronic charge parameters obtained from a diffraction study of the charge density distribution in a crystal, a mathematical procedure is presented for deriving the electrostatic potential. The procedure allows the mapping of electrostatic potential for a molecule or group of molecules removed from the crystal structure but with each molecule retaining the effects of polarization owing to the original crystal environment. The method is applied for the neurotransmitter gamma-aminobutyric acid. The potential for a gamma-aminobutyric acid molecule is analyzed in terms of a simple model that is suitable for rapid computations concerned with Coulombic molecular interactions. Outside the molecular envelope at 1.2 A from the atomic nuclei, the total potential is well represented by a sum of spherical atom contributions with V(r) = (q/r) + exp(-beta r2). The most important aspherical component in the potential is the dipole contribution from the hydrogen atoms. This can be represented as V(r, phi) = (0.162 cos phi)/(r2 + 0.615). Here, V is in e/A, r is the distance from each nucleus in A, q is the experimentally determined net atomic charge in electron units, and phi is the angle between r and the bond X-H. We obtain beta = 1.47, 1.66, 1.83 A-2 for C, N, and O respectively. For H, no term in beta is needed.

Biophysical Phenomena↗