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PubMed1993

Probes of membrane electrostatics: synthesis and voltage-dependent partitioning of negative hydrophobic ion spin labels in lipid vesicles.

Two spin-labeled derivatives of the hydrophobic anion trinitrophenol have been synthesized and characterized in lipid vesicles. In the presence of lipid vesicles, the electron paramagnetic resonance (EPR) spectra of these probes are a composite of both membrane-bound and aqueous populations; as a result, the membrane-aqueous partitioning can be determined from their electron paramagnetic resonance spectra. The effect of transmembrane potentials on the membrane-aqueous partitioning of these spin-labeled hydrophobic ions was examined in phosphatidylcholine vesicles formed by extrusion. Inside positive membrane potentials promote an increase in the binding of these probes that is quantitatively accounted for by a simple thermodynamic model used previously to describe the partitioning of paramagnetic phosphonium ions. The transmembrane migration rates of these ions are dependent on the dipole potential, indicating that these ions transit the membrane in a charged form. The partitioning of the probe is also sensitive to the membrane surface potential, and this dependence is accurately accounted for using the Gouy-Chapman Stern formalism. As a result of the membrane dipole potential, these probes exhibit a stronger binding and a more rapid transmembrane migration rate compared with positive hydrophobic ion spin labels and provide a new set of negatively charged hydrophobic ion probes to investigate membrane electrostatics.

Biophysical Phenomena↗
PubMed1993

Torque and switching in the bacterial flagellar motor. An electrostatic model.

A model is presented for the rotary motor that drives bacterial flagella, using the electrochemical gradient of protons across the cytoplasmic membrane. The model unifies several concepts present in previous models. Torque is generated by proton-conducting particles around the perimeter of the rotor at the base of the flagellum. Protons in channels formed by these particles interact electrostatically with tilted lines of charges on the rotor, providing "loose coupling" between proton flux and rotation of the flagellum. Computer simulations of the model correctly predict the experimentally observed dynamic properties of the motor. Unlike previous models, the motor presented here may rotate either way for a given direction of the protonmotive force. The direction of rotation only depends on the level of occupancy of the proton channels. This suggests a novel and simple mechanism for the switching between clockwise and counterclockwise rotation that is the basis of bacterial chemotaxis.

Bacterial Physiological Phenomena↗
PubMed1994

An electrostatic spatial resonance model for coaxial helical structures with applications to the filamentous bacteriophages.

A model is presented that treats the symmetry matching problem in structures made of two interacting coaxial helices of point charges. The charges are sources of a potential field that mediates a non-specific attractive interaction between the helices. The problem is represented in Fourier space, which affords the most generality. It is found that coaxial helices with optimally mated symmetries can lock into spatial resonance configurations that maximize their interaction. The resonances are represented as vectors in a discrete three-dimensional space. Two algebraic relations are given for the four symmetry parameters of two helices in resonance. One-start inner helices interacting with coaxial one-start or NR-start outer helices are considered. Applications are made to the filamentous bacteriophages Ff, Pf1, Xf, and Pf3. The interaction given by the linearized Poisson-Boltzmann equation is calculated in this formalism to allow comparison of the electrostatic free energy of interaction of different resonance structures. Experimental nucleotide/subunit ratios are accounted for, and models for the DNA-protein interfaces are presented, with particular emphasis on Pf1.

Amino Acid Sequence↗
PubMed1994

Electrostatic forces contribute to interactions between trp repressor dimers.

The trp repressor of Escherichia coli (TR), although generally considered to be dimeric, has been shown by fluorescence anisotropy of extrinsically labeled protein to undergo oligomerization in solution at protein concentrations in the micromolar range (Fernando, T., and C. A. Royer 1992. Biochemistry. 31:3429-3441). Providing evidence that oligomerization is an intrinsic property of TR, the present studies using chemical cross-linking, analytical ultracentrifugation, and molecular sieve chromatography demonstrate that unmodified TR dimers form higher order aggregates. Tetramers and higher order species were observed in chemical cross-linking experiments at concentrations between 1 and 40 microM. Results from analytical ultracentrifugation and gel filtration chromatography were consistent with average molecular weight values between tetramer and dimer, although no plateaus in the association were evident over the concentration ranges studied, indicating that higher order species are populated. Analytical ultracentrifugation data in presence of corepressor imply that corepressor binding destabilizes the higher order aggregates, an observation that is consistent with the earlier fluorescence work. Through the investigation of the salt and pH dependence of oligomerization, the present studies have revealed an electrostatic component to the interactions between TR dimers.

Bacterial Proteins↗
PubMed1995

Electrostatics of hemoglobins from measurements of the electric dichroism and computer simulations.

Hemoglobins from normal human cells, from sickle cells, and from horse were investigated by electrooptical methods in their oxy and deoxy forms. The reduced linear dichroism measured as a function of the electric field strength demonstrates the existence of permanent dipole moments in the range of 250-400 Debye units. The reduced limiting dichroism is relatively small (< or = 0.1); it is negative for hemoglobin from sickle cells and positive for the hemoglobins from normal human cells and from horse. The dichroism decay time constants are in the range from about 55 to 90 ns. Calculations of the electrooptical data from available crystal structures are given according to models of various complexity, including Monte Carlo simulations of proton fluctuations with energies evaluated by a finite difference Poisson-Boltzmann procedure. The experimental dipole moments are shown to be consistent with the results of the calculations. In the case of human deoxyhemoglobin, the root mean square dipole is higher than the mean dipole by a factor of about 4.5, indicating a particularly large relative contribution due to proton fluctuations. The ratio of the root mean square dipole to the mean dipole is much smaller (approximately 1.1 to approximately 1.5) for the other hemoglobin molecules. The calculations demonstrate that the dichroism decay time constants are not simply determined by the size/shape of the proteins, but are strongly influenced by the orientation of the dipole vector with respect to the axis of maximal absorbance. The comparison of experimental and calculated electrooptical data provides a useful test for the accuracy of electrostatic calculations and/or for the equivalence of structures in crystals and in solutions.

Animals↗
PubMed1995

Calculations of the electrostatic potential adjacent to model phospholipid bilayers.

We used the nonlinear Poisson-Boltzmann equation to calculate electrostatic potentials in the aqueous phase adjacent to model phospholipid bilayers containing mixtures of zwitterionic lipids (phosphatidylcholine) and acidic lipids (phosphatidylserine or phosphatidylglycerol). The aqueous phase (relative permittivity, epsilon r = 80) contains 0.1 M monovalent salt. When the bilayers contain < 11% acidic lipid, the -25 mV equipotential surfaces are discrete domes centered over the negatively charged lipids and are approximately twice the value calculated using Debye-Hückel theory. When the bilayers contain > 25% acidic lipid, the -25 mV equipotential profiles are essentially flat and agree well with the values calculated using Gouy-Chapman theory. When the bilayers contain 100% acidic lipid, all of the equipotential surfaces are flat and agree with Gouy-Chapman predictions (including the -100 mV surface, which is located only 1 A from the outermost atoms). Even our model bilayers are not simple systems: the charge on each lipid is distributed over several atoms, these partial charges are non-coplanar, there is a 2 A ion-exclusion region (epsilon r = 80) adjacent to the polar headgroups, and the molecular surface is rough. We investigated the effect of these four factors using smooth (or bumpy) epsilon r = 2 slabs with embedded point charges: these factors had only minor effects on the potential in the aqueous phase.

Biophysical Phenomena↗
PubMed1996

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.

Animals↗
PubMed1996

Electrostatic coupling between retinal isomerization and the ionization state of Glu-204: a general mechanism for proton release in bacteriorhodopsin.

The pKa values of ionizable groups that lie between the active site region of bacteriorhodopsin (bR) and the extracellular surface of the protein are reported. Glu-204 is found to have an elevated pKa in the resting state of bR, suggesting that it corresponds to the proton-releasing group in bR. Its elevated pKa is predicted to be due in part to strong repulsive interactions with Glu-9. Following trans-cis isomerization of the retinal chromophore and the transfer of a proton to Asp-85, polar groups on the protein are able to interact more strongly with the ionized state of Glu-204, leading to a substantial reduction of its pKa. This suggests a general mechanism for proton release in which isomerization and subsequent charge separation initially produce a new electrostatic balance in the active site of bR. Here it is proposed that those events in turn drives a conformational change in the protein in which the ionized state of Glu-204 can be stabilized through interactions with groups that were previously inaccessible. Whether these groups should be identified with polar moieties in the protein, bound waters, or Arg-82 is an important mechanistic question whose elucidation will require further study.

Bacteriorhodopsins↗
PubMed1997

Electrostatic binding of proteins to membranes. Theoretical predictions and experimental results with charybdotoxin and phospholipid vesicles.

We previously applied the Poisson-Boltzmann equation to atomic models of phospholipid bilayers and basic peptides to calculate their electrostatic interactions from first principles (Ben-Tal, N., B. Honig, R. M. Peitzsch, G. Denisov, and S. McLaughlan. 1996. Binding of small basic peptides to membranes containing acidic lipids. Theoretical models and experimental results. Biophys. J. 71:561-575). Specifically, we calculated the molar partition coefficient, K (the reciprocal of the lipid concentration at which 1/2 the peptide is bound), of simple basic peptides (e.g., pentalysine) with phospholipid vesicles. The theoretical predictions agreed well with experimental measurements of the binding, but the agreement could have been fortuitous because the structure(s) of these flexible peptides is not known. Here we use the same theoretical approach to calculate the membrane binding of two small proteins of known structure: charybdotoxin (CTx) and iberiotoxin (IbTx); we also measure the binding of these proteins to phospholipid vesicles. The theoretical model describes accurately the dependence of K on the ionic strength and mol % acidic lipid in the membrane for both CTx (net charge +4) and IbTx (net charge +2). For example, the theory correctly predicts that the value of K for the binding of CTx to a membrane containing 33% acidic lipid should decrease by a factor of 10(5) when the salt concentration increases from 10 to 200 mM. We discuss the limitations of the theoretical approach and also consider a simple extension of the theory that incorporates nonpolar interactions.

Biophysical Phenomena↗
PubMed1997

Computation of molecular electrostatics with boundary element methods.

In continuum approaches to molecular electrostatics, the boundary element method (BEM) can provide accurate solutions to the Poisson-Boltzmann equation. However, the numerical aspects of this method pose significant problems. We describe our approach, applying an alpha shape-based method to generate a high-quality mesh, which represents the shape and topology of the molecule precisely. We also describe an analytical method for mapping points from the planar mesh to their exact locations on the surface of the molecule. We demonstrate that derivative boundary integral formulation has numerical advantages over the nonderivative formulation: the well-conditioned influence matrix can be maintained without deterioration of the condition number when the number of the mesh elements scales up. Singular integrand kernels are characteristics of the BEM. Their accurate integration is an important issue. We describe variable transformations that allow accurate numerical integration. The latter is the only plausible integral evaluation method when using curve-shaped boundary elements.

Biophysical Phenomena↗
PubMed1997

Electrostatic effects on electron-transfer kinetics in the cytochrome f-plastocyanin complex.

In a complex of two electron-transfer proteins, their redox potentials can be shifted due to changes in the dielectric surroundings and the electrostatic potentials at each center caused by the charged residues of the partner. These effects are dependent on the geometry of the complex. Three different docking configurations (DCs) for intracomplex electron transfer between cytochrome f and plastocyanin were studied, defined by 1) close contact of the positively charged region of cytochrome f and the negatively charged regions of plastocyanin (DC1) and by (2, 3) close contact of the surface regions adjacent to the Fe and Cu redox centers (DC2 and DC3). The equilibrium energetics for electron transfer in DC1-DC3 are the same within approximately +/-0.1 kT. The lower reorganization energy for DC2 results in a slightly lower activation energy for this complex compared with DC1 and DC3. The long heme-copper distance (approximately 24 A) in the DC1 complex drastically decreases electronic coupling and makes this complex much less favorable for electron transfer than DC2 or DC3. DC1-like complexes can only serve as docking intermediates in the pathway toward formation of an electron-transfer-competent complex. Elimination of the four positive charges arising from the lysine residues in the positive patch of cytochrome f, as accomplished by mutagenesis, exerts a negligible effect (approximately 3 mV) on the redox potential difference between cyt f and PC.

Biophysical Phenomena↗
PubMed1997

Theoretical study of the electrostatic and steric effects on the spectroscopic characteristics of the metal-ligand unit of heme proteins. 2. C-O vibrational frequencies, 17O isotropic chemical shifts, and nuclear quadrupole coupling constants.

The quantum chemical calculations, vibronic theory of activation, and London-Pople approach are used to study the dependence of the C-O vibrational frequency, 17O isotropic chemical shift, and nuclear quadrupole coupling constant on the distortion of the porphyrin ring and geometry of the CO coordination, changes in the iron-carbon and iron-imidazole distances, magnitude of the iron displacement out of the porphyrin plane, and presence of the charged groups in the heme environment. It is shown that only the electrostatic interactions can cause the variation of all these parameters experimentally observed in different heme proteins, and the heme distortions could modulate this variation. The correlations between the theoretically calculated parameters are shown to be close to the experimentally observed ones. The study of the effect of the electric field of the distal histidine shows that the presence of the four C-O vibrational bands in the infrared absorption spectra of the carbon monoxide complexes of different myoglobins and hemoglobins can be caused by the different orientations of the different tautomeric forms of the distal histidine. The dependence of the 17O isotropic chemical shift and nuclear quadrupole coupling constant on pH and the distal histidine substitution can be also explained from the same point of view.

Carbon Monoxide↗
PubMed1998

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.

Amino Acid Sequence↗
PubMed1998

Evaluation of the electrostatic field strength at the site of exocytosis in adrenal chromaffin cells.

Exocytosis in secretory cells consists of release from intracellular storage granules directly into the extracellular space via fusion of the granule membrane with the plasma membrane of the cell. It is considered here as comprising two distinct processes. One is the close apposition of granule and plasma membranes. The other arises from interactions between the two membranes during the process of apposition, leading to the formation of a fusion pore. In the following it is shown for the case of the adrenal medullary chromaffin cell that the fusion pore can be ascribed to electroporation of the granule membrane, triggered by the strong electric field existing at the site of exocytosis. Based on an electric surface charge model of the cytoplasmic side of the plasma membrane, resulting from the negatively charged phosphatidylserine groups, it is found that the electrostatic field strength at the site of exocytosis reaches values on the order of 10(8) V/m at small intermembrane distances of 3 nm and lower. The field strength increases with the size of the disc-shaped plasma membrane region generating the electric field, reaching an approximate limit for a radius of 10 nm, at a surface charge density of 5.4 x 10(-2) C/m2. According to previous experimental evaluations of threshold field strength, this field is sufficiently strong to cause membrane electroporation. This step is a precondition for the subsequent membrane fusion during the ongoing process of apposition, leading to secretion.

Animals↗
PubMed1998

Anomalous mole fraction effect, electrostatics, and binding in ionic channels.

Ionic channels bathed in mixed solutions of two permeant electrolytes often conduct less current than channels bathed in pure solutions of either. For many years, this anomalous mole fraction effect (AMFE) has been thought to occur only in single-file pores containing two or more ions at a time. Most thinking about channels incorporates this view. We show here that the AMFE arises naturally, as an electrostatic consequence of localized ion specific binding, if the average current through a channel is described by a theory (Poisson-Nernst-Planck, PNP) that computes the average electric field from the average concentration of charges in and near the channel. The theory contains only those ion-ion interactions mediated by the mean field, and it does not enforce single filing. The AMFE is predicted by PNP over a wide range of mean concentrations of ions in the channel; for example, it is predicted when (on the average) less, or much less, than one ion is found in the channel's pore. In this treatment, the AMFE arises, in large measure, from a depletion layer produced near a region of ion-specific binding. The small excess concentration of ions in the binding region repels all nearby ions of like charge, thereby creating a depletion layer. The overall conductance of the channel arises in effect from resistors in series, one from the binding region, one from the depletion zone, and one from the unbinding region. The highest value resistor (which occurs in the depletion zone) limits the overall series conductance. Here the AMFE is not the result of single filing or multiple occupancy, and so previous views of permeation need to be revised: the presence of an AMFE does not imply that ions permeate single file through a multiply occupied pore.

Binding Sites↗
PubMed1998

Formation of giant liposomes promoted by divalent cations: critical role of electrostatic repulsion.

Spontaneous formation of giant unilamellar liposomes in a gentle hydration process, as well as the adhesion energy between liposomal membranes, has been found to be dependent on the concentration of divalent alkali cations, Ca2+ or Mg2+, in the medium. With electrically neutral phosphatidylcholine (PC), Ca2+ or Mg2+ at 1-30 mM greatly promoted liposome formation compared to low yields in nonelectrolyte or potassium chloride solutions. When negatively charged phosphatidylglycerol (PG) was mixed at 10%, the yield was high in nonelectrolytes but liposomes did not form at 3-10 mM CaCl2. In the adhesion test with micropipette manipulation, liposomal membranes adhered to each other only in a certain range of CaCl2 concentrations, which agreed with the range where liposome did not form. The adhesion range shifted to higher Ca2+ concentrations as the amount of PG was increased. These results indicate that the divalent cations bind to and add positive charges to the lipids, and that membranes are separated and stabilized in the form of unilamellar liposomes when net charges on the membranes produce large enough electrostatic repulsion. Under the assumption that the maximum of adhesion energy within an adhesive range corresponds to exact charge neutralization by added Ca2+, association constants of PC and PG for Ca2+ were estimated at 7.3 M(-1) and 86 M(-1), respectively, in good agreement with literature values.

Calcium↗
PubMed1999

A self-consistent, microenvironment modulated screened coulomb potential approximation to calculate pH-dependent electrostatic effects in proteins.

An improved approach is presented for calculating pH-dependent electrostatic effects in proteins using sigmoidally screened Coulomb potentials (SCP). It is hypothesized that a key determinant of seemingly aberrant behavior in pKa shifts is due to the properties of the unique microenvironment around each residue. To help demonstrate this proposal, an approach is developed to characterize the microenvironments using the local hydrophobicity/hydrophilicity around each residue of the protein. The quantitative characterization of the microenvironments shows that the protein is a complex mosaic of differing dielectric regions that provides a physical basis for modifying the dielectric screening functions: in more hydrophobic microenvironments the screening decreases whereas the converse applies to more hydrophilic regions. The approach was applied to seven proteins providing more than 100 measured pKa values and yielded a root mean square deviation of 0.5 between calculated and experimental values. The incorporation of the local hydrophobicity characteristics into the algorithm allowed the resolution of some of the more intractable problems in the calculation of pKa. Thus, the divergent shifts of the pKa of Glu-35 and Asp-66 in hen egg white lysozyme, which are both about 90% buried, was correctly predicted. Mechanistically, the divergence occurs because Glu-35 is in a hydrophobic microenvironment, while Asp-66 is in a hydrophilic microenvironment. Furthermore, because the calculation of the microenvironmental effects takes very little CPU time, the computational speed of the SCP formulation is conserved. Finally, results from different crystal structures of a given protein were compared, and it is shown that the reliability of the calculated pKa values is sufficient to allow identification of conformations that may be more relevant for the solution structure.

Algorithms↗
PubMed2003

Electrostatic interactions across the dimer-dimer interface contribute to the pH-dependent stability of a tetrameric malate dehydrogenase.

Malate dehydrogenase (MDH) from the moderately thermophilic bacterium Chloroflexus aurantiacus (CaMDH) is a tetrameric enzyme, while MDHs from mesophilic bacteria usually are dimers. Using site-directed mutagenesis, we show here that a network of electrostatic interactions across the extra dimer-dimer interface in CaMDH is important for thermal stability and oligomeric integrity. Stability effects of single point mutations (E25Q, E25K, D56N, D56K) varied from -1.2 degrees C to -26.8 degrees C, and depended strongly on pH. Gel-filtration experiments indicated that the 26.8 degrees C loss in stability observed for the D56K mutant at low pH was accompanied by a shift towards a lower oligomerization state.

Amino Acid Substitution↗