Elastic, electrostatic and electrokinetic forces influencing membrane curvature

Many cellular and intracellular processes critically depend on membrane shape, but the shape generating mechanisms are still to be fully understood. In this study we evaluate how electrostatic/electrokinetic forces contribute to membrane curvature. Membrane bilayer had finite thickness and was either elastically anisotropic or anisotropic overall, but isotropic per sections (heads and tails). The physics of the situation was evaluated using a coupled system of elastic and electrostatic/electrokinetic (Poisson-Nernst-Planck) equations. The fixed charges present only on the upper membrane surface lead to the accumulation of counter-ions and depletion of co-ions that decay spatially very rapidly (Debye length<1nm), as does the potential and electric field. Spatially uneven electric field and the permittivity mismatch also induce charges at the membrane-solution interface, which are not fixed but influence the electrostatics nevertheless. Membrane bends due to - Coulomb force (caused by fixed membrane charges in the electric field) and the dielectric force (due to the non-uniform electric field and the permittivity mismatch between the membrane and the solution). Both act as membrane surface forces, and both depend supra-linearly on the fixed charge density. Regardless of sign of the fixed charges, the membrane bends toward the charged (upper) surface owing to the action of the Coulomb force, but this is opposed by the smaller dielectric force. The spontaneous membrane curvature becomes very pronounced at high fixed charge densities, leading to very small spontaneous radii (<50nm). In conclusion the electrostatic/electrokinetic forces contribute significantly to the membrane curvature.     

Electrostatic potential and Born energy of charged molecules interacting with phospholipid membranes: calculation via 3-D numerical solution of the full Poisson equation.

Understanding the physicochemical basis of the interaction of molecules with lipid bilayers is fundamental to membrane biology. In this study, a new, three-dimensional numerical solution of the full Poisson equation including local dielectric variation is developed using finite difference techniques in order to model electrostatic interactions of charged molecules with a non-uniform dielectric. This solution is used to describe the electric field and electrostatic potential profile of a charged molecule interacting with a phospholipid bilayer in a manner consistent with the known composition and structure of the membrane. Furthermore, the Born interaction energy is then calculated by appropriate integration of the electric field over whole space. Numerical computations indicate that the electrostatic potential profile surrounding a charge molecule and its resultant Born interaction energy are a function of molecular position within the membrane and change most significantly within the polar region of the bilayer. The maximum interaction energy is observed when the charge is placed at the center of the hydrophobic core of the membrane and is strongly dependent on the size of the charge and on the thickness of the hydrocarbon core of the bilayer. The numerical results of this continuum model are compared with various analytical approximations for the Born energy including models established for discontinuous slab dielectrics. The calculated energies agree with the well-known Born analytical expression only when the charge is located near the center of a hydrocarbon core of greater than 60 A in thickness. The Born-image model shows excellent agreement with the numerical results only when modified to include an appropriate effective thickness of the low dielectric region. In addition, a newly derived approximation which considers the local mean dielectric provides a simple and continuous solution that also agrees well with the numerical results.     

Effect of planar dielectric interfaces on fluorescence emission and detection. Evanescent excitation with high-aperture collection.

We consider the effect of planar dielectric interfaces (e.g., solid/liquid) on the fluorescence emission of nearby probes. First, we derive an integral expression for the electric field radiated by an oscillating electric dipole when it is close to a dielectric interface. The electric field depends on the refractive indices of the interface, the orientation of the dipole, the distance from the dipole to the interface, and the position of observation. We numerically calculate the electric field intensity for a dipole on an interface, as a function of observation position. These results are applicable to fluorescent molecules excited by the evanescent field of a totally internally reflected laser beam and thus very close to a solid/liquid interface. Next, we derive an integral expression for the electric field radiated when a second dielectric interface is also close to the fluorescent molecule. We numerically calculate this intensity as observed through the second interface. These results are useful when the fluorescence is collected by a high-aperture microscope objective. Finally, we define and calculate a "dichroic factor," which describes the efficiency of collection, in the two-interface system, of polarized fluorescence. The limit when the first interface is removed is applicable for any high-aperture collection of polarized or unpolarized fluorescence. The limit when the second interface is removed has application in the collection of fluorescence with any aperture from molecules close to a dielectric interface. The results of this paper are required for the interpretation of order parameter measurements on fluorescent probes in supported phospholipid monolayers (Thompson, N.L., H. M. McConnell, and T. P. Burghardt, 1984, Biophys. J., 46:739-747).     

The effect of the lipid bilayer state on fluorescence intensity of fluorescein-PE in a saturated lipid bilayer

Fluorescein-PE is a fluorescence probe that is used as a membrane label or a sensor of surface associated processes. Fluorescein-PE fluorescence intensity depends not only on bulk pH, but also on the local electrostatic potential, which affects the local membrane interface proton concentration. The pH sensitivity and hydrophilic character of the fluorescein moiety was used to detect conformational changes at the lipid bilayer surface. When located in the dipalmitoylphosphatidylcholine (DPPC) bilayer, probe fluorescence depends on conformational changes that occur during phase transitions. Relative fluorescence intensity changes more at pretransition than at the main phase transition temperature, indicating that interface conformation affects the condition in the vicinity of the membrane. Local electrostatic potential depends on surface charge density, the local dielectric constant, salt concentration and water organisation. Initial increase in fluorescence intensity at temperatures preceding that of pretransition can be explained by the decreased value of the dielectric constant in the lipid polar headgroups region related in turn to decreased water organisation within the membrane interface. The abrupt decrease in fluorescence intensity at temperatures between 25 degrees C and 35 degrees C (DPPC pretransition) is likely to be caused by an increased value of the electrostatic potential, induced by an elevated value of the dielectric constant within the phosphate group region. Further increase in the fluorescence intensity at temperatures above that of the gel-liquid phase transition correlates with the calculated decreased surface electrostatic potential. Above the main phase transition temperature, fluorescence intensity increase at a salt concentration of 140 mM is larger than with 14 mM. This results from a sharp decline of the electrostatic potential induced by the phosphocholine dipole as a function of distance from the membrane surface.     

Effect of pore structure on energy barriers and applied voltage profiles. II. Unsymmetrical channels.

This paper examines "realistic" pores, i.e., ones that are neither symmetric nor of uniform diameter. Methods are described that permit estimation of the image potential for an ion in an aqueous pore spanning a lipid membrane and for the electric field produced in such a pore when a transmembrane potential is applied. They are used to model features of the delayed rectifier potassium channel. Constraints on the geometry of the exterior mouth, the dielectric properties of the narrow part of the pore and the conduction mechanism are determined for this channel.     

A Computational Study of the Giant Local Electric Field Enhancement in Al-Au-Ag Trimetallic Three-Layered Nanoshells

The surface plasmon resonance (SPR)-induced local field effect in Al-Au-Ag trimetallic three-layered nanoshells has been studied theoretically. Because of having three kinds of metal, three plasmonic bands have been observed in the absorption spectra and the local electric field factor spectra. The local electric field enhancement and the corresponding resonance wavelength for different plasmon coupling modes and spatial positions of the Al-Au-Ag nanoshells with various geometry dimensions are investigated to find the maximum local electric field enhancement. The calculation results indicate that the giant local electric field enhancement could be stimulated by the plasmon coupling in the middle Au shell or the outer Ag shell and could be optimized by increasing the Ag shell thickness and decreasing the Au shell thickness. What is more, the local electric field enhancement also nonmonotonously depends on the dielectric constant of the environment; the local electric field intensity will be weakened when the surrounding dielectric constant is too small or too large.

     

Dielectric properties of the polar head group region of zwitterionic lipid bilayers.

A theoretical model describing the dielectric properties of the lipid membrane-water interface region was developed. The rotating polar head groups (e.g. phosphatidylcholine) were simulated as a collection of interacting dipoles imbedded in a nonhomogeneous dielectric. The interactions between the nearest neighborhood were explicitly taken into account, while the other interactions were evaluated by means of the continuum theories. The values of the dielectric constant, its anisotropy and the spontaneous polarization of the interface were evaluated. As an application, we calculated the energy of interaction between an ion and the membrane polar head group region. The results indicate a small spontaneous polarization of the interface (1-1.7 Debyes per lipid molecule) due to the tilting angle of the choline residue with respect to the membrane surface. This dipolar field partially compensates that of opposite orientation originating from the ester group region, giving calculated overall dipolar potentials in better agreement with the experimental data. Our model suggests also a very strong dielectric anisotropy of the interface region, the component of the dielectric constant perpendicular to the membrane plane being much smaller than the parallel component.     

Polarized fluorescent emission from probes near dielectric interfaces

The electromagnetic field surrounding and emitted by a dipolar molecular probe very near to a dielectric interface is the sum of the real dipole field and the field of the image dipole induced inside the dielectric interface. The total charge distribution, made up of the real and image dipoles in close proximity to each other, approximates a quadrupole distribution and emits a light intensity pattern similar to that of an oscillating electric quadrupole. The electromagnetic field emitted by this system contains information that can be directly related to the spatial and orientational distributions of the dipole near the interface. Experimental methods are discussed that utilize this system for determining the spatial and orientational distribution of fluorescent probes in biological material.     

Dielectric Breakdown of Cell Membranes

With human and bovine red blood cells and Escherichia coli B, dielectric breakdown of cell membranes could be demonstrated using a Coulter Counter (AEG-Telefunken, Ulm, West Germany) with a hydrodynamic focusing orifice. In making measurements of the size distributions of red blood cells and bacteria versus increasing electric field strength and plotting the pulse heights versus the electric field strength, a sharp bend in the otherwise linear curve is observed due to the dielectric breakdown of the membranes. Solution of Laplace's equation for the electric field generated yields a value of about 1.6 V for the membrane potential at which dielectric breakdown occurs with modal volumes of red blood cells and bacteria. The same value is also calculated for red blood cells by applying the capacitor spring model of Crowley (1973. Biophys. J. 13:711). The corresponding electric field strength generated in the membrane at breakdown is of the order of 4 · 10⁶ V/cm and, therefore, comparable with the breakdown voltages for bilayers of most oils. The critical detector voltage for breakdown depends on the volume of the cells. The volume-dependence predicted by Laplace theory with the assumption that the potential generated across the membrane is independent of volume, could be verified experimentally. Due to dielectric breakdown the red blood cells lose hemoglobin completely. This phenomenon was used to study dielectric breakdown of red blood cells in a homogeneous electric field between two flat platinum electrodes. The electric field was applied by discharging a high voltage storage capacitor via a spark gap. The calculated value of the membrane potential generated to produce dielectric breakdown in the homogeneous field is of the same order as found by means of the Coulter Counter. This indicates that mechanical rupture of the red blood cells by the hydrodynamic forces in the orifice of the Coulter Counter could also be excluded as a hemolysing mechanism. The detector voltage (or the electric field strength in the orifice) depends on the membrane composition (or the intrinsic membrane potential) as revealed by measuring the critical voltage in E. coli B harvested from the logarithmic and stationary growth phases. The critical detector voltage increased by about 30% for a given volume on reaching the stationary growth phase.     

Brownian dynamics simulation of the lateral distribution of charged membrane components

Brownian dynamics simulations were performed to study the contribution of electric interactions between charged membrane components to their lateral distribution in a two-dimensional viscous liquid (bilayer lipid membrane). The electrostatic interaction potential was derived from an analytical solution of the linearized Poisson-Boltzmann equation for point charges in an electrolyte solution — membrane — electrolyte solution system. Equilibrium as well as dynamic quantities were investigated. The lateral organization of membrane particles, modelled by mobile cylinders in a homogeneous membrane separating two electrolyte solutions was described by spatial distribution functions, diffusion coefficients and cluster statistics. Disorder, local order and crystal-like arrangements were observed as a function of the particle charge, the closest possible distances between the charges and the particle density. The simulations revealed that the system is very sensitive to the position of the charges with respect to the electrolyte solution — membrane interface. Electrostatic interactions of charges placed directly on the membrane surface were almost negligible, whereas deeper charges demonstrated pronounced interaction. Biologically relevant parameters corresponded at most to local and transient ordering. It was found that lateral electric forces can give rise to a preferred formation of clusters with an even number of constituents provided that the closest possible charge-charge distances are small. It is concluded that lateral electrostatic interactions can account for local particle aggregations, but their impact on the global arrangement and movement of membrane components is limited. Correspondence to: D. Walther     

Probing biological interfaces by tracing proton passage across them.

The properties of water at the surface, especially at an electrically charged one, differ essentially from those in the bulk phase. Here we survey the traits of surface water as inferred from proton pulse experiments with membrane enzymes. In such experiments, protons that are ejected (or captured) by light-triggered enzymes are traced on their way between the membrane surface and the bulk aqueous phase. In several laboratories it has been shown that proton exchange between the membrane surface and the bulk aqueous phase takes as much as about 1 ms, but could be accelerated by added mobile pH-buffers. Since the accelerating capacity of the latter decreased with increase in their electric charge, it was suggested that the membrane surface is separated from the bulk aqueous phase by a barrier of electrostatic nature. In terms of ordinary electrostatics, the barrier could be ascribed to dielectric saturation of water at a charged surface. In terms of nonlocal electrostatics, the barrier could result from the dielectric overscreening in the surface water layers. It is discussed how the interfacial potential barrier can affect the reactions at interface, especially those coupled with biological energy conversion and membrane transport.     

Frequency-Dependent Polarization Properties of Local Electric Field in Gold–Dielectric Multi-Nanoshells

The polarization properties of the local electric field in the gold–dielectric–gold multilayer nanoshells are investigated by theoretical calculation based on the quasi-static approximation. The calculation results show that the complete polarized incident light does not only stimulate the same directional polarized local electric field. The polarized angle of the local field may changes from 0° to 90° as the wavelength and location are changed. The distributions of local field polarization are different in dielectric layer or gold shell and display different features in different plasmonic hybridization mode. As the incident wavelength is increased, the hot spot of polarizing angle moves monotonously in the middle dielectric shell, whereas moves nonmonotonously in the gold shell and surrounding environment. In the gold shell, the gap between hot spots of polarizing angle may occur at the resonance frequency. However, the hot spots of polarizing angle always occur at the resonance frequencies in the surrounding environment. These interesting results show that the single-molecule detection based on metal nanostructure induced surface-enhanced Raman scattering and surface enhanced fluorescence could be optimized by adjusting the incident light polarization and frequency.     

Origin of the rising phase of gating currents

It is suggested that the delayed rise of gating currents may result from a dielectric relaxation process within the membrane, not of the gating systems themselves but of molecules in the neighborhood of the gating systems. Such dielectric relaxation may prevent the electric fields at the locations of the gates from rapidly attaining their final, "clamped," values. Calculations based on this concept, using the Hodgkin Huxley m-process as an example, are shown to lead to gating currents whose shapes are similar to those observed experimentally. One possible interpretation in terms of membrane structure is proposed.     

Hybrid Dielectric-Plasmonic Nanocomposite Arrays for Bulk and Local Refractive Index Sensing

Plasmonics - Plasmonics-based biosensors are often limited by material losses in the form of joule heating while all dielectric nanoparticles systems have relatively smaller local electric field...     

Theoretical evaluation of the distributed power dissipation in biological cells exposed to electric fields

The paper deals with the power dissipation caused by exposure of biological cells to electric fields of various frequencies. With DC and sub-MHz AC frequencies, power dissipation in the cell membrane is of the same order of magnitude as in the external medium. At MHz and GHz frequencies, dielectric relaxation leads to dielectric power dissipation gradually increasing with frequency, and total power dissipation within the membrane rises significantly. Since such local increase can lead to considerable biochemical and biophysical changes within the membrane, especially at higher frequencies, the bulk treatment does not provide a complete picture of effects of an exposure. In this paper, we theoretically analyze the distribution of power dissipation as a function of field frequency. We first discuss conductive power dissipation generated by DC exposures. Then, we focus on AC fields; starting with the established first-order model, which includes only conductive power dissipation and is valid at sub-MHz frequencies, we enhance it in two steps. We first introduce the capacitive properties of the cytoplasm and the external medium to obtain a second-order model, which still includes only conductive power dissipation. Then we enhance this model further by accounting for dielectric relaxation effects, thereby introducing dielectric power dissipation. The calculations show that due to the latter component, in the MHz range the power dissipation within the membrane significantly exceeds the value in the external medium, while in the lower GHz range this effect is even more pronounced. This implies that even in exposures that do not cause a significant temperature rise at the macroscopic, whole-system level, the locally increased power dissipation in cell membranes could lead to various effects at the microscopic, single-cell level.     

Electrorotation--a new method for investigating membrane events during thrombocyte activation. Influence of drugs and osmotic pressure

The measurement of the spin of cells in rotating high-frequency electric fields ('electrorotation') make possible the investigation of dielectric membrane properties of single cells. This method was applied to membrane permeability changes accompanying thrombocyte activation and compared with light-scattering data. Describing the dielectric behavior of platelets by a single-shell model and assuming a sufficiently low membrane conductivity of 1 X 10(-7) S/m we found for nonactivated platelets a membrane capacity of 5.5 mF/m2 and the conductivity of the internal medium was estimated to be 0.12 S/m. Upon activation, the electrorotation decreased continuously, with half-times in the range of few minutes. This could be explained assuming a 500-fold increase in membrane conductivity. The application of both local anesthetics and virostatics inhibited the decrease of electrorotation, as did hypertonic osmotic pressure. In all cases this was accompanied by inhibition of platelet aggregation. Hypotonic solutions induced self-aggregation and spontaneous loss of electrorotation. It was concluded that the increase in permeability of the granule membrane is a crucial step in the release reaction and that the electrorotation method is able to detect the incorporation of the granule membranes into the plasma membrane during activation. The advantage of this electrorotation method is that it enables measurements on a single-cell level, thus avoiding interactions between platelets.     

Annexin V membrane interaction: an electrostatic potential study

The possible role of electrostatic interactions for membrane binding and pore formation of annexin V has been analysed on the basis of a simple dielectric model. It is suggested that the binding of phospholipids to annexin V is regulated, at least initially, by the protein's electrostatic potential. The calculations show that a strong local gradient of the electrostatic potential exists at the membrane-protein interface and a membrane pore may be generated by electroporation. The observed specificity and regulation of ion conduction is suggested to reside in the protein part of the pore. On the basis of the three-dimensional structures of the protein and its hypothetical membrane complex, and electrophysiological measurements, a mechanical model of the transmembrane voltage regulation of the annexin's ion conduction properties is proposed.     

Proton transfer dynamics at the membrane/water interface: dependence on the fixed and mobile pH buffers, on the size and form of membrane particles, and on the interfacial potential barrier

Crossing the membrane/water interface is an indispensable step in the transmembrane proton transfer. Elsewhere we have shown that the low dielectric permittivity of the surface water gives rise to a potential barrier for ions, so that the surface pH can deviate from that in the bulk water at steady operation of proton pumps. Here we addressed the retardation in the pulsed proton transfer across the interface as observed when light-triggered membrane proton pumps ejected or captured protons. By solving the system of diffusion equations we analyzed how the proton relaxation depends on the concentration of mobile pH buffers, on the surface buffer capacity, on the form and size of membrane particles, and on the height of the potential barrier. The fit of experimental data on proton relaxation in chromatophore vesicles from phototropic bacteria and in bacteriorhodopsin-containing membranes yielded estimates for the interfacial potential barrier for H(+)/OH(-) ions of approximately 120 meV. We analyzed published data on the acceleration of proton equilibration by anionic pH buffers and found that the height of the interfacial barrier correlated with their electric charge ranging from 90 to 120 meV for the singly charged species to >360 meV for the tetra-charged pyranine.     

Evaluation of the influence of the internal aqueous solvent structure on electrostatic interactions at the protein-solvent interface by nonlocal continuum electrostatic approach

The dielectric properties of the polar solvent on the protein-solvent interface at small intercharge distances are still poorly explored. To deconvolute this problem and to evaluate the pair-wise electrostatic interaction (PEI) energies of the point charges located at the protein-solvent interface we used a nonlocal (NL) electrostatic approach along with a static NL dielectric response function of water. The influence of the aqueous solvent microstructure (determined by a strong nonelectrostatic correlation effect between water dipoles within the orientational Debye polarization mode) on electrostatic interactions at the interface was studied in our work. It was shown that the PEI energies can be significantly higher than the energies evaluated by the classical (local) consideration, treating water molecules as belonging to the bulk solvent with a high dielectric constant. Our analysis points to the existence of a rather extended, effective low-dielectric interfacial water shell on the protein surface. The main dielectric properties of this shell (effective thickness together with distance- and orientation-dependent dielectric permittivity function) were evaluated. The dramatic role of this shell was demonstrated when estimating the protein association rate constants.