Electrical Bistability of the Motoneuronal Dendritic Membrane Determined by Non-inactivating Inward Currents: a Model Study

We investigated features of the spatial pattern of electrical bistable states of dendrites using a computer model of an abducens motoneuron with the dendritic branching reconstructed in detail. The dendritic membrane has an N-shaped current-voltage relation (I-V curve) determined mainly by the presence of L-type calcium channels. Such channels, according to indirect experimental data, are present in the dendrites of these cells together with glutamatergic NMDA-type channels also capable of determining electrical bistability of the membrane and the corresponding specific patterns of electrical activity generated by such neurons. For our model, we obtained steady-state local I-V curves and transferred spatial distribution maps of the membrane potential difference (surface density of transmembrane currents), as well as increments of the axial dendritic current, to three-dimensional images of the reconstructed branching dendrites. The latter increments determine the contribution of a dendritic site in general axial current delivering the charge to the trigger zone of a neuron. The simulation results showed that incorporation of non-inactivating calcium channels into dendritic membrane leads to the origination of a pattern of spatial distribution of bistable electrical states in the dendrites, which were not described earlier. Such features are most important under conditions of a stable state of high depolarization of the relevant parts of the dendrites. In this case, the respective feature was the existence of a zone of maximum density of the inward transmembrane current, which covers areas of first-order branching of all dendrites. Since the greatest relative contribution to the total current belongs to the inward calcium current, the above zone of first branchings can be considered a “hot spot” zone characterized by increased entry of Ca²⁺. This may have important functional consequences for local intracellular calcium signaling.     

The osmotic flow of an electrolyte through a charged porous membrane

A pore model in which the pore wall has a continuous distribution of electrical charge is used to investigate the osmotic flow through a charged permeable membrane separating electrolyte solutions of unequal concentrations. The pore is treated as a long, circular, cylindrical duct. The analysis is based on a continuum formulation in which a dilute electrolyte solution is described by the coupled Nernst-Planck/Poisson creeping flow equations. Account is taken of the significant size of the electrolyte ions (assumed to be rigid spheres) when compared with the diameter of the membrane pores. Analytical solutions for the ion concentrations, hydrostatic pressure and electrostatic potential in the electrolyte solutions are given and an intra-pore flow solution is derived. A mathematical expression for the osmotic reflection coefficient as a function of the solute ion: pore diameter ratio λ and the solute fluxes is obtained. Approximate solutions are quoted which relate the solute fluxes and the solution electrostatic potentials at the membrane surfaces to the bulk solution concentrations, the membrane pore charge and pore geometry. The osmotic reflection coefficient is thus determined as a function of these parameters.     

A quantitative analysis of the voltage-current relationships of fixed charge membranes and the associated property of "punch-through"

A theoretical analysis of the voltage-current relationship is carried out in a membrane consisting of two fixed charge regions, of opposite sign, in contact. This is achieved by applying the diffusion equations to this system in conjunction with the Poisson-Boltzmann equation. The latter has been successfully applied by Mauro to determine the profiles of the electrostatic potential in his treatment of the capacitative property of such a system. It is shown that the system displays the property of rectification and is very similar in many respects to a solid state P-N junction diode. It is also shown that for the case of reverse bias, an electrical breakdown phenomena can occur. This is referred to as the “punch-through” effect. “Punch-through” was observed in experiments on the electrical characteristics of the membranes of Chara australis and Nitella sp. The experimental results are discussed in relation to the theoretical analysis.     

Extracellular electrical signals in a neuron-surface junction: model of heterogeneous membrane conductivity

Signals recorded from neurons with extracellular planar sensors have a wide range of waveforms and amplitudes. This variety is a result of different physical conditions affecting the ion currents through a cellular membrane. The transmembrane currents are often considered by macroscopic membrane models as essentially a homogeneous process. However, this assumption is doubtful, since ions move through ion channels, which are scattered within the membrane. Accounting for this fact, the present work proposes a theoretical model of heterogeneous membrane conductivity. The model is based on the hypothesis that both potential and charge are distributed homogeneously on the membrane surface, concentrated near channel pores, as the direct consequence of the inhomogeneous transmembrane current. A system of continuity equations having non-stationary and quasi-stationary forms expresses this fact mathematically. The present work performs mathematical analysis of the proposed equations, following by the synthesis of the equivalent electric element of a heterogeneous membrane current. This element is further used to construct a model of the cell-surface electric junction in a form of the equivalent electrical circuit. After that a study of how the heterogeneous membrane conductivity affects parameters of the extracellular electrical signal is performed. As the result it was found that variation of the passive characteristics of the cell-surface junction like conductivity of the cleft and the cleft height could lead to different shapes of the extracellular signals.     

Donnan potential and surface potential of a charged membrane.

A model is presented for the electrical potential distribution across a charged biological membrane that is in equilibrium with an electrolyte solution. We assume that a membrane has charged surface layers of thickness d on both surfaces of the membrane, where the fixed charges are distributed at a uniform density N within the layers, and that these charged layers are permeable to electrolyte ions. This model unites two different concepts, that is, the Donnan potential and the surface potential (or the Gouy-Chapman double-layer potential). Namely, the present model leads to the Donnan potential when d much greater than 1/k' (k' is the Debye-Hückel parameter of the surface charge layer) and to the surface potential as d----0, keeping the product Nd constant. The potential distribution depends significantly on the thickness d of the surface charge layer when d less than or approximately equal to 1/k'.     

Potential dependence of the “electrically silent” anion exchange across the plasma membrane ofXenopus oocytes mediated by the band-3 protein of mouse red blood cells

Summary Mouse erythroid band-3 protein was incorporated into the plasma membrane ofXenopus oocytes by microinjection of poly(A)⁺-mRNA from spleens of anemic mice. Subsequently, the efflux of microinjected³⁶Cl was continuously followed in single oocytes in a perfusion chamber the bottom of which was formed by the window of a Geiger-Müller tube. During the flux measurements, the membrane potential was clamped to different holding potentials. The efflux increased over the voltage range of –10 to –100 mV by a factor of about 1.5. Since the membrane potential cannot act as a driving force of anion exchange, it is suggested that the observed slight potential dependence is related to a recruitment of the anion-loaded transport protein by the electrical field, thereby changing the steady-state distribution between inwardly and outwardly facing anion binding sites of the transport molecules.The experimental data are discussed in terms of ping-pong kinetics, assuming that the potential dependence is primarily due to an effect of the electrical field in the membrane on the ratelimiting interconversion of inwardly and outwardly oriented anion binding sites. The results are compatible with the assumption that in the oocyte membrane the substrate-loaded band-3 molecules are preferentially inwardly oriented, and that the transition from the inwardly to the outwardly oriented conformation is associated with a reorientation of an effective charge of 0.1 elementary charge.During progesterone-induced maturation of the oocytes, several endogenous transport systems change their activity drastically. The mouse band-3 protein in the oocyte membrane also undergoes activity changes; however, these changes do not seem to involve direct regulation by specific metabolic processes. They can be explained as a consequence of the depolarization of the membrane potential associated with the maturation process.     

Surface potential on the periplasmic side of the photosynthetic membrane of Rhodopseudomonas sphaeroides

Membrane surface potential on the periplasmic side of the photosynthetic membrane was estimated in cells, spheroplasts and chromatophores of Rhodopseudomonas sphaeroides. When the membrane potential (potential difference between bulk aqueous phases) was kept constant in the presence of carbonylcyanide m-chlorophenylhydrazone, addition of salt to a suspension of cells or spheroplasts induced a red shift in the carotenoid absorption spectrum which indicated a change in the intramembrane electrical field. The spectral shift is explained by a rise in electrical potential at the outside surface of the photosynthetic membrane due to a decrease in extent of the negative surface potential.The spectral shift occurred in the direction opposite to that in chromatophores, indicating that the sidedness of the membrane of cells or spheroplasts is opposite to that of chromatophores. The dependences of the extent of the potential change on concentration and valence of cations of salts agreed with the Gouy-Chapman relationship on the electrical diffuse double layer. The charge density on the periplasmic surface of the photosynthetic membrane was estimated to be ?2.9 · 10^?3 elementary charge per Ų, while that on the cytoplasmic side surface was calculated as ?1.9 · 10^?3 elementary charge per Ų (Matsuura, K., Masamoto, K., Itoh, S. and Nishimura, M. (1979) Biochim. Biophys. Acta 547, 91–102). Surface potential on the periplasmic side of the photosynthetic membrane was estimated to be about ?50 mV at pH 7.8 in the presence of 0.1 M monovalent salt.     

Theoretical evaluation of a possible nature of the outer membrane potential of mitochondria

A possibility of generation of the outer membrane potential in mitochondria has been suggested earlier in the literature, but the potential has not been directly measured yet. Even its nature, metabolic impact and a possible range of magnitudes are not clear, and require further theoretical and experimental analysis. Here, using simple mathematical model, we evaluated a possible contribution of the Donnan and metabolically derived potentials to the outer membrane potential, concluding that the superposition of both is most probable; exclusively Donnan origin of the potential is doubtful because unrealistically high concentrations of charged macromolecules are needed for maintaining its relatively high levels. Regardless of the mechanism(s) of generation, the maximal possible potential seems to be less than 30 mV because significant osmotic gradients, created at higher values, increase the probability of the outer membrane rupture. New experimental approaches for direct or indirect determination of true value of the outer membrane potential are suggested here to avoid a possible interference of the surface electrical potential of the inner membrane, which may change as a result of the extrusion of matrix protons under energization of mitochondria.     

Radiation-inactivation analysis of the oligomeric structure of the renal sodium/d-glucose symporter

The radiation-inactivation size (RIS) of the rat renal brush-border membrane sodium/d-glucose cotransporter was estimated from the loss of transport activity in irradiated membrane vesicles. The RIS depended on the electrochemical conditions present when measuring transport activity. A RIS of 294±40 kDa was obtained when transport was measured in the presence of a sodium electrochemical gradient. Under sodium equilibrium conditions, the RIS was 84±25 kDa in the presence of a glucose gradient, and 92±20 kDa in its absence. In the absence of a sodium gradient, but in the presence of an electrical potential gradient, the RIS increased to 225±49 kDa. The 294 kDa result supports earlier suggestions that the Na⁺ gradient-dependent glucose transport activity is mediated by a tetramer. Individual monomers appear, however, to carry out glucose transport under equilibrium exchange conditions or when a glucose gradient serves as the only driving force. The electrical potential gradient-driven glucose transport RIS appears to involve three functional subunits.     

Basal lamina secreted by MDCK cells has size- and charge-selective properties

The role electrical charge plays in determining glomerular permeability to macromolecules remains unclear. If the glomerular basement membrane (GBM) has any significant role in permselectivity, physical principles would suggest a negatively charged GBM would reject similarly charged more than neutral species. However, recent in vivo studies with negative and neutral glomerular probes showed the opposite. Whether this observation is due to unique characteristics of the probes used or is a general physiological phenomenon remains to be seen. The goal of this study was to use the basement membrane deposited by Madin-Darby canine kidney epithelial cells as a simple model of a biologically derived, negatively charged filter to evaluate size- and charge-based sieving properties. Fluorescein isothiocyanate-labeled carboxymethylated Ficoll 400 (FITC-CM Ficoll 400) and amino-4-methyl-coumarin-labeled Ficoll 400 (AMC Ficoll 400) were used as negatively charged and neutral tracer molecules, respectively, during pressure-driven filtration. Streaming potential measurement indicated the presence of fixed, negative charge in the basal lamina. The sieving coefficient for neutral Ficoll 400 decreased by ～0.0013 for each 1-? increment in solute radius, compared with a decrease of 0.0023 per ? for the anionic Ficoll 400. In this system, molecular charge played a significant role in determining the sieving characteristics of the membrane, pointing to solute charge as a potential contributor to GBM permselectivity.     

A reconstruction of charge movement during the action potential in frog skeletal muscle.

The transfer of intramembrane charge during an action potential at 4 degrees C was reconstructed for a model representing the electrical properties of frog skeletal muscle by a cylindrical surface membrane and 16 concentric annuli ("shells") of transverse tubular membrane of equal radial thickness. The lumina of the transverse tubules were separated from extracellular fluid by a fixed series resistance. The quantity, geometrical distribution and steady-state and kinetic properties of charge movement components were described by equations incorporating earlier experimental results. Introducing such nonlinear charge into the distributed model for muscle membrane diminished the maximum amplitude of the action potential within the transverse tubules by 2 mV but increased the maximum size of the after-depolarization by 3-5 mV and also its duration. However, these changes were small in comparison to the 135-mV deflection represented by the action potential. They therefore did not justify altering the values of the electrical parameters adopted by Adrian R.H., and L.D. Peachey (1973. J. Physiol. [Lond.]. 235:103-131.) and used in the present calculations. Cable properties significantly affected the time course and extent of charge movement in each shell during action potential propagation into the tubular system. Q beta charge moved relatively rapidly in all annuli, and did so without significant latency (approximately 0.3 ms) after the surface action potential upstroke. Its peak displacement varied between 53 and 58% (the range representing the difference fiber edge/fiber axis) of the total Q beta charge. This was attained at 5.4-7.3 ms after the stimulus, depending on depth within the tubules. In contrast, q gamma moved after a 1.7-2.9 ms latency and achieved a peak displacement of up to 22-34% of available charge. Both charge movement species could be driven by repetitive (47.7 Hz) action potentials without buildup of charge transfer. Such stimulus frequencies would normally cause tetanus. Latencies in q gamma charge movement in response to an action potential were resolved into (a) propagation of tubular depolarization required to gain the "threshold" of q gamma charge (0.8-1.5 ms) and (b) dielectric loss processes. The latter took consistently around 1.5 ms throughout the tubular system. Taken with (c) the earlier reports of a minimal latency in delta [Ca2+] signals attributed to tubulo-cisternal coupling following voltage sensing (approximately 2 ms: Zhu, P.H., I. Parker, and R. Miledi., 1986. Proc. R. Soc. Lond. B. Biol. Sci. 229:39-46.).(ABSTRACT TRUNCATED AT 400 WORDS)     

Das Membranpotenzial. Biophysik im Experiment

The membrane potential Every living cell is surrounded by a cell membrane separating the cell's contents from the environment. It enables the generation of an electrical potential difference, the membrane potential or membrane voltage. Simple experiments using model membranes (ion exchanger membranes) help to understand the characteristics and the generation of the membrane potential, as well as analysis of the data by the theoretical equations derived by Nernst, Goldman, Hodgkin and Huxley.     

Modeling electrically active viscoelastic membranes

The membrane protein prestin is native to the cochlear outer hair cell that is crucial to the ear's amplification and frequency selectivity throughout the whole acoustic frequency range. The outer hair cell exhibits interrelated dimensional changes, force generation, and electric charge transfer. Cells transfected with prestin acquire unique active properties similar to those in the native cell that have also been useful in understanding the process. Here we propose a model describing the major electromechanical features of such active membranes. The model derived from thermodynamic principles is in the form of integral relationships between the history of voltage and membrane resultants as independent variables and the charge density and strains as dependent variables. The proposed model is applied to the analysis of an active force produced by the outer hair cell in response to a harmonic electric field. Our analysis reveals the mechanism of the outer hair cell active (isometric) force having an almost constant amplitude and phase up to 80 kHz. We found that the frequency-invariance of the force is a result of interplay between the electrical filtering associated with prestin and power law viscoelasticity of the surrounding membrane. Paradoxically, the membrane viscoelasticity boosts the force balancing the electrical filtering effect. We also consider various modes of electromechanical coupling in membrane with prestin associated with mechanical perturbations in the cell. We consider pressure or strains applied step-wise or at a constant rate and compute the time course of the resulting electric charge. The results obtained here are important for the analysis of electromechanical properties of membranes, cells, and biological materials as well as for a better understanding of the mechanism of hearing and the role of the protein prestin in this mechanism.     

Excitation trapping and charge separation in Photosystem II in the presence of an electrical field

To investigate the effects of a membrane potential on excitation trapping and charge separation in Photosystem II we have studied the chlorophyll fluorescence yield in osmotically swollen chloroplasts subjected to electrical field pulses. Significant effects were observed only in those membrane regions where a large membrane potential opposing the photochemical charge separation was built up. When the fluorescence yield was low, close to F₀, a much higher yield, up to F_max, was observed during the presence of the membrane potential. This is explained by an inhibition by the electrical field of electron transfer to the quinone acceptor Q, resulting in a decreased trapping of excitations. A field pulse applied when the fluorescence yield was high, Q and the donor side being in the reduced state, had the opposite effect: the fluorescence was quenched nearly to F₀. This field-induced fluorescence quenching is ascribed to reversed electron transfer from Q^? to the intermediate acceptor, pheophytin. Its field strength dependence suggests that the midpoint potential difference between pheophytin and Q is at most about 300 mV. Even then it must be assumed that electron transfer between pheophytin and Q spans 90% of the potential difference across the membrane.     

Effects of Polarization of the Receptor Membrane and of the First Ranvier Node in a Sense Organ

It has previously been shown that the site of production of the generator potential in Pacinian corpuscles is the receptor membrane of the non-myelinated ending, and the site of initiation of the nerve impulse, the adjacent (first) Ranvier node. Effects of membrane polarization of these sites were studied in the present work. Nerve ending and first Ranvier node were isolated by dissection, electric activity was recorded from, and polarizing currents were passed through them. All observations were done at steady levels of polarization, seconds after onset of current flow. The following results were obtained: The amount of charge transferred through the excited receptor membrane is a function of the electrical gradients across the membrane. The generator potential in response to equal mechanical stimuli increases with resting potential of the receptor membrane. The refractory state of the generator potential is not affected by polarization. The electrical threshold for impulse firing at the first Ranvier node (measured by the minimal amplitude of generator potential which elicits a nodal impulse) is nearly minimal at normal resting potential of the node. Both, hyperpolarization and depolarization lead to a rise in nodal threshold. For any level of polarization of nodal and receptor membrane, the threshold for production of impulses by adequate (mechanical) stimulation appears determined by the generator potential-stimulus strength relation and by the electrical threshold of the node.     

Salt-induced pH changes in spinach chloroplast suspension. Changes in surface potential and surface pH of thylakoid membranes

A pH decrease in chloroplast suspension in media of low salt concentration was observed when a salt was added at pH values higher than 4.4, while at lower pH values a pH increase was observed. The salt-induced pH changes depended on the valence and concentration of cations of added salts at neutral pH values (higher than 4.4) and on those of anions at acidic pH values (lower than 4.4). The order of effectiveness was trivalent > divalent > monovalent. The pH value change by salt addition was affected by the presence of ionic detergents depending on the sign of their charges. These characteristics agreed with those expected from the Gouy-Chapman theory on diffuse electrical double layers. The results were interpreted in terms of the changes in surface potential, surface pH and the ionization of surface groups which result in the release (or binding) of H⁺ to (or from) the outer medium.The analysis of the data of KCl-induced pH change suggests that the change in the surface charge density of thylakoid membranes depends mainly on the ionization of carboxyl groups, which is determined by the surface pH. When the carboxyl groups are fully dissociated, the surface charge density reaches ?1.0 ± 0.1 · 10^?3 elementary charge/square Å.Dependence of the estimated surface potential on the bulk pH was similar to that of electrophoretic mobility of thylakoid membrane vesicles.     

RECTIFICATION AND INDUCTANCE IN THE SQUID GIANT AXON

Previous measurements have shown that the electrical properties of the squid axon membrane are approximately equivalent to those of a circuit containing a capacity shunted by an inductance and a rectifier in series. Selective ion permeability of a membrane separating two electrolytes may be expected to give rise to the rectification. A quasi-crystalline piezoelectric structure of the membrane is a plausible explanation of the inductance. Some approximate calculations of behavior of an axon with these membrane characteristics have been made. Fair agreement is obtained with the observed constant current subthreshold potential and impedance during the foot of the action potential. In a simple case a formal analogy is found between the calculated membrane potential and the excitability defined by the two factor formulations of excitation. Several excitation phenomena may then be explained semi-quantitatively by further assuming the excitability proportional to the membrane potential. Some previous measurements and subthreshold potential and excitability observations are not consistent with the circuit considered and indicate that this circuit is only approximately equivalent to the membrane.     

Apparent cooperativity of amino acid transport in Halobacterium halobium: Effect of electrical potential

Active serine accumulation in cell envelope vesicles from Halobacterium halobium proceeds by co-transport with Na⁺ and can be induced by either transmembrane electrical potential or transmembrane Na⁺ concentration difference. It was shown earlier that in the former case the initial transport rate is a fourth-power function of the magnitude of the electrochemical potential difference of sodium ions, and in the latter, a second-power function. A possible interpretation of this finding is cooperativity of sodium-transporting sites in the transport carrier. When both kinds of driving force are imposed simultaneously on the vesicles, fourth-power dependence on the total potential difference of sodium ions is obtained, suggesting that the transport carrier is regulated by the electrical potential. Heat treatment of the vesicles at 48 ° partially inactivates transport and abolishes this effect of the electrical potential.     

Electronic sizing and counting of bacteria

An electronic apparatus is described that permits rapid determination of the concentration and size distribution of bacteria in electrolyte suspensions by a resistance method. The resulting size-concentration distribution may be displayed on an oscilloscope and recorded with an X–Y plotter and an electric typewriter-tape punch unit. The paper tape is analyzed with a computer program. Comparisons are made between electronic measurements of bacterial cell concentration and size distribution and values obtained by other methods. Effects of heat-killing and disruption of the cell membrane on the electrical counting characteristics of the organisms are discussed.     

Effect of membrane charge on flow and protein transport during ultrafiltration

Although several recent studies have demonstrated the importance of electrostatic interactions in ultrafiltration, there have been few quantitative studies of the effects of membrane charge density on protein transport and membrane hydraulic permeability. Data were obtained using a series of charge-modified cellulose membranes, with the surface charge density controlled by varying the extent of addition of a quaternary amine functionality. The membrane charge was evaluated from streaming potential measurements. Protein transmission decreased by a factor of 100 as the membrane zeta potential increased from 0.3 to 6.6 mV. The protein sieving data were in good agreement with a partitioning model accounting for electrostatic effects, while the hydraulic permeability data were consistent with a flow model accounting for the effects of counter-electroosmosis. The results provide the first quantitative analysis of the effects of membrane charge density on the performance of ultrafiltration membranes.