Electrokinetic membrane processes in relation to properties of excitable tissues. I. Experiments on oscillatory transport phenomena in artificial membranes

An artificial system is studied consisting of salt solutions of different concentrations separated by a porous, "charged" membrane, through which a constant electric current is passed. Experiments on such systems demonstrate rhythmic variations of the transmembrane potential and the membrane resistance, which are concomitant with an oscillatory streaming of water solution across the membrane. The repetitive oscillations can be of a damped or undamped type dependent on the "stimulating" current density. A qualitative discussion of the mechanism of the oscillations is given. It centers around the periodic resistance changes in the membrane, which result from a complicated interplay between the driving forces present. The importance of electro-osmotic effects is emphasized. A few comparisons relating to possible electrophysiological implications are presented. In the metastable state of this membrane oscillator, "make" and "break" responses can be triggered by electric as well as by mechanical (pressure) "stimuli."     

The cylindrical cell with a time-variant membrane resistance. Measuring passive parameters.

The passive electrical properties of a cable can be measured by injecting a step of current at a point and fitting the resulting potentials at several positions along the cable with analytic solutions of the cable equation. An error analysis is presented for this method (which is based on constant membrane resistance) when the membrane resistance is not constant, but increases linearly with time. The increase of rm produces a "creep" in the membrane potential at long times, as observed in cardiac, skeletal, and smooth muscle. The partial differential equation describing the time-varying cable was solved numberically for a step of current and these "data" were fit by standard constant-resistance methods. Comparing the resulting parameter values with the known true values, we suggest that a correction of the standard methods is not satisfactory for resistance changes of the kind observed; instead, the cable equation must be solved again for the particular form of rm(t). The practical implementation of a method by Adrian and Peachey for measuring the membrane capacitance and an approximate method for estimating the rate-of-change of membrane resistance are discussed in appendices.     

Electrical Signs of New Membrane Production during Cleavage of Rana pipiens Eggs

Rana pipiens eggs dividing normally in diluted Ringer's solution show an increase in transmembrane potential inside negative, a decrease in resistance, and no change in total surface membrane capacitance at the appearance of a division furrow. Furrows of eggs in solutions with the tonicity of full Ringer develop partially, then regress so that the surface is again spherical. The potential and resistance changes are greater and substantial increases in capacitance occur when furrowing is so inhibited. It is proposed that the electrical changes at division are due to the introduction of new plasma membrane, between the blastomeres, having selective permeability to K and a low resistance compared to the outer spherical membrane. A narrow gap between blastomeres limits current flow through new membrane during normal division. A direct exposure of new membrane to the bathing medium when furrowing is disrupted results in larger changes in potential and resistance and permits the capacitance of new membrane to be detected.     

Further studies of the effect of calcium on the time course of action of carbamylcholine at the neuromuscular junction

The rate at which the postjunctional membrane of muscle fibers becomes desensitized to the action of carbamylcholine is increased after the muscle has been soaked in solutions containing increased concentrations of calcium. Some further aspects of this effect of calcium were investigated by measuring changes in the input resistance of single fibers of the frog sartorius during local perfusion of the neuromuscular junction with 2.73 x 10^-3 M carbamylcholine in isolated muscles immersed in 165 mM potassium acetate. It was found that (a) sudden changes in the local concentration of calcium brought about by perfusing fibers with carbamylcholine solutions containing 20 mM calcium, 40 mM oxalate, or 40 mM EDTA were followed within 20 sec by marked changes in the rate of desensitization; (b) prior to 13 sec after the introduction of carbamylcholine, however, no effect on the input resistance could be detected even though the muscle had been presoaked in 10 mM calcium; (c) the ability of high concentrations of calcium to bring about rapid desensitization disappears when a lower concentration of carbamylcholine (0.137 x 10^-3 M) is applied to the muscle fiber. These findings suggest that calcium present in the extracellular fluid can act directly on the postjunctional membrane to promote the desensitization process and that an increased permeability of the membrane to calcium brought about by the presence of carbamylcholine is a factor which contributes to this action.     

A Theoretical Analysis of the Capacitance of Muscle Fibers Using a Distributed Model of the Tubular System

A model is developed to predict the changes in total capacitance (i.e. total charge stored divided by surface membrane potential) of the tubular system of muscle fibers. The tubular system is represented as a punctated disc and the area of membrane across which current flows is represented as a punctated annulus, the capacitance of the muscle fiber being proportional to this area. The area can be determined from a distributed model of the tubular system, in which the only resistance to radial current flow is presumed to be in the lumen of the tubules. Calculations are made of the variation of capacitance expected as the conductivity of the bathing solution is varied. These calculations include the effects of fixed charge in the tubular lumen and the effects of changes in the shape and volume of the tubular system in solutions of low conductivity. The calculated results fail to fit comparable experimental data, although they do qualitatively account for the known variation of the radial spread of contraction with conductivity of the bathing medium. It is pointed out that the existence of a significant "access resistance" at the mouth of the tubules might explain the discrepancy between theory and experiment.     

The contributions of normal and anomalous osmosis to the osmotic effects arising across charged membranes with solutions of electrolytes

The osmotic effect arising across a porous membrane separating the solution of an electrolyte from water (or a more dilute solution) is ordinarily due to both normal osmosis, as it occurs also with non-electrolytes, and to "anomalous" osmosis. It is shown that the normal osmotic component cannot be measured quantitatively by the conventional comparison with a non-electrolytic reference solute. Anomalous osmosis does not occur with electroneutral membranes. Accordingly, with membranes which can be charged and discharged reversibly (without changes in geometrical structure), such as many proteinized membranes, the osmotic effects caused by an electrolyte can be measured both when only normal osmosis arises (with the membrane in the electroneutral state) and when normal as well as anomalous osmosis occurs (with the membrane in a charged state). The difference between these two effects is the true anomalous osmosis. Data are presented on the osmotic effects across an oxyhemoglobin membrane in the uncharged state at pH 6.75 and in two charged states, positive at pH 4.0 and negative at pH 10.0, with solutions of a variety of electrolytes using a concentration ratio of 2:1 over a wide range of concentrations. The rates of the movement of liquid across the membrane against an inconsequentially small hydrostatic head are recorded instead of, as conventional, the physiologically less significant pressure rises after a standard time.     

Osmotic Flow of Water across Permeable Cellulose Membranes

Direct measurements have been made of the net volume flow through cellulose membranes, due to a difference in concentration of solute across the membrane. The aqueous solutions used included solutes ranging in size from deuterated water to bovine serum albumin. For the semipermeable membrane (impermeable to the solute) the volume flow produced by the osmotic gradient is equal to the flow produced by the hydrostatic pressure RT ΔC, as given by the van't Hoff relationship. In the case in which the membrane is permeable to the solute, the net volume flow is reduced, as predicted by the theory of Staverman, based on the thermodynamics of the steady state. A means of establishing the amount of this reduction is given, depending on the size of the solute molecule and the effective pore radius of the membrane. With the help of these results, a hypothetical biological membrane moving water by osmotic and hydrostatic pressure gradients is discussed.     

The electrical resistance of epithelia in the presence of osmotic and hydrostatic pressure gradients

The electrical resistance has been determined for aqueous channels through thick walls which separate electrolyte solutions of different concentrations under hydrostatic and osmotic pressure gradients. It is shown that the variation of the conductivity of epithelial layers under various constraints can be subjected to a similar analysis. Although the treatment is quantitative, concomitant morphological changes in the tissue could also take place which would introduce a non-predictive element. An awareness of both effects appears essential, when osmotic and/or hydrostatic pressure gradients are applied across epithelia.     

Osmoprotective effect of ubiquinone in lipid vesicles modelling the E. coli plasma membrane

Bacteria need to be able to adapt to sudden changes in their environment, including drastic changes in the surrounding osmolarity. As part of this adaptation, the cells adjust the composition of their cytoplasmic membrane. Recent studies have shown that ubiquinones, lipid soluble molecules involved in cell respiration, are overproduced by bacteria grown in hyperosmotic conditions and it is thus believed that these molecules can provide with osmoprotection. Hereby we explore the mechanisms behind these observations. Liposomes with a lipid headgroup composition mimicking that of the cytoplasmic membrane of E. coli are used as suitable models. The effect of ubiquinone-10 (Q10) on water transport across the membranes is characterized using a custom developed fluorescence-based experimental approach to simultaneously determine the membrane permeability coefficient and estimate the elastic resistance of the membrane towards deformation. It is shown that both parameters are affected by the presence of ubiquinone-10. Solanesol, a molecule similar to Q10 but lacking the quinone headgroup, also provides with osmoprotection although it only improves the resistance of the membrane against deformation. The fluorescence experiments are complemented by cryogenic transmission electron microscopy studies showing that the E. coli membrane mimics tend to flatten into spheroid oblate structures when osmotically stressed, suggesting the possibility of lipid segregation. In agreement with its proposed osmoprotective role, the flattening process is hindered by the presence of Q10.     

Membrane viscoelasticity.

In this paper, we develop a theory for viscoelastic behavior of large membrane deformations and apply the analysis to the relaxation of projections produced by small micropipette aspiration of red cell discocytes. We show that this relaxation is dominated by the membrane viscosity and that the cytoplasmic and extracellular fluid flow have negligible influence on the relaxation time and can be neglected. From preliminary data, we estimate the total membrane "viscosity" when the membrane material behaves in an elastic solid manner. The total membrane viscosity is calculated to be 10(-3) dyn-s/cm, which is a surface viscosity that is about three orders of magnitude greater than the surface viscosity of lipid membrane components (as determined by "fluidity" measurements). It is apparent that the lipid bilayer contributes little to the fluid dynamic behavior of the whole plasma membrane and that a structural matrix dominates the viscous dissipation. However, we show that viscous flow in the membrane is not responsible for the temporal dependence of the isotropic membrane tension required to produce lysis and that the previous estimates of Rand, Katchalsky, et al., for "viscosity" are six to eight orders of magnitude too large.     

Analysis of the effects of calcium or magnesium on voltage-clamp currents in perfused squid axons bathed in solutions of high potassium

Isolated axons from the squid, Dosidicus gigas, were internally perfused with potassium fluoride solutions. Membrane currents were measured following step changes of membrane potential in a voltage-clamp arrangement with external isosmotic solution changes in the order: potassium-free artificial seawater; potassium chloride; potassium chloride containing 10, 25, 40 or 50, mM calcium or magnesium; and potassium-free artificial seawater. The following results suggest that the currents measured under voltage clamp with potassium outside and inside can be separated into two components and that one of them, the predominant one, is carried through the potassium system. (a) Outward currents in isosmotic potassium were strongly and reversibly reduced by tetraethylammonium chloride. (b) Without calcium or magnesium a progressive increase in the nontime-dependent component of the currents (leakage) occurred. (c) The restoration of calcium or magnesium within 15–30 min decreases this leakage. (d) With 50 mM divalent ions the steady-state current-voltage curve was nonlinear with negative resistance as observed in intact axons in isosmotic potassium. (e) The time-dependent components of the membrane currents were not clearly affected by calcium or magnesium. These results show a strong dependence of the leakage currents on external calcium or magnesium concentration but provide no support for the involvement of calcium or magnesium in the kinetics of the potassium system.     

The Effect of Surface Charge on the Voltage-Dependent Conductance Induced in Thin Lipid Membranes by Monazomycin

Differences in the behavior of phosphatidylethanolamine (PE) and phosphatidylglycerol (PG) thin lipid membranes treated with monazomycin are shown to be due to the negative surface charge on PG membranes. We demonstrate that shifts of the conductance-voltage (g-V) characteristic of PG films produced by changes of univalent or divalent cation concentrations result from changes of the membrane surface potential on one or both sides. In particular, if divalent cations are added to the aqueous phase not containing monazomycin, the resulting asymmetry of the surface potentials results in an intramembrane potential difference not recordable by electrodes in the bulk phases. Nevertheless, this intramembrane potential difference is "seen" by the monazomycin, and consequently the g-V characteristic is shifted along the voltage axis. These changes are accounted for by diffuse double layer theory. Thus we find it unnecessary to invoke specific binding of Mg⁺⁺ or Ca⁺⁺ to the negative charges of PG membranes to explain the observation that concentrations of these ions some 100-fold lower than that of the univalent cation present produce large shifts of the g-V characteristic. We suggest that analogous shifts of g-V characteristics in axons produced by changes of divalent cation concentration are also best explained by diffuse double layer theory.     

Analysis of tracheal mechanics and applications.

We have developed a mathematical model for a tracheal ring that consists of a "horseshoe" of cartilage with its tips joined by a membrane. The ring is subjected to a uniform transmural pressure (Ptm) difference. The model was used to calculate the cross-sectional area (A) of the trachea. Whereas the mechanics of the deformation of the cartilage were analyzed using elastica theory, the posterior membrane was treated as a simple membrane that is inextensible under changes in Ptm. The membrane can be specified to be of any length less than baseline and thus can represent a posterior membrane under tension. The cartilage can have specifiable nonuniform unstressed curvature as well as nonuniform bending stiffness. We have investigated the effect on the tracheal A-Ptm curve of posterior membrane length and tensile force in the membrane, cartilage shape and elasticity, and localized weakening of the cartilage. The model predictions are in good agreement with magnetic resonance imaging data from rabbit tracheas and show that the shape of the horseshoe as well as the posterior membrane force are important determinants of tracheal compliance.     

Charge pulse studies of transport phenomena in bilayer membranes. I. Steady-state measurements of actin- and valinomycin-mediated transport in glycerol monooleate bilayers.

A charge pulse technique has been applied to studies of transport phenomena in bilayer membranes. The membrane capacitance can be rapidly charged (in less than a microsecond). The charge then decays through the membrane's conductive mechanism-no current flows through the solution or external circuitry. The resulting voltage decay is thus a manifestation of membrane and boundary layer phenomena only. There are a number of advantages to this approach over conventional voltage or current-clamp techniques: the rise-time of the voltage perturbation is not limited by the time constant deriving from the membrane capacitance and solution resistance, thus permitting study of extremely rapid rate processes; the membrane is exposed to high voltage for relatively short times and thus can be subjected to higher voltages without breakdown; the steady-state current-voltage behavior of the membrane can be deduced from a single charge pulse experiment; the charge (and therefore the integral of the ion flux through the membrane) is monitored allowing detection of rate processes too rapid to follow directly. In this paper we present what is primarily a steady-state analysis of actin (non-, mon-, din-, trin-)-mediated transport of ammonium ion and valinomycin-mediated transport of cesium and potassium ions through glycerol monooleate bilayers. We introduce the concept of the "intercept discrepancy", a method for measuring charge lost through extremely rapid rate processes. Directly observable pre-steady-state phenomena are also discussed but will be the main subject of part II.     

Studies on the electrical properties of a single plant cell; internodal cell of Nitella flexilis

Impedance changes of single plant cells of Nitella flexilis were studied under different environmental conditions. With the analysis presented changes in resistance of the protoplasmic membrane and of cell sap can be studied independently and simultaneously. Under "transcellular osmosis," the resistance of the protoplasmic membrane and of the cell sap increase at the part of the cell where water enters, while they decrease where water goes out. Ethanol of low concentration (below 8 per cent) first decreases and later increases the resistance of the protoplasmic membrane. Concentrated ethanol (over 10 per cent), however, brings about a large decrease in resistance of the protoplasmic membrane. Its time course is not simple, but undulatory changes occur. When ethanol is applied to one part of the cell, the resistance of the protoplasmic membrane shows a different type of change, which may be attributed to the local osmotic effect of ethanol; injury generally occurs with comparatively low concentration. Methanol, ethanol, and propanol have almost the same effect upon the cell, while butanol is toxic at the same concentration. When the cell dies, the resistance of the protoplasmic membrane decreases greatly, while the resistance of the cell sap increases to a level (several hundred kilo ohms or more), expected when external solution and cell sap are freely mixed with each other.     

A modified cable model for neuron processes with non-constant diameters.

The neuron axon cable model is expanded and developed to describe the linear subthreshold transmembrane potential of any circular cross section, thin membrane neuron fiber whose radius can be expressed as an analytic function of position, r(x). The transmembrane time constant is shown under the condition of space clamp to be independent of changes in geometry. Three typical neuron geometries are modeled (dendrite-soma, soma-axon, and dendrite-soma-axon) and the solutions to the resulting differential equations are numerically evaluated. The geometry-induced effects ate attributed to changes in current density and physiological correlates of the effects are proposed.     

Responses of neurons to extreme osmomechanical stress

Neurons are often regarded as fragile cells, easily destroyed by mechanical and osmotic insult. The results presented here demonstrate that this perception needs revision. Using extreme osmotic swelling, we show that molluscan neurons are astonishingly robust. In distilled water, a heterogeneous population of Lymnaea stagnalis CNS neurons swelled to several times their initial volume, yet had a ST₅₀ (survival time for 50% of cells) >60 min. Cells that were initially bigger survived longer. On return to normal medium, survivors were able, over the next 24 hr, to rearborize.Reversible membrane capacitance changes corresponding to about 0.7 F/cm² of apparent surface area accompanied neuronal swelling and shrinking in hypo- and hyperosmotic solutions; reversible changes in cell surface area evidently contributed to the neurons' ability to accommodate hydrostatic pressures then recover. The reversible membrane area/capacitance changes were not dependent on extracellular Ca²⁺.Neurons were monitored for potassium currents during direct mechanical inflation and during osmotically driven inflation. The latter but not the former stimulus routinely elicited small potassium currents, suggesting that tension increases activate the currents only if additional disruption of the cortex has occurred.Under stress in distilled water, a third of the neurons displayed a quite unexpected behavior: prolonged writhing of peripheral regions of the soma. This suggested that a plasma membrane-linked contractile machinery (presumably actomyosin) might contribute to the neurons' mechano-osmotic robustness by restricting water influx. Consistent with this possibility, 1 mM, N-ethylmaleimide, which inhibits myosin ATPase, decreased the ST₅₀ to 18 min, rendered the survival time independent of initial size, and abolished writhing activity.For neurons, active mechanical resistance of the submembranous cortex, along with the mechanical compliance supplied by insertion or eversion of membrane stores may account for the ability to withstand diverse mechanical stresses. Mechanical robustness such as that displayed here could be an asset during neuronal out-growth or regeneration.This work was supported by a NSERC Canada research grant to CEM.