A comment on Martin's relation.

In the limit of slowly varying synaptic conductance changes, a quantity proportional to the quantal content of a synaptic potential is provided by Martin's formula: 1/(VO/Vp-1), where Vp is the peak amplitude of the synaptic potential and Vo is the synaptic equilibrium potential. If the synaptic conductance change is not slowly varying on the time scale of the postsynaptic cell's membrane time constant, Martin's formula overestimates the effects of nonlinear summation and provides an upper limit for the actual quantal content. In the limit of rapidly varying synaptic conductance changes the quantity ln(1/[1-Vp/Vo]) is proportional to the quantal content. This formula underestimates the effects of nonlinear summation and gives a lower limit for the quantal content for cases in which the synaptic conductance is not rapidly varying. These two formulas used together provide upper and lower bounds to the correction for nonlinear summation of postsynaptic potentials.     

Opioids activate both an inward rectifier and a novel voltage-gated potassium conductance in the hippocampal formation

Opioid receptors were found to activate two different types of membrane potassium conductance in acutely dissociated neurons from the CA1/subiculum regions of the adult rat hippocampal formation. Opioid-responsive neurons were distinguished based on their morphology and electrophysiological responses. In one population of neurons having a multipolar, nonpyramidal cell shape, mu-selective opioid agonists increased an inward rectifying potassium current. Opioid activation of the inward rectifying conductance resulted in small outward potassium currents at resting membrane potentials and increased inward currents at hyperpolarized potentials. In a second population of nonpyramidal neurons, mu opioid agonists increased a novel voltage-gated potassium current. This current was blocked by internal CsCl2, unaffected by external BaCl2 or CdCl2, irreversibly activated by intracellular GTP-gamma-S, and inactivated by sustained depolarization. In contrast to the inward rectifying conductance, the voltage-gated conductance was not activated at resting membrane potentials or hyperpolarized potentials. The opioid-activated, voltage-gated conductance represents a new class of G protein-regulated potassium current in the brain.     

On the voltage-dependent action of tetrodotoxin.

The use of the maximum rate-of-rise of the action potential (Vmax) as a measure of the sodium conductance in excitable membranes is invalid. In the case of membrane action potentials, Vmax depends on the total ionic current across the membrane; drugs or conditions that alter the potassium or leak conductances will also affect Vmax. Likewise, long-term depolarization of the membrane lessens the fraction of total ionic current that passes through the sodium channels by increasing potassium conductance and inactivating the sodium conductance, and thereby reduces the effect of Vmax of drugs that specifically block sodium channels. The resultant artifact, an apparent voltage-dependent potency of such drugs, is theoretically simulated for the effects of tetrodotoxin on the Hodgkin-Huxley squid axon.     

Embryonic mesenchymal cells share the potential for smooth muscle differentiation: myogenesis is controlled by the cell's shape.

Undifferentiated embryonic mesenchymal cells are round/cuboidal in shape. During development, visceral myogenesis is shortly preceded by mesenchymal cell elongation. To determine the role of the cell's shape on smooth muscle development, undifferentiated embryonic mesenchymal cells from intestine (abundant visceral muscle), lung (some visceral muscle) or kidney (no visceral muscle) were plated under conditions that maintained cell rounding or promoted elongation. Regardless of their fate in vivo, all the cells differentiated into smooth muscle upon elongation as indicated by the expression of smooth muscle-specific proteins and the development of membrane potentials of -60 mV and voltage-dependent Ca2+ currents, characteristic of excitable cells. Smooth muscle differentiation occurred within 24 hours and was independent of cell proliferation. Regardless of their fate in vivo, all the round cells remained negative for smooth muscle markers, had membrane potentials of -30 mV and showed no voltage-activated current. These cells, however, differentiated into smooth muscle upon elongation. The role of the cell's shape in controlling smooth muscle differentiation was not overcome by treatment with retinoic acid, TGF-beta1, PDGF BB or epithelial-conditioned medium (all modulators of smooth muscle differentiation). These studies suggest that the mesenchymal cell shape plays a main role in visceral myogenesis.     

Pressure regulation of the electrical properties of growing Arabidopsis thaliana L. root hairs.

Actively growing Arabidopsis thaliana L. (Columbia wild type) root hairs were used to examine the interplay between cell turgor pressure and electrical properties of the cell: membrane potential, conductance, cell-to-cell coupling, and input resistance. Pressure was directly modulated using a pressure probe or indirectly by changing the extracellular osmolarity. Direct modulation of pressure in the range of 0 to about 15 x 10(5) Pa (normal turgor pressure was 6.8 +/- 2.0 x 10(5) Pa, n = 29) did not affect the membrane potential, conductance, coupling, or input resistance. Indirect modulation of turgor pressure by adding (hyperosmotic) or removing (hypo-osmotic) 200 mM mannitol/sorbitol affected the potential and conductance but not cell-to-cell coupling. Hypo-osmotic treatment depolarized the potential about 40 mV from an initial potential of about -190 mV and increased membrane conductance, consistent with an increase in anion efflux from the cell. Hyperosmotic treatment hyperpolarized the cell about 25 mV from the same initial potential and decreased conductance, consistent with a decline in cation influx. The results are likely due to the presence of an "osmo-sensor," rather than a "turgor-sensor," regulating the cell's response to osmotic stress.     

Effects of physostigmine on the voltage dependent ionic conductances of skeletal muscle fibres

The voltage dependent ionic conductances were studied by analysing the phase plane trajectories of action potentials evoked by electrical stimulation of the sartorius muscles of the frog (Rana esculenta). The delayed outward potassium current was measured also under voltage clamp conditions on muscle fibres of either the frog (Rana esculenta) or Xenopus laevis. On analysing the effect of physostigmine decreasing the peak amplitude, the rate of both the rising and falling phases of the action potentials, it was revealed that the alkaloid at a concentration of 1 mmol/l reduced significantly both the delayed potassium conductance and the outward ionic current values during the action potentials. The inhibition of sodium conductance and inward ionic current was less expressed. The maximum value of delayed potassium conductance measured under voltage clamp conditions was decreased by 1 mmol/l physostigmine. The time constant determined from the development of delayed potassium conductance was increased at a given membrane potential. The voltage vs. n relationship describing the membrane potential dependence of the delayed rectifier was not influenced by physostigmine. It has been concluded that physostigmine changes the time course of the action potentials by decreasing the value of both voltage dependent ionic conductances and by slowing down their kinetics. It is discussed that results obtained from the phase plane analysis of complex pharmacological effects can only be accepted with some restrictions.     

Electrophysiology of identified neurosecretory and non-neurosecretory cells in the cockroach pars intercerebralis

Two cell types can be distinguished with intracellular recording from the pars intercerebralis of the American cockroach (Periplaneta americana). The first type, which corresponds morphologically to the medial neurosecretory cell, always had spontaneously occurring, overshooting action potentials. These action potentials are probably endogenously produced. Tetrodotoxin experiments revealed that sodium is the dominant ion of the action potential. The action potentials are followed by a relatively long after-hyperpolarization. The input resistance of these cells ranged from 120 to 390 M omega. A mathematical model, based on cellular morphology and response to current pulses, revealed a membrane time constant of about 100 msec and an axonal:somatic conductance ratio of approximately 13. Area-specific membrane resistance was estimated at 33 k omega cm2. These cells also often had reversible and spontaneous inhibitory postsynaptic potentials. The second cell type, which is non-neurosecretory, never produced spontaneous action potentials and rarely had synaptic potentials. Action potentials could be evoked by current injection into the cell body or by extracellular stimulation of their axons in the posteroventral portion of the the protocerebrum. These action potentials also depend on sodium ions. Their input resistance ranged from 16 to 35 M omega. They had a membrane time constant of approximately 15 msec and an axonal:somatic conductance ratio of about 9. Their area specific membrane resistance was estimated at 14 k omega cm2.     

Fusion of membranes during fertilization. Increases of the sea urchin egg''s membrane capacitance and membrane conductance at the site of contact with the sperm

The early events of fertilization that precede and cause activation of an egg have not been fully elucidated. The earliest electrophysiological change in the sea urchin egg is a sperm-evoked increase of the egg's membrane conductance. The resulting depolarization facilitates entry of the fertilizing sperm and precludes the entry of supernumerary sperm. The sequence of the increase in the egg's membrane conductance, gamete membrane fusion, egg activation, and sperm entry, including causal relationships between these events, are not known. This study reports the use of whole egg voltage clamp and loose patch clamp to monitor simultaneously changes of membrane conductance and capacitance at the site of sperm-egg contact. Measurements were made during sperm-egg interactions where sperm entry readily proceeded or was precluded by maintaining the egg's membrane potential either at large, negative values or at positive values. Whenever the sperm evoked an increase of the egg's membrane conductance, that increase initiated abruptly, was localized to the site of sperm attachment, and was accompanied by a simultaneous abrupt increase of the membrane capacitance. This increase of capacitance indicated the establishment of electrical continuity between gametes (possibly fusion of the gametes' plasma membranes). If sperm entry was blocked by large negative membrane potentials, the capacitance cut off rapidly and simultaneously with a decrease of the membrane conductance, indicating that electrical continuity between gametes was disrupted. When sperm entry was precluded by positive membrane potentials, neither conductance nor capacitance increased, indicating that sperm entry was halted before the fusion of membranes. A second, smooth increase of capacitance was associated with the exocytosis of cortical granules near the sperm in eggs that were activated. Electrical continuity between the gametes always preceded activation of the egg, but transient electrical continuity between the gametes alone was not always sufficient to induce activation.     

Voltage oscillations in the barnacle giant muscle fiber.

Barnacle muscle fibers subjected to constant current stimulation produce a variety of types of oscillatory behavior when the internal medium contains the Ca++ chelator EGTA. Oscillations are abolished if Ca++ is removed from the external medium, or if the K+ conductance is blocked. Available voltage-clamp data indicate that the cell's active conductance systems are exceptionally simple. Given the complexity of barnacle fiber voltage behavior, this seems paradoxical. This paper presents an analysis of the possible modes of behavior available to a system of two noninactivating conductance mechanisms, and indicates a good correspondence to the types of behavior exhibited by barnacle fiber. The differential equations of a simple equivalent circuit for the fiber are dealt with by means of some of the mathematical techniques of nonlinear mechanics. General features of the system are (a) a propensity to produce damped or sustained oscillations over a rather broad parameter range, and (b) considerable latitude in the shape of the oscillatory potentials. It is concluded that for cells subject to changeable parameters (either from cell to cell or with time during cellular activity), a system dominated by two noninactivating conductances can exhibit varied oscillatory and bistable behavior.     

Model of ion transport regulation in chloride-secreting airway epithelial cells. Integrated description of electrical, chemical, and fluorescence measurements.

An electrokinetic model was developed to calculate the time course of electrical parameters, ion fluxes, and intracellular ion activities for experiments performed in airway epithelial cells. Model variables included cell [Na], [K], [Cl], volume, and membrane potentials. The model contained apical membrane Cl, Na, and K conductances, basolateral membrane K conductance, Na/K/2 Cl and Na/Cl symport, and 3 Na/2 K ATPase, and a paracellular conductance. Transporter permeabilities and ion saturabilities were determined from reported ion flux data and membrane potentials in intact canine trachea. Without additional assumptions, the model predicted accurately the measured short-circuit current (Isc), cellular conductances, voltage-divider ratios, open-circuit potentials, and the time course of cell ion composition in ion substitution experiments. The model was used to examine quantitatively: (a) the effect of transport inhibitors on Isc and membrane potentials, (b) the dual role of apical Cl and basolateral K conductance in cell secretion, (c) whether the basolateral symporter requires K, and (d) the regulation of apical Cl conductance by cAMP and Ca-dependent signaling pathways. Model predictions gave improved understanding of the interrelations among transporting systems and in many cases gave surprising predictions that were not obvious without a detailed model. The model developed here has direct application to secretory or absorptive epithelial cells in the kidney thick ascending limb, cornea, sweat duct, and intestine in normal and pathophysiological states such as cystic fibrosis and cholera.     

Ion channels in the plasma membrane of protoplasts from the halophytic angiosperm Zostera muelleri

Patch clamp studies show that there may be as many as seven different channel types in the plasma membrane of protoplasts derived from young leaves of the halophytic angiosperm Zostera muelleri. In whole-cell preparations, both outward and inward rectifying currents that activate in a timeand voltage-dependent manner are observed as the membrane is either depolarized or hyperpolarized. Current voltage plots of the tail currents indicate that both currents are carried by K⁺. The channels responsible for the outward currents have a unit conductance of approximately 70 pS and are five times more permeable to K⁺ than to Na⁺. In outside-out patches we have identified a stretch-activated channel with a conductance of 100 pS and a channel that inwardly rectifies with a conductance of 6 pS. The reversal potentials of these channels indicate a significant permeability to K⁺. In addition, the plasma membrane contains a much larger K⁺ channel with a conductance of 300 pS. Single channel recordings also indicate the existence of two Cl^– channels, with conductances of 20 and 80 pS with distinct substates. The membrane potential difference of perfused protoplasts showed rapid action potentials of up to 50 mV from the resting level. The frequency of these action potentials increased as the external osmolarity was decreased. The action potentials disappeared with the addition of Gd³⁺, an effect that is reversible upon washout.We would like to thank K. Morris and D. McKenzie for technical assistance and the Australian Research Council for financial support.     

Diphtheria toxin at low pH depolarizes the membrane, increases the membrane conductance and induces a new type of ion channel in Vero cells.

Receptor-dependent translocation of diphtheria toxin across the surface membrane of Vero cells was studied using patch clamp techniques. Translocation was induced by exposing cells with surface-bound toxin to low pH. Whole cell current and voltage clamp recordings showed that toxin translocation was associated with membrane depolarization and increased membrane conductance. The conductance increase was voltage independent, with a reversal potential of approximately 15 mV. This value was unaffected by changing the Cl- gradient across the membrane and microfluorometric measurements showed that the cytosolic Ca2+ concentration was only marginally elevated by the translocation. The conductance increase is thus mainly due to monovalent cations. Exposing outside-out and cell-attached patches with bound toxin to low pH induced a new type of ion channel in the membrane. The channel current was inward at negative membrane potentials and the single channel conductance was approximately 30 pS. This value is about three times larger than for receptor-independent channels induced by diphtheria toxin or toxin fragments in artificial lipid membranes.     

A theoretical study on the sucrose gap technique as applied to multicellular muscle preparations. II. Methodical errors in the determination of outward currents.

This paper presents a mathematical model for analyzing systematic errors associated with the membrane conductance of multicellular muscle preparations as determined in a sucrose gap apparatus. The errors arise because of the interdiffusion of sucrose and saline in the interstitial fluid spaces, which results (a) in spatial variations of equilibrium potentials, membrane conductance, and solution conductivity, and (b) in the existence of a liquid junction potential. The model was applied to simulate the measurement of outward currents predominantly carried by potassium ions; time variations were not considered. Output current/voltage (I/V) curves were computed and compared with the membrane I/V relationship used in the computation. The output curves look very much like experimental results but are distorted considerably from the membrane I/V relationship: (a) under favorable conditions (negligible shunt current), the membrane current is overestimated over the entire range of membrane potential, (b) regions with negative slope conductance of I/V relations with "anomalous rectifier" properties are found to be less pronounced or even absent, and (c) resting potentials may be either increased or reduced. The origin of these errors is related to currents emerging from the sucrose compartment (local circuit as well as externally applied currents). Their dependence on several experimental parameters is discussed.     

Conductance increases produced by bath application of cholinergic agonists to Electrophorus electroplaques

When solutions containing agonists are applied to the innervated face of an Electrophorus electroplaque, the membrane's conductance increases. The agonist-induced conductance is increased at more negative membrane potentials. The "instantaneous" current-voltage curve for agonist-induced currents is linear and shows a reversal potential near zero mV; chord conductances, calculated on the basis of this reversal potential, change epsilon-fold for every 62-mV change in potential when the conductance is small. Conductance depends non-linearly on small agonist concentrations; at all potentials, the dose-response curve has a Hill coefficient of 1.45 for decamethonium (Deca) and 1.90 for carbamylcholine (Carb). With agonist concentrations greater than 10(-4) M Carb or 10(-%) M Deca, the conductance rises to a peak 0.5-1.5 min after introduction of agonist, then declines with time; this effect resembles the "desensitization" reported for myoneural junctions. Elapid alpha-toxin, tubocurarine, and desensitization reduce the conductance without changing the effects of potential; the apparent dissociation constant for tubocurarine is 2 X 10(-7) M. By contrast, procaine effects a greater fractional inhibition of the conductance at high negative potentials.     

Modulation of membrane potential by an acetylcholine-activated potassium current in trout atrial myocytes

Application of the current-clamp technique in rainbow trout atrial myocytes has yielded resting membrane potentials that are incompatible with normal atrial function. To investigate this paradox, we recorded the whole membrane current (I(m)) and compared membrane potentials recorded in isolated cardiac myocytes and multicellular preparations. Atrial tissue and ventricular myocytes had stable resting potentials of -87 +/- 2 mV and -83.9 +/- 0.4 mV, respectively. In contrast, 50 out of 59 atrial myocytes had unstable depolarized membrane potentials that were sensitive to the holding current. We hypothesized that this is at least partly due to a small slope conductance of I(m) around the resting membrane potential in atrial myocytes. In accordance with this hypothesis, the slope conductance of I(m) was about sevenfold smaller in atrial than in ventricular myocytes. Interestingly, ACh increased I(m) at -120 mV from 4.3 pA/pF to 27 pA/pF with an EC(50) of 45 nM in atrial myocytes. Moreover, 3 nM ACh increased the slope conductance of I(m) fourfold, shifted its reversal potential from -78 +/- 3 to -84 +/- 3 mV, and stabilized the resting membrane potential at -92 +/- 4 mV. ACh also shortened the action potential in both atrial myocytes and tissue, and this effect was antagonized by atropine. When applied alone, atropine prolonged the action potential in atrial tissue but had no effect on membrane potential, action potential, or I(m) in isolated atrial myocytes. This suggests that ACh-mediated activation of an inwardly rectifying K(+) current can modulate the membrane potential in the trout atrial myocytes and stabilize the resting membrane potential.     

Theory of electromechanical effects in nerve

The electromechanical transduction mechanisms operating in nerve membranes are considered theoretically. For mechanical-to-electrical transduction (mechanical generator potentials), a model is proposed in which the surface charge on the membrane mediates stress-induced changes in the intramembrane electric field, thus opening transmembrane ion conductance channels or reducing the ion selectivity of the membrane via leak conductance pathways. For electrical-to-mechanical transduction (axon diameter change with excitation), an investigation into two well-known electrostatic properties of dielectrics, electrostriction and piezoelectricity, in the context of the nerve membrane is undertaken which predicts a few percent change in axon dimensions for voltage- and space-clamped axons.     

Disopyramide phosphate effects on slow and depressed fast responses

We studied the effects of disopyramide phosphate on explanted neonatal rat ventricle cells exhibiting depressed fast responses or naturally occurring slow response action potentials together with automatic activity. Disopyramide suppressed the spontaneous activity at a concentration of 2.5 micrograms/mL with a half-maximal value of 10 micrograms/mL. Before spontaneous activity was lost, there was an increase in beating rate possibly related to membrane depolarization. In depressed fast and slow response action potentials there was an increase in action potential duration (APD) which was consistently found both at the level of the plateau and at 90% repolarization. Comparison of the APD increase observed after disopyramide treatment and that after exposure to 20 mM tetraethylammonium suggested a block of a potassium conductance as a possible cause underlying the change in APD. The Vmax values of the depressed fast response decreased at constant membrane potential and this was attributed to the local anesthetic effect of the drug. In addition, we report two novel findings: (i) a decrease of Vmax of the slow response action potentials which may be secondary to membrane depolarization, and (ii) an increase in the duration of slow action potentials, possibly caused by inhibition of a potassium conductance.     

"Action potentials" in Neurospora crassa, a mycelial fungus.

Occasional spontaneous "action potentials" are found in mature hyphae of the fungus Neurospora crassa. They can arise either from low-level sinusoidal oscillations of the membrane potential or from a linear slow depolarization which accelerates into a rapid upstroke at a voltage 5-20 mV depolarized from the normal resting potential (near-180 mV). The "action potentials" are long-lasting, 1-2 min and at the peak reach a membrane potential near-40 mV. A 2-to 8-fold increase of membrane conductance accompanies the main depolarization, but a slight decrease of membrane conductance occurs during the slow depolarization. Two plausible mechanisms for the phenomenon are (a) periodic increases of membrane permeability to inorganic ions, particularly H+ or Cl- and (b) periodic decreases in activity of the major electrogenic pump (H+) or the Neurospora membrane, coupled with a nonlinear (inverse signoid) current-boltage relationship. Identification of action potential-like disturbances in fungi means that such behavior has now been found in all major biologic taxa which have been probed with suitable electrodes. As yet there is no obvious function for the events in fungi.     

Anion-sensitive sodium conductance in the apical membrane of toad urinary bladder

Membrane potentials and the electrical resistance of the cell membranes and the shunt pathway of toad urinary bladder epithelium were measured using microelectrode techniques. These measurements were used to compute the equivalent electromotive forces (EMF) at both cell borders before and after reductions in mucosal Cl- concentration ([Cl]m). The effects of reduction in [Cl]m depended on the anionic substitute. Gluconate or sulfate substitutions increased transepithelial resistance, depolarized membrane potentials and EMF at both cell borders, and decreased cell conductance. Iodide substitutions had opposite effects. Gluconate or sulfate substitutions decreased apical Na conductance, where iodide replacements increased it. When gluconate or sulfate substitutions were brought about the presence of amiloride in the mucosal solution, apical membrane potential and EMF hyperpolarized with no significant changes in basolateral membrane potential or EMF. It is concluded that: (a) apical Na conductance depends, in part, on the anionic composition of the mucosal solution, (b) there is a Cl- conductance in the apical membrane, and (c) the electrical communication between apical and basolateral membranes previously described is mediated by changes in the size of the cell Na pool, most likely by a change in sodium activity.     

Expression of voltage-gated calcium channels augments cell susceptibility to membrane disruption by nanosecond pulsed electric field

We compared membrane permeabilization by nanosecond pulsed electric field (nsPEF) in HEK293 cells with and without assembled CaV1.3 L-type voltage-gated calcium channel (VGCC). Individual cells were subjected to one 300-ns pulse at 0 (sham exposure); 1.4; 1.8; or 2.3 kV/cm, and membrane permeabilization was evaluated by measuring whole-cell currents and by optical monitoring of cytosolic Ca²⁺. nsPEF had either no effect (0 and 1.4 kV/cm), or caused a lasting (>80 s) increase in the membrane conductance in about 50% of cells (1.8 kV/cm), or in all cells (2.3 kV/cm). The conductance pathway opened by nsPEF showed strong inward rectification, with maximum conductance increase for the inward current at the most negative membrane potentials. Although these potentials were below the depolarization threshold for VGCC activation, the increase in conductance in cells which expressed VGCC (VGCC+ cells) was about twofold greater than in cells which did not (VGCC− cells). Among VGCC+ cells, the nsPEF-induced increase in membrane conductance showed a positive correlation with the amplitude of VGCC current measured in the same cells prior to nsPEF exposure. These findings demonstrate that the expression of VGCC makes cells more susceptible to membrane permeabilization by nsPEF. Time-lapse imaging of nsPEF-induced Ca²⁺ transients confirmed permeabilization by a single 300-ns pulse at 1.8 or 2.3 kV/cm, but not at 1.4 kV/cm, and the transients were expectedly larger in VGCC+ cells. However, it remains to be established whether larger transients reflected additional Ca²⁺ entry through VGCC, or were a result of more severe electropermeabilization of VGCC+ cells.