Electrical Interactions via the Extracellular Potential Near Cell Bodies

Ephaptic interactions between a neuron and axons or dendrites passing by its cell body can be, in principle, more significant than ephaptic interactions among axons in a fiber tract. Extracellular action potentials outside axons are small in amplitude and spatially spread out, while they are larger in amplitude and much more spatially confined near cell bodies. We estimated the extracellular potentials associated with an action potential in a cortical pyramidal cell using standard one-dimensional cable theory and volume conductor theory. Their spatial and temporal pattern reveal much about the location and timing of currents in the cell, especially in combination with a known morphology, and simple experiments could resolve questions about spike initiation. From the extracellular potential we compute the ephaptically induced polarization in a nearby passive cable. The magnitude of this induced voltage can be several mV, does not spread electrotonically, and depends only weakly on the passive properties of the cable. We discuss their possible functional relevance.     

Admittance change of squid axon during action potentials. Change in capacitive component due to sodium currents.

Since the discovery of Cole and Curtis (1938. Nature (Lond.). 142:209 and 1939. J. Gen. Physiol. 22:649) that the imaginary components, i.e., capacitive and inductive components, of the admittance of squid axon membrane remained unchanged during the action potential, there have been numerous studies on impedance and admittance characteristics of nerves. First of all, it is now known that the dielectric capacitance of the membrane is frequency dependent. Second, the recent observation of gating currents indicates that dipolar molecules may be involved in the onset of ionic currents. Under these circumstances, the author felt it necessary to reinvestigate the membrane admittance characteristics of nerve axons. The measurements by Cole and Curtis were performed mainly at 20 kHz, indicating that their observation was limited only to the passive membrane capacitance. To detect the change in the capacitive component during the action potential, we performed transient admittance measurements at lower frequencies. However, the frequency range of the measurements was restricted because of the short duration of the normal action potential. In addition, a change in the inductive component obscured the low frequency behavior of the capacitance. To use wider frequency range and simplify the system by eliminating the inductive component, the potassium current was blocked by tetraethyl ammonium, and the increase in the capacitive component was reinvestigated during the long action potential. The admittance change under this condition was found to be mostly capacitive, and conductance change was very small. The increase in the capacitive component was from 1.0 to 1.23 muF/cm2.     

Augmentation and suppression of action potentials by estradiol in the myometrium of pregnant rat.

The purpose of this study was to investigate the actions of estradiol on spontaneous and evoked action potentials in the isolated longitudinal smooth muscle cells of the pregnant rat. Single cells were obtained by enzymatic digestion from pregnant rat longitudinal myometrium. Action potentials and currents were recorded by whole-cell current-clamp and voltage-clamp methods, respectively. The acute effects of 17beta-estradiol on action potentials and inward and outward currents were investigated. The following results were obtained. The average resting membrane potential of single myometrial cells was -54 mV (n = 40). In many cells, an electrical stimulation evoked a membrane depolarization, and action potentials were superimposed on the depolarization. In some cells, spontaneous action potentials were observed. Estradiol (30 microM) slightly depolarized the membrane (ca. 5 mV) and attenuated the generation of action potentials by reducing the frequency and amplitude of the spikes. Afterhyperpolarization was also attenuated by estradiol (30 microM). On the other hand, in 5 of 35 cells, estradiol increased the first spike amplitude and action potential duration, while frequency of the spike generation and afterhyperpolarization were inhibited. In voltage-clamped muscle cells, estradiol inhibited both inward and outward currents. Acute inhibition or augmentation of spike generation by estradiol is due to the balance of inhibition of inward and outward currents. Inhibition of both currents also prevented afterhyperpolarization, causing potential-dependent block of Ca spikes.     

Slowing of the time course of the excitation of squid giant axons in viscous solutions

Summary The time course of excitation of intracellularly perfused squid giant axons was slowed as the solution viscosity was raised by adding neutral molecules, i.e., glucose and glycerol. By twofold increase of the solution viscosity, the duration of action potential was prolonged to 2.7-fold and the maximum rate of rise decreased to one-half. At the same time, the membrane resistance at resting state increased by 60%. These effects were reversible. The time course of inward and outward currents was slowed also. When the solution viscosity increased to twofold, the time to peak inward current increased by 80%, and the amplitudes of peak inward and steady outward currents decreased by 60% and by 70%, respectively. These effects were not specific for the sodium or the potassium channel. Effects of solution viscosity occurred in both hypotonic and hypertonic solutions. Q₁₀ values of temperature dependence of the time course of the action potential were equal in any viscous solutions. These effects in viscous solutions were explained by the change in solution viscosity but not by the change in solution osmolarities, ionic activities, or solution resistivity.     

Spontaneous and GABA-induced single channel currents in cultured murine spinal cord neurons

Intracellular and patch clamp recordings were made from embryonic mouse spinal cord neurons growing in primary cell culture. Outside-out membrane patches obtained from these cells usually showed spontaneous single channel currents when studied at the resting potential (-56 +/- 1.5 mV). In 18 out of 30 patches tested, spontaneous single channel activity was abolished by making Tris+ the major cation on both sides of the membrane. The remaining patches continued to display spontaneous single channel currents under these conditions. These events reversed polarity at a patch potential of 0 mV and displayed a mean single channel conductance of 24 +/- 1.2 pS. Application of the putative inhibitory transmitter gamma-aminobutyric acid (0.5-10 microM) to outside-out patches of spinal cord cell membrane induced single channel currents in 10 out of 15 patches tested. These channels had a primary conductance of 29 +/- 2.8 pS in symmetrical 145 mM Cl- solutions. Frequency distributions for the open times of these channels were well fit by the sum of a fast exponential term ("of") with a time constant tau of = 4 +/- 1.3 ms and a slow exponential term ("os") with a time constant tau os = 24 +/- 8.1 ms. Frequency distributions for channel closed times were also well fit by a double exponential equation, with time constants tau cf = 2 +/- 0.2 ms and tau cs = 62 +/- 20.9 ms.     

Effects of several sea anemone and scorpion toxins on excitability and ionic currents in the giant axon of the cockroach

The membrane effects of 4 sea anemone and 6 scorpion toxins have been studied under current clamp and voltage clamp conditions. Micromolar concentrations of the purified toxins were applied externally on single giant axons of the american cockroach. Periplaneta americana in a double oil-gap arrangement and the effects on the resting potential, action potential and underlying currents analysed. The 4 sea anemone toxins (Condylactis toxin, Anemonia toxin 2, Anthopleurin toxin A and Parasicyonis toxin) were found to considerably prolong the action potential. This effect is frequency dependent and long plateau spikes (100-500 ms in duration) are consistently seen for frequencies lower than 0.2 Hz. This effect is due to a considerable delay in the turning-off of the sodium current during square membrane depolarizations associated, for large concentrations, with a decrease in the potassium conductance. Toxin effects on the sodium current are not prevented by pretreatment with STX. From the 4 purified toxins extracted from the venom of the scorpion, Androctonus australis Hector, 3 (Mammal toxins 1 and 2 and crustacean toxin) were found to have sea anemone toxin like effects and to induce long duration plateau action potentials. As for sea anemone toxins, this effect is due to a lengthening of the falling phase of the sodium current associated with a small decrease in the potassium conductance. The 4th toxin (insect toxin or ITAaH) depolarizes the membrane and induces repetitive firing of short action potentials.(ABSTRACT TRUNCATED AT 250 WORDS)     

Further studies on the functional properties of spinal axons in vivo

Mammalian spinal tracts in situ demonstrate a phase of marked hyperexcitability during hypoxia or on the application of an excess of potassium or citrate ion. This is in keeping with the fact that they also show post-spike supernormality as well as hyperexcitability under cathodal polarization (17). Behavior of this kind indicates that central axons carry a well developed L fraction of membrane properties. The rhythmic state in central axons in situ, unlike peripheral nerve or spinal root, is not induced by the action of excess potassium ion. This appears to be related to the absence of a positive after-potential in dorsal columns (17). However, sodium citrate can elicit autonomous firing in central axons. When synchronized by an applied stimulus the resulting periodic oscillations have a fundamental frequency (340 to 400 C.P.S.) which is significantly greater than that of peripheral nerve.     

A gradient model of cardiac pacemaker myocytes

We have formulated a spatial-gradient model of action potential heterogeneity within the rabbit sinoatrial node (SAN), based on cell-specific ionic models of electrical activity from its central and peripheral regions. The ionic models are derived from a generic cell model, incorporating five background and exchange currents, and seven time-dependent currents based on three- or four-state Markov schemes. State transition rates are given by non-linear sigmoid functions of membrane potential.

By appropriate selection of parameters, the generic model is able to accurately reproduce a wide range of action potential waveforms observed experimentally. Specifically, the model can fit recordings from central and peripheral regions of the SAN with RMS errors of 0.3987 and 0.7628 mV, respectively. Using a custom least squares parameter optimisation routine, we have constructed a spatially-varying gradient model that exhibits a smooth transition in action potential characteristics from the central to the peripheral region, whilst ensuring individual membrane currents remain physiologically accurate. Smooth transition action potential characteristics include maximum diastolic potential, overshoot potential, upstroke velocity, action potential duration and cycle length. The gradient model is suitable for developing higher dimensional models of the right atrium, in which action potential heterogeneity within nodal tissue may be readily incorporated.     

The frequency response function and sinusoidal threshold properties of the Hodgkin-Huxley model of action potential encoding

The behaviour of the space-clamped Hodgkin-Huxley model has been studied using bandlimited white noise (0–50 Hz) as the input membrane current and taking the output as a point process in time given by the peaks of the action potentials. The frequency response and coherence functions were measured by use of the Fourier transform and digital filtering of the spike train. The results obtained are in good agreement with those already published for the simple integrator and leaky integrator models of neuronal encoding, as well as the earlier studies on the response of the Hodgkin-Huxley model to steady currents. In addition, the threshold of the model to sinusoidal membrane currents has been measured as a function of frequency over the range of 0.1–100 Hz. This shows a relatively constant level up to 2 Hz and then a clear minimum at 60 Hz, in agreement with measured thresholds of squid axons. These results are discussed in terms of the possible contributions of action potential encoding mechanisms to the frequency responses and sinusoidal thresholds which have been measured for rapidly adapting receptors.     

Subthreshold Behavior and Phenomenological Impedance of the Squid Giant Axon

The oscillatory behavior of the cephalopod giant axons in response to an applied current has been established by previous investigators. In the study reported here the relationship between the familiar "RC" electrotonic response and the oscillatory behavior is examined experimentally and shown to be dependent on the membrane potential. Computations based on the three-current system which was inferred from electrical measurements by Hodgkin and Huxley yield subthreshold responses in good agreement with experimental data. The point which is developed explicitly is that since the three currents, in general, have nonzero resting values and two currents, the "Na" system and the "K" system, are controlled by voltage-dependent time-variant conductances, the subthreshold behavior of the squid axon in the small-signal range can be looked upon as arising from phenomenological inductance or capacitance. The total phenomenological impedance as a function of membrane potential is derived by linearizing the empirically fitted equations which describe the time-variant conductances. At the resting potential the impedance consists of three structures in parallel, namely, two series RL elements and one series RC element. The true membrane capacitance acts in parallel with the phenomenological elements, to give a total impedance which is, in effect, a parallel R, L, C system with a "natural frequency" of oscillation. At relatively hyperpolarized levels the impedance "degenerates" to an RC system.     

Ion-channel noise places limits on the miniaturization of the brain's wiring

The action potential (AP) is transmitted by the concerted action of voltage-gated ion channels. Thermodynamic fluctuations in channel proteins produce probabilistic gating behavior, causing channel noise. Miniaturizing signaling systems increases susceptibility to noise, and with many cortical, cerebellar, and peripheral axons <0.5 mum diameter [1, 2 and 3], channel noise could be significant [4 and 5]. Using biophysical theory and stochastic simulations, we investigated channel-noise limits in unmyelinated axons. Axons of diameter below 0.1 microm become inoperable because single, spontaneously opening Na channels generate spontaneous AP at rates that disrupt communication. This limiting diameter is relatively insensitive to variations in biophysical parameters (e.g., channel properties and density, membrane conductance and leak) and will apply to most spiking axons. We demonstrate that the essential molecular machinery can, in theory, fit into 0.06 microm diameter axons. However, a comprehensive survey of anatomical data shows a lower limit for AP-conducting axons of 0.08-0.1 microm diameter. Thus, molecular fluctuations constrain the wiring density of brains. Fluctuations have implications for epilepsy and neuropathic pain because changes in channel kinetics or axonal properties can change the rate at which channel noise generates spontaneous activity.     

Ca2+-activated K+ currents regulate odor adaptation by modulating spike encoding of olfactory receptor cells

The olfactory system is thought to accomplish odor adaptation through the ciliary transduction machinery in olfactory receptor cells (ORCs). However, ORCs that have lost their cilia can exhibit spike frequency accommodation in which the action potential frequency decreases with time despite a steady depolarizing stimulus. This raises the possibility that somatic ionic channels in ORCs might serve for odor adaptation at the level of spike encoding, because spiking responses in ORCs encode the odor information. Here I investigate the adaptational mechanism at the somatic membrane using conventional and dynamic patch-clamp recording techniques, which enable the ciliary mechanism to be bypassed. A conditioning stimulus with an odorant-induced current markedly shifted the response range of action potentials induced by the same test stimulus to higher concentrations of the odorant, indicating odor adaptation. This effect was inhibited by charybdotoxin and iberiotoxin, Ca2+-activated K+ channel blockers, suggesting that somatic Ca2+-activated K+ currents regulate odor adaptation by modulating spike encoding. I conclude that not only the ciliary machinery but also the somatic membrane currents are crucial to odor adaptation.     

Synchronization of Na/K pump molecules by an oscillating electric field

Synchronization of the Na/K pump molecules in a cell membrane was studied in frog skeletal muscle fibers using double Vaseline-gap voltage-clamp techniques. We found that the pumping rate of naturally random-paced pump molecules can be artificially synchronized by a pulsed, symmetric, oscillating membrane potential with a frequency comparable to the physiological turnover rate. The synchronized pump currents show separated outward and inward components, where the magnitude of the outward component is about three times the randomly-paced pump currents, and the magnitude-ratio of the outward to inward pump currents is close to 3:2, which reflects the stoichiometric ratio of the pump molecules. Once synchronized, the pumping rate is restricted to the field frequency, and the pump currents are mainly dependent on the field frequency, but not the field strength. In contrast to previous work, which by restraining the pumps at a presteady state succeeded in triggering the steps of the pump cycle only individually and between interruptions, here we synchronize the pumps running continuously and in a normal running mode.     

Propagation of action potentials in squid giant axons. Repetitive firing at regions of membrane inhomogeneities

Effects of reduction in potassium conductance on impulse conduction were studied in squid giant axons. Internal perfusion of axons with tetraethylammonium (TEA) ions reduces G K and causes the duration of action potential to be increased up to 300 ms. This prolongation of action potentials does not change their conduction velocity. The shape of these propagating action potentials is similar to membrane action potentials in TEA. Axons with regions of differing membrane potassium conductances are obtained by perfusing the axon trunk and one of its two main branches with TEA after the second branch has been filled with normal perfusing solution. Although the latter is initially free of TEA, this ion diffuses in slowly. Up until a large amount of TEA has diffused into the second branch, action potentials in the two branches have very different durations. During this period, membrane regions with prolonged action potentials are a source of depolarizing current for the other, and repetitive activity may be initiated at transitional regions. After a single stimulus in either axon region, interactions between action potentials of different durations usually led to rebound, or a short burst, of action potentials. Complex interactions between two axon regions whose action potentials have different durations resembles electric activity recorded during some cardiac arrhythmias.     

Singar1, a novel RUN domain-containing protein, suppresses formation of surplus axons for neuronal polarity

Although neuronal functions depend on their robust polarity, the mechanisms that ensure generation and maintenance of only a single axon remain poorly understood. Using highly sensitive two-dimensional electrophoresis-based proteomics, we identified here a novel protein, single axon-related (singar)1/KIAA0871/RPIPx/RUFY3, which contains a RUN domain and is predominantly expressed in the brain. Singar1 expression became up-regulated during polarization of cultured hippocampal neurons and remained at high levels thereafter. Singar1 was diffusely localized in hippocampal neurons and moderately accumulated in growth cones of minor processes and axons. Overexpression of singar1 did not affect normal neuronal polarization but suppressed the formation of surplus axons induced by excess levels of shootin1, a recently identified protein located upstream of phosphoinositide-3-kinase and involved in neuronal polarization. Conversely, reduction of the expression of singar1 and its splicing variant singar2 by RNA interference led to an increase in the population of neurons bearing surplus axons, in a phosphoinositide-3-kinase-dependent manner. Overexpression of singar2 did not suppress the formation of surplus axons induced by shootin1. We propose that singar1 ensures the robustness of neuronal polarity by suppressing formation of surplus axons.     

Sodium flux ratio in Na/K pump-channels opened by palytoxin

Palytoxin binds to Na(+)/K(+) pumps in the plasma membrane of animal cells and opens an electrodiffusive cation pathway through the pumps. We investigated properties of the palytoxin-opened channels by recording macroscopic and microscopic currents in cell bodies of neurons from the giant fiber lobe, and by simultaneously measuring net current and (22)Na(+) efflux in voltage-clamped, internally dialyzed giant axons of the squid Loligo pealei. The conductance of single palytoxin-bound "pump-channels" in outside-out patches was approximately 7 pS in symmetrical 500 mM [Na(+)], comparable to findings in other cells. In these high-[Na(+)], K(+)-free solutions, with 5 mM cytoplasmic [ATP], the K(0.5) for palytoxin action was approximately 70 pM. The pump-channels were approximately 40-50 times less permeable to N-methyl-d-glucamine (NMG(+)) than to Na(+). The reversal potential of palytoxin-elicited current under biionic conditions, with the same concentration of a different permeant cation on each side of the membrane, was independent of the concentration of those ions over the range 55-550 mM. In giant axons, the Ussing flux ratio exponent (n') for Na(+) movements through palytoxin-bound pump-channels, over a 100-400 mM range of external [Na(+)] and 0 to -40 mV range of membrane potentials, averaged 1.05 +/- 0.02 (n = 28). These findings are consistent with occupancy of palytoxin-bound Na(+)/K(+) pump-channels either by a single Na(+) ion or by two Na(+) ions as might be anticipated from other work; idiosyncratic constraints are needed if the two Na(+) ions occupy a single-file pore, but not if they occupy side-by-side binding sites, as observed in related structures, and if only one of the sites is readily accessible from both sides of the membrane.     

Ionic dependence of sodium currents in squid axons analyzed in terms of specific ion "channel" interactions.

Inward sodium currents were measured from voltage-clamped giant axons externally perfused with artificial seawater (ASW) solutions containing various concentrations of sodium and potassium ions. The data was analyzed under the assumption that under a constant membrane potential sodium conductance is determined by a specific ion-channel site (SIS) reaction. The sodium current density values were expressed in terms of SIS-reaction rates which were compared, by means of minimization techniques, with those computed for various saturation reaction mechanisms. The following conclusions were drawn: 1) The dependence of peak inward sodium current on external sodium and potassium concentrations can be described in terms of saturation reactions. 2) The experimental data fit well the kinetics of a positive cooperative homotropic reaction, involving at least two allosteric active sites. One of these sites may be catalytic while the other, either catalytic or regulatory. 3) The inhibitory effect of external potassium on inward sodium current, can be described by a reversible competitive or noncompetitive inhibition mechanism. The values of the dissociation constant of the inhibitor-site "complex" (Ki) were found to be close to the external potassium concentration under physiological conditions.     

Voltage noise influences action potential duration in cardiac myocytes

Stochastic gating of ion channels introduces noise to membrane currents in cardiac muscle cells (myocytes). Since membrane currents drive membrane potential, noise thereby influences action potential duration (APD) in myocytes. To assess the influence of noise on APD, membrane potential is in this study formulated as a stochastic process known as a diffusion process, which describes both the current-voltage relationship and voltage noise. In this framework, the response of APD voltage noise and the dependence of response on the shape of the current-voltage relationship can be characterized analytically. We find that in response to an increase in noise level, action potential in a canine ventricular myocytes is typically prolonged and that distribution of APDs becomes more skewed towards long APDs, which may lead to an increased frequency of early after-depolarization formation. This is a novel mechanism by which voltage noise may influence APD. The results are in good agreement with those obtained from more biophysically-detailed mathematical models, and increased voltage noise (due to gating noise) may partially underlie an increased incidence of early after-depolarizations in heart failure.     

Electrical characteristics of frog atrial trabeculae in the double sucrose gap.

The electrical behavior of small single frog atrial trabeculae in the double sucrose gap has been investigated. The currents injected during voltage clamp experiments did not behave as predicted from the assumption of spatial uniformity of the voltage across a Hodgkin-Huxley membrane. Much of the difference is due to the geometrical complexities of this tissue. Nonetheless, two transient inward currents have been identified, the faster of which is blocked by tetrodotoxin (TTX). The magnitude of the slower transient varies markedly between preparations but always increases in a given preparation with increase of external calcium. The fast transient current traces, at small to intermediate depolarizations, are often marred by the presence of notches and secondary peaks due most probably to the loss of space clamp conditions. In many preparations these could be removed by reducing the current magnitude through application of a partially-blocking dose of TTX. Conversely, in the preparations whose fast transient was fully blocked by TTX, notches and secondary peaks in the slow transient could by induced through increasing calcium concentration and thereby the slow current magnitude. Previously used techniques for the measurement of the reversal potential of the fast inward transient have been shown to be invalid. In so far as they can be measured, the reversal potentials of the fast and slow inward transient are in the same neighborhood, i.e. around 120 mV from rest. The true values may be quite a bit apart. The total charge flow in the capacitive transient was measured for different sized nodes and preparations. From these data and estimates of plasma membrane area per unit trabecular volume, specific membrane capacitances of around 3 muF/cm2 were calculated for small bundles. The apparent ion current densities on this basis are approximately 1/10 of those measured in axons. The capacitive current occurring in small bundles decayed as the sum of at least three exponential functions of time. On the basis of these data and the anomalously large stable node widths, we suggest a coaxial core model of the preparation with the inner elements in series with an additional large extracellular resistance.     

Characteristics of sodium tail currents in Myxicola axons. Comparison with membrane asymmetry currents.

Sodium currents after repolarization to more negative potentials after initial activation were digitally recorded in voltage-clamped Myxicola axons compensated for series resistance. The results are inconsistent with a Hodgkin-Huxley-type kinetic scheme. At potentials more negative than -50 mV, the Na+ tails show two distinct time constants, while at more positive potentials only a single exponential process can be resolved. The time-course of the tail currents was totally unaffected when tetrodotoxin (TTX) was added to reduce gNa to low values, demonstrating the absence of any artifact dependent on membrane current. Tail currents were altered by [Ca++] in a manner consistent with a simple alteration in surface potential. Asymmetry current "off" responses are well described by a single exponential. The time constant for this response averaged 2.3 times larger than that for the rapid component of the Na+ repolarization current and was not sensitive to pulse amplitude or duration, although it did vary with holding potential. Other asymmetry current observations confirm previous reports on Myxicola.