Depletion and accumulation of potassium in the extracellular clefts of cardiac Purkinje fibers during voltage clamp hyperpolarization and depolarization: experiments in sodium-free bathing media

Voltage clamp hyperpolarization and depolarization result in currents consistent with depletion and accumulation of potassium in the extracellular clefts o cardiac Purkinje fibers exposed to sodium-free solutions. Upon hyperpolarization, an inward current that decreased with time (id) was observed. The time course of tail currents could not be explained by a conductance exhibiting voltage-dependent kinetics. The effect of exposure to cesium, changes in bathing media potassium concentration and osmolarity, and the behavior of membrane potential after hyperpolarizing pulses are all consistent with depletion of potassium upon hyperpolarization. A declining outward current was observed upon depolarization. Increasing the bathing media potassium concentration reduced the magnitude of this current. After voltage clamp depolarizations, membrane potential transiently became more positive. These findings suggest that accumulation of potassium occurs upon depolarization. The results indicate that changes in ionic driving force may be easily and rapidly induced. Consequently, conclusions based on the assumption that driving force remains constant during the course of a voltage step may be in error.     

Automaticity in cardiac cells.

Automaticity is the result of dynamic changes in transmembrane currents during electrical diastole. It is readily demonstrated in most cardiac cell types. In all four cardiac cell types studied by the voltage clamp technique (Purkinje, ventricular, atrial, and sino-atrial node fibers), the major change detected during diastolic depolarization is a decrease in outward current. This decrease in a repolarizing current (largely potassium mediated) permits an inward current (sodium and/or calcium mediated) to depolarize the cell.All four cardiac cell types appear to possesess a time-dependent potassium conductance which controls the decrease in outward current over the ?70 to ?30 mV potential range. Purkinje fibers manifest an additional conductance which is responsible for automaticity in this type of cell at potentials between ?100 and ?70 mV.     

Effects of D-600 on intramembrane charge movement of polarized and depolarized frog muscle fibers

Intramembrane charge movement has been measured in frog cut skeletal muscle fibers using the triple vaseline gap voltage-clamp technique. Ionic currents were reduced using an external solution prepared with tetraethylammonium to block potassium currents, and O sodium + tetrodotoxin to abolish sodium currents. The internal solution contained 10 mM EGTA to prevent contractions. Both the internal and external solutions were prepared with impermeant anions. Linear capacitive currents were subtracted using the P-P/4 procedure, with the control pulses being subtracted either at very negative potentials, for the case of polarized fibers, or at positive potentials, for the case of depolarized fibers. In 63 polarized fibers dissected from Rana pipiens or Leptodactylus insularis frogs the following values were obtained for charge movement parameters: Qmax = 39 nC/microF, V = 36 mV, k = 18.5 mV. After depolarization we found that the total amount of movable charge was not appreciably reduced, while the voltage sensitivity was much changed. For 10 fibers, in which charge movement was measured at -100 and at 0 mV, Qmax changed from 46 to 41 nC/microF, while V changed from -41 to -103 mV and k changed from 20.5 to 30 mV. Thus membrane depolarization to 0 mV produces a shift of greater than 50 mV in the Q-V relationship and a decrease of the slope. Membrane depolarization to -20 and -30 mV, caused a smaller shift of the Q-V relationship. In normally polarized fibers addition of D-600 at concentrations of 50-100 microM, does not cause important changes in charge movement parameters. However, the drug appears to have a use-dependent effect after depolarization. Thus in depolarized fibers, total charge is reduced by approximately 20%. D-600 causes no further changes in the voltage sensitivity of charge movement in fibers depolarized to 0 mV, while in fibers depolarized to -20 and -30 mV it causes the same effects as that obtained with depolarization to 0 mV. These results are compatible with the idea that after depolarization charge 1 is transformed into charge 2. D-600 appears to favor the conversion of charge 1 into charge 2. Since D-600 also favors contractile inactivation, charge 2 could represent the state of the voltage sensor for excitation-contraction coupling in the inactivated state.     

Single potassium channel conductance in the frog node of Ranvier.

The single K+-channel conductance was calculated from the variance of the spontaneous potassium noise currents in voltage clamped frog node. Essential for this calculation is the mean potassium conductance during the noise measurement. So far this quantity has been underestimated, apparently due to K+-ion accumulation. With the proper values, the single K+-channel conductance is an increasing function of membrane voltage.     

Dynamics of potassium ion currents in squid axon membrane. A re-examination.

The original experiments of Cole and Moore (1960. Biophys. J. 1:161-202.), using conditioning and test membrane potentials to examine the dynamics of the potassium channel conductance in the squid axon, have been extended to test voltage levels by the use of tetrodotoxin to block the sodium conductance. The potassium currents for test voltage levels from -20 to +85 mV were superposable by translation along the time axis for all conditions tested: (a) with depolarizing conditioning voltages; (b) with hyperpolarizing conditioning voltages; and (c) in normal and in high potassium external media. The only deviations from superposition seen were when the internal sodium concentration was abnormally high and the potassium currents showed saturation at high levels of depolarization. Some restoration toward normal kinetics could be obtained by rapidly repeated depolarizations.     

Single channel currents in adrenocortical cells

Single channel currents have been recorded from cell-attached patches of tumoral adrenocortical cells. Our experiments suggest the existence of three sets of potassium channels in the surface membrane of these cells. All channel types can be recorded in a given membrane patch but some patches have only one type of single channel currents. One channel type has a unitary conductance of about 103 pS. The other two channels have smaller conductances and opposite voltage dependence. In one case channels open on depolarization and have a single channel conductance of 31.6 pS. In the other case the probability of being in the open state increases on hyperpolarization and the single channel conductance is of 21 pS. These channels seem to be similar to the delayed and anomalous rectifying potassium channels seen in other preparations. The role of membrane ionic permeability in steroid release induced by ACTH is discussed.     

Potassium ion accumulation at the external surface of the nodal membrane in frog myelinated fibers.

Potassium accumulation associated with outward membrane potassium current was investigated experimentally in myelinated fibers and analyzed in terms of two models-three-compartment and diffusion in an unstirred layer. In the myelinated fibers, as in squid giant axons, the three-compartment model satisfactorily describes potassium accumulation. Within this framework the average space thickness, theta, in frog was 5,900 +/- 700 A, while the permeability coefficient of the external barrier, PK, was (1.5 +/- 0.1) X 10(-2) cm/s. The model of ionic diffusion in an unstirred aqueous layer adjacent to the axolemma, as an alternative explanation for ion accumulation, was also consistent with the experimental data, provided that D, the diffusion constant, was (1.8 +/- 0.2) X 10(-6) cm/s and l, the unstirred layer thickness, was 1.4 +/- 0.1 micron, i.e., similar to the depth of the nodal gap. An empirical equation relating the extent of potassium accumulation to the amplitude and duration of depolarization is given.     

Potassium ion accumulation in a periaxonal space and its effect on the measurement of membrane potassium ion conductance

Summary Potassium currents of various durations were obtained from squid giant axons voltage-clamped in artificial seawater solutions containing sufficient tetrodotoxin to block the sodium conductance completely. From instantaneous potassium current-voltage relations, the reversal potentials immediately at the end of these currents were determined. On the basis of these reversal potential measurements, the potassium ion concentration gradient across the membrane was shown to decrease as the potassium current duration increased. The kinetics of this change was shown to vary monotonically with the potassium ion efflux across the membrane estimated from the integral over time of the potassium current divided by the Faraday, and to be independent of both the external sodium ion concentration and the presence or absence of membrane series resistance compensation. It was assumed that during outward potassium current flow, potassium ions accumulated in a periaxonal space bounded by the membrane and an external diffusion barrier. A model system was used to describe this accumulation as a continuous function of the membrane currents. On this basis, the mean periaxonal space thickness and the permeability of the external barrier to K⁺ were found to be 357 Å and 3.21×10^–4 cm/sec, respectively. In hyperosmotic seawater, the value of the space thickness increased significantly even though the potassium currents were not changed significantly. Values of the resistance in series with the membrane were calculated from the values of the permeability of the external barrier and these values were shown to be roughly equivalent to series resistance values determined by current clamp measurements. Membrane potassium ion conductances were determined as a function of time and voltage. When these were determined from data corrected for the potassium current reversal potential changes, larger maximal potassium conductances were obtained than were obtained using a constant reversal potential. In addition, the potassium conductance turn-on with time at a variety of membrane potentials was shown to be slower when potassium conductance values were obtained using a variable reversal potential than when using a constant reversal potential.     

Different effects of blocked potassium channels on action potentials, accommodation, adaptation and anode break excitation in human motor and sensory myelinated nerve fibres: computer simulations

 Action potentials and electrotonic responses to 300-ms depolarizing and hyperpolarizing currents for human motor and sensory myelinated nerve fibres have been simulated on the basis of double cable models. The effects of blocked nodal or internodal potassium (fast or slow) channels on the fibre action potentials, early and late adaptations to 30-ms suprathreshold slowly increasing depolarizing stimuli have been examined. The effects of the same channels on accommodation after the termination of a prolonged (100 ms) hyperpolarizing current pulse have also been investigated. By removing the nodal fast potassium conductance the action potentials of the sensory fibres are considerably broader than those of the motor neurons. For both types of fibres, the blocked nodal slow potassium channels have a substantially smaller effect on the action potential repolarization. When the suprathreshold depolarizing current intensity is increased, the onset of the spike burst occurs sooner, which is common in the behaviour of the fibres. The most striking differences in the burst activity during early adaptation have been found between the fibres when the nodal fast potassium channels are blocked. The results obtained confirm the fact that the motor fibres adapt more quickly to sustained depolarizing current pulses than the sensory ones. The results also show that normal human motor and sensory fibres cannot be excited by a 100-ms hyperpolarizing current pulse, even at the threshold level. When removing the potassium channels in the nodal or internodal axolemma, the posthyperpolarization increase in excitability is small, which is common in the behaviour of the fibres. However, anode break excitation can be simulated in the fibres with simultaneous removal of the potassium channels under the myelin sheath, and this is more pronounced in the human sensory fibres than in motor fibres. This phenomenon can also be found when the internodal and some of the nodal (fast or slow) potassium channels are simultaneously blocked. Received: 8 November 1999 / Accepted in revised form: 29 February 2000     

Interactions of aminopyridines with potassium channels of squid axon membranes.

The effects of aminopyridines on ionic conductances of the squid giant axon membrane were examined using voltage clamp and internal perfusion techniques. 4-Aminopyridine (4-AP) reduced potassium currents, but had no effect upon transient sodium currents. The block of potassium channels by 4-AP was substantially less with (a) strong depolarization to positive membrane potentials, (b) increasing the duration of a given depolarizing step, and (c) increasing the frequency of step depolarizations. Experiments with high external potassium concentrations revealed that the effect of 4-AP was independent of the direction of potassium ion movement. Both 3- and 2-aminopyridine were indistinguishable from 4-AP except in potency. It is concluded that aminopyrimidines may be used as tools to block the potassium conductance in excitable membranes, but only within certain specific voltage and frequency limits.     

Potassium ion currents in the crayfish giant axon. Dynamic characteristics.

The kinetics of the voltage-sensitive potassium channel in crayfish axon have been examined. The conductance increase after a step depolarization from rest can be described by a first-order kinetic process raised to the third power. When conditioning voltage levels preceded the test pulse, the steady-state conductance was found to be independent of initial conditions. Depolarizing conditioning voltages in general allowed superposition of test voltage potassium currents by a shift along the time axis. Hyperpolarizing conditioning voltages produced a delay in onset of conductance during the test pulse and changed the kinetics so that superposition was not possible. The delay increased during the hyperpolarization with a first-order lag having a time constant in the range of 1.5-3 ms. Return to the resting level caused recovery from the delayed state to follow a single exponential decay with a time constant of 1.9-2.2 ms. The steady state delay vs. voltage curves were not saturated at potentials as negative as -180 mV.     

Increased excitability of acidified skeletal muscle: role of chloride conductance

Generation of the action potentials (AP) necessary to activate skeletal muscle fibers requires that inward membrane currents exceed outward currents and thereby depolarize the fibers to the voltage threshold for AP generation. Excitability therefore depends on both excitatory Na+ currents and inhibitory K+ and Cl- currents. During intensive exercise, active muscle loses K+ and extracellular K+ ([K+]o) increases. Since high [K+]o leads to depolarization and ensuing inactivation of voltage-gated Na+ channels and loss of excitability in isolated muscles, exercise-induced loss of K+ is likely to reduce muscle excitability and thereby contribute to muscle fatigue in vivo. Intensive exercise, however, also leads to muscle acidification, which recently was shown to recover excitability in isolated K(+)-depressed muscles of the rat. Here we show that in rat soleus muscles at 11 mM K+, the almost complete recovery of compound action potentials and force with muscle acidification (CO2 changed from 5 to 24%) was associated with reduced chloride conductance (1731 +/- 151 to 938 +/- 64 microS/cm2, P < 0.01) but not with changes in potassium conductance (405 +/- 20 to 455 +/- 30 microS/cm2, P < 0.16). Furthermore, acidification reduced the rheobase current by 26% at 4 mM K+ and increased the number of excitable fibers at elevated [K+]o. At 11 mM K+ and normal pH, a recovery of excitability and force similar to the observations with muscle acidification could be induced by reducing extracellular Cl- or by blocking the major muscle Cl- channel, ClC-1, with 30 microM 9-AC. It is concluded that recovery of excitability in K(+)-depressed muscles induced by muscle acidification is related to reduction in the inhibitory Cl- currents, possibly through inhibition of ClC-1 channels, and acidosis thereby reduces the Na+ current needed to generate and propagate an AP. Thus short term regulation of Cl- channels is important for maintenance of excitability in working muscle.     

Transfer properties of neuronal dendrites with tonically activated conductances

The somatopetal current transfer was studied in the mathematical models of a reconstructed brainstem motoneuron with tonically activated excitatory synaptic inputs uniformly distributed over dendritic arborization. The soma and axon provided a constant passive leak. The extrasynaptic dendritic membrane was either passive or active (of a Hodgkin-Huxley type). The longitudinal membrane current density (per unit path length) was used as an estimate of the current transfer effectiveness of different dendritic paths. Introduction of a steady uniform voltage-independent conductance per unit membrane area simulated such a synaptic activation. This actions always produced a spatially inhomogeneous membrane depolarization decaying from the distal dendritic tips toward the soma. The reason for such an inhomogeneity was the preponderance of somatopetal over somatofugal input conductance at every site in the dendrites with sealed distal ends and a leaky somatic end. In active dendrites, partial voltage-dependent extrasynaptic conductances followed this depolarization according to their activation-inactivation kinetics. The greater the local depolarization, the greater the contribution of the non-inactivating potassium conductance to the total membrane conductance. The contribution of the inactivated sodium conductance was one order of magnitude smaller. Correspondingly, the effective equilibrium potential of the total transmembrane current became spatially inhomogeneous and shifted to the potassium equilibrium potential. In the passive dendrites, the equilibrium potential remained spatially homogeneous. Inhomogeneities of the dendritic geometry (abrupt change in the diameter and, especially, asymmetrical branching) caused characteristic perturbations in the voltage gradient, so that the path profiles of the voltage, conductances, and currents diverged. This indicated a geometry-induced separation of the dendritic paths in their transfer effectiveness. Active dendrites of the same geometry were less effective than passive ones due to the effect of the potassium conductance associated with the hyperpolarizing equilibrium potential.     

Distribution of Kv1-like potassium channels in the electromotor and electrosensory systems of the weakly electric fish Apteronotus leptorhynchus

The electromotor and electrosensory systems of the weakly electric fish Apteronotus leptorhynchus are model systems for studying mechanisms of high-frequency motor pattern generation and sensory processing. Voltage-dependent ionic currents, including low-threshold potassium currents, influence excitability of neurons in these circuits and thereby regulate motor output and sensory filtering. Although Kv1-like potassium channels are likely to carry low-threshold potassium currents in electromotor and electrosensory neurons, the distribution of Kv1 alpha subunits in A. leptorhynchus is unknown. In this study, we used immunohistochemistry with six different antibodies raised against specific mammalian Kv1 alpha subunits (Kv1.1-Kv1.6) to characterize the distribution of Kv1-like channels in electromotor and electrosensory structures. Each Kv1 antibody labeled a distinct subset of neurons, fibers, and/or dendrites in electromotor and electrosensory nuclei. Kv1-like immunoreactivity in the electrosensory lateral line lobe (ELL) and pacemaker nucleus are particularly relevant in light of previous studies suggesting that potassium currents carried by Kv1 channels regulate neuronal excitability in these regions. Immunoreactivity of pyramidal cells in the ELL with several Kv1 antibodies is consistent with Kv1 channels carrying low-threshold outward currents that regulate spike waveform in these cells (Fernandez et al., J Neurosci 2005;25:363-371). Similarly, Kv1-like immunoreactivity in the pacemaker nucleus is consistent with a role of Kv1 channels in spontaneous high-frequency firing in pacemaker neurons. Robust Kv1-like immunoreactivity in several other structures, including the dorsal torus semicircularis, tuberous electroreceptors, and the electric organ, indicates that Kv1 channels are broadly expressed and are likely to contribute significantly to generating the electric organ discharge and processing electrosensory inputs.     

Gating of Na channels. Inactivation modifiers discriminate among models

Macroscopic Na currents were recorded from N18 neuroblastoma cells by the whole-cell voltage-clamp technique. Inactivation of the Na currents was removed by intracellular application of proteolytic enzymes, trypsin, alpha-chymotrypsin, papain, or ficin, or bath application of N-bromoacetamide. Unlike what has been reported in squid giant axons and frog skeletal muscle fibers, these treatments often increased Na currents at all test pulse potentials. In addition, removal of inactivation gating shifted the midpoint of the peak Na conductance-voltage curve in the negative direction by 26 mV on average and greatly prolonged the rising phase of Na currents for small depolarizations. Polypeptide toxins from Leiurus quinquestriatus scorpion and Goniopora coral, which slow inactivation in adult nerve and muscle cells, also increase the peak Na conductance and shift the peak conductance curve in the negative direction by 7-10 mV in neuroblastoma cells. Control experiments argue against ascribing the shifts to series resistance artifacts or to spontaneous changes of the voltage dependence of Na channel kinetics. The negative shift of the peak conductance curve, the increase of peak Na currents, and the prolongation of the rise at small depolarization after removal of inactivation are consistent with gating kinetic models for neuroblastoma cell Na channels, where inactivation follows nearly irreversible activation with a relatively high, voltage-independent rate constant and Na channels open only once in a depolarization. As the same kind of experiment does not give apparent shifting of activation and prolongation of the rising phase of Na currents in adult axon and muscle membranes, the Na channels of these other membranes probably open more than once in a depolarization.     

Ionic mechanisms of pacemaker activity in cardiac Purkinje fibers.

Rhythmic activity in cardiac Purkinje fibers can be analyzed by using the voltage clamp technique to study pacemaker currents. In normally polarized preparations, pacemaker activity can be generated by two distinct ionic mechanisms. The standard pacemaker potential (phase 4 depolarization) involves a slow potassium current, IK2. Following action potential repolarization, the IK2 channels slowly deactivate and thus unmask a steady background inward current. The resulting net inward current causes the slow pacemaker depolarization. Epinephrine accelerates the diastolic depolarization by promoting more complete and more rapid deactivation of IK2 over the pacemaker range of potentials. The catecholamine acts rather selectively on the voltage dependence of the gating mechanism, without altering the basic character of the pacemaker process. The nature of the pacemaker depolarization is altered by intoxication with high concentrations of cardiac glycosides or aglycones. These compounds promote spontaneous impulses in Purkinje fibers by a mechanism that supersedes the ordinary IK2 pacemaker. The digitalis-induced depolarization is generated by a transient inward current that is either absent or very small in untreated preparations. The transient inward current is largely carried by sodium ions. Its unusual time course probably reflects an underlying subcellular event, the oscillatory release of calcium ions from intracellular stores.     

Influence of chloride, potassium, and tetraethylammonium on the early outward current of sheep cardiac Purkinje fibers

In voltage clamp studies of cardiac Purkinje fibers, a large early outward current is consistently observed during depolarizations to voltages more positive than -20 mV. After the outward peak of the current, the total membrane current declines slowly. Dudel et al. (1967. Pfluegers Arch. Eur. J. Physiol. 294:197--212) reduced the extracellular chloride concentration and found that the outward peak and the decline of the current were abolished. They concluded that the total membrane current at these voltages was largely determined by a time- and voltage-dependent change in the membrane chloride conductance. We reinvestigated the chloride sensitivity of this current, taking care to minimize possible sources of error. When the extracellular chloride concentration was reduced to 8.6% of control, the principal effect was a 20% decrease in the peak amplitude of the outward current. This implies that the membrane chloride conductance is not the major determinant of the total current at these voltages. The reversal potential of current tails obtained after a short conditioning depolarization was not changed by alterations in the extracellular chloride or potassium concentrations. We suspect that the tail currents contain both inward and outward components, and that the apparent reversal potential of the net tail current largely reflects the kinetics of the outward component, so that this experiment does not rule out potassium as a possible charge carrier. The possibility that potassium carries much of the early outward current was further investigated using tetraethylammonium, which blocks potassium currents in nerve and skeletal muscle. This drug substantially reduced the early outward current, which suggests that much of the early outward current is carried by potassium ions.     

Whole-cell currents in single and confluent M-1 mouse cortical collecting duct cells

M-1 cells, derived from a microdissected cortical collecting duct of a transgenic mouse, grown to confluence on a permeable support, develop a lumen-negative amiloride-sensitive transepithelial potential, reabsorb sodium, and secrete potassium. Electron micrographs show morphological features typical of principal cells in vivo. Using the patch clamp technique distinct differences are detected in whole-cell membrane current and voltage (Vm) between single M-1 cells 24 h after seeding vs cells grown to confluence. (a) Under control conditions (pipette: KCl- Ringer; bath: NaCl-Ringer) Vm averages -42.7 +/- 3.4 mV in single cells vs -16.8 +/- 4.1 mV in confluent cells. Whole-cell conductance (Gcell) in confluent cells is 2.6 times higher than in single cells. Cell capacitance values are not significantly different in single vs confluent M-1 cells, arguing against electrical coupling of confluent M- 1 cells. (b) In confluent cells, 10(-4)-10(-5) M amiloride hyperpolarizes Vm to -39.7 +/- 3.0 mV and the amiloride-sensitive fractional conductance of 0.31 shows a sodium to potassium selectivity ratio of approximately 15. In contrast, single cells express no significant amiloride-sensitive conductance. (c) In single M-1 cells, Gcell is dominated by an inwardly rectifying K-conductance, as exposure to high bath K causes a large depolarization and doubling of Gcell. The barium-sensitive fraction of Gcell in symmetrical KCl-Ringer is 0.49 and voltage dependent. (d) In contrast, neither high K nor barium in the apical bath affect confluent M-1 cells, showing that confluent cells lack a significant apical K conductance. (e) Application of 500 microM glibenclamide reduces whole-cell currents in both single and confluent M-1 cells with a glibenclamide-sensitive fractional conductance of 0.71 and 0.83 in single and confluent cells, respectively. Glibenclamide inhibition occurs slower in confluent M-1 cells than in single cells, suggesting a basolateral action of this lipophilic drug on ATP-sensitive basolateral K channels in M-1 cells. (f) A component of the whole-cell conductance in M-1 cells appears as a deactivating outward current during large depolarizing voltage pulses and is abolished by extracellular chloride removal. The deactivating chloride current averages 103.6 +/- 16.1 pA/cell, comprises 24% of the outward current, and decays with a time constant of 179 +/- 13 ms. The outward to inward conductance ratio obtained from deactivating currents and tail currents is 2.4, indicating an outwardly rectifying chloride conductance.     

Ionic basis of the receptor potential in primary endings of mammalian muscle spindles

The effect of changing the ionic composition of bathing fluid on the receptor potential of primary endings has been examined in isolated mammalian spindles whose capsule was removed in the sensory region. After impulse activity is blocked by tetrodotoxin, ramp-and-hold stretch evokes a characteristic pattern of potential change consisting of a greater dynamic depolarization during the ramp phase and a smaller static depolarization during the hold phase. After a high-velocity ramp there is a transient post-dynamic undershoot to below the static level. On release from hold stretch, the potential shows a postrelease undershoot relative to base line. The depolarization produced by stretch is rapidly decreased by the removal of Na+ and Ca2+. Addition of normal Ca2+ partly restores the response. Stretch appears to increase the conductance to Na+ and Ca2+ in the sensory terminals. The postdynamic undershoot is diminished by raising external K+ and blocked by tetraethylammonium (TEA). It apparently results from a voltage-dependent potassium conductance. The postrelease undershoot is decreased by raising external K+, but is not blocked by TEA. It is presumably caused by a relative increase in potassium conductance on release. Substitution of isethionate for Cl- or the addition of ouabain does not alter the postdynamic and postrelease undershoots.     

Influence of intercellular clefts on potential and current distribution in a multifiber preparation.

A theoretical model is presented for current and voltage clamp of multifiber bundles in a double sucrose gap. Attention is focused on methodological errors introduced by the intercellular cleft resistance. The bundle is approximated by a continuous geometry. Voltage distribution, as a function of radial distance and time, is defined by a parabolic partial differential equation which is specified for different membrane characteristics. Assuming a linear membrane, analytical solutions are given for current step and voltage step conditions. The theoretical relations (based on Bessel functions) may be used to calculate membrane conductance and capacity from experimental clamp data. The case of a nonlinear membrane with standard Hodgkin-Huxley kinetics for excitatory Na current is treated assuming maximum Na conductances (gNa) of 120, 10, and 1 mmho/cm2. Numerical simulations are presented for potential and current distribution in a bundle of 60 microns diameter during depolarizing voltage steps. Adequate voltage control is restricted to the peripheral fibers of the bundle whereas the membrane potential of the inner fibers deviates from the command level during early inward current, tending to the Na equilibrium potential. In the peak current-voltage diagram the loss of voltage control is reflected by an increased steepness of the negative region and a decreased slope conductance of the positive region. With gNa = 120 mmho/cm2, the positive slope conductance is approximately 25% of the slope expected from ideal space clamping. With the lower values of gNa, the slope conductance ratio is in the order of 50%. Implications of the results for an experimental voltage clamp analysis of early inward current on multifiber preparations are discussed.