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The Journal of Neuroscience, September 15, 1998, 18(18):7436-7451
Critical Role of Axonal A-Type K+ Channels and Axonal Geometry in the Gating of Action Potential Propagation along CA3 Pyramidal Cell Axons: A Simulation Study
Irina L. Kopysova1, 2, 3 and Dominique Debanne1 1 Unité de Neurocybernétique Cellulaire, UPR 9041 Centre National de la Recherche Scientifique, 13009 Marseille, France, 2 Innovationskolleg Theoretische Biologie, Humboldt-Universität zu Berlin, 10115 Berlin, Germany, and 3 Unité de Neurobiologie Expérimentale et Théorie des Systèmes Complexes, UPR 9081 Centre National de la Recherche Scientifique, 75231 Paris, France
ABSTRACT
Top
Abstract
Introduction
A model of CA3 pyramidal cell axons was used to study a new mode of gating of action potential (AP) propagation along the axon that depends on the activation of A-type K+ current (Debanne et al., 1997
). The axonal membrane contained voltage-dependent Na+ channels, K+ channels, and A-type K+ channels. The density of axonal A-channels was first determined so that (1) at the resting membrane potential an AP elicited by a somatic depolarization was propagated into all axon collaterals and (2) propagation failures occurred when a brief somatic hyperpolarization preceded the AP induction. Both conditions were fulfilled only when A-channels were distributed in clusters but not when they were homogeneously distributed along the axon. Failure occurs in the proximal part of the axon. Conduction failure could be determined by a single cluster of A-channels, local decrease of axon diameter, or axonal elongation. We estimated the amplitude and temporal parameters of the hyperpolarization required for induction of a conduction block. Transient and small somatic hyperpolarizations, such as simulated GABAA inhibitory postsynaptic potentials, were able to block the AP propagation. It was shown that AP induction had to occur with a short delay (<30 msec) after the hyperpolarization. We discuss the possible conditions in which such local variations of the axon geometry and A-channel density may occur and the incidence of AP propagation failures on hippocampal network properties.
Key words: hippocampus; modeling; conduction failure; neural networks; short-term plasticity; A-current
INTRODUCTION
The main function of the axon is to conduct action potentials (APs) from the cell body to the nerve terminals, thus allowing a spread of activity over long distances in the brain (Ramon y Cajal, 1911
Conduction failures have been found in various types of neurons when APs are elicited at a frequency >10-30 Hz (Parnas, 1972
A novel form of gating that requires the activation of a fast A-type K+ current has recently been reported in CA3 pyramidal cells in vitro (Debanne et al., 1997
Propagation failures were induced in only 30% of the cases (Debanne et al., 1997
The first aim of this study was to simulate experimental gating of AP propagation. In a second step, we determined the incidence of local variations in A-channel density and in the morphology of CA3 pyramidal cell axons on AP conduction. We then estimated the minimal hyperpolarization required to induce a propagation block. Finally, we discussed which physiological hyperpolarization can provide favorable conditions for conduction failure.
The present experimental results have been published previously (Debanne et al., 1997
MATERIALS AND METHODS
Experimental data
Briefly, pairs of cells were recorded intracellularly in hippocampal slice cultures (Gähwiler, 1981Morphology of the modeled cell
The modeled structure included a soma, the principal axon, and main axon collaterals but was devoid of dendrites (see Fig. 2B). The axon was a reduced version of a CA3 pyramidal cell axon labeled in vivo, with geometrical parameters described by Li et al. [(1994
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Table 1. Morphological parameters of the structure Biophysics of the modeled cell
Properties of simulated A-current. Steady-state gating parameters of simulated A-current are shown in Figure 1A. The voltage dependence of activation and inactivation was abrupt, as reported for hippocampal neurons (Numann et al., 198770 mV (Segal et al., 1984
Simulations reproduced the results of voltage-clamp experiments in the hippocampus in vitro with different characteristics of the hyperpolarizing prepulse (Segal et al., 1984
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Figure 1. Properties of A-current in an isolated compartment of membrane. A, Activation and inactivation curves of A-current. Note that at the RMP (vertical arrow), most of the channels were inactivated. B, Level of the hyperpolarization and recovery from inactivation in simulations of voltage-clamp-mode experiments. The holding potential was
Distribution of A-channels. In the model, a parameter of A-channel density, GA, was expressed as a function of the maximal conductance GA,max: GA = GA,max · a · b, where a and b are the variables of activation and inactivation, respectively (see and Fig. 1A). In patch-clamp experiments, the density of A-current in the soma of CA3 pyramidal neurons has been found to vary between 0.055 and 0.377 mA/cm2 (Klee et al., 1995
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Table 2. Distribution of ionic channels
RESULTS
Propagation of the AP elicited from RMP
We first determined the configuration of the model that allowed successful propagation of the AP into all axonal collaterals under inactivation of the A-current (i.e., at the RMP).
We considered homogeneous distribution of A-channels along the whole axon. The parameter GA,max varied between 0.5 and 5 mS/cm2 (Fig. 2A). AP elicited by a somatic depolarizing step of current was successfully propagated into all axon branches when GA,max was set up to 2.5 mS/cm2 (Fig. 2A,B). When A-channel density had been increased to 2.6 mS/cm2, AP failed in several branches [12 and 16 (Fig. 2A,C)]. The number of axon collaterals exhibiting failures increased with A-channel density. With GA,max of 4.5 and 5 mS/cm2, the AP was still initiated at the area of AP generation but did not reach any terminal (Fig. 2A).
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Figure 2. Propagation of the AP along the axon with different distributions of A-channels. A, Homogeneous distribution. Amplitudes of the AP in the area of the spike generation (branch 1) and in five axonal collaterals (2, 7, 10, 12, and 16; see B) as a function of the density of A-channels. At low density (GA,max 2.5 mS/cm2), the AP propagated into all axonal terminals. At GA,max = 2.6 mS/cm2 conduction failed in branch 16 of the principal axon and collateral 12 was obtained. With further increase of GA,max, more terminals were blocked, and at GA,max = 4.5 mS/cm2 the AP failed to reach any terminal. B, Details of AP propagation within the whole axonal arborization when A-channels were distributed homogeneously with a low density (GA,max = 2.5 mS/cm2). Action potentials were elicited by a brief current-induced depolarization (inflection on the rising phase of the AP). C, Propagation failed in the principal axon (16) and in the collateral 12 (blue traces) when A-channel density was increased to 2.6 mS/cm2. D, Successful propagation when hot spots of A-channels (GA,max = 4.1 mS/cm2) at the branch points were added to a low homogeneous density of A-channels (GA,max = 1.2 mS/cm2).
AP propagation from the cell body to all nerve terminals was also successful when hot spots of A-channels (GA,max = 4.1 mS/cm2) at the branch points were added to homogeneously (GA,max = 1.2 mS/cm2) distributed A-channels (Fig. 2D). The presence of the hot spots of A-channels at the bifurcations decreased the AP amplitude at the branch point between branches 9 and 11 (Fig. 2, compare B,D). The AP, however, was able to recover and propagate actively into all axon terminals.
AP propagation after a somatic hyperpolarization
Propagation of the AP elicited after a hyperpolarizing prepulse was tested in the two configurations that allowed a successful propagation from the RMP [i.e., homogeneous density with GA,max = 2.5 mS/cm2 (Fig. 2B), and clustered distribution (Fig. 2D)]. The configuration that did not allow successful propagation from the RMP (GA,max = 2.6 mS/cm2) was discarded.
The AP was elicited after a hyperpolarizing current prepulse applied at the soma (Fig. 3A,B). The delay between the onset of the depolarizing step of the current and the spike was 1.2 msec. With homogeneously distributed A-channels, the AP propagated into all terminals, although locally (in branches 9, 11, and 13) the amplitude of the AP was reduced (Fig. 3A). The propagation failure was not possible to obtain even when the hyperpolarization was increased to
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Figure 3. Propagation of the AP after a hyperpolarizing prepulse. A, Simulations for homogeneous distribution of A-channels (GA,max = 2.5 mS/cm2). AP was elicited after a 20 msec hyperpolarizing prepulse of 9.5 mV. No conduction failure was induced. B, Clustered distribution as in Figure 2D. The same hyperpolarization induced propagation failures along the principal axon (branch 16) and collateral 12 but not in adjacent collaterals (2, 7, and 10). C, Selective conduction block in CA3 cells of hippocampal slice cultures. Pairs of two monosynaptically CA3 pyramidal cells were recorded intracellularly. Presynaptic AP induced in the cell (1) at the RMP evoked an EPSP in cell (2). When cell (1) was phasically hyperpolarized, no EPSP was elicited in the cell (2). The electrode was then removed from the cell (2) and inserted in the cell (3). Even in the presence of phasic hyperpolarization, the presynaptic AP always evoked an EPSP. AP thus failed in the axonal collateral of cell (1) to cell (2), but not in the branch to cell (3).
Determination of the location of propagation failure
The location of AP failure is very difficult to determine experimentally because it would require multiple electrophysiological recordings from the axon. These recordings can be performed in large crustacean axons (Grossman et al., 1979a
A-channels are inactivated at the RMP. To produce a propagation block, A-channels have to recover from inactivation. This can be achieved only if axonal membrane is hyperpolarized (Fig. 1B). Therefore it is important to determine how far in the axon a somatic hyperpolarization can be spread electrotonically.
The model showed that a steady-state somatic hyperpolarization of 9.5 mV applied at the soma attenuated along the principal axon within the first 200 µm (Fig. 4A). Downstream from the first bifurcation point (100 µm), the level of the hyperpolarization was already attenuated by almost 50%. Only 8.5% of the hyperpolarization remained behind the third bifurcation. Hyperpolarization was attenuated almost completely at 240 µm (210 µm from the soma), suggesting that AP failure could occur only along this proximal part of the axon.
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Figure 4. Location of the AP failure along the principal axon. A, Electrotonic attenuation along the principal axon of a steady-state hyperpolarization to
To determine the location of the conduction failure more precisely, we compared the amplitudes of the AP, A-currents, and Na+ currents in the soma (Fig. 4B) and at four points along the proximal part of the principal axon (Fig. 4C). Simulations were performed with and without the hyperpolarizing prepulse. Because the level of the hyperpolarization in the very proximal area was only slightly attenuated (Fig. 4A), the preliminary hyperpolarization drastically increased the A-current (26% at the area of spike generation) (Fig. 4C, first recording point). This increase, however, had only a small influence on the amplitude of the AP because of the high density of Na+ channels in this area, which were also deinactivated by the hyperpolarization (see Na+ currents in Fig. 4C). Compared with control, a delay of ~1 msec in the generation of the AP was observed. Downstream from the first bifurcation point (Fig. 4C, second recording point), somatic hyperpolarization was still able to significantly increase the A-current (up to 14%). The proximity of the area of the AP initiation kept the amplitude of the AP almost unchanged. Reduction of ~1 mV in the AP amplitude was found at this level. Farther away from the area of the spike generation, the hyperpolarization-induced increase in the A-current played a more important role. Behind the second bifurcation (Fig. 4C, third recording point), the small increase in the A-current (only 7%) led to a 1.5 mV reduction in the AP amplitude. The AP was dramatically attenuated between second and third bifurcation (Fig. 4C, fourth recording point). Indeed, behind the third bifurcation, the AP amplitude was 8 mV smaller than under control conditions (oblique arrow).
We conclude that propagation failure occurred in the axonal branches that meet two conditions. First, the area must still be under the influence of the somatic hyperpolarization and therefore be proximal. Second, it must be remote from the area of high density of Na+ channels so that the effect of the A-current expresses. In other words, the failure occurred in the axonal region where the potassium inhibition dominated the sodium activation. In the next experiments, we studied how the modifications in the density of A-channels and in the axonal geometry affected the AP propagation.
Single clusters of A-channels determine propagation failure
We first tested the consequences of removing a single proximal hot spot of A-channels on the conduction properties. To examine this question, we used the configuration illustrated in Figure 3B (and reproduced by a dashed line in Fig. 5). Because the area between the second and third branch points was a region of low safety for AP propagation, we chose to remove the hot spot at the second branch point (indicated by a dashed circle). When the hot spot was removed, the AP was conducted successfully to the end of the principal axon (Fig. 5).
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Figure 5. Effect of removal of a single cluster on propagation failure. The control configuration was indicated by a dashed line. When the cluster of A-channel was removed from the second branch point (indicated by the dashed circle), the AP propagated successfully into all axon terminals (solid line).
These results show that A-channel activation is required for AP conduction to be blocked and that a single cluster of A-channels in the area of AP failure might influence the AP propagation along the axon (see Discussion).
Role of the axonal morphology
In a second step, we tested the consequences of geometrical modifications within the proximal part of the axon. In organotypic slice cultures, propagation failures were found in approximately one-third of CA3 pyramidal cell axons (Debanne et al., 1997
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Figure 6. Effect of axon elongation and reduction of the axonal diameter on propagation failure. A, Control configuration. B, The length of axonal branch 9 was increased from 50 (a, b in A) to 100 µm (a, b' in B). As a result, the AP propagated into all axonal collaterals. C, The diameter was decreased by 0.1 µm in three branches labeled by × (9, 10, and 11). Propagation into the whole axonal arborization was achieved.
When the length of branch 9 (limited by branch points a and b) was increased by 50 µm, propagation failures were suppressed (Fig. 6B). Similarly, conduction was successful in the whole axonal tree when the axon diameter was reduced by 0.1 µm in the axonal branches labeled by × (Fig. 6C).
Time courses of the AP were calculated for each 10 µm along branches 3 and 9, and along the first 20 µm of branches 10 and 11. AP amplitudes were measured and compared for the three configurations in Figure 6. Close to the area of AP initiation (70 µm from the soma), AP amplitudes were identical in all configurations (Fig. 7). Under control conditions (black triangles), the amplitude of the AP decreased along the axon, with larger gradients at the vicinity of each branch point (a and b). Behind the second branching point (150 µm), the difference in the AP amplitudes in branches 10 and 11 was ~4 mV. AP was sufficiently high to activate Na+ channels in the right branch (10) but not in the left (11).
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Figure 7. Comparison of AP amplitudes in three morphological configurations shown in Figure 6: control, with elongated branch and with decreased diameters. Part of the modeled structure included branches 3 and 9 and the first 20 µm of branches 10 and 11. Labeling of the branch points a, b, and b' is the same as in Figure 6. In the control (filled triangles), the amplitude decreased in the vicinity of branch points a and b. The amplitude was sufficient to allow active propagation into branch 10 but not into branch 11. When the distance between the two branch points was increased (a, b', empty circles), the amplitude of the AP was able to recover after passing the bifurcation a (110 µm). Approaching b', the AP amplitude decreased. Active propagation, however, was achieved in both branches after b' (200 µm). For decreased diameters (filled circles), the amplitude drop was also weaker than in control, and active propagation into both collaterals (10 and 11) was observed.
In contrast with the control situation, the AP amplitude was locally preserved when the axon was elongated between a and b (empty circles). In this configuration the branching point b was replaced by b'. The distance between two successive clusters of A-channels (at a and b') was increased. After the first bifurcation (100-140 µm), the AP amplitude increased and then progressively decreased while approaching the second bifurcation (b'). The AP was able to propagate into both the principal axon (11) and the collateral (10).
When the axon diameter was decreased (filled circles) in the branch between the bifurcations a and b, the input impedance increased by 15%. As a result, when the AP reached the bifurcation a, its amplitude was less attenuated than in control (black triangles). Behind the bifurcation b, APs in both daughter branches were sufficiently high to allow active propagation up to the end of these collaterals.
In all cases, the amplitude of the AP in branch 11 was smaller than in 10 because of the proximity of the next bifurcation (see the whole structure in Fig. 6).
Required minimal amplitude and duration of the hyperpolarization for conduction block
Physiological hyperpolarizations are limited in both duration and amplitude by several factors, such as the kinetics of transmitter release, access, degradation or buffering of the second messengers, kinetics of activation and inactivation of the channels involved, and the equilibrium potentials of the ions that flow through the channels.
To know whether physiological hyperpolarizations suffice to induce a conduction block, we estimated the minimal duration and amplitude of a current-induced hyperpolarization to produce a conduction failure. In addition to the GA,max = 4.1 mS/cm2 used before, we considered two other densities of A-channels in the hot spots: GA,max = 4 and 4.05 mS/cm2.
As expected from inactivation properties of the A-channels, the level required for hyperpolarization was lower for larger durations of the hyperpolarization (Fig. 8B). For example, when the A-channel density at the branch points was 4.05 mS/cm2, a 10 msec hyperpolarization had to be as large as
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Figure 8. Amplitude and duration of the hyperpolarization required for the conduction failure. For different durations of the hyperpolarizing prepulse (10-50 msec), the minimal level of the hyperpolarization allowing a conduction failure was determined. Three densities of the A-channels in the hot spots were considered (GA,max = 4, 4.05, and 4.1 mS/cm2). The hyperpolarization required for deinactivation of the A-channels decreased when the duration increased. Note the saturation for durations larger than 40 msec. The required hyperpolarization increased significantly with a small decrease in the A-channel density. For a 10 msec prepulse, hyperpolarizations deeper than
Because GA,max = 4.1 mS/cm2 was found to provide a conduction block even with very small levels of hyperpolarization, we used a smaller value of GA,max (4.05 mS/cm2) in the next computations.
Role of the delay between the hyperpolarization and AP induction
In all previous examples, depolarizing currents were applied with a fixed delay of 1 msec after the offset of the hyperpolarizing current. We examined the role of this delay on AP conduction along the principal axon (Fig. 9). For these computations, the amplitude of the hyperpolarization at the soma was set to 30 mV. For small delays of 1-25 msec (Fig. 9A,B), no signal reached the terminal of the principal axon. AP propagation was successful, however, when the delay was increased to 35 msec (Fig. 9C). Similarly, for a delay of 25 msec, propagation recovered when a short subthreshold depolarization (5 msec, 4.4 mV) followed the hyperpolarizing prepulse (Fig. 9D). In all cases, the time course of A-current was calculated (Fig. 9A-D, second trace). The amplitude of A-current decreased when the delay was increased (Fig. 9E). At 25 msec, this amplitude was much smaller when the subthreshold depolarization was added.
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Figure 9. Critical delay between the hyperpolarization and AP induction (GA,max = 4.05 mS/cm2). A, Time courses of the transmembrane potential (Vm,soma, top traces) and density of A-current (VA,soma, middle traces) in the soma, and potential in terminal 16 of the principal axon (Vm,terminal, bottom traces) were calculated for different delays between the hyperpolarization and AP induction. Hyperpolarizing prepulse was 30 mV and its duration was 20 msec. A conduction block along the principal axon was observed when hyperpolarizing prepulse preceded the AP by 1 msec. B, Similar results were obtained for a delay of 25 msec. C, When the delay was increased to 35 msec, propagation into the principal axon was successful. D, When a 5 msec subthreshold depolarization was added to the configuration in B (25 msec delay), the AP propagated normally along the principal axon. E, Graph of the peak amplitude of A-current during the AP (shown in A-D) as a function of the delay. Note that for a delay of 25 msec, the peak amplitude was significantly reduced when a small depolarization event was added. F, Experimental results. Two monosynaptically coupled CA3 pyramidal cells were recorded intracellularly. When the hyperpolarizing prepulse preceded the AP by 15 msec in the cell (1), no EPSP was elicited in the cell (2). Propagation failure was not observed when the delay was increased to 35 msec.
Similar critical values were observed in experiments [Fig. 9F and Debanne et al. (1997)
AP propagation block after GABAA IPSPs
The preceding computations showed that relatively small hyperpolarizations were able to block the AP conduction in the axon. We therefore tested whether a simulated GABAA IPSP of small amplitude would block AP propagation. In the absence of any IPSP, the AP reached both the end of the collateral (Fig. 10A, trace 2) and the principal axon (Fig. 10A, trace 3). A somatic GABAA-like IPSP of 5.5 mV was generated at the soma by an increase in Cl
-conductance with the profile of an
-function (Fig. 10B, trace 1). Because of a fast attenuation along the principal axon, the IPSP did not influence the membrane potential at the terminals (Fig. 10B, traces 2 and 3). A selective failure in the principal axon (Fig. 10C, trace 3) but not in the collateral (Fig. 10C, trace 2) was obtained when the AP was evoked after the onset of the simulated IPSP (Fig. 10C).
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Figure 10. Conduction block induced by a somatic IPSP (GA,max = 4.05 mS/cm2). A, GABAA-receptor synaptic input was placed on the soma. Without synaptic activation, the AP elicited at the soma (1) propagated into both collateral (2) and principal axon (3). B, Membrane potentials in the soma (1), collateral (2), and principal axon (3) in response to activation of the synaptic input. No hyperpolarization was detected in the collateral and principal axon. C, The AP failed to propagate into the principal axon (arrow on trace 3) when it was elicited at the maximum of the IPSP (see trace 1). It was still able to propagate into the collateral (2). D, Experimental conduction block. Two pyramidal cells were recorded intracellularly in areas CA3 (1) and CA1 (2). Similar effects were observed for the current-induced (right) and synaptically induced (left) hyperpolarizations of the cell (1). When the hyperpolarization preceded the presynaptic AP by <10 msec (top), no EPSP was observed postsynaptically (arrows). When the delay between the hyperpolarizing prepulse and the presynaptic AP was >30 msec (bottom), an EPSP was elicited for both types of hyperpolarization, indicating normal AP conduction into the presynaptic axon. The complex response before the unitary EPSP in the cell (2) resulted from activation of Schaffer collaterals.
Comparable conduction block was observed experimentally [Debanne et al. (1997)
Density and kinetics of Na+ channels
Because the exact measurements of density and kinetic properties of Na+ channels in the axons of the hippocampal pyramidal neurons are lacking, it was important to study how the model behavior depends on the parameters of Na+ channels.
In the first set of experiments we varied the density of Na+ channels (parameter GNa,max) on the soma and along the axon around the value of 50 mS/cm2 used in previous simulations. The maximum density of A-channels in the bifurcation hot spots (parameter GA,max) that allowed the successful propagation into all axonal terminals at the RMP was determined for each value of GNa,max. The values of the maximum possible GA,max in the hot spots as function of the density of Na+ channels are presented in Figure 11A (top). For GNa,max lower than 35 mS/cm2, the AP failed to propagate into some axonal terminals even when hot spots were suppressed and A-channels were homogeneously distributed (GA,max = 1.2 mS/cm2) along the whole axon. With an increase of GNa,max the maximal possible density of A-channels increased almost linearly. Ratio GNa,max/GA,max was calculated for different GNa,max and presented in Figure 11A (middle). It was suggested that both successful propagation at the RMP and hyperpolarization-induced block of spike propagation could be obtained more easily at higher density of Na+ channels when the ratio GNa,max/GA,max was higher. Results of the estimations of the hyperpolarization required for conduction failure into the principal axon are presented in Figure 11A (bottom). One can notice from the comparison of the middle and bottom of Figure 11A that the required level of the hyperpolarization was determined by the ratio GNa,max/GA,max. For GNa,max = 35 mS/cm2, when GNa,max/GA,max was 16.5, the required hyperpolarization was
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Figure 11. Role of the density and kinetics of Na+ channels. A, Variation of the density. The density of Na+ channels (GNa,max) varied between 35 and 60 mS/cm2 in the soma and along the axon. In the area of spike generation the density of Na+ channels was 30 times higher. Top, The density of A-channels (GA,max) in the hot spots was calculated from the condition of successful spike propagation into all axonal collaterals at the RMP. GA,max increases with the increase of GNa,max. Middle, The ratio GNa,max/GA,max was calculated from the data presented in the top. To higher density of Na+ channels corresponded higher GA,max and lower GNa,max/GA,max. Bottom, The level of the hyperpolarization required to induce a failure of the spike propagation into the principal axon. The duration of the hyperpolarization was 20 msec. For GNa,max >40 mS/cm2, the required level of the hyperpolarization was found to be lower than
In the next set of simulations, we studied the role of the kinetic properties of Na+ current. We considered the cases when the time constants of both activation and inactivation of Na+ channels were multiplied by a scale factor ranging from 0.1 to 2. The results of simulated propagation of the AP into five axonal terminals for different kinetics of Na+ channels are presented in Figure 11B. For all considered kinetics, a somatic depolarizing step of current induced generation of the AP in the area of spike generation in the axon (Fig. 11B, open circles). The AP successfully propagated into all axon terminals when time constants were multiplied by a scale factor ranging from 1 to 2. When the kinetics of Na+ channels were accelerated (multiplied by a scale factor ranging from 0.4 to 0.9), AP propagation failed in several branches (10, 12, and 16). The number of axon collaterals exhibiting conduction failure increased with further acceleration of the Na+ channel kinetics. When time constants of activation and inactivation of Na+ channels were decreased tenfold, the AP was still initiated at the area of AP generation but did not reach any terminal (Fig. 11B).
The level of the hyperpolarization required for conduction failure was influenced only slightly when the time constants of activation and inactivation of Na+ channels were increased two times. For both control and twofold slower Na+ kinetics, propagation failure in the principal axon was observed when a 20 msec hyperpolarizing prepulse of 6 mV preceded the AP (data not shown).
DISCUSSION
We provide theoretical evidence that axonal A-current can be deinactivated by somatic hyperpolarization in the physiological range and consequently induces a conduction block. This type of gating differs from previous studies (Smith, 1980
Ionic channel densities and AP propagation
Successful propagation and hyperpolarization-induced conduction failure were obtained only if A-channels were clustered. With homogeneous distributions, it was not possible to reproduce experimental observations, i.e., successful propagation when the AP was elicited from RMP, and failure when the AP was preceded by a hyperpolarization. APs elicited from RMP failed in several branches when the density was high, and no conduction failure could be induced by the conditioning hyperpolarization when the density was low. Although these configurations do not account for the experimentally observed gating, both cases should retain attention. It is plausible that two-thirds of the CA3 cells that did not show the conduction failures (Debanne et al., 1997
Despite the growing knowledge about the different subunits of the family of A-type channels (Dolly and Parcej, 1996
According to our findings, clustered distribution of A-channels appears crucial for this form of gating. In the hippocampus, hot spots of A-channels are found in the axons of granule cells (Cooper et al., 1998
One of the most important conclusions of our study is that only a few clusters of A-channels at some strategic points in the proximal axonal arborization determine whether the AP propagates. The removal of only one cluster allows normal AP conduction in the whole axonal arborization. Moreover, a small modification in A-channel density at the branch points strongly modified the threshold for the conduction block (Fig. 8). This suggests that the local modulation of A-channel efficacy can regulate the output signal of the neuron in some target areas. In dendrites of hippocampal neurons, reduction of A-channel density is sufficient to modify the back-propagating AP (Hoffman et al., 1997
When can such modulation occur? The activity of A-channels is controlled by numerous neurotransmitters such as GABA (Gage, 1992
Our results must be qualified in two important ways. We used a homogeneous distribution of Na+ channels with one proximal hot spot. The presence of this hot spot has recently been reported in cultures of dissociated hippocampal cells (Dargent et al., 1998
Where does the failure occur?
We showed that failure could occur only if in the axon two conditions were met. The critical region had to be proximal to allow deinactivation of A-channels by the hyperpolarization, but it also had to be far enough from the area of high density of Na+ channels (i.e., area of spike generation). We found that this region was in the proximal part of the axonal arborization (Fig. 4). This conclusion was corroborated by the speed at which 4-aminopyridine in the presynaptic recording pipette blocked conduction failures. The effect of the blocking agent occurred within 2 min after somatic impalement (Debanne et al., 1997
This evaluation, however, must be qualified in three different ways. The location of AP failure was determined for a given structure and for a limited hyperpolarization (~10 mV). It is well established that changes in parameters such as axonal morphology, membrane resistivity, and amplitude of the applied hyperpolarization would modify the attenuation profiles of the steady-state voltages (Rall, 1989
Temporal requirements for AP block
Two temporal parameters are critical for the A-current-dependent block of AP propagation: the duration of the preliminary hyperpolarization and the time interval between hyperpolarization and AP induction. Both parameters are determined by the time constant of A-current inactivation. These temporal requirements determine the optimal profile of the membrane potential to produce conduction failures, i.e., prolonged hyperpolarization followed by fast depolarizing transition. Our results suggest that slow IPSPs and AHPs, or summated fast IPSPs evoked at high frequency, would be more efficient than single fast IPSPs to produce conduction failure. Moreover, introduction of a subthreshold depolarization between the prepulse and the AP was sufficient to restore propagation at short delays that had not permitted conduction. This result underscores the importance of the recent history of neuronal activity for the propagation of APs along the axon. Any depolarizing event in the neuron (such as EPSPs) could accelerate the A-channel inactivation and consequently reduce the critical time interval during which A-current can induce conduction block.
Physiological hyperpolarizations that produce conduction failures
GABAA receptor-mediated IPSP of a few millivolts blocked AP propagation both experimentally and in the simulations. It is interesting to note that the amplitude of the simulated IPSP was smaller than the threshold for conduction block when a hyperpolarization was induced by current. This apparent discrepancy resulted from the additive effect of the shunt of the chloride conductance underlying the IPSP. It further demonstrates that current injections that are usually used to mimic EPSPs or IPSPs cannot account for complex mechanisms of gating of AP propagation that involve synaptic shunting.
Other physiological hyperpolarizations such as AHPs may also produce conduction failures. Failures have been observed in cell pairs that exhibited current-induced conduction blocks when single presynaptic APs were elicited at a frequency of 1 Hz (D. Debanne, unpublished observations). Vincent and Marty (1996)
Consequences for the function of hippocampal networks
Conduction failures mediated by A-current activation may affect the function of the hippocampal networks at several levels.
First, for two monosynaptically coupled neurons, conduction failures produce a functional disconnection, as reported by Debanne et al. (1997)
For a branching axon that contacts different postsynaptic neurons, it was important to show that AP failed preferentially in some collaterals. Selective conduction blocks were shown to determine receptive field properties in sensory neurons of the leech (Gu, 1991
Finally, the studied phenomenon could have important consequences in the whole hippocampal network. It has been proposed that networks of interneurons entrain cortical, synchronized theta (4-7 Hz), and gamma (40 Hz) activity (Lytton and Sejnowski, 1991
àlek et al., 1997
FOOTNOTES Received Feb. 23, 1998; revised June 24, 1998; accepted July 1, 1998.
This work was supported by Centre National de la Recherche Scientifique and Deutsche Forschungsgemeinschaft (I.L.K.) and a Fondation pour la Recherche Médicale grant (D.D.). We thank Drs. H. Bras, Y. Frégnac, B. H. Gähwiler, N. C. Guérineau, A. Herz, S. Korogod, T. Launay, and S. Tyc-Dumont for helpful discussions and constructive criticisms on this manuscript. We are particularly indebted to Professors B. H. Gähwiler and S. M. Thompson for collaboration on the experiments performed at the Brain Research Institute (University of Zurich, Switzerland) that are briefly reported here for comparison.
Correspondence should be addressed to Dr. Dominique Debanne, Unité de Neurocybernétique Cellulaire, UPR 9041 Centre National de la Recherche Scientifique, 280 Boulevard Sainte Marguerite, 13009 Marseille, France.
APPENDIX The transmembrane voltage V along the modeled structure was calculated solving the cable equation numerically:
(A1) where x is a coordinate and a(x) the diameter of the structure. Cm denotes the capacity per unit area (1 µF/cm2). Ri is the resistivity of the cytoplasm (100
· cm). Im, Isyn, and Iinj are densities of transmembrane ionic current, postsynaptic current, and polarizing current injected in the first compartment of the soma, respectively.
For each compartment of the soma, Im was represented as:
and for each compartment of the axon as:
(A2) where INa denotes the current through excitable Na+ channels, IK the delayed rectif
(A3)
