Modeling Action Potential Initiation and Back-Propagation in Dendrites of Cultured Rat Motoneurons

Hans-R. Lüscher and Matthew E. Larkum

Department of Physiology, University of Bern, CH-3012 Bern, Switzerland

    ABSTRACT
Abstract
Introduction
Methods
Results
Discussion
References

Lüscher, Hans-R. and Matthew E. Larkum. Modeling action potential initiation and back-propagation in dendrites of cultured rat motoneurons. J. Neurophysiol. 80: 715-729, 1998. Regardless of the site of current injection, action potentials usually originate at or near the soma and propagate decrementally back into the dendrites. This phenomenon has been observed in neocortical pyramidal cells as well as in cultured motoneurons. Here we show that action potentials in motoneurons can be initiated in the dendrite as well, resulting in a biphasic dendritic action potential. We present a model of spinal motoneurons that is consistent with observed physiological properties of spike initiation in the initial segment/axon hillock region and action potential back-propagation into the dendritic tree. It accurately reproduces the results presented by Larkum et al. on motoneurons in organotypic rat spinal cord slice cultures. A high Na+-channel density of &gmacr;Na = 700 mS/cm2 at the axon hillock/initial segment region was required to secure antidromic invasion of the somato-dendritic membrane, whereas for the orthodromic direction, a Na+-channel density of &gmacr;Na = 1,200 mS/cm2 was required. A "weakly" excitable (&gmacr;Na = 3 mS/cm2) dendritic membrane most accurately describes the experimentally observed attenuation of the back-propagated action potential. Careful analysis of the threshold conditions for action potential initiation at the initial segment or the dendrites revealed that, despite the lower voltage threshold for spike initiation in the initial segment, an action potential can be initiated in the dendrite before the initial segment fires a spike. Spike initiation in the dendrite depends on the passive cable properties of the dendritic membrane, its Na+-channel density, and local structural properties, mainly the diameter of the dendrites. Action potentials are initiated more easily in distal than in proximal dendrites. Whether or not such a dendritic action potential invades the soma with a subsequent initiation of a second action potential in the initial segment depends on the actual current source-load relation between the action potential approaching the soma and the electrical load of the soma together with the attached dendrites.

    INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References

Early work on the cat and toad motoneurons in vivo (Araki and Otani 1955; Brock et al. 1953; Coombs et al. 1957; Fuortes et al. 1957) suggested that action potentials are initiated in the axon hillock and initial segment region. It was shown that action potentials recorded from the somata of motoneurons have at least two components: a smaller initial segment (IS) spike and a larger somato-dendritic (SD) spike. The antidromic spike, set up by muscle nerve stimulation, sometimes failed to evoke the SD component, leaving the IS spike in isolation. The IS spike always preceded the SD spike independent of orthodromic or antidromic stimulation. This observation led to the hypothesis that the action potential is initiated at the initial segment. It was shown with voltage-clamp recordings that this region has a lower threshold for action potential initiation than the soma (Araki and Terzuolo 1962), and it was speculated that the axon hillock and initial segment might have a sodium channel density as high as the node of Ranvier (Dodge and Cooley 1973). Support for this suggestion came from electron microscopy studies showing morphological membrane similarities between the initial segment and the node of Ranvier (Palay et al. 1968; Peters et al. 1968). Recent modeling studies on cortical pyramidal neurons provided theoretical justification for high Na+-channel density at the axon hillock and initial segment (Mainen et al. 1995; Rapp et al. 1996). However, attempts to directly measure Na+-channel density in the axon hillock and initial segment of subicular pyramidal neurons have failed to confirm a higher channel density in those structures, and it therefore was suggested that the action potential actually might be initiated at the first nodes of Ranvier rather than at the axon hillock and initial segment (Colbert and Johnston 1996).

In principle, the machinery for dendritic action potentials is present in most neurons in the form of voltage-activated sodium and calcium channels as was shown with direct recordings from the dendrites of a number of different neurons (Häusser et al. 1995; Larkum et al. 1996; Spruston et al. 1995; Stuart and Sakmann 1994). There is widespread agreement that the decremental back-propagation of the action potential into the dendritic tree after initiation in the region of the axon is boosted by fast voltage-activated sodium channels, albeit with varying effectiveness across different cell types (Häusser et al. 1995; Larkum et al. 1996; Spruston et al. 1995; Stuart and Sakmann 1994). In addition, it has been shown that action potential initiation may shift from the axon hillock/initial segment region into the dendrites under certain circumstances. In particular, high-intensity stimulation of distal dendrites in layer V neocortical pyramidal dendrites can initiate dendritic regenerative responses before somatic action potentials (Stuart and Sakmann 1996). Several recent studies provide direct evidence that distal synaptic input can evoke dendritic calcium spikes while the soma and initial segment of the same cells remain subthreshold for action potential initiation (Magee et al. 1995; Schiller et al. 1996; Yuste et al. 1994). However, triple recordings from soma, dendrite and axon have revealed that the fast sodium action potentials always are recorded first in the axon before the soma whether or not slower regenerative responses occurred in the dendrite (Stuart and Sakmann 1996). Thus these dendritically located regenerative processes can be distinguished functionally from authentic action potentials; although they provide added richness to the computation involved in determining spike initiation, they do not in themselves represent a form of output.

The dendrites of cultured spinal neurons, the focus of this study, seem to behave similarly to other CNS neurons with regard to action potential back-propagation (Larkum et al. 1996). In most instances the action potential is initiated first near the soma, probably at the initial segment, and is propagated back into the dendrites in a decremental manner. The back-propagated action potential also is boosted by fast voltage-activated sodium channels. Under certain circumstances, however, fast sodium action potentials could be elicited in the dendrites before a second action potential was initiated in the initial segment.

The aim of this simulation study is first to reproduce the results presented by Larkum et al. (1996) on the action potential propagation and initiation in the dendrites of spinal motoneurons. We demonstrate the importance of the axon hillock and initial segment for secure invasion of the soma by the antidromic action potential. In addition, we address the question of whether the large observed scatter in the amplitude of the back-propagated action potential can be explained by geometric factors alone or whether differences in the sodium channel densities in different dendrites must be assumed. Simulations are used to explore threshold conditions for action potential initiation in the dendrites and initial segment under the assumption of uniformly but "weakly" excitable dendrites. Finally, we investigate the influence of dendritic stimulus location with a view to determining if regenerative activity could arise in the dendrites before the initiation of an action potential at the initial segment.

    METHODS
Abstract
Introduction
Methods
Results
Discussion
References

Multicompartmental single-neuron models were implemented using the simulation program NEURON (Hines 1993) with integration time steps of 25 µs. Two different types of models were considered. One was a simplified five-compartment model consisting of an axon, initial segment, axon hillock, soma, and one tapering dendrite. The second type consisted of reconstructed motoneurons filled with biocytin from organotypic spinal cord slice cultures of rats. Presumed motoneurons were identified by their ventral location, size, and morphology of the dendritic apparatus. However, no unequivocal identification of motoneurons is possible in organotypic slice cultures (Larkum et al. 1996).

Morphology of dendrites and axon

A computer-assisted tracing system (Eutectic 3D NTS, Eutectic Electronics, Raleigh, NC) was used to reconstruct the biocytin filled motoneurons. The dendritic morphology of these motoneurons has been described elsewhere (Ulrich et al. 1994). Because the axon in these cells could not be determined with certainty, the neurite most likely to be the axon was removed for the simulation, and a new unmyelinated axon with defined morphology was attached to the soma. There was no significant variation if different neurites were chosen as the axon. At the developmental stage these cultures were used for the experiments [14-20 days in vitro (DIV)], the axon is not yet myelinated. First signs of myelination with Sudan-black staining only could be seen after 3 wk in culture (unpublished observation). An axon hillock and an initial segment were interposed between the soma and the axon proper. The axon hillock was 8 µm long and tapered from 3 to 0.8 µm. The diameter of the initial segment and axon was 0.8 µm throughout the entire length. The length of the initial segment was assumed to be 10 µm. The axon hillock and initial segment were modeled with 8 and 10 compartments, respectively. The axon proper was 500 µm long and was modeled with 50 compartments. In the absence of reliable morphological data on the axon, we adapted the dimensions used to model the axon of neocortical pyramidal cells by Mainen et al. (1995) and scaled them to the diameters of neurites measured in our cultured cells. The same axonal structure was attached to the soma of the simplified model.

For modeling purposes, a spatial discretization of <= 20 µm per compartment was observed for all dendritic sections except for the axon hillock, initial segment, and axon as mentioned earlier.

Passive electrical properties

The cable and passive membrane properties of these motoneurons were determined by cable analysis and compartmental modeling and are published elsewhere (Ulrich et al. 1994). Briefly, the motoneuron had a mean input resistance of 498 ± 374 (SD) MOmega , and a mean membrane time constant (tau m) of 22 ± 4.6 ms. The specific membrane capacitance (Cm), estimated from the charge of the capacitive current transient during a voltage step and the total surface area, was 1.08 ± 0.3 µF/cm2. Experimental voltage transients due to brief current pulses were fitted with simulated voltage transients from compartmental computer models to derive Rm and Ri. Ri of 308 ± 39 Omega cm and a uniform membrane resistivity (Rm) of 17,502 ± 3,054 Omega cm2 led to the best match between fitted and experimental transients.

Channel properties

In the motoneurons studied, the back-propagated action potential is supported by voltage-activated fast Na+-channels (Larkum et al. 1996). The voltage-activated Ca2+ channels that also are present in motoneuron dendrites (Larkum et al. 1996) were not included in the model. Because the model was not required to reproduce repetitive firing behavior, the multiple K+-channels present in motoneurons for shaping firing properties (Viana et al. 1993) were not considered. Instead, a single voltage-dependent potassium conductance with one n gate was used to provide for spike repolarization (Mainen et al. 1995; Rapp et al. 1996).

No data are available for the Na+-channel kinetics in motoneuron dendrites. We used standard Hodgkin and Huxley formalism (Hodgkin and Huxley 1952) with parameter values for the equations describing the Na+ and K+ currents precisely as given in Mainen et al. (1995): ENa = +60 mV and EK = -80 mV, and resting potential was -70 mV. All simulations were done at 20°C, corresponding approximately to the room temperature at which the experiments were performed. The steady-state values for minfinity and tau m are given by minfinity  = alpha /(alpha  + beta ) and tau m = 1/(alpha  + beta ), respectively. The forward reaction rate is described by alpha (Vm) = [A(Vm - V1/2)]/[1 - e(Vm-V1/2)/k] with A = 0.182, V1/2 = -35, and k = 9 for the m gate and A = 0.024, V1/2 = -50, and k = 5 for the h gate. The backward reaction rate is beta (Vm) = [-A(Vm - V1/2)]/[1 - e(Vm-V1/2)/k] with A = 0.124, V1/2 = -35, and k = 9 for the m gate and A = 0.0091, V1/2 = -75, and k = 5 for the h gate. tau h was described analogously to tau m. tau h was described explicitly by hinfinity  = 1/(1 e(Vm-V1/2)/k) with V1/2 = -65 and k = 6.2. Because of the overlap of hinfinity and minfinity , a significant amount of steady-state Na+ conductance is present producing a substantial window current. With &gmacr;Na = 40 pS/µm2, a voltage step from -70 to -10 mV yielded a peak current density of 0.8 pA/µm2 peaking at 0.59 ms.

Na+-channel distribution

The Na+-channel density in the soma and dendrite of motoneurons has not yet been determined. Following Hugenard et al. (1989) and Stuart and Sakmann (1994), we assumed a uniform Na+-channel density for somatic and dendritic membrane. We have evaluated three alternatives: passive soma and dendrites, weakly excitable soma and dendrites with &gmacr;Na = 3 mS/cm2, and fully excitable soma and dendrite with &gmacr;Na = 12 mS/cm2. These Na+-channel densities have been used throughout the simulation study unless otherwise noted.

Following Mainen et al. (1995) we used a Na+-channel density of &gmacr;Na = 3,000 mS/cm2 for the initial segment and the axon hillock. The unmyelinated axon was simulated with &gmacr;Na = 12 mS/cm2. The ratio &gmacr;Na: &gmacr;K = 3.33 was the same as in the original Hodgkin-Huxley model and kept constant over all compartments of the model. This ensured complete repolarization of the action potential. Spike width at half-amplitude was ~2.0 ms with the above distribution of Na+ and K+ channels.

    RESULTS
Abstract
Introduction
Methods
Results
Discussion
References

In this section, we present only the results of simulations. It is organized as follows: first we explore the importance of the initial segment and axon hillock for spike initiation. In the second part, we evaluate three alternative models and compare them to the experimental results. The three models are: passive soma and dendrite, "weakly" excitable soma and dendrites, and "normally" excitable soma and dendrites. In all three cases, there is a high Na+-channel density in the axon hillock and initial segment. We further explore the influence of the location of current injection into the dendrites on the ability to evoke dendritic action potentials. We then investigate the different threshold conditions for action potential initiation in the dendrites and the initial segment. Last, the influence of the active and passive membrane properties of the dendrites on the threshold behavior is explored.

Initial segment and action potential invasion

It is a well-established experimental observation that action potentials elicited in the muscle nerve may fail to invade the soma propagating antidromically, especially at depolarized membrane potentials. This may lead to the remnants of an abortive spike in the soma, which is called an IS spike (Brock et al. 1953). This observation is usually the indication of a poor impalement at the soma with a large concomitant leak conductance. The current produced by the initial segment thus is shunted through the introduced leak leading to insufficient depolarization at the somatic membrane to cross threshold for an action potential. Even without a leak introduced by a microelectrode, the impedance mismatch caused by the unfavorable geometry at the transition from the axon to the soma, which corresponds to a large step increase in the core conductor geometry (Goldstein and Rall 1974), makes this location prone to action potential propagation failure. The same would be true for an action potential traveling down a dendrite toward the soma because it would face a very similarly unfavorable geometric arrangement.

Figures 1 and 2 show simulations of a motoneuron with a weakly excitable soma-dendritic membrane (&gmacr;Na = 3 mS/cm2) and an axon hillock, initial segment, and axon with a uniform Na+-channel density (&gmacr;Na = 12 mS/cm2). The action potential is initiated at the end of the axon by injection of a current pulse (Fig. 1A, right-arrow). The stimulus started at 1.0 ms and lasted for 15 ms; current amplitude was 0.15 nA. The resulting potential profiles along the axon (from the soma to the end of the axon) are shown in Fig. 1B (right-arrow, stimulus location). The first potential profile is plotted 0.5 ms after onset of stimulus current. Delta t for each subsequent potential profile is 0.5 ms. The potential profiles are sequentially numbered. It can be seen readily that the action potential amplitude gets dramatically smaller within 100 µm from the soma and completely fails to invade the axon hillock as well as the soma. The small remaining depolarization in the soma spreads electrotonically into the dendrites (Fig. 1C). Figure 1D shows the action potential midway at the axon (Fig. 1A, Right-arrow  A) and the progressively smaller remnants of the failing action potential as it passes through the initial segment, the soma and then to the dendritic recording locations D1 and D2.


View larger version (27K):
[in this window]
[in a new window]
 
FIG. 1. Failure of the retrograde axonal action potential to invade the soma. &gmacr;Na = 3 mS/cm2 for soma-dendritic membrane; &gmacr;Na = 12 mS/cm2 for axon, initial segment, and axon hillock. Stimulus current: duration, 15 ms; amplitude, 0.15 nA; stimulus started 1.0 ms after the onset of simulation. A: reconstructed motoneuron with an artificial axon. right-arrow, site of stimulation. Right-arrow , recording sites. B: potential profiles along the axon, initial segment, axon hillock, and soma. First potential profile is plotted 0.5 ms after stimulus onset. Subsequent potential profiles are plotted at an interval of 0.5 ms. Numbers denote the temporal sequence after simulation onset. right-arrow, site of stimulation. C: potential profiles along the 2 dendrites indicated with x and y in A. First flat line plots the potential profile 0.5 ms after stimulus onset. D: superimposed recordings of the electrotonic remnants of the failing action potential. Full-size action potential recorded in the axon is shown becoming progressively smaller at the initial segment (thick stippled line), at the soma (thin solid line), and at the dendritic locations D1 and D2 (thick solid line and thin stippled line, respectively).


View larger version (23K):
[in this window]
[in a new window]
 
FIG. 2. Failure of the dendritic action potential to invade the soma. &gmacr;Na = 3 mS/cm2 for soma-dendritic membrane; &gmacr;Na = 12 mS/cm2 for axon, initial segment, and axon hillock. A: reconstructed motoneuron with an artificial axon. right-arrow, site of dendritic stimulation. Stimulus current: duration, 15 ms; amplitude, 0.15 nA; stimulus started 1.0 ms after the onset of simulation. Right-arrow , recording sites. B: potential profiles along the axon, initial segment, axon hillock, and soma. First flat potential profile is plotted 0.5 ms after stimulus onset. Subsequent potential profiles are plotted at intervals of 0.5 ms. C: potential profiles along the 2 dendrites indicated with x and y in A. First line plots the potential profile 1.5 ms after simulation onset (corresponding to 0.5 ms after stimulus onset). Numbers refer to the time elapsed after simulation onset. D: superimposed recordings of the action potential at the site of current injection (thick solid line), at the soma (thin solid line), and at dendritic site D2 (stippled line).

Figure 2 illustrates the situation where the stimulus is applied to a dendrite at location D1 (Fig. 2A, right-arrow), again using weakly excitable soma-dendritic membrane. The stimulus is capable of eliciting an abortive action potential (Fig. 2D, thick solid line). The amplitude of the action potential increases as it spreads out into the dendrite approaching the sealed boundary condition (Fig. 2D, dashed line). However, the action potential does not invade the soma (Fig. 2D, thin solid line). This asymmetric behavior can best be seen in the shape of the potential profiles along the dendritic path x to y in Fig. 2C (right-arrow, site of stimulation). The first potential profile is plotted 0.5 ms after the onset of stimulation. Delta t between each potential profile is 0.5 ms. The potential profiles are sequentially numbered from 1 to 13. The potential drops very steeply toward the soma, which represents a big electrical load draining the longitudinal current. The small depolarization reached in the axon hillock and initial segment is insufficient for action potential initiation. Potential profile 13 (6.5 ms after onset of stimulation) clearly shows how the back-propagated action potential increases as it approaches the dendritic tip.

The question now arises as to how large &gmacr;Na must be in the axon hillock and initial segment to secure action potential propagation from the axon back in to the soma and for a dendritic action potential out into the axon. The transition between failure and success for an action potential traveling antidromically toward the soma is found between &gmacr;Na = 600 mS/cm2 (no action potential at the soma) and &gmacr;Na = 700 mS/cm2 (action potential at the soma) in both the axon hillock and initial segment. For an action potential traveling from a dendrite toward the soma, as shown in Fig. 2, the values are between &gmacr;Na = 1,200 mS/cm2 (no action potential at the axon hillock/initial segment) and 1,300 mS/cm2 (action potential at the axon hillock/initial segment). The larger Na+-channel density found to secure propagation from dendrite to soma is expected because much less inward current is produced by the action potential in the dendrite mainly due to the lower Na+-channel density in the somato-dendritic membrane compared with the axon. This smaller current, however, must negotiate a similar impedance mismatch as in the case of the antidromic invasion. Following Mainen et al. (1995), we have chosen for the axon hillock and initial segment in all the following simulations a &gmacr;Na = 3,000 mS/cm2. This high value guarantees safe propagation of action potential from the axon as well as from the dendrites in both directions.

Action potential initiation and dendritic back-propagation

The situation with a high Na+-channel density in the axon hillock and initial segment (&gmacr;Na = 3,000 mS/cm2) is illustrated in Figs. 3 and 4 for an antidromic and orthodromic action potential, respectively. The organization of these figures is similar Figs. 1 and 2. Stimulus current was applied at the site indicated (Fig. 3, A and B, right-arrow). The potential profiles in Fig. 3, B and C, are sequentially labeled. The first potential profile is plotted 0.5 ms after onset of stimulation. Delta t is 0.5 ms. Inspecting the potential profiles at different time instances along the axon (Fig. 3B) reveals that the amplitude of the action potential still drops as it reaches the transition from the axon to the initial segment. In this case, however, the membrane potential is depolarized sufficiently to reach threshold due to the high Na+-channel density in the initial segment. The action potential then propagates actively into the axon hillock and subsequently into the soma. From there it propagates further into the dendrites with decreasing amplitude reaching a minimum at a distance of about half the entire dendritic length. The amplitude recovers, albeit not to the full amplitude, as it approaches the end of the dendrites. This propagation behavior is illustrated in Fig. 3C, which plots the potential profiles at different times along the two dendrites marked with x and y in Fig. 3A. The action potentials recorded from the axon hillock, the soma and sites D1 and D2 (from Fig. 3A) are plotted successively as a function of time in Fig. 3D.


View larger version (34K):
[in this window]
[in a new window]
 
FIG. 3. High Na+-channel density at initial segment and axon hillock ensures success of the retrograde axonal action potential to invade the soma. &gmacr;Na = 3 mS/cm2 for soma-dendritic membrane; &gmacr;Na = 12 mS/cm2 for axon, and &gmacr;Na = 3,000 mS/cm2 for initial segment and axon hillock. A: reconstructed motoneuron with an artificial axon. right-arrow, site of stimulation. Stimulus current: duration, 15 ms; amplitude, 0.15 nA; stimulus started 1.0 ms after the onset of simulation. Right-arrow , recording sites. B: potential profiles along the axon, initial segment, axon hillock, and soma. First potential profile is plotted 0.5 ms after stimulus onset. Subsequent potential profiles are plotted at intervals of 0.5 ms. C: potential profiles along the 2 dendrites indicated with x and y in A. First line plots the potential profile 1.5 ms after simulation onset (corresponding to 0.5 ms after stimulus onset). Numbers refer to the time elapsed after simulation onset. D: superimposed recordings of the action potential at the initial segment (thick stippled line), at the soma (thin solid line), and at the dendritic locations D1 and D2 (thick solid line and thin stippled line, respectively).


View larger version (39K):
[in this window]
[in a new window]
 
FIG. 4. High Na+-channel density at initial segment and axon hillock ensures success of the dendritic action potential to invade the soma. &gmacr;Na = 3 mS/cm2 for soma-dendritic membrane; &gmacr;Na = 12 mS/cm2 for axon; and &gmacr;Na = 3,000 mS/cm2 for initial segment and axon hillock. A: reconstructed motoneuron with an artificial axon. right-arrow, site of dendritic stimulation. Stimulus current: duration, 15 ms; amplitude, 0.15 nA; stimulus started 1.0 ms after the onset of simulation. Right-arrow , recording sites. B: potential profiles along the axon, initial segment, axon hillock, and soma. First flat potential profile is plotted 0.5 ms after stimulus onset. Subsequent potential profiles are plotted at an interval of 0.5 ms. C: potential profiles along the two dendrites indicated with x and y in A. First line plots the potential profile 1.5 ms after simulation onset (corresponding to 0.5 ms after stimulus onset). First 12 profiles are plotted as thin lines. Numbers denote the temporal sequence after simulation onset. D: superimposed recordings of the action potential at the site of current injection (D1; thick solid line), at the soma (thin solid line), at dendritic site D2 (thin stippled line), and at the initial segment (thick stippled line). Further explanation is in the text.

Figure 4 illustrates a rather complex, multistep process for spike initiation and propagation. Here, the same model as in Fig. 3 is simulated but the stimulus is applied to the dendrite instead to the axon (Fig. 4, A and C, right-arrow). The potential profiles are plotted in steps of 0.5 ms and are numbered sequentially. Potential profile no. 1 starts 0.5 ms after the onset of the stimulus. Again, the potential profile along the dendrites x and y drops steeply from the site of current injection toward the soma (Fig. 4C). The abortive spike develops into a larger spike as it propagates out into the dendrite approaching the end of the dendrite (potential profiles numbered from 1 to 12 with thin solid lines). Despite the steep drop in potential from the site of injection to the soma, the initial segment is depolarized sufficiently to elicit an action potential (potential profile 13 in Fig. 4B), which then propagates in both directions along the axon hillock (potential profile 14 in Fig. 4B) and later the axon (potential profiles 15-18, Fig. 4B). The somatic action potential spreads into the other dendrite (labeled y in Fig. 4A) in a decremental manner but increases its amplitude as it approaches the end of the dendrite (Fig. 4C, potential profiles 15-23, thick lines). At the site of current injection the action potential develops in two phases (Fig. 4D, filled heavy line, right-arrow, and *). First an abortive spike is generated as in Fig. 2, C and D, that increases in amplitude as it approaches the tip of the dendrite marked with x (potential profiles 1-12 in Fig. 5C, thin lines). Shortly after, an action potential is elicited in the initial segment and axon hillock propagating back into the soma and dendrites (Fig. 4D, *). This spike does not propagate actively beyond the site of current injection because the membrane is refractory from the first actively propagated spike. We investigated this point in more detail later (Fig. 8). Because somatic and dendritic spikes are initiated almost simultaneously, the membrane potential in between D1 and the soma is at any time close to isopotential and rises simultaneously as can be seen in Fig. 4C (shaded area).


View larger version (16K):
[in this window]
[in a new window]
 
FIG. 5. Summary of back-propagating action potential for 3 different models. Inset: motoneuron was stimulated at the soma; the peak amplitude of the back-propagated action potential was measured at 4 equally spaced locations in every section of the dendritic tree. Stimulus current: duration, 15 ms; amplitude, 0.15 nA. &gmacr;Na = 12 mS/cm2 for axon; &gmacr;Na = 3,000 mS/cm2 for initial segment and axon hillock. A: "fully" excitable soma-dendritic membrane with &gmacr;Na = 12 mS/cm2. B: "weakly" excitable soma-dendritic membrane with &gmacr;Na = 3 mS/cm2. C: passive soma-dendritic membrane.


View larger version (15K):
[in this window]
[in a new window]
 
FIG. 8. Same simulation as illustrated in Fig. 7 but with decreasing Na+-channel densities to simulate QX-314 experiments (see text). Results of 4 simulations are shown. Following Na+-channel densities for the somato-dendritic membrane were used: &gmacr;Na = 4 mS/cm2, &gmacr;Na = 3 mS/cm2, &gmacr;Na = 2 mS/cm2, and &gmacr;Na = 1 mS/cm2. A: action potentials recorded at the dendritic, current injection site (thick line) and initial segment (thin line). Amplitude of the dendritically evoked action potential decreases with decreasing Na+-channel density. Stimulus remains subthreshold at a Na+-channel density of &gmacr;Na = 1 mS/cm2. B: onset of phase plane loops recorded from initial segment. Numbers 1-4 indicate direction of decreasing Na+-channel densities. C: onset of phase plane loops recorded from dendritic, current injecting location. Numbers 1-4 indicate direction of decreasing Na+-channel densities. Threshold for action potential initiation in the dendrite is not reached if the Na+-channel density drops to &gmacr;Na = 1 mS/cm2 (4 in C).

For the remainder of the results, the axon, axon hillock and initial segment are simulated with &gmacr;Na = 12 mS/cm2 and &gmacr;Na = 3,000 mS/cm2, respectively.

The attenuation of the back-propagated action potential in three different models is summarized in Fig. 5. The inset in Fig. 5A illustrates the simulated motoneuron. In each model, the motoneuron always was stimulated at the soma. The peak amplitude of the back-propagated action potential was measured at four equally spaced locations in every section of the dendritic tree and plotted against the distance from the soma. In Fig. 5A, the dendrites and soma were excitable with a uniformly distributed Na+-channel density of &gmacr;Na = 12 mS/cm2. The action potential amplitude remained virtually constant along the dendritic branches. In Fig. 5B, the dendrites and soma were chosen to be weakly excitable &gmacr;Na = 3 mS/cm2. The action potential amplitude first decreased and then remained constant or increased slightly as it approached the end of the dendrites. Areas of scatter in the attenuation can be seen that were the result of differing dendritic branch lengths and diameters. Figure 5C illustrates the case with a passive soma and dendrites.

Threshold conditions at initial segment and dendrite

According to the results presented earlier, we believe that a weakly excitable soma-dendritic tree describes the experimental results most accurately (cf. Fig. 5 and Fig. 3 from Larkum et al. 1996). To study threshold conditions at the initial segment and at dendritic locations under these conditions, we used a reduced model of the motoneuron with a geometry illustrated in Fig. 6H. Here, the dendrite and soma were weakly excitable with a uniform &gmacr;Na = 4 mS/cm2. The Na+-channel density of the axon hillock and initial segment was &gmacr;Na = 3,000 mS/cm2. In the axon Na+-channel density was &gmacr;Na = 12 mS/cm2. Current (duration = 15 ms, amplitude = 0.15 nA) was injected into the dendrite at the location indicated with an arrow (St in Fig. 6H). The resulting action potentials were recorded at the site of current injection (thick solid line) at the soma (thin solid line) and at the initial segment (stippled line) and plotted superimposed in Fig. 6A. The action potential starts first in the initial segment and propagates in a decremental manner back into the dendrite. Figure 6, B and C, shows phase plane plots of the total current (Itot = IC + Ipas + INa + IK) versus membrane potential recorded at the initial segment and dendritic location respectively. Figure 6, D and E, illustrates the onsets of the loops in the same phase plots but at a much higher resolution. In a distributed structure, the usual definition of threshold for action potential initiation is the first transition from outward to inward of the integral of membrane current over the surface of the structure (Jack et al. 1975). We define the first transition from outward (positive) current to inward (negative) current at the site of current recording as the local threshold for the onset of a regenerative response. The phase plane loop recorded at the initial segment (Fig. 6B) is dominated at first by a large inward current during the rising phase of the action potential that is followed by an outward current during repolarization. At the dendritic location, the phase plane loop is first dominated by a large outward current (Fig. 6C). This outward current reflects the current produced by the approaching action potential that is initiated in the initial segment and spreads from the soma toward the dendritic location. As the action potential passes under the recording site, a relatively small inward current is recorded. This inward current shows the active nature of the back-propagated action potential. By inspecting the two phase plane loops at the onset of current injection, it can be seen that the outward current produced by the injected current depolarizes the membrane at both sites. However, the outward current only reaches threshold in the initial segment where it is followed by a large inward current. In contrast, at the dendritic location the outward current has a vertical trajectory along the voltage axis without crossing and then increases again as soon as the leading edge of the action potential elicited at the initial segment spreads into the dendrite.


View larger version (21K):
[in this window]
[in a new window]
 
FIG. 6. Threshold conditions and action potential initiation at initial segment in a reduced model. Stimulus is applied to the dendrite (right-arrow, St) in H; duration, 15 ms, amplitude, 0.15 nA; stimulus starts 1 ms after onset of simulation. Weakly excitable soma-dendritic membrane with &gmacr;Na = 4 mS/cm2; &gmacr;Na = 12 mS/cm2 for axon; &gmacr;Na = 3,000 mS/cm2 for initial segment and axon hillock. A: superimposed action potentials record from initial segment (dotted line), from soma (thin solid line), and at the site of current injection (thick solid line). B: phase plane trajectory plotting total current Itot = IC + Ipas + INa + IK vs. membrane potential calculated at initial segment. Negative current indicates net inward current. Right-arrow , loop direction. C: same phase plane trajectory but calculated at site of current injection at the dendrite. Notice the different loop rotation in C, indicating that the current sensed by the dendritic electrode during action potential initiation in the initial segment is directed outwardly and thus passive. At the time the back-propagated action potential passes underneath the dendritic electrode, an inward current is detected, indicating that the action potential is indeed actively back-propagated. D: onset of the phase plane loop illustrated in B at a different voltage and current scale. Threshold for action potential initiation is reached at the transition from net outward current to net inward current. E: onset of phase plane loop illustrated in C at different voltage and current scale. Note that threshold for action potential initiation is not reached at the site of current injection. F: time course of the Na+-activation variable (m) calculated at the dendritic location (site of current injection; solid line) and at the initial segment (stippled line). G: time course of the Na+-inactivation variable (h) calculated at the dendritic location (site of current injection; solid line) and at the initial segment (stippled line).

Figure 6, F and G, plots the Na+-activation variable (m) and inactivation variable (h), respectively (solid line at dendritic location, stippled line at the initial segment). The activation variable rises first slowly at the dendritic location. At the initial segment the activation variable increases steeply after a short delay, peaking earlier than at the dendritic location. The inactivation variable at the dendritic location drops slowly to ~0.5 before the back-propagated action potentials spreads into the dendrite (Fig. 6G). This leaves enough sodium channels for active, but decremental back-propagation of the action potential.

This analysis is repeated in Fig. 7 for dendritic current injection at a more distal location. The same reduced model is used as for Fig. 6 and the location of current injection is indicated with an arrow (St). The current pulse (duration = 15 ms, amplitude = 0.15 nA) injected into the dendrite is this time capable of eliciting a small dendritic action potential at the site of current injection (Fig. 7A, thick line). The same current initiates a full-sized action potential in the initial segment (Fig. 7A, stippled line), which is back-propagated into the dendrite. Figure 7B illustrates the phase plane loop of the total current versus membrane potential for the initial segment. It is dominated by the large inward current during the action potential. Figure 7C illustrates the phase plane loop at the site of current injection. A small inward current is seen during the abortive spike elicited at this site during stimulation. The ensuing outward current reflects the current flowing toward the stimulation site produced by the action potential initiated in the initial segment and axon hillock. Just before this back-propagated action potential passes under the electrode, the current flow is again reversed. However, there is no net inward current suggesting that the action potential is not propagated in a regenerative fashion, due to refractoriness of the membrane following the local, abortive spike. Figure 7, D and E, shows the onsets of the phase plane loops recorded at the initial segment and dendritic location, respectively. In contrast to the case illustrated in Fig. 6, the outward current at the site of stimulation is followed by an inward current, indicating that threshold for initiation of an action potential is indeed reached at about -45 mV (Fig. 7E, Th1). At the initial segment, threshold for initiating an action potential is reached at about -68 mV (Fig. 7D, Th2). If the two threshold values obtained from the phase plane plots are inserted into the membrane voltage versus time plots (Fig. 7A), it becomes evident that although the threshold is much higher at the dendritic location (which is expected because of the low Na+-channel density in the dendritic membrane) than in the initial segment, the higher threshold is reached at a much earlier time than the lower threshold. It is not only the magnitude of the threshold that determines where an action potential is initiated but also the time at which threshold is reached at different sites.


View larger version (19K):
[in this window]
[in a new window]
 
FIG. 7. Similar illustration as Fig. 6. Only difference is that the stimulus is applied at a more distal dendritic location (right-arrow, St). A: action potential is initiated 1st in the dendrite and later at a lower threshold in the initial segment. B: entire phase plane loop of total current vs. membrane voltage calculated at initial segment. C: phase plane loop of total current vs. membrane voltage calculated at the site of current injection (St in H). D: onset of phase plane loop at initial segment plotted at different current and voltage scale. E: onset of phase plane loop at site of dendritic current injection plotted at different current and voltage scale. At both sites, the phase plane loop shows a transition from net outward current to net inward current, indicating that threshold for action potential initiation is reached at either sites. Although threshold is much higher (less negative membrane potential) at the dendritic, current-injecting site than at the initial segment, threshold is reached earlier at the dendritic location than in the initial segment (A). F: time course of the Na+-activation variable (m) calculated at the dendritic location (site of current injection; solid line) and at the initial segment (stippled line). G: time course of the Na+-inactivation variable (h) calculated at the dendritic location (site of current injection; solid line) and at the initial segment (stippled line).

The phase plane loop in Fig. 7C suggests that no regenerative back-propagation of this action potential occurs. This suggestion is further addressed in Fig. 7, F and G, plotting the Na+-activation variable (m) and inactivation variable (h), respectively (solid line at dendritic location, stippled line at the initial segment). The activation variable rises slowly during the first dendritic action potential. Its value is close to one at the moment the second action potential is initiated in the initial segment. Relaxation of the activation variable is strongly delayed at the dendritic site as compared with the initial segment location. The inactivation variable drops slowly during the first dendritic action potential, approaching almost zero. The Na+-channels at the dendritic location thus are inactivated completely at the moment the action potential is elicited at the initial segment. This demonstrates that the action potential is passively back-propagated due to the fact that the dendritic action potentials leave the membrane refractory.

Two main factors determine whether or not an action potential can be elicited in the dendrite. First, the Na+-channel density determines the local dendritic threshold and, second, the cable properties of the dendritic segment, between the dendritic location of current injection and the initial segment, determine at which site threshold is crossed first.

In Fig. 8, we present a simulation reproducing the experiments illustrated in Fig. 5 of Larkum et al. (1996). The simulation is done on the reduced model as illustrated in Fig. 7. In the original experiment, the dendritic current-injecting electrode contained the intracellular sodium channel blocker QX-314. Immediately after breakthrough at the dendritic site, the action potential was initiated in the dendrite and later in the soma. As the drug diffused into the cell, the action potential initiated in the dendrite decreased and finally was blocked completely, leaving only the back-propagated action potential. The peak amplitude of the back-propagated action potential declined with increasing diffusion time. The delay between stimulus onset and action potential initiation in the initial segment increased over the time of drug diffusion. QX-314 application was simulated approximately by reducing the Na+-channel density in the dendrite. In Fig. 8A, four pairs of recordings (dendritic recordings: thick solid lines, somatic recordings: thin solid lines) with the following Na+-channel density superimposed (&gmacr;Na = 4 mS/cm2, &gmacr;Na = 3 mS/cm2, &gmacr;Na = 2 mS/cm2, and &gmacr;Na = 1 mS/cm2). With decreasing Na+-channel density, the action potential initiated in the dendrite gets smaller and finally disappears, exactly as seen in the corresponding experiment. The onset of the phase-plane loop, plotting total current versus membrane voltage, is illustrated for the initial segment and dendritic current-injection site in Fig. 8, B and C, respectively. Although threshold is reached at more negative membrane voltages (but later in time) in the initial segment with decreasing Na+-channel density in the dendrite, threshold is reached at less negative membrane voltages in the dendrite and does not reach threshold at all at a Na+-channel density of &gmacr;Na = 1 mS/cm2 (no transition occurs from inward to outward current in the current trajectory).

In Fig. 9, we investigate the influence of Ri on the threshold for action potential initiation at the dendritic current-injection site and at the initial segment. The simulation was performed with the reduced model illustrated in Figs. 6 and 7. A current pulse (duration = 15 ms; amplitude = 0.15 nA) was injected at the middle of the dendrite. Ri was changed from 300 to 50 Omega cm with a step size of 50 Omega cm. Selected examples are shown in Fig. 9, A-C, for 300, 150, and 50 Omega cm, respectively (thick line, dendritic recording; thin line, somatic recording; doted line, initial segment). With high intracellular resistivity, the action potential could be initiated at the dendritic site. It started earlier and reached a higher amplitude with Ri = 300 Omega cm than with lower intracellular resistivities. With Ri = 50 Omega cm, no action potential could be initiated at the site of current injection in the dendrite. Inspecting the onset of the phase plane loops, which plot total current versus membrane potential in the initial segment (Fig. 9D) and the dendritic site (Fig. 9E), reveals that the threshold decreased (more negative values) in the initial segment with decreasing intracellular resistivity (Fig. 9D). The outward current loop showed two phases at higher Ri and reached much higher values at high Ri than at low Ri (Fig. 9D). This additional outward current reflects the excess current (added to the stimulus current) produced by the action potential initiated in the dendrite. This excess current boosts the membrane potential to threshold, which is reached earlier in time but at a higher level (less negative values). For Ri = 50 Omega cm, the current-voltage trajectory at the site of current injection never reached transition from outward to inward current and thus did not reach threshold (thick solid line in Fig. 9E). The maximal inward current decreases with decreasing intracellular resistivity.


View larger version (21K):
[in this window]
[in a new window]
 
FIG. 9. Same simulation as depicted in Fig. 7 but with different Ri. Soma-dendritic membrane weakly excitable with &gmacr;Na = 3 mS/cm2. A: action potential recorded from initial segment (dotted line), soma (thin solid line), and dendritic location (thick solid line). Ri = 300 Omega cm. B: same as A but Ri = 150 Omega cm. C: same as A but Ri = 50 Omega cm. No dendritic action potential can be elicited. D: onset of phase plane loops recorded at initial segment for different values for Ri labeled on the different trajectories. E: onset of phase plane loops recorded at initial segment for different values of Ri. Same line styles as in D. Trajectory for Ri = 50 is identified. Note that with the exception of the trajectory calculated for Ri = 50, all other trajectories cross from outward to inward current indicating action potential initiation at the dendritic location.

This analysis of threshold behavior predicts that action potential should be elicited easily in the thin distal dendrites. Figure 10 illustrates a simulation where the current was applied at successively more distally located sites in the dendrites. The sites of current injection (duration: 15 ms; amplitude: 0.15 nA) are indicated with arrows and labeled with letters from B to H (Fig. 10A) corresponding to the recordings illustrated in Fig. 10, B-H (somatic recording, solid line; recording from site of current injection, stippled line). Because of the increasing input resistance at more distal locations, the stimulus induced depolarization increased. Moving from stimulus location B to H, an action potential was first elicited at location E, and the amplitude of the dendritic action potential increased at more distal sites. The exact distance where an action potential can be successfully initiated in the dendrites depends on the passive cable properties, the Na+-channel density as well as on local geometric properties of the dendritic tree.


View larger version (17K):
[in this window]
[in a new window]
 
FIG. 10. Stimulus location and ability to initiate an action potential in the dendrite. A: motoneuron with weakly excitable somato-dendritic membrane (&gmacr;Na = 3 mS/cm2). Sites of current injection (duration, 15 ms; amplitude, 0.15 nA) are indicated (right-arrow) and labeled with letters from B to H corresponding to the recordings illustrated in B-H (somatic recording, solid line; recording from site of current injection, dotted line).

    DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References

We have presented a model of spinal motoneurons that is consistent with observed physiological properties of spike initiation in the initial segment/axon hillock region and action potential back-propagation into the dendritic tree. It accurately reproduces the results presented by Larkum et al. (1996) on motoneurons in organotypic rat spinal cord slice cultures. Our model builds on the pioneering work of Cooley and Dodge (1966) and Moore et al. (1983) on the possible site of action potential initiation in spinal motoneurons of the cat. Because of a lack of specific data on sodium and potassium channel kinetics and corresponding channel densities for motoneurons, we adopted the respective data from Mainen et al. (1995) and Rapp et al. (1996) used for models of spike initiation in neocortical pyramidal cells. For the time being, we consider this an acceptable adaptation because the basic findings on spike initiation and dendritic back-propagation are surprisingly similar in the two types of neurons. The following discussion is structured according to the presentation of the data in the result section.

Anti- and orthodromic action potential invasion of the soma

It is well known that a propagating action potential changes its shape and conduction velocity while approaching a change in core conductor geometry and eventually may fail to propagate beyond a sufficiently large increase in axon diameter (Goldstein and Rall 1974; Lüscher and Shiner 1990a,b). Although the details of the geometry determine the impedance match or mismatch at a core conductor inhomogeneity, many additional factors, e.g., active membrane properties and intra- and/or extracellular ion accumulation, are finally critical for the success or failure of action potential propagation (Lüscher et al. 1994). Our simulations show that in the case of a uniformly excitable neuron, the soma together with the dendritic apparatus represents too big an electrical load to ensure safe action potential propagation in both the orthodromic and the antidromic direction. To overcome the impedance mismatch for an action potential propagating from the axon back into the somato-dendritic apparatus, the initial segment and axon hillock must provide additional current. This can be achieved with a high density of sodium channels in that region. Mainen et al. (1995) used a sodium channel density in the initial segment and axon hillock that was 1,000 times higher than that in the somato-dendritic membrane. In our simulation, a sodium channel density 200 times higher than in the dendrite was sufficient to secure antidromic invasion of the somato-dendritic membrane. For the orthodromic action potential traveling down a dendrite, the situation is different. The initial segment and axon hillock region must have a very low voltage threshold because the small remaining current from the failing dendritic action potential as it approaches the soma can depolarize the axon hillock and initial segment region only very little. A 400-fold increase in the sodium channel density of the axon hillock and initial segment region compared with the somato-dendritic membrane was required for safe propagation of a action potential from a dendrite through the soma down into the axon. Strictly speaking, the action potential propagating from the dendrite toward the soma always fails but is reinitiated in the initial segment/axon hillock region provided that the Na+-channel density is sufficiently high. In the absence of precise morphological data on the initial segment and axon hillock, the simulations cannot, however, provide realistic estimates of the required sodium channel densities. The sodium channel density could be reduced by assuming a different type of sodium channel in the axon hillock/initial segment region (Rapp et al. 1996). In the adult brain stem motoneuron, it has been shown that the action potential can be initiated with, as well as without, a simultaneous activation of the axon hillock/initial segment membrane, indicating that the first nodes of Ranvier can provide sufficient current for action potential initiation (Gogan et al. 1983). Attempts to measure the Na+-channel density in the initial segment of subicular pyramidal neurons also have failed to confirm a significantly higher Na+-channel density in this structure compared with the soma. This observation supports the earlier suggestion that the action potential might be initiated at the heminode or the first node or nodes of Ranvier rather than at the axon initial segment (Colbert and Johnston 1996; Coombs et al. 1957). At the developmental stage we studied the cultured motoneurons, myelin still was absent and no nodes of Ranvier close to the soma could provide the current necessary for secure anti- or orthodromic propagation.

Action potential initiation and dendritic back-propagation

Although safe antidromic invasion of the soma may not be of any functional significance, the high Na+-channel density necessary in the axon hillock and the initial segment also can serve as a spike initiation zone. It was found experimentally that the site of action potential initiation was always in the initial segment region even when current was injected into the soma or proximal dendrite despite an active boosting of the subsequently back-propagating action potential. The simulations demonstrate that a weakly but homogeneously excitable dendrite reproduces the observed data on the dendritically back-propagated action potential well. With a weakly excitable dendritic tree, the amplitude of the action potential decreases with increasing distance from the soma. The amplitude tends to increase as the action potential approaches the sealed end of the dendritic terminations. There is no need to postulate a decrement in the sodium channel density (cf. Rapp et al. 1996) or an increased density of a transient A-type potassium channel along the dendritic path (Hoffman et al. 1997) to explain the observed decremental back-propagation of the action potential. We cannot, of course, rule out that potassium channels in the dendrites and/or a gradient in the sodium channel density shapes the action potential as it propagates back into the dendritic tree. These important dendritic membrane properties await experimental verification in the motoneuron.

For motoneurons, Larkum et al. (1996) observed a much larger scatter in the peak amplitude of the back-propagated action potential plotted against distance from the soma than Stuart and Sakmann (1994) found for the apical dendrite of cortical pyramidal neurons. The small scatter present in the simulated neuron (Fig. 5) was due to structural inhomogeneities. The much larger scatter in the data seen in the actual experiments (Fig. 3 in Larkum et al. 1996) is most likely the result of different sodium channel densities in different dendrites of the same neuron and/or across different neurons. The much more homogeneous structure of the apical dendrite of pyramidal neurons would lead to much less scatter in the data as has been seen in the actual experiments (Stuart and Sakmann 1994). It also should be noted that the scatter is greatest in the case with "weakly excitable" somato-dendritic membrane as compared with both the passive case and the "strongly excitable" case. Thus a difference in the mean sodium channel density in the dendrites across different cell types also might partly account for differences in the scatter.

Threshold conditions at initial segment and dendrites

Despite the fact that the axon hillock/initial segment region has a much lower voltage threshold for action potential initiation compared with the soma-dendritic membrane (due to the much higher sodium channel density in that region), the simulations predict that action potentials can be initiated in the dendrites before the initial segment fires a spike. This means that the higher voltage threshold in the dendrite can be reached earlier than the lower voltage threshold in the axon hillock/initial segment region. Anything that speeds up membrane depolarization during current injection in the dendrite facilitates spike initiation. Most importantly, anything that hinders intracellular current flow from the dendrite to the soma and initial segment favors action potential initiation in the dendrite over action potential initiation in the initial segment. Given that the intracellular resistance to axial current flow is a function of Ri and the diameter of the dendrite, it follows necessarily that both parameters play a decisive role for dendritic action potential initiation as our simulations have demonstrated. Action potentials can more easily be initiated in thin than in thick dendrites because the current injected into the thin dendrites will locally depolarize the membrane, whereas, on the other hand, the same current injected into a thick dendrite will flow mostly intracellularly along the dendrite into the soma. The same reasoning would apply to the observation that action potentials can be initiated in the distal but not in the proximal dendrites.

It is not only the intracellular resistance that determines where the action potential is initiated. The membrane resistivity plays an important role as well. This parameter has not been studied in our simulation, but it is obvious that a high Rm would favor current flow along the dendrite into the soma and the initial segment region. On the other hand, a high Rm value also would lead to a higher local input resistance with a concomitant large local depolarization. A large Rm together with a large Cm, however, would lead to a slow local depolarization that would favor spike initiation in the initial segment over spike initiation in the dendrite. Cm would play a more prominent role for transient synaptic input with regard to its ability to evoke a dendritic spike. A high Cm would locally dampen the voltage swing produced by a synaptic current.

In contrast to Stuart and Sakmann (1994), Regehr et al. (1993) observed synaptically evoked action potentials in the apical dendrites of cortical pyramidal neurons. Our simulations would predict that action potentials indeed could be initiated in thin distal dendrites. Whether or not these action potentials would propagate down the dendrite and invade the soma with subsequent initiation of a second action potential in the initial segment would depend on the actual current source-load relation between the action potential approaching the soma and the electrical load of the soma together with the attached passive dendrites. Initiation of dendritic regenerative potentials in distal dendrites of cortical pyramidal neurons has recently been confirmed experimentally (Stuart et al. 1997).

In addition to the passive electrotonic structure of the neuron, the local sodium channel density plays an important role for spike initiation in the dendrite as well. This has been demonstrated experimentally with local intracellular application of QX-314 (Larkum et al. 1996) and in this simulation study where a reduction of sodium channel density in the dendrites abolished dendritic spike initiation (Fig. 8). It was shown that the somato-dendritic membrane of motoneurons becomes more excitable after axotomy, and evidence for sodium channel "hot spots" has been reported in the dendrites of chromatolyzed motoneurons in the cat (Eccles et al. 1958). It has been proposed that excitatory synaptic potentials might be able to elicit action potentials in dendrites of denervated motoneurons (Eccles et al. 1958; Kuno and Llinàs 1970; Traub and Llinàs 1977). This suggests that sodium channels redistribute over the somato-dendritic membrane during the response to axotomy. It, however, is considered unlikely that sodium channel hot spots capable of eliciting dendritic action potentials exist in normal, adult motoneurons.

Importance of the dendritic back-propagated action potentials

For motoneurons, no evidence exists that the back-propagated action potential may induce changes in the synaptic potentials according to the degree of coincidence between action potential and excitatory postsynaptic potential, as has been reported for layer V neocortical pyramidal neurons (Markram et al. 1997) and hippocampal pyramidal neurons (Magee and Johnston 1997). So far, actively back-propagated action potentials in motoneurons have only been observed in cultured cells (Larkum et al. 1996), and only indirect evidence exists for dendritic action potentials in motoneurons of adult cats (Araki and Terzuolo 1961; Fatt 1957; Terzuolo and Araki 1961). The back-propagated action potential in motoneurons activates dendritic voltage-dependent Ca2+ channels, similar to the hippocampal (Spruston et al. 1995) and neocortical pyramidal cells (Markram et al. 1995). This mechanism endows the motoneuron with the potential machinery for retrograde signaling. At the present time, it can only be speculated as to what this back propagated signal might convey in the motoneuron. It is possible, however, that this signaling might play an important role during development in the period the spinal network is being established.

    ACKNOWLEDGEMENTS

  We thank Drs. Streit and Wannier for helpful discussions and critical reviewing of the manuscript.

  This research was supported by the Swiss National Science Foundation (Grant 3100-042055.94).

    FOOTNOTES

   Present address of M. Larkum: MPI für Med. Forschung, Abteilung Zellphysiologie, D-69120 Heidelberg, Germany.

  Address reprint requests to: H.-R. Lüscher, Dept. of Physiology, University of Bern, CH-3012 Bern, Switzerland.

  Received 26 January 1998; accepted in final form 5 May 1998.

    REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References

0022-3077/98 $5.00 Copyright ©1998 The American Physiological Society