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The Journal of Neuroscience, February 1, 2001, 21(3):1007-1021
Presynaptic Inhibition and Antidromic Spikes in Primary Afferents
of the Crayfish: A Computational and Experimental Analysis
Daniel
Cattaert1,
Frédéric
Libersat2, and
Abdeljabbar
El Manira3
1 Laboratoire Neurobiologie et Mouvements, Centre
National de la Recherche Scientifique, 13402 Marseille Cedex 20, France, 2 Department of Life Sciences and Zlotowski Center
for Neuroscience, Ben Gurion University of the Negev, Beer Sheva,
84105, Israel, and 3 The Nobel Institute for
Neurophysiology, Department of Neuroscience, Karolinska Institutet,
S-171 77 Stockholm, Sweden
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ABSTRACT |
Primary afferent depolarizations (PADs) are associated with
presynaptic inhibition and antidromic discharges in both vertebrates and invertebrates. In the present study, we have elaborated a realistic
compartment model of a primary afferent from the coxobasipodite chordotonal organ of the crayfish based on anatomical and
electrophysiological data. The model was used to test the validity of
shunting and sodium channel inactivation hypotheses to account for
presynaptic inhibition. Previous studies had demonstrated that GABA
activates chloride channels located on the main branch close to the
first branching point. We therefore focused the analysis on the effect of GABA synapses on the propagation of action potentials in the first
axonal branch. Given the large diameters of the sensory axons in the
region in which PADs were likely to be produced and recorded, the model
indicates that a relatively large increase in chloride conductance (up
to 300 nS) is needed to significantly reduce the amplitude of sensory
spikes. The role of the spatial organization of GABA synapses in the
sensory arborization was analyzed, demonstrating that the most
effective location for GABA synapses is in the area of transition from
active to passive conduction. This transition is likely to occur on the
main branch a few hundred micrometers distal to the first
branching point. As a result of this spatial organization, antidromic
spikes generated by large-amplitude PADs are prevented from propagating distally.
Key words:
presynaptic inhibition; primary afferent
depolarization; antidromic discharge; crayfish; simulation; compartment
model
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INTRODUCTION |
The effectiveness of sensory
synaptic transmission is modulated by presynaptic inhibition, which is
associated with primary afferent depolarizations (PADs) in both
vertebrates and invertebrates (Clarac and Cattaert,
1999 ; Rudomin and Schmidt, 1999). PADs are mediated by the activation of GABA receptors, which increase the conductance to chloride. During rhythmic motor activity, PADs occur in
bursts during a given phase of the motor cycle and can reach sufficient
large amplitude to generate action potentials that propagate
antidromically (El Manira et al., 1991; Gossard et al., 1991; Cattaert et al., 1992). These
action potentials do not propagate toward the axon terminals and thus
do not produce any postsynaptic response (El Manira et al.,
1991; Cattaert et al., 1992). Although
presynaptic inhibition of sensory transmission has been extensively
studied in the mammalian spinal cord, the underlying mechanisms have
not been examined experimentally. Using computer simulations, several
possible mechanisms have been proposed to account for PAD-associated
presynaptic inhibition, including shunting of the afferent
action potentials (Segev, 1990) and the inactivation of sodium and calcium channels (Graham and Redman, 1994; Walmsley et al., 1995; Lamotte
d'Incamps et al., 1998).
In the crayfish, intra-axonal recording from stretch receptor afferents
[coxobasipodite chordotonal organ (CBCO)] showed that these receive
bursts of GABA-mediated PADs during locomotion that can generate
antidromic action potentials (El Manira et al., 1991; Cattaert et al., 1992). These PADs are
attributable to an increased chloride conductance and reduce the
amplitude of afferent action potentials and the resulting EPSPs in
postsynaptic target neurons (Cattaert et al., 1992).
Using anatomical and electrophysiological techniques, we have shown
recently that the GABAergic synaptic inputs mediating PADs were mainly
located at the first branching point of the sensory axons
(Cattaert and El Manira, 1999). Furthermore, experimental data suggest that PADs mediate their inhibitory effects mainly through shunting mechanisms and not via inactivation of voltage-gated channels (Cattaert and El Manira,
1999).
Taking advantage of the detailed data available on presynaptic
mechanisms in crayfish sensory axons, we have now developed a realistic
simulation model of presynaptic inhibition in crayfish primary
afferents to determine the following: (1) the importance of the
localization of GABAergic synapses in relation to active versus passive
propagation zones; (2) the respective roles of inactivation and
shunting mechanisms in the reduction of spike amplitude; and (3) how
antidromic action potentials elicited by PADs are prevented from
propagating distally. We find that shunting mechanisms can account for
the decrease of afferent action potential amplitude. We also show that
effect of the shunt is more efficient if the conductance increase is
located close to the zone of transition from active to passive
properties, and the same shunting phenomenon is responsible for
preventing antidromic action potentials from propagating distally.
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MATERIALS AND METHODS |
Histology of sensory axons. An in vitro
preparation of the thoracic locomotor nervous system was used as
described previously (Sillar and Skorupski, 1986;
Chrachri and Clarac, 1989). Sensory nerve activity was
recorded with platinum en passant electrodes, connected to home-made
amplifiers (gain of 10,000-100,000×). Intracellular recordings from
CBCO terminals (CBTs) within the ganglion were performed with
micropipettes filled with carboxyfluoresceine (5% in K acetate 0.2 M), using an Axoclamp 2A amplifier (Axon Instruments, Foster City, CA). CBTs were identified on the basis of two criteria. First, injection of depolarizing current pulses elicited antidromic spikes in CBTs that were one to one correlated with extracellular spikes recorded on the CBCO sensory nerve. Second, orthodromic spikes
produced by the CBCO sensory neurons were correlated with intracellular
spikes at a fixed delay in CBTs. The CBTs analyzed in this study fired
action potentials attributable to the existence of spontaneous activity
in CBCO sensory neurons. An eight channel stimulator (A.M.P.I.,
Jerusalem, Israel) was used to trigger intracellular pulses in CBTs
during the identification procedure. Data were displayed and printed on
a four-channel digital oscilloscope (Yokogawa, Tokyo, Japan) and stored
on tape (DTR 1800; Biologic, Claix, France). Anatomical data are based
on recordings from five identified CBTs.
After identification of CBCO neurons, they were filled with either
carboxyfluoresceine (Sigma, St. Louis, MO) or dextrane fluoresceine
(Molecular Probes, Eugene, OR) by injecting negative current pulses
( 8 nA, 500 msec, 1 Hz) for 45 min. The preparation was then fixed for
1 hr in a solution of 4% paraformaldehyde in 0.1 M sodium
phosphate, pH 7.4, at 4°C and then rinsed eight times in PBS
over approximately 2 hr. Tissues were dehydrated in graded ethanol (30, 50, 70, and 95%, absolute ethanol, 10 min each), cleared with methyl
salycilate (5 min; Sigma, St. Louis, MO), mounted in Permount (Fisher
Scientific, Houston, TX), and viewed with a Leica TCS 4D (Leica,
Heildelberg, Germany) laser scanning confocal microscope (Fig.
1A) equipped with a
krypton-argon mixed gas laser. Forty to 50 optical sections 1 µm
apart with a Leica 25× oil or 50× water immersion lenses were taken
from single whole-mount preparations. In some experiments, the ganglion
was not fixed and was observed in a confocal microscope directly after
injecting the fluorescent dye. This procedure was used to avoid
shrinkage.
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Figure 1.
Architecture of CBCO sensory arborization in the
ganglion. A, Projection file computed from a confocal image
stack taken from a sensory afferent. B, Reconstructed
representation of the same sensory afferent shown in A. C,
Same as B but rotated 90° in the y-axis.
D, Dendrogram showing the branching structure of the sensory
afferent shown in A. The number on the
top of specific segments indicates the diameter, and the
number below indicates the length of this segment.
E, Histogram showing the decrease in diameter with the
distance in the first branch of three representative examples of
sensory afferents; all three branches are aligned to their origin on
the main tree trunk of the sensory afferent, which has been
arbitrarily defined as zero.
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Three-dimensional reconstruction of sensory axon. The
branching of sensory neurons were reconstructed (Fig. 1B,C)
and analyzed in three dimensions with a commercial 3-D system
(Neurolucida; MicroBrightField Inc., Colchester, VT), directly from the
confocal image stack. Each reconstructed sensory afferent was
represented by a set of data points consisting of the x, y,
and z coordinates and the diameters of the tapered branch.
Each reconstruction was approximately 500-600 digitized points.
Suitable software from Neurolucida computed various morphometric
parameters and generated various graphic representations of the
afferent (e.g., dendrograms) (Fig. 1D).
Simulations. The propagation of action potentials into
axonal terminals was simulated using a compartment model program
("SWIM") (Ekeberg et al., 1991). The properties of
each compartment can be defined independently. The simulated axons were
composed of excitable compartments and passive compartments. Specific
compartments received synaptic inputs. Excitable compartments were
described by standard (Hodgkin and Huxley, 1952) channel
kinetic equations.
In the crayfish, sensory axons are not myelinated, their
diameters ranging from 7 to 15 µm in the largest area (that is, at the entry region of the ganglion, before the first branching point) (Fig. 1A-C). Generally, the diameter of the
fiber remains constant (5-6 µm) for ~150 µm after the branch and
then progressively decreases to ~3 µm at a distance of 600-800
µm from the first branching site (Fig. 1D). Because output
synapses are located on axonal branches and GABA synapses seem to be
located on the main axon close to the first branch (Cattaert and
El Manira, 1999), we were mainly interested in simulating the
propagation of events in the main branch around the first branch (100 µm on each side) and in the first branch (400 µm). The diameter of
the first branch was ~2 µm (Fig. 1E) and generally
comprised between 3 (proximal part of the branch) and 1 (300 µm more
distal) µm. To give the model a realistic behavior, we have included
500 µm of axon (used for spike propagation outside of the ganglion)
and a distal process of 300 µm that plays a key role in the
distribution of currents at the first branching point.
After several trials, we fixed the length of compartments to 20 µm.
Longer compartments (up to 100 µm) gave similar results but did not
allow to precisely localize where antidromic spikes were produced.
Smaller compartments (up to 5 µm) did not significantly improve the
results. The axonal model consisted of 72 compartments (Fig.
2). The first 25 compartments (length of
20 µm and diameter of 10 µm) were used to simulate the sensory
axons outside the ganglion. Five compartments (length of 20 µm and
diameter of 4-10 µm) were used to simulate the 100 µm of axon
before the first branching point, and the last 20 compartments (length
of 20 µm, diameter of 4-10 µm) were used to simulate the distal
processes of the sensory main axon. The first axonal branch was
composed of 20 compartments (length of 20 µm and diameter of 2 µm).
Two more compartments were used to mimic conduction in the remainder of
the main axon and in the branch end. Terminals were modeled as sealed
ends. In most of the runs, an orthodromic action potential was
initiated at the proximal end of the axon, and it traveled toward the
distal processes of the terminal. The temporal integration step was 100 µsec. To avoid the sealed effect produced in the first axonal
compartment from interfering with the analysis, we started the
observations at a distance of 400 µm from the first branching point
(Fig. 2). Therefore, only 400 µm on each side of the branching point
have been represented in all diagrams, corresponding to positions 0 (the more proximal axonal compartment analyzed) to 800 (the most distal
compartment in the main axon and in the branch) µm.
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Figure 2.
Compartment model of a CBCO sensory arborization.
In this model, we have only considered the first axonal branch of the
sensory neuron (see inset). The input resistance of the
model was monitored by injecting an hyperpolarizing current pulse (5
nA, 15 msec) in the vicinity of the first branch. A decrease of input
resistance from 7.8 (1) to 2.3 (2) M was
obtained when a 300 nS chloride conductance was used to simulated the
activation of GABA synapses at the same location.
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Passive properties. The intracompartmental potential,
E, is described by the differential equation:
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(1)
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where Ileak is the passive leakage
current:
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(2)
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and Eleak and
Gleak are the equilibrium potential and
the leak conductance, respectively. Icore is the axial current to neighboring compartments summed over all neighbors:
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(3)
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The parameter Gcore (in
S) denotes the core conductance from the compartment in
question to the neighboring compartment:
where diam and l are diameter and
length of the compartment (in centimeters), respectively, and
Ra is the specific resistance of the axoplasm
(in ohm centimeter).
Ich and Isyn in
Equation 1 are intrinsic and synaptic currents, respectively.
Intracellular current injection can be modeled by adding current to the
compartment. The parameter cm (microfarads) describes
the capacitance of the compartment:
(area is the membrane surface of the
compartment in square centimeters, and Cm is the
specific capacitance in microfarads per square centimeter.)
All compartments had the same specific membrane resistance
(Rm) as estimated from experimental data
(see Results). Several values were tested (from 2000 to 8000 cm2). All computations were performed assuming a
specific capacitance, Cm of 1 µF/cm2 and a specific axoplasmic resistance,
Ra, of 75 cm (calculated from
electrophysiological measurements; see Results).
Synaptic inhibition was modeled with a conductance in the postsynaptic
compartment. The activation level of the postsynaptic channel,
s, ranges from 0 to 1 when the synapse is "closed" or "open," respectively. The maximum conductance
Gsyn is fixed, but the value of the actual
conductance, Gsyn·s, varies with
s, that is, when the synapse opens and closes. The kinetics
of s are controlled by two parameters: the duration and the
decay time. In most of the simulations (see Figs. 3-8), the duration
of GABA-mediated PADs was fixed to 2 msec and the decay time to 20 msec
to fit to experimental data (Cattaert and El Manira, 1999). To analyze the contribution of sodium channels
inactivation to presynaptic inhibition, long-duration PADs were
produced (duration, 300 msec; decay time, 20 msec) (see Fig. 11).
The synaptically induced current that enters the postsynaptic
compartment is calculated by:
in which Esyn is the equilibrium
potential for chloride ions.
Sodium and potassium channels. Sodium
(Na+) current is computed as:
The activation variable m is described by:
with rate functions  m and
 m:
The inactivation variable h is computed in a similar
way.
with rate functions h and
h:
In most computations, we used the following values for the
Na+ channel parameters:
Activation m:
Inactivation h:
These values were adjusted from the "SWIM" model
(Ekeberg et al., 1991) to produce no inactivation of
Na+ channels at membrane potentials more
hyperpolarized than 58 mV, as shown by the experimental data
(Cattaert and El Manira, 1999). By using these
parameters, the simulated PADs did not produce any inactivation of
Na+ channels and thereby allowed for the analysis of
the role of shunting mechanisms in presynaptic inhibition (see Fig.
11A-D). Large PADs can depolarize the membrane potential
above 58 mV and reach the threshold for Na+
channel inactivation. To analyze the contribution of
Na+ channels inactivation in PAD-mediated decrease
in afferent spike amplitude, simulations were performed with the
inactivation threshold shifted toward hyperpolarized membrane potential
(see Fig. 11E-H) by using the following parameters:
A h = 0.08 mV 1
msec1; Bh = 50
mV; Ch = 1 mV; and
A h = 0.4 mV1
msec1; Bh = 36
mV; Ch = 2 mV.
The maximum conductance density for Na+ channels in
a given compartment was GNa (S) = 16.7 mS·cm2 (unless stated otherwise). The
equilibrium potential for Na+ ions was set at
ENa = +50 mV.
Potassium (K+) current is computed as:
Its activation variable, n, is described by the
equation:
with rate functions n and
n:
In all computations, we used the following values for the
K+ channel parameters:
The maximum conductance density for a given compartment was
GK (S) = 8.3
mS·cm2 (unless otherwise stated). The
equilibrium potential for K+ ions was
EK = 80 mV.
The conductance densities we used for Na+ and
K+ channels (16.7 mS·cm2 and
8.3 mS·cm2, respectively) were smaller than in
Hodgkin and Huxley (HH) model (120 mS·cm2 and 36 mS·cm2, respectively). They were adjusted to the
minimum required to get an active conduction in the simulated sensory
axon. Using HH values, we obtained qualitatively similar results,
except that the spikes had a short duration and were thereby more
attenuated in passive conduction compartments because of low-pass
filter effect. Such characteristics partially masked the relative
effects of PADs. To not minimize the effect of K+
channels during trains of spikes, the Na/K ratio was set to 1:2 instead
of 1:3.33 as in the HH model. However, we did not observe any
noticeable difference when simulations were done with the Na/K ratio of
1:3.33 (data not shown).
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RESULTS |
Morphological characteristics of sensory axons
To construct a realistic model of the crayfish CBCO axons,
three-dimensional confocal reconstructions were performed from sensory
axons injected with carboxyfluoresceine or dextrane fluoresceine. The
CBCO sensory axons have a characteristic morphology with a main axon
giving rise to a small branch at the first axonal branching point (Fig.
1A,B). Ninety degree rotation in the y-axis of
the reconstructed CBCO axon shows that the branches project mostly laterally in the ganglion (Fig. 1C). Figure 1D
shows a dendrogram of the different branches of a reconstructed CBCO
sensory axon. The length of the main axon ranged between 600 and 800 µm, whereas that of the branch ranged between 100 and 200 µm. The
diameter of the main axon was between 7 and 10 µm in fixed
preparations (6-15 µm in fresh preparations) and decreases after
the first branch to 3-4 µm in fixed preparations (Fig.
1D) or 4-7 µm in fresh preparations. The diameter of the
branch also decreases with distance and was approximately 2 µm within
the 200 µm after the branch (in fresh and fixed preparations) (Fig.
1E).
Simulation of a CBT
A model axon was built based on the morphological data (Fig. 2).
The location and strength of GABA synapses mediating presynaptic inhibition used in these simulations is based on anatomical and physiological data (Cattaert and El Manira, 1999). Using
conventional intracellular recordings, the input resistance
(rinput) of CBTs at the first branching
point was 6.5 ± 0.85 M and the length constant ( ) was
~1000 µm, for an axon diameter of 8.5 µm (Fig. 2). These
parameters were used to build a model of CBCO sensory axons. Using
infinite cable theory, passive parameters in the model were calculated
as follows.
In an infinite cable, the input resistance
(rinput) is equal to:
where =  is the length
constant, in which rm is the membrane resistance
for a unit length (cm), and ra is the
axoplasmic resistance per unit length
(cm1).
From these estimations, the specific resistance of the
axoplasm (Ra),
was assumed to be 75 cm, and the specific membrane
resistance (Rm),
was set to be in the range of 3000-4000
cm2. However, this parameter is difficult to
measure precisely with sharp microelectrodes. Thus, to test how it
would affect the simulations, we have tested the effect of different
Rm values (2000, 4000, and 8000 cm2).
The measured time constant ( m) was 3.3 msec; therefore, the specific membrane capacitance
(Cm),
was assumed to be 1 µFcm2.
Validation of the model: adjustment to real parameter values
(rinput, , and
GCl)
The compartment model was examined in the case of infinite cable
configuration to ensure that the length constant () obtained from
simulations is similar to that obtained by theoretical calculation using infinite cable theory. The values obtained by simulation and
theoretical calculations were similar for the different diameters and
Rm values tested as shown in Table
1.
Estimations of the length constant () were made by measuring
the propagation (attenuation of amplitude Vx
with distance x) of a depolarizing current pulse (+2.5 nA,
40 msec) of initial amplitude V0.
Estimations of the length constant () by theoretical
calculations were made with the formula:
This validated model was used in the finite cable configuration,
which corresponds to anatomical data. The calculated parameters were,
therefore, adjusted to fit experimental measurements of input
resistance (rinput) and the length
constant (), both in the absence and presence of PADs simulated as
an increased chloride conductance. The input resistance was measured by
injecting a hyperpolarizing current pulse (5 nA, 15 msec) (Fig. 2).
The 5 nA pulse produced a 37.5 mV hyperpolarization
(rinput of 7.8 M). Comparable values
were obtained experimentally in the in vitro preparation
(El Manira and Clarac, 1991; Cattaert et al.,
1992).
In in vitro experiments, when GABA receptors were activated
by pressure ejection of GABA, we observed a 67% reduction of the input
resistance of sensory axons (Cattaert et al., 1992).
Simulations of input resistance were performed with the model presented
in Figure 2, when the GABA conductance was activated. To obtain a change comparable with the results obtained experimentally, the chloride conductance associated with the GABA synapse was set to 300 nS. In the following simulations, different values of GABA synapse
conductance (100, 200, 300, 400, 500, and 600 nS) were tested.
Propagation of spikes and PADs
The experimental data allowed a reasonably good estimation of most
of the parameters in the area accessible to intracellular recordings.
However, Rm was difficult to estimate with
certainty in thin-diameter axons. Therefore, the experimental values of input resistance were likely underestimated (or overestimated). For
these reasons, the passive propagation of spikes and PADs was studied
using different Rm values of 2000, 4000, and
8000 cm2 (only results with 2000 and 8000 cm2 in the realistic model of sensory axon are
presented in Fig. 3). In addition, the
topological analysis of different CBCO fibers demonstrated that axon
diameters ranged between 10 and 4 µm within the 200 µm after the
first branching point. Therefore, simulations of spike and PAD
propagation were done with axon diameters of 10 and 4 µm. The passive
propagation of spikes and PADs was comparable in large-diameter axons.
For example, in a 10 µm axon with Rm of 2000 cm2, PAD attenuated from 25 to 17 mV (32%
attenuation) between locations 300 and 800 (Fig. 3A1), and
the spike attenuated from 99 to 67 mV (32% attenuation) (Fig.
3B1). However, in thin branches (2 µm), PADs propagate
better than spikes. PADs amplitude decreased from 23 to 11.5 mV (50%
attenuation) (Fig. 3A1), whereas spike amplitude decreased
from 99 to 35 mV (65% attenuation) (Fig. 3B1). The
difference between the spatial attenuation of spikes and that of PADs
increased in thin branches with increasing
Rm; for Rm of 8000 cm2 in a 2 µm diameter branch, PAD attenuated
from 25 to 19.5 mV (22% attenuation) (Fig. 3A2), and spike
attenuated from 99 to 47 mV (53% attenuation) (Fig.
3B2).
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Figure 3.
Incidence of axon diameter and specific membrane
resistance (Rm) on propagation of PADs
(A) and spikes (B), in the case of finite axon
length. Each diagram represents the peak value of the events (PAD or
spike) measured at different locations along the axon (0-300 µm,
axon; 400 µm, branching; 400-900 µm, distal processes). The distal
process of the axon was also simulated with three different values of
diameter (4 µm, open circles; 7 µm, open
triangles; 10 µm, open squares). In each case, the
branch diameter was 2 µm (small symbols), and the diameter
of the axon was 10 µm (in location 0-400 µm; large
symbols).
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In this configuration, the characteristics of the passive propagation
of PADs in axon with different diameters (2, 4, and 10 µm) tended to
become similar when Rm was increased from 2000 to 8000 cm2 (Fig. 3, compare A1,
A2). On the other hand, the spike spatial attenuation
remained dependent on the axon diameter regardless of the
Rm value used, as shown by the curves
corresponding to 2, 4, and 10 µm that did not tend to converge when
Rm was increased (Fig. 3, compare B1,
B2). The difference in the passive propagation of spikes and
PADs can be summarized as follows. PADs tended to invade all branches
with reduced attenuation compared with spikes, which were more
attenuated as they propagated in the fine branches.
Shunting of spikes by PADs
In these simulations, a GABA-mediated chloride conductance of 300 nS was required to produce a decrease of input resistance (67%)
similar to that obtained experimentally (Cattaert et al., 1992). The chloride conductance required is directly related to the diameter of the sensory axon at the site of the GABAergic synapses
and also depends on whether GABAergic synapses are in a zone with
active or passive propagation. These questions are addressed in the
simulations illustrated in Figures 4 and
5.
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Figure 4.
Incidence of axon diameter on the shunting effect
of increased chloride conductance. The increase in chloride conductance
was induced on the main axon, at the level of the branch (location 400 µm). A, Simulation of a small (4 µm) diameter main axon.
B, Simulation of a large (10 µm) diameter main axon. In
both cases, and in all simulations presented here, the diameter of the
branch was fixed to 2 µm according to anatomical data (see Fig. 1).
Each diagram represents the peak value of the spike measured at
different locations along the main axon (large symbols) and
the branch (small symbols). The propagation of spike in the
absence of PAD is represented by open symbols; the
propagation of spike in the presence of PAD is represented by
gray symbols. In insets are represented the spike
shapes recorded at locations indicated by a, b, and c.
C, Evolution of the shunting effect produced by increasing
chloride conductance from 0 to 600 nS, when specific membrane
resistance was fixed to 2000 (1) and 8000 (2)
cm2. Both diagrams represent the peak value of
the spike at location b (branching point; large
symbols) and c (branch; small symbols), for
three values of main axon diameter (4 µm, square; 7 µm,
triangle; 10 µm, circle).
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Effect of axon diameter
In all the following simulations, a 100 mV spike was initiated at
location 0. Figure 4A illustrates the propagation of action potentials in a 4 µm diameter axon in which active propagation of
spikes occurs up to 100 µm after the first branching point (gray part of the axon). Figure 4A1
shows the propagation of action potentials along the main axon and the
branch in the absence (open circles) and presence
(filled circles) of PAD. In inset, three superimposed profiles of spikes recorded at location 0 (a), 400 (b), and 700 (c) µm are shown. The left
traces (open circle) have been obtained in the absence
of PAD, and the right traces (filled circle) have been obtained in the presence of a 300 nS PAD. In the
presence of PAD, the spike appears above the PAD, and the shunting
mechanism is partly compensated by the amplitude of the PAD.
Three different axon diameter values (4, 7, and 10 µm) were
tested in the simulations. Shunting effects were always larger at the
site of the GABA synapse first branching point (location b
in the drawing and graphs) than in the branch (location c)
in which output synapses are likely to be located (Cattaert and
El Manira, 1999). Increasing the axon diameter reduced the
shunting effect of PADs on the spike amplitude. The effect of diameter on shunting efficacy in an axon with Rm of 2000 cm2 was examined by comparing 4 and 10 µm axon
diameters (Fig. 4A). In the absence of PAD, the spike
amplitude at the first branching point (location b on the
drawing and graphs) was 90.4 and 97.4 mV with an axon diameter of 4 (Fig. 4A1) and 10 (Fig. 4A2) µm, respectively. In the presence of a 600 nS chloride conductance, the
spike amplitude decreased to 48.0 (Fig. 4A1) and 72.7 (Fig. 4A2) mV, which represents 53 and 74.6% of the
control amplitude, respectively. The shunting thus decreased the spike
amplitude by 47% in a 4 µm axon and only by 25.4% in a 10 µm axon.
When spike amplitudes were measured at location c on
the branch (Fig. 4A1), the spike peak was 37.8 mV in
a 4 µm axon in the absence of PAD and was reduced to 24.4 mV by a 600 nS PAD. This represents a 37.8-24.4 = 13.4 mV (35.5%) shunting
effect. In a 10 µm axon (Fig. 4A2), the spike peak
was 40.9 mV at location c on the branch in the absence of
PAD and was reduced to 33.2 mV using a 600 nS PAD. This represents a
40.9-33.2 = 7.7 mV (18.8%) shunting effect. Thus, increasing the
axon diameter by a factor of 2.5 reduced the shunting effect by ~50%
at locations b and c. These results suggest that
the diameter of the axon at the site of the GABA synapse plays an
important role in determining the efficacy of the shunt.
Effect of Rm
To determine the extent to which Rm
affected the shunting effect of PADs on spike amplitude, we compared
the effect of PADs at two Rm values: 2000 (Fig.
4A) and 8000 (Fig. 4B) cm2.
We present here only effects at location c because they are similar to those at location b. With an
Rm value of 2000 cm2 and
an axon diameter of 4 µm, the amplitude of the spike at a distal
location c was 37.8 mV (62.2% attenuation) in the absence of PAD and was reduced to 24.4 mV when a 600 nS increase in chloride conductance was applied at the branching point (Fig.
4A1). This shows that the spike was shunted by
37.8-24.4 = 13.4 mV (35.5%). When Rm value
was increased to 8000 cm2, and the spike
amplitude at location c was 48.9 mV (51.1% attenuation) in
the absence of PAD and 33.5 mV when a 600 nS increase in chloride conductance was applied at the branching point (Fig.
4B1). The spike was thus shunted by 48.9-33.5 = 15.4 mV (31.5%) because of the inhibitory synapse. Thus, a fourfold
increase in Rm resulted in an increase of the
shunting only by 2 mV (4%), indicating that Rm
plays a minor role in determining the efficacy of shunting.
To generalize this result, we have tested different chloride
conductances and different axon diameters at two different
Rm values (Fig. 4C). The results show
that the shunting is always more efficient in small-diameter axons (4 µm). Large Rm values improved the propagation
of both unshunted and shunted spikes in small branches. Consequently,
there was no dramatic increase of the shunting effect (measured in
small branches), regardless of the value of the chloride conductance
(100-600 nS).
Effect of active and passive propagation at the GABA
synapse site
The preceding simulations were performed with the GABA synapse
occurring at a site with active propagation. To determine how the
shunting is affected when it occurs at a site with passive propagation,
we have used the same parameters as in Figure 4 but with spikes being
passively propagated (absence of Na+ and
K+ channels) from location 200 µm. In a 4 µm
axon with a Rm value of 2000 cm2, the spike peak was 19.1 mV at location
c on the branch in the absence of PAD (Fig. 5A1)
and was reduced to 15.8 mV when a 600 nS chloride conductance increase
applied at the branching point (location 400 µm). This shows that the
spike was shunted by 19.1-15.8 = 3.3 mV. When the axon diameter
was increased to 10 µm, the peak potential measured at location
c was 29.8 and 22.7 mV in the absence and presence of a 600 nS PAD, respectively (Fig. 5A2). That is a 7.1 mV decrease
at location c. Thus, when the GABA synapse was located at a
passive site, the shunting effect was relatively more efficient in
large-diameter than in small-diameter axons.
Increasing the Rm value to 8000 cm2 (Fig. 5B) resulted in increasing
electrotonic propagation of both not shunted and shunted spikes. In a 4 µm axon diameter, the spike peak at location c was 31.2 mV
in the absence of PAD and decreased to 22.5 with a 600 nS PAD (Fig.
5B1). This represents a 31.2-22.5 = 8.7 mV shunting effect. In a 10 µm axon diameter, the spike peak was 45 mV in the
absence of PAD and 37.5 mV in the presence of a 600 nS PAD (Fig.
5B2). The spike was then shunted by 45-37.5 = 7.5 mV.
Thus, in small branches, increasing Rm increased
the passive propagation of both unshunted (control) and shunted spikes.
However, the effect on control spikes was larger.
The above results hold true for all chloride conductances
tested (100 to 600 nS) (Fig. 5C). However, in contrast with
the situation presented in Figure 4C, the inhibitory effect
in the small-diameter (4 µm) axon model is less than that obtained
with large-diameter (10 µm) axon model. In small-diameter axons (4 µm), spikes are rapidly attenuated as they propagate passively toward
distal sites (Fig. 5A1,B1). When a 300 nS PAD was
elicited, the peak potential decreased from 40.6 to 32.1 mV in location b and from 19.1 to 16.5 mV in location c (Fig.
5C1, open circles). Increasing the chloride
conductance to 600 nS further reduced spike peak (29.9 mV) at location
b but had less effect on the spike peak (15.8 mV) measured
at location c. Increasing the conductance from 400 to 600 nS
did not have any further shunting effect on the spike peak at location
c. This is because of PAD being better conveyed than spikes
in passive axonal branches (Fig. 3); consequently, in the more distal
sites (c), most of the depolarization is attributable to the
PAD rather than to the spike (Fig. 5A1,B1,
insets). Increasing Rm (Fig.
5B,C2) only slightly improved the passive propagation of spikes but largely improved the propagation of PADs that becomes the
main constituent in the measure of the peak. In all cases, GABA
synapses located in passive conduction sites produced less shunting
effects than those located in active sites.
Effect of PAD on active spike propagation
The respective roles of the two features, membrane depolarization
and shunting, that accompany activation of GABA synapses on CBCO
terminals were tested in a series of simulations (axon diameter of 4 µm; Rm of 2000 cm2)
(Fig. 6). In the previous figures (Figs.
4, 5), the spike amplitude was measured as the sum of that PAD and
spike. To estimate the relative effect of the depolarization and the
shunt associated with the PAD, the spike amplitude was measured in two
different ways: (1) from the resting membrane potential (70 mV) to
the peak of the spike (Fig. 6A1,1), or (2)
from the top of the PAD to the peak of the spike (Fig.
6A1,2). For a given increase of chloride
conductance, the reversal potential for chloride ion (ECl) was either 40 mV (in this case a
PAD was produced) or 70 mV, the resting membrane potential (in this
case, no PAD was produced, although the shunting effect remained). This
was done to isolate the effect of shunt from the effect of
depolarization. An example of such simulations with
ECl of 40 mV (thick trace) and 70
mV (thin trace) is shown in Figure 6, A2 and
A3. The respective effects of the two chloride equilibrium
potentials are compared in two ways (Fig.
6A2,A3) using measure 1 and 2, respectively. Spikes were measured at two locations (as in Figs. 4, 5):
at the first branching point (Fig. 6B1,b) and
at a more distal location in a thin branch (Fig.
6B2,c). Various values of chloride conductance from 100 to 600 nS were used.
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Figure 6.
Contribution of PAD to spike propagation. PADs
were applied close to the transition from active to passive conduction.
Active conduction was achieved up to location 500 µm (see
schema at the top), and a 300 nS GABA synapse was
simulated at the branching point at location 400 µm. A1,
In these simulations, the monitoring of the spike was measured as
either its peak value (1) corresponding to the sum of the
PAD plus the spike, or its amplitude (2). A2, The
equilibrium potential for chloride was fixed to 40 mV (thick
trace) or to 70 mV (thin trace). A3,
Aligning the two traces with respect to the base of the
spike demonstrates that the depolarization induced by a 40 mV
equilibrium potential PAD contributes to the spike propagation.
B1, B2, Incidence of increasing chloride
conductance on spike propagation in the case of pure shunting
(ECl of 70 mV; filled circles) and
when PADs are produced (ECl of 40 mV;
filled triangles) at the branching point of the main axon
(B1) and in the distal part of the branch (B2).
For GCl > 200 nS, spike propagation is
abruptly prevented (arrowhead) in the case of pure shunting,
whereas this abrupt change is not observed when PADs are produced. The
filled squares represent the peak value of spikes (that is
the parameter represented in all other figures) in the case of PADs
associated with a 40 mV chloride equilibrium potential. C,
Spike propagation along the main axon during PAD (C1) and
pure shunting (C2) and in the absence of presynaptic
inhibition (C3). In the configuration represented here (4 µm main branch, Rm of 2000 cm2), chloride conductance larger than 230 nS
produce a failure of spike conduction (C4). For 230 nS, the failure is not complete, and the spike recovers partially in
the more distal compartments that possess sodium channels.
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Whatever the chloride conductance used, the peak of the spike (measure
1) was always larger with ECl of 40 mV
(squares) than with ECl of 70 mV
(circles) at both locations b and c.
When PADs were produced by a large chloride conductance increase (600 nS), the peak value of a concomitant spike measured distally at
location c is affected by the PAD (Fig.
6A1; see also Fig. 4, insets). If we now
consider solely the amplitude of the spike (measure 2), a pure shunting
mechanism (ECl of 70 mV) resulted in an abrupt decrease of spike amplitude when chloride conductance was increased over 200 nS (see recording shown in Fig. 6A3 using a
300 nS chloride conductance). This effect, observed at both locations
b and c (Fig. 6B), was unexpected if
PADs inactivate sodium channels, and a 300 nS chloride conductance
should have resulted in a larger decrease of spike amplitude for
ECl of 40 mV than for
ECl of 70 mV. However, in the present
simulation, the decrease in spike amplitude was larger for
ECl of 70 mV than for
ECl of 40 mV. This is attributable to failure
of spike propagation for ECl of 70 mV when
GCl is above 230 nS. This phenomenon is
illustrated in Figure 6C1-C4. Each figure represents
recordings made at nine locations regularly spaced from site 0 (the
most proximal; top trace) to site 800 µm (the most distal;
bottom trace) on the main axon. The branching point (site
400 µm at which PADs are produced) is represented by the thick
trace. When a 300 nS GCl with a 40 mV
ECl is used, the spike amplitude is smaller at
that site but partially recovers in the next distal (Fig.
6C1; see also Fig. 4A1). When
ECl is fixed at the resting membrane
potential (70 mV), the reduction of the spike amplitude is greater at
the branching point (Fig. 6C2) and does not recover in the
next distal site. Failure of spikes occurs with
GCl above 230-240 nS (Fig.
6B1, arrowhead). In the absence of PAD
(GCl of 0 nS) (Fig. 6C3), distal spikes are actively propagated up to site 500 µm (trace
immediately below the thick trace) and then
progressively attenuate (Fig. 4A1). The amplitude of
the spike at a given location not only involves the activation of local
sodium channels but also the sodium channels of neighboring sites. Any
phenomenon that reduces the depolarization of preceding compartments
would delay the spike in the preceding compartment and reduce the
amplitude of the spike in the current compartment. These two features
are illustrated in Figure 6C4. A GCl
of 230 nS was used, with ECl fixed at the resting potential (70 mV). In such conditions, an incoming spike fails to generate a spike in the first branching point compartment (thick trace). In the more distal compartments, the
depolarization produced by the failed spike at last reaches the
threshold for spiking and a second (distal) delayed spike is produced.
If the chloride conductance was above 230 nS, the depolarization was not sufficient to generate a distal spike (Fig. 6C2). Note
that such failures were never observed when ECl
was 40 mV.
These results demonstrate that, in the transition from an active to a
passive propagating zone, PADs have conflicting effects: (1) locally,
they dramatically reduce the propagating spike attributable to a
shunting effect, and (2) they facilitate the propagation of the shunted
spike to the more distal active compartments (up to 100 µm more
distal to the first branching point). The consequence of this latter
effect is that, in the absence of a depolarization accompanying the
increase of GCl, an abrupt increase in
the efficacy of presynaptic inhibition with increasing
GCl occurs (Fig. 6B, arrowhead). From these results, it is likely that
presynaptic inhibition mediated by PADs mainly involves a shunting
mechanism and very little, if any, inactivation of sodium channels (see Discussion).
Effect of PAD position
To determine the effect of the location of the synaptic input
mediating PADs along sensory axons on shunting and thereby on presynaptic inhibition, we compared the effect of PADs occurring at two
different compartments. When PADs were elicited at a compartment 100 µm more proximally (300 µm) from the branching point, the spike
amplitude was reduced in this compartment (Fig.
7A). However, because of the
existence of active conductances, the spikes regenerated between the
site of PADs and the branching point (Fig. 7A). In a 4 µm
axon and Rm of 4000 cm2, a
300 nS increase in conductance reduced the spike amplitude from 108 (control spike; open circles) to 71 (shunted spike;
filled circles) mV at the GABA synapse location
(b). However, at the branching point (c), because
of the presence of Na+ channels, the amplitude of
the shunted spike was partially restored (80 mV). This configuration
could work in an all or none manner if the GABA synapse is placed even
more proximally.
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Figure 7.
Incidence of PAD location on presynaptic
inhibition. A GABA synapse was simulated by an increase of chloride
conductance (GCl of 300 nS;
ECl of 40 mV) at locations 300 (A)
and 400 (branching point; B) µm. In these simulations, the
diameter of the main axon was fixed to 4 µm, and the intrinsic
membrane resistance, Rm, was 4000 cm2. Active conduction is achieved up to location
500 µm. Propagation of spikes along the main axon (large
circles) and in the branch (small circles) are
represented as their peak values at various locations of axonal tree,
in the absence (1-5; open symbols) and presence
(a-e; gray symbols) of PAD.
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In contrast, chloride conductance increase (GCl
of 300 nS) occurring at the branching point (Fig. 7B)
markedly reduced the amplitude of spikes at the branching point.
Because experimental data indicate that there is no active propagation
in the branch (Cattaert and El Manira, 1999), spikes
fail in the branch (Fig. 7B). However, because of the
presence of active compartments up to location 500 µm in the main
axon, a partial recovery of the spike occurs in the main axon. In this
configuration, activation of the GABA synapses
(GCl of 300 nS; ECl of
40 mV) results in a significant decrease of the spike amplitude in
the branch.
Origin and propagation of antidromic spikes
Simultaneous intracellular recordings made from a sensory terminal
of a CBCO and a postsynaptic motoneuron demonstrated that large PADs
were often capable of triggering antidromic spikes (El Manira et
al., 1991; Cattaert et al., 1992). Such
antidromic spikes were very attenuated when recorded distally (100-200
µm more distal to the first branching point) and never elicited any response in the postsynaptic motoneuron (El Manira et al.,
1991; Cattaert et al., 1992). To test whether
the shunting hypothesis could explain these observations, we have
simulated large PADs (ECl of 35 mV) that could
produce antidromic spikes.
Whatever the Rm value tested (2000, 4000, and
8000 cm2), antidromic spikes were elicited when
ECl was set to 35 mV (Fig. 8). When Rm was
low (2000 cm2 in Fig. 8A), it was more
difficult to elicit antidromic spikes because of the powerful shunting
effect in the compartments around the GABA synapse and the fact that
the depolarization is less propagated. As a result, in the compartments
close to the GABA synapse, a large depolarization occurred because of
the equilibrium potential for Cl
(ECl of 35 mV), but the spikes that should have
been elicited by this depolarization were shunted
(GCl of 300 nS), and a slight nonpropagated
transient was observed (Fig. 8A,c, first small
peak indicated by an asterisk on the
top of the PAD). However, the amplitude of this incomplete
spike was large enough to depolarize more distant compartments up to
spike threshold, and a full spike was generated in those compartments
(Fig. 8A,b). In turn, this full spike invaded the first
branching point compartment (location c), but because of the
massive local shunt and the Na+ channels being
inactivated, this spike was not propagated distally (Fig.
8A,d,e).
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Figure 8.
Production and propagation of antidromic spikes
elicited by large PADs. Large PADs were elicited at location 400 µm
(branching point), by increasing chloride conductance
(GCl of 300 nS; ECl of
35 mV). Same disposition as in Figure 7. A, Rm
of 2000 cm2. B, Rm of 8000 cm2. In A at location c, a
nonpropagated spike is observed (asterisk) before the
electrotonic image of the propagated spike (arrow). These
two events are also observed at location c for the second
spike in B (see Results for explanations).
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With Rm high (8000 cm2),
antidromic spikes were elicited more easily, because the depolarization
propagates better (Fig. 8, compare A1-A5 with
B1-B5, see orthodromic spike propagation). When a large PAD
was elicited close to the branching point, the membrane potential
reached the threshold for spiking in nonshunted compartments more
rapidly, so that the nonpropagated transient was not observed in the
GABA synapse compartment (Fig. 8B,c). However, in such a
configuration, the distal propagation of the spike generated by the PAD
was greater than with Rm of 2000 cm2 (Fig. 8, compare A,B). Note that
with Rm of 8000 cm2, two
spikes were elicited by the PAD, with the second one being much more
attenuated that the first one because of the inactivation of
Na+ channels.
These simulations demonstrate that spikes elicited by PADs are very
attenuated in the distal compartments. The attenuation of distal
propagation of such spikes increases with lower
Rm values. When Rm was
set at 2000 cm2, the distal propagation of
PAD-triggered spikes was totally prevented. The result from the
simulation supports the experimental observations, which demonstrates
that PAD-triggered spikes do not elicit any EPSP in postsynaptic
motoneuron (El Manira et al., 1991;
Cattaert et al., 1992).
Validation of the simulation results
The simulation of the propagation of antidromic spikes suggests
that spikes triggered by large PADs would be generated in proximal
parts of the sensory axon (Fig. 8). These simulations also predicted
that, at the GABA synaptic site (Fig. 8A,c), only a
nonpropagated transient would be generated (asterisk).
Therefore, we have performed intracellular recordings from sensory
axons to test this prediction (Figs. 9,
10). When
antidromic spikes generated by PADs were recorded in the proximal part
of the axon (400 µm before the first branching point), only full
spikes were |
TOP
ABSTRACT
INTRODUCTION
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![&agr;<SUB>n</SUB>=<FR><NU>A<SUB>&agr;<SUB>n</SUB></SUB>(E−B<SUB>&agr;<SUB>n</SUB></SUB>)</NU><DE>1−e<SUP>[(B<SUB>&agr;<SUB>n</SUB></SUB>−E)/C<SUB>&agr;<SUB>n</SUB></SUB>]</SUP></DE></FR> &bgr;<SUB>n</SUB>=<FR><NU>A<SUB>&bgr;<SUB>n</SUB></SUB>(B<SUB>&bgr;<SUB>n</SUB></SUB>−E)</NU><DE>1−e<SUP>[(E−B<SUB>&bgr;<SUB>n</SUB></SUB>)/C<SUB>&bgr;<SUB>n</SUB></SUB>]</SUP></DE></FR>.](/content/vol21/issue3/fulltext/1007/img018.gif)
