Reduction of presynaptic action potentials by PAD: model and experimental study

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Journal of Computational Neuroscience 5, 141–156 (1998) c 1998 Kluwer Academic Publishers. Manufactured in The Netherlands. °

Reduction of Presynaptic Action Potentials by PAD: Model and Experimental Study BORIS LAMOTTE D’INCAMPS URA CNRS 1448, Universit´e Ren´e Descartes, 45 rue des Saints-P`eres, 75270 Paris Cedex 06, France CLAUDE MEUNIER AND MARIE-LAURE MONNET UMR CNRS 7644, Centre de Physique Th´eorique, Ecole Polytechnique, 91128 Palaiseau Cedex, France ´ LENA JAMI AND DANIEL ZYTNICKI URA CNRS 1448, Universit´e Ren´e Descartes, 45 rue des Saints-P`eres, 75270 Paris Cedex 06, France [email protected]

Received March 19, 1997; Revised October 7, 1997; Accepted October 17, 1997 Action Editor: Segev

Abstract. A compartmental model of myelinated nerve fiber was used to show that primary afferent depolarization (PAD), as elicited by axo-axonic synapses, reduces the amplitude of propagating action potentials primarily by interfering with ionic current responsible for the spike regeneration. This reduction adds to the effect of the synaptic shunt, increases with the PAD amplitude, and occurs at significant distances from the synaptic zone. PAD transiently enhances the sodium current activation, which partly accounts for the PAD-induced fiber hyperexcitability, and enhances sodium inactivation on a slower time course, thus reducing the amplitude of action potentials. In vivo, intraaxonal recordings from the intraspinal portion of group I afferent fibers were carried out to verify that depolarizations reduced the amplitude of propagating action potentials as predicted by the model. This article suggests PAD might play a major role in presynaptic inhibition. Keywords: computer study, compartmental model, nerve, afferent fibers, sodium current inactivation 1.

Introduction

In anaesthetized cats, sustained contractions of an ankle extensor muscle generate sustained Ib afferent discharges from tendon organs. In contrast, the inhibitory potentials elicited by this afferent input in homonymous motoneurons quickly subside, as if information arising from tendon organs was filtered out during contractions (Zytnicki et al., 1990). Primary afferent depolarizations (PADs), recorded from the intraspinal portion of Ib afferent fibers during homonymous muscle contractions (Lafleur et al., 1992) indicated presynaptic inhibition of Ib terminals (see Devanandan et al., 1966), which

might account for the filtering out of Ib input during contraction. Most of the available data on presynaptic inhibition of group I afferents in the spinal cord were obtained from studies of Ia afferents. Presynaptic inhibition occurs at axo-axonic synapses contacting the intraspinal arborizations of afferent fibers where it is mediated primarily through activation of GABAA receptors, possibly with a contribution of GABAB receptors (Stuart and Redman, 1992; see also Eccles et al., 1963b; Curtis and Lodge, 1982; Rudomin et al., 1983). Activation of GABAA receptors increases the chloride membrane conductance, thereby inducing a shunt of ionic currents

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in the axonal membrane, plus a PAD that passively spreads along the fiber. The resulting reduction in the amplitude of afferent action potentials (Segev, 1990; Cattaert et al., 1992; Graham and Redman, 1994) is likely to reduce calcium influx in, and transmitter release from, terminal boutons. The shunt of ionic currents might by itself reduce the spike height, but recent computer studies suggest that relatively large synaptic conductances are required to induce a significant reduction of action potential (Segev, 1990; Graham and Redman, 1994). Considering the activation of a single axo-axonic synapse (located on an en passant bouton), Graham and Redman (1994) compared the effects of a purely shunting synapse (that is, with a reversal potential equal to the resting membrane potential) to those of a PADgenerating synapse (that is, with a reversal potential higher than the resting potential). They found that PAD does contribute to the reduction of spike height but concluded that it does not elicit a sufficient decrease of afferent action potentials to significantly reduce the transmitter release (see also Jackson and Zhang, 1995; Walmsley et al., 1995). The Ia collateral studied by Walmsley et al. (1995), bearing only three axo-axonic synapses on 36 boutons, received only weak presynaptic inhibition. In contrast, 30 of 35 Ia boutons examined by Pierce and Mendell (1993) in the S1/L7 ventral horn bore a total of 90 axo-axonic synapses. Moreover, in a recent confocal microscope study carried out by our group, two Ib collaterals, located in the lumbosacral spinal cord, were found to receive at least 59 axo-axonic synapses (Lamotte d’Incamps et al., 1997). In keeping with these morphological data, it seems a reasonable assumption that the coactivation of several axo-axonic synapses located on neighboring branches may result in spatiotemporal summation of individual PADs. The resulting collective PAD might then be large enough to elicit antidromic action potentials, as observed in group I fibers during fictive locomotion (Gossard et al., 1991) or in unmyelinated chordotonal afferents of crayfish (Cattaert et al., 1992). In this latter preparation, in which recording sites were close to axoaxonic synapses, large PADs of 15 to 20 mV were observed. These data justified the present reexamination, both in a model and experimentally, of the contribution of PAD to the reduction of action potential amplitude. In a first step, we designed a simple compartmental model to study the effects of large PADs (in the 1.5 to 36 mV range), generated by a single “equivalent”

axo-axonic synapse, on action potentials propagating along an intraspinal myelinated branch of an afferent fiber. This equivalent synapse was meant to mimick the coactivation of a group of GABAergic axo-axonic synapses. Using this simple model, we could show that a 15 to 20 mV PAD may by itself depress afferent action potentials by as much as 35 to 45%. Our computations further allowed investigation of (1) the relationship between the depression of a propagating action potential and PAD amplitude, (2) the reduced height of antidromic action potentials generated when PAD amplitude reaches the fiber discharge threshold, (3) the effects of PAD at distances from the site where it is generated, (4) the effects of a depolarizing current on a propagating action potential, and (5) the ionic mechanisms responsible for the reduction of action potentials by PAD. We also examined the reasons why PAD can simultaneously reduce action potentials and increase the fiber excitability, as observed by Wall (1958) (see also Schmidt, 1973; Rudomin, 1990). In a second step, we verified experimentally, using intra-axonal recordings from the intraspinal portion of group I fibers in anaesthetized cats, that depolarizations, induced either by a neuronal pathway known to mediate presynaptic inhibition or by injection of depolarizing current through the micropipette, reduced the amplitude of incoming action potentials, as predicted by the model. Altogether, our theoretical and experimental results are consistent with the hypothesis that PAD actually plays a major role in presynaptic inhibition.

2. 2.1.

Methods The Model of Myelinated Fiber

We modeled an intraspinal collateral of a myelinated group I fiber (Fig. 1) comprising 30 internodal segments separated by Ranvier nodes. The terminal zone at one end (left in Fig. 1) was a Ranvier node receiving electrical stimulation that elicited action potentials. The other end (right in Fig. 1) was a Ranvier node bearing an axo-axonic synapse. The dimensions of Ranvier nodes and internodal segments were taken from the mean values measured by Nicol and Walmsley (1991) on a Ia collateral in the midlumbar spinal cord. The axoplasmic diameter of the fiber was 1 µm while the internodal zones were surrounded by a 0.25 µm thick myelin sheath giving a total fiber diameter of 1.5 µm. Lengths of internodal zones and Ranvier nodes were

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Figure 1. Schematic representation of the myelinated fiber model. (See detailed description in the text) The PAD, elicited by activation of an axo-axonic synapse located at the right end of the fiber, passively spread from right to left. Afferent action potential was elicited by a square pulse (0.5 nA × 200 µs) applied at the left-end node 6 ms after the onset of synaptic activation. The effects of PAD on the action potential were observed from different recording points along the fiber. Recording point 1 was at the terminal compartment, recording points 2 and 3 at nodes located 315 µm and 1650 µm, respectively, from the terminal ending.

60 and 3 µm, respectively, resulting in a total length of 1893 µm for the model. We verified that for these parameters the saltatory conduction of action potentials was not affected by boundary effects in a central portion of the model representing 70% of the total length. Values for electrical parameters were derived from available data obtained in frog and rabbit myelinated axon preparations in vitro (Dodge and Frankenhauser, 1958; Chiu et al., 1979; and see Tasaki, 1982) as listed in Table 1. The axoplasmic resistivity was the same as used by Segev (1990). The membrane conductances of internodal segments and Ranvier nodes as well as the membrane capacitance of Ranvier nodes were in the range of experimental data (Dodge and Frankenhauser, 1958; Chiu et al., 1979). The membrane capacitance Table 1.

of internodal segments was computed by rescaling the mean value measured on a frog sciatic axon—that is, 5 · 10−3 µF · cm−2 with outer and inner diameters of 14 and 10 µm, respectively (Tasaki, 1982). A membrane capacitance of 4.15 · 10−2 µF · cm−2 was found (see also Graham and Redman, 1994). For Ranvier nodes, the sodium and potassium equilibrium potentials as well as the maximal conductances were those measured by Dodge and Frankenhauser (1958) with classical voltage-clamp techniques. 2.2.

Compartmentalization and Numerical Integration

The alternation of Ranvier nodes and internodal zones with contrasted electrical properties implied the use

Electrical parameters for each type of compartment. Ranvier node

Axoplasmic resistivity (Ä · cm) Membrane conductance (mS · cm−2 )

90

Internodal segment

Terminal zone

90

90

20a,b

8.23 · 10−2 (a,b)

2a,b

4.15 · 10−2

2

Resting membrane potential (mV)

−65

−65

−65

Sodium equilibrium potential (mV)

+50a

—

+50

Potassium equilibrium potential (mV)

−77a

—

−77

1200a

0

1200

90a

0

90

−65.385

−65

−65.385

Time constant (ms)

0.1

0.5

0.1

Space constant (µm)

37.3

581

37.3

Membrane capacitance

(µF · cm−2 )

Maximal sodium conductance

(mS · cm−2 )

Maximal potassium conductance (mS · cm−2 ) Leak equilibrium potential (mV)

a Dodge b Chiu

and Frankenhauser (1958). et al. (1979).

20

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of a compartmental model: the axon was subdivided into segments with electrotonic lengths shorter than 0.1 times the space constant so that the membrane was nearly isopotential along a compartment (Segev et al., 1989). Each Ranvier node was modeled as a single compartment, and each internodal zone as three successive compartments of 20 µm each. The electrotonic lengths were then 0.08 and 0.034 times the space constant for Ranvier node and internodal zone, respectively (see Table 1). In total the model comprised 121 compartments. Sealed-end boundary conditions were imposed at both ends. The numerical integration of the system of equations was performed using a fully object oriented simulator recently developed by Guillon, Meunier, and Monnet (unpublished work). The method chosen for the computation was the second order implicit Crank-Nicholson algorithm with a time step of 1 µs (see Crank, 1975; Tuckwell, 1988; Mascagni, 1989). Similar methods were used for the branched model (see details in the legend of Fig. 6). 2.3.

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The Sodium and Potassium Voltage-Dependent Currents

Voltage-dependent sodium and potassium currents were responsible for the generation of action potentials at the Ranvier nodes. The sodium current was fast activating and slowly inactivating while the potassium current was slowly activating. These currents were described, as in the Hodgkin-Huxley model (1952), by Eqs. (1) and (2), respectively: INa = gNa · (VNa − V ) · m 3 · h IK = gK · (VK − V ) · n , 4

(1) (2)

where gNa and gK were the maximal conductances, VNa and VK the reversal potentials for sodium and potassium currents respectively (see Table 1), m and h the activation and inactivation variables of the sodium current, and n the activation variable of the potassium current. The kinetics of each of the gating variables (x = m, h, n) followed a voltage-dependent relaxation equation of the form τx (V ) ·

dx = x∞ (V ) − x, dt

(3)

where x stands for one of the gating variable. The steady-state value x ∞ (V ) and the time constant τx (V ) were expressed in terms of the rate functions

Table 2. Numerical values for the parameters in the αx (V ) and βx (V ) functions.

A (ms) V1/2 (threshold, mV) z γ τmin (ms)

m

h

n

1.0 −40.0 −2.6 0.5 0.175

16.67 −62.0 +3.4 0.37 1.0

10 −53.0 −1.4 0.78 1.35

αx (V ) and βx (V ): x∞ (V ) =

αx (V ) αx (V ) + βx (V )

(4)

and µ

¶ θ , τmin , τx (V ) = Sup αx (V ) + βx (V )

(5)

with θ a dimensionless parameter. When the membrane potential exceeded a limit value (in the −30 mV to 0 mV range, depending on the gating variable m, h θ or n) the time constant αx (V )+β was nearly zero x (V ) which is not realistic. τx (V ) was then fixed at a nonnull constant τmin (see Table 2). The functions αx (V ) and βx (V ) were modeled using the formalism introduced by Borg-Graham (1991) for the description of voltage-dependent ionic currents. The functions αx (V ) and βx (V ) then read αx (V ) = 1/A · e

−zγ (V −V1/2 ) F RT

(6)

and βx (V ) = 1/A · e

z(1−γ )(V −V1/2 ) F RT

,

(7)

where R = 8.32 J · K−1 · mol−1 is the gas constant, F = 96.5 kC the Faraday constant, and T the absolute temperature (in K). A (expressed in ms) is a time constant. The activation or inactivation threshold V1/2 (expressed in mV) is the value of V for which the sigmoidal steady-state activation (or inactivation) function x∞ (V ) equals 0.5. The dimensionless parameter z acts both on the slope of the function x∞ (V ) at V1/2 and the peak width of τx (V ). The dimensionless parameter γ skews the shape of the function τx (V ). The parameters A, V1/2 , z, and γ were set independently for each gating variable m, n, and h to obtain voltage dependences close to those of the Hodgkin-Huxley model (see Table 2).

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Contribution of PAD to Reduction of APs For θ set at 0.28, the computed action potentials compared quite well with action potentials recorded in cat with central temperature maintained at 38◦ C. In particular, the duration of computed action potentials was 1.3 ms, which was very close to the duration (1.2 ms) of in vivo action potentials (see Fig. 7). The axonal conduction velocity was 2 m · s−1 —that is, in the same range as in Graham and Redman (1994, their Table 1). 2.4.

The Axo-Axonic Synapse

The activation of the axo-axonic synapse elicited in the terminal zone a synaptic current which followed the Eq. (8): ISyn = e ·

t −(t/τ ) · gSyn · (VSyn − V ), ·e τ

(8)

where gsyn is the maximal synaptic conductance in the 1 to 240 nS range, Vsyn is the synaptic reversal potential in the −65 to −35 mV range, and τ is the synaptic time constant here set at 2 ms. PADs then lasted less than 20 ms (see Fig. 2A2 for an example). The duration of the PAD mostly depended on the time course of the synaptic activation given by Eq. (8), while it was very little affected by the membrane properties, as membrane time constants were fast for all compartments (see Table 1). Under physiological circumstances, it

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is likely that the repetitive activation of axo-axonic synapses distributed over the intraspinal arborization of the fiber results in a long-lasting PAD as it is the case, for instance, of contraction-induced PADs on Ib fibers (Lafleur et al., 1992). In the present computer work, we did not try to get such a long-lasting PAD because we were studying the effects of the depolarization on an action potential—that is, a transient phenomenon of 2 ms duration: for the present study, a duration of 20 ms was sufficient. It was verified, however, that longer durations did not elicit other effects on the action potential than those reported in this article. The synaptic reversal potentials compared with those measured by Cattaert et al. (1992) in the sensory terminal of crayfish chordotonal organ (from −40 to −25 mV) as well as with the equilibrium potential of chloride ions (−61 mV) in the nerve terminals of rat posterior pituitary (Zhang and Jackson, 1995). When the synaptic reversal potential was set at the resting membrane potential (−65 mV), the activation of the synapse only elicited shunting effects on the action potential and did not generate any PAD (“shunting” synapse). When the synaptic reversal potential was set above the resting membrane potential, the synaptic activation induced a PAD whose peak amplitude depended on both the maximal synaptic conductance and

Figure 2. Effects of PAD on an action potential (as seen from recording point 1 in Fig. 1). A1 : Thin line: control action potential in absence of synaptic activation. Bold line: afferent action potential superimposed on the PAD (Vsyn = −55 mV, gsyn = 50 nS). A2 : Time course of PAD in absence of afferent action potential. B: Afferent action potential when axo-axonic synapse was active but did not generate any PAD (shunting synapse, Vsyn = −65 mV, gsyn = 50 nS). Horizontal bars indicate duration of axo-axonic synapse activation. Dots under A1 and B traces, electrical stimulation eliciting the afferent action potential.

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the synaptic reversal potential. At the fiber terminal, the PAD amplitude was in the 1.5 to 36 mV range. The median value was in keeping with the mean depolarization (14 mV) induced by local application of GABA (50 µM) in cell-attached patches of rat pituitary nerve terminals (Zhang and Jackson, 1995). 3.

Results

Figure 2 shows the effects of the activation of the axoaxonic synapse on an action potential reaching the terminal zone. In this instance, the synaptic reversal potential and the maximal synaptic conductance were set at −55 mV and 50 nS, respectively, and a primary afferent depolarization (PAD) was generated by the synaptic activation. The PAD quickly developed to reach an amplitude of 10 mV at the terminal compartment 1 ms after the onset of activation (see Fig. 2A2 ). It then slowly declined and disappeared after 15 ms. Six milliseconds after the onset of synaptic activation, an electrical stimulation was applied to the other end of the fiber eliciting an action potential that propagated to the terminal compartment in 0.9 ms. There, it appeared superimposed on the declining portion of the PAD with an amplitude of 64 mV (bold trace in Fig. 2A1 )—that is, 39% less than the 105 mV amplitude of the control action potential elicited in the absence of synaptic activation (thin trace in Fig. 2A1 ). It is apparent from Fig. 2A1 that part of this reduction was due to the superimposition of the action potential on a preexisting level of depolarization (that is, the PAD). However, most of the reduction of the action potential amplitude was due to the fact that the peak of the action potential reached a lower level when the axo-axonic synapse was activated (bold trace in Fig. 2A1 ) than when it was silent (thin trace in Fig. 2A1 ). 3.1.

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Contribution of the PAD to the Reduction of the Action Potential Amplitude

Was this reduction solely due to the shunting effect of the axo-axonic synapse, or was it also due to the PAD? To answer this question, a new simulation was carried out with the peak synaptic conductance again set at 50 nS but with a reversal potential of −65 mV (that is, the resting membrane potential). With these parameters, the synaptic activation induced the same shunting effect but no PAD (see Section 2, Methods). In such conditions, the action potential reached the terminal

with an amplitude of 81 mV (Fig. 2B)—that is, a reduction of only 23%, with respect to the control, which could be ascribed to the shunt of ionic currents elicited by the membrane conductance increase during synaptic activation (see also Segev, 1990). The comparison of the two simulations (Figs. 2A1 and 2B) indicated that the PAD by itself contributes to the decrease of spike height (see also Graham and Redman, 1994; Jackson and Zhang, 1995); this effect comes in addition to the shunt effect. The decrease in action potential amplitude was very substantial when the axo-axonic activation elicited a large PAD as exemplified in Fig. 3. In this instance, a PAD of 23 mV reached the discharge threshold of the fiber. Interestingly, the action potential thus generated at the terminal compartment had an amplitude of only 13 mV (bold trace, asterisk in Fig. 3A) indicating a partial block that was probably due to the combined effects of shunt and PAD. Nevertheless, this partial block did not prevent the action potential from propagating antidromically along the fiber (see thin trace, asterisk in Fig. 3). Figure 3 shows also the effects of such a large PAD on an action potential propagating in the usual orthodromic direction: on arrival at the terminal compartment, the action potential shown in Fig. 3A was superimposed on a 16 mV PAD and had an amplitude of 21 mV only (bold trace, arrow). During another simulation (Fig. 3B), made under purely shunting conditions (synaptic reversal potential and maximal synaptic conductance set at −65 mV and 94 nS, respectively), the action potential had a higher amplitude (60 mV), indicating that the PAD by itself elicited a large supplementary reduction (60 − 21 = 39 mV—that is, 37% of the control action potential). Additional observations further support the view that PAD contributes to the decrease of action potential amplitude. First, the effect of PAD on spike height was found to increase with the amplitude of PAD. This relationship was investigated by running simulations with increased conductances and/or reversal synaptic potentials. Under purely shunting conditions (Fig. 4A, open circles)—that is, when the synaptic activation did not generate any PAD (see Section 2, Methods)—the action potential amplitude was found to decrease with increasing conductance of the equivalent axo-axonic synapse. For peak synaptic conductances up to 95 nS, this reduction was linear with a slope of −0.47 mV/nS. Conductances in the 95 to 150 nS range caused reductions with a steeper slope (−0.75 mV/nS). For peak

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Figure 3. Effects on afferent action potential of axo-axonic activation inducing a large PAD. Bold trace: events observed from terminal compartment. Thin trace: events observed from recording point 3 in Fig. 1. Reversal potential and peak synaptic conductance of synapse, −45 mV and 94 nS, respectively. The PAD was large enough to generate an action potential (pointed by asterisks). Note that despite its small initial size (bold trace, asterisk), this action potential propagated antidromically along the fiber and fully regenerated, as observed from recording point 3 (thin trace, asterisk). Dots indicates that afferent potential was elicited 6 ms after the onset of synaptic activation in order to avoid collision with the antidromic spike. This afferent action potential propagated orthodromically in 0.9 ms to the terminal compartment where it superimposed on a 16 mV PAD (bold trace, arrow).

Figure 4. A: Relationship between synaptic conductance and action potential amplitude. All measurements made from recording point 1 in Fig. 1, for two values of synaptic reversal potential: −65 mV (open circles—that is, shunting synapse) and −35 mV (full circles). Action potentials were superimposed on the declining phase of synaptic activation at a time were the effective conductance was 0.4 times the peak synaptic conductance. Downward and upward arrows point to amplitudes measured for a peak synaptic conductance of 60 nS and a reversal synaptic potential of −65 mV and −35 mV, respectively. The difference between these two values is the additional, PAD-induced, reduction of action potential amplitude. B: Relationship between PAD amplitude and PAD-induced additional reduction of action potential amplitude. PAD generated with a synaptic reversal potential of −35 mV and measured just before onset of afferent action potential. The bisecting line is the expected contribution of PAD to the decrease of spike height if the decrease were only due to a passive reduction of driving force by membrane depolarization. The vertical dashed line indicates difference between passive and PAD-induced reductions of spike amplitude.

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conductances over 150 nS, the action potential was very small. When synaptic activation generated a PAD (synaptic reversal potential above resting potential), the relationship between membrane conductance and action potential amplitude was altered (see Fig. 4A, full circles): regardless of the synaptic conductance, the reduction of the action potential amplitude was larger in presence than in absence of PAD, especially for conductances under 100 nS. For instance, the shunt elicited by a 60 nS conductance reduced the spike height by only 39 mV (downward arrow in Fig. 4A), whereas under the same shunting condition, a 22 mV PAD further reduced the spike height by 55 mV (upward arrow in Fig. 4A). Conversely, for conductances over 150 nS, the reduction induced by the PAD was much smaller than the reduction induced by the shunt effect (Fig. 4A). In Fig. 4B, the extra reduction of spike height induced by PAD itself—that is, the difference between the amplitude of the action potential for the shunting synapse (Fig. 4A, open circles) and for the PADgenerating synapse (Fig. 4A, filled circles)—is plotted as a function of PAD amplitude. For PADs under 20 mV, the extra reduction of spike height was found to increase linearly (slope 2.7 mV/mV) with the amplitude of the PAD. Conversely, for PADs over 20 mV, the extra reduction steeply decayed with increasing PAD amplitude. This was explained by the fact that large PADs were caused by large conductances (above 100 nS) that already depressed the action potential by their sole shunting effect (see Fig. 4A, open circles). In these conditions the PAD by itself could only elicit a weak extra reduction of the action potential amplitude. Second, the action of the PAD is not a purely passive one. The bisecting line in Fig. 4B indicates the passive reduction of the spike height that would be expected if the reduction resulted only from the decreased driving force due to the membrane depolarization. PADs under 25 mV elicited a reduction of action potential amplitude larger than expected if the effects were exclusively passive. For instance, a PAD of 18 mV reduced the spike height by 51 mV that is 33 mV more than the expected passive reduction (Fig. 4B, vertical dashed line). Third, the effect of PAD could be directly demonstrated when the action potential was observed at distances from the axo-axonic synapse where the synaptic shunt was negligible. Figure 5 shows the changes in the amplitude of the action potential as it travels along the fiber under different conditions: (a) in absence of axoaxonic synapse activation, the amplitude of the action potential slightly increased from 103 mV to 106 mV

Figure 5. Amplitude of afferent action potential during conduction along the axon: (a) without synaptic activation, (b) during activation of a shunting synapse (Vsyn = −65 mV, gsyn = 50 nS—that is, same conditions as in Fig. 2B), (c, bold line) when a PAD was induced by synaptic activation (Vsyn = −55 mV, gsyn = 50 nS—that is, same conditions as in Fig. 2A1 ), and (e, dashed line) during injection (at recording point 1) of a depolarizing 4.25 · 10−2 nA current pulse. Afferent action potentials elicited as described in the legend of Fig. 1. Continuous curves obtained by linear interpolation between measurement points in the center of compartments. The crinkled appearance of the lines is due to alternation of action potential generation at successive nodes and passive decay in the internodes. (d) Passive decay of PAD along the axon. Vsyn = −55 mV, gsyn = 50 nS, i.e., same conditions as in Fig. 2A1 . PAD measured just before onset of afferent action potential. Horizontal dashed line indicates resting membrane potential. The spatial attenuation of PAD fits with an exponential function decreasing with a space constant of 177 µm— that is, a value close to the mean space constant (155 µm) that can be analytically computed when considering a myelinated branch of infinite length (Basser, 1993).

when reaching the terminal zone because of sealed-end effects (see also Segev, 1990); (b) conversely, under shunting conditions, the action potential amplitude decreased to 81 mV when reaching the terminal zone; a reduction of the action potential was visible up to a distance of 315 µm from the synaptic site: this was the maximal extent of the shunting effect of the synapse; and (c) action potentials were reduced in amplitude on a longer spatial range in presence of PAD: a 0.5 mV reduction of the incoming action potential was already observed at a distance of 650 µm from the axo-axonic synapse. Such reduction would be too small to affect synaptic transmission if an en passant synapse was

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located at this place. Still, it illustrated clearly that generation of a PAD at the axo-axonic synapse interfered with an incoming action potential on a long spatial range. The spatial attenuation curve of a PADgenerating axo-axonic synapse (Fig. 5c) was fitted with an exponential function decaying with a characteristic length of 100 µm (that is, significantly larger than the 55 µm characteristic length for the spatial attenuation of the shunt effect, Fig. 5b). These long-range effects were due to a spread of the PAD over relatively long distances. In the case illustrated by Fig. 5, a PAD of 7 mV generated at the synaptic zone was attenuated by 50% at a distance of 125 µm from the synapse, and at 650 µm it fell to 0.2 mV (Fig. 5d). Our results therefore suggest that the PAD can act on action potentials, from the synaptic zone to sites about 300 µm beyond the spatial extent of the shunt. This is in keeping with the passive cable theory where the spatial decrement of shunt effect is limited to half the space constant, as

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verified using a straightforward analytical computation (see also Koch et al., 1990). Finally, the depressing action of the PAD was indirectly confirmed by simulations in which a pure depolarization of the fiber—that is, not associated with a shunt effect—was elicited by injecting a long current pulse of small amplitude at recording point 1 (see Fig. 1). For instance, a depolarization of 7.5 mV elicited a 12.5 mV reduction of the spike height (not illustrated). As this depolarization diffused along the fiber, we verified that the spatial extent of its effect (see Fig. 5e, dashed line) was very similar to that of the PAD generated by the axo-axonic synapse. A second model, incorporating a branching point, showed that the PAD could also reduce the amplitude of an afferent action potential in a branch where the PAD diffused. As exemplified in Fig. 6, a PAD generated by the activation of an axo-axonic synapse located at the end of one daughter branch spread with

Figure 6. Effects of PAD on action potential propagation in a model incorporating a branching point. The parent and daughter branches each included four internodal zones separated by nodes. Geometrical and electrical features of compartments as in the main model for the parent branch (see Section 2, Methods). For the two identical daughter branches, inner and outer diameters and length of internodal segments were, respectively, 15 µm, 0.6 and 1 µm; node diameter, 0.6 µm; membrane conductance and capacitance of inernodal segment, 0.13 mS · cm−2 and 0.066 µF · cm−2 , respectively. Consequently, space constants for internodal segments and nodes in daughter branches were, respectively, 366 and 29.6 µm. Internodal segments in daughter branches implemented as three successive compartments of 5 µm length. Afferent action potential elicited as described in Fig. 1. Axo-axonic synapse (Vsyn = −45 mV, G syn = 60 nS) located at the end of the upper daughter branch. Depressed action potential (bold traces) observed from different locations pointed by arrows. Superimposed thin traces are the corresponding control action potentials recorded in absence of activation of the axo-axonic synapse. Note that the baseline difference between depressed and control action potential is the amplitude of the PAD that spread to the corresponding recording point. Further comments in the text.

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some attenuation up to the branching point (4.6 mV amplitude at this level, b) and from there both to the parent branch (a, 2.3 mV) and to the daughter branch that did not bear any axo-axonic synapse (c, 2.6 mV). In contrast, the synaptic shunting action remained confined to the branch bearing the synapse. Depression of afferent action potential was observed in all the locations where PAD was present. This depression was found to be proportional to the local amplitude of the PAD as predicted by the unbranched model (see Fig. 4B). At the end of the branch devoid of axo-axonic synapse, the action potential was reduced by 6 mV (c). 3.2.

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in the recorded fibers consistently decreased by 0.3 to 1.8 mV. In the example of Fig. 7A, the conditioning stimulation of PBST and Q nerves at two times group

Experimental Verification of Model Predictions

Electrophysiological experiments, using in vivo intraaxonal records from the intraspinal portion of group I afferent fibers to investigate the effects of PAD on propagating action potentials, were made to test the model predictions. Experimental animals were adult cats deeply anesthetized with sodium pentobarbitone (Sagatal, May & Baker, initial dose 45 mg kg−1 i.p., supplemented whenever necessary by additional i.v. doses of 4 mg kg−1 ) and paralyzed with gallamine triethiodide (Flaxedil, Spécia, 8 mg kg−1 h−1 i.v.). The methods for intra-axonal recording from identified afferent fibers, as well as the care taken to permanently monitor the adequacy of anesthesia and artificial ventilation, were fully described in Lafleur et al. (1992). It is known that, in cats, inputs from knee flexor (posterior biceps-semitendinosus, PB-St) or extensor (quadriceps, Q) muscles elicit PADs in group I afferent fibers from triceps surae (TS), an ankle extensor muscle (Eccles et al., 1962; Jimenez et al., 1988). We therefore elicited afferent action potentials in TS group I fibers by single electrical pulses on the nerve and tested whether the amplitude of these action potentials was depressed upon stimulation of PB-St or/and Q nerves by trains of eight pulses at 330 s−1 . This test could be carried out only on fibers where (1) the resting membrane potential (−40 to −60 mV) was stable throughout the recording session and (2) the amplitude of the control action potential (in absence of PAD) was between 40 and 75 mV. In two experiments, these conditions were satisfied for 6 group I fibers from TS in which conditioning PB-St and Q stimulation elicited PADs of 0.2 to 0.8 mV peak amplitude at the recording point (that is, the common range of PAD amplitudes reported under similar experimental conditions) (see, e.g., Jimenez et al., 1988). During the development of PADs, the amplitudes of action potentials traveling

Figure 7. A: Intra-axonal recordings from a TS group I fiber showing the effects of PAD on orthodromic action potential (19 averaged sweeps). Open circles under intra-axonal trace indicate 300 Hz electrical stimulation (at two times group I threshold) of Q and PBST nerves, eliciting PAD in the TS fiber. Dots indicate stimulation of TS nerve. Action potentials cut (double bars) to fit within the figure. Amplitude of control action potential, 75 mV. Lower dashed line, resting membrane potential (−70 mV). Upper dashed line, level of control action potential peak. Downward arrow shows that peak of test action potential was 0.7 mV less than the control. Upward arrow, 0.8 mV PAD elicited by conditioning stimulation. Axonal conduction velocity of afferent fiber, 110 m · s−1 . B: Effects of current-induced depolarization on incoming action potentials in a group I fiber of sciatic nerve (five averaged sweeps). Upper trace, membrane potential recorded from the intraspinal portion of the fiber. Lower trace, depolarizing current injected through the recording microelectrode. Rectangular pulses of 1 nA × 60 ms in A and 2 nA × 60 ms in B. Dots under current trace, electrical stimulation of sciatic nerve eliciting an orthodromic action potential. Stimulation before onset of depolarizing current elicited control spike, and second stimulation, 45 ms after onset of depolarization, elicited the test spike (arrow). Note that control spike amplitude was higher in B than in A, probably because of improved recording conditions. In B, note that an action potential (asterisk) was fired at the onset of depolarization when membrane potential reached the fiber discharge threshold. Axonal conduction velocity of afferent fiber, 75 m · s−1 .

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I threshold elicited in a TS fiber a depolarization of 0.8 mV with respect to the resting membrane potential (bottom dashed line). This depolarization reduced the amplitude of a test action potential by 1.5 mV with respect to a control spike. The reduction in spike amplitude was larger than the amplitude of the PAD (upward arrow) because the peak of the action potential was lowered by 0.7 mV (downward arrow). This reduction of peak amplitude was predicted by our model (see Figs. 2A and 3A) and suggested that the PAD partly acted by disturbing the kinetics of voltage dependent conductances responsible for the action potential regeneration (see below). Our results contrasted with early observations of Eccles et al. (1963a), who found that “when superimposed on the PAD the spike potential was reduced by an amount approximately equivalent to the depolarization.” During in vivo experiments, intra-axonal recordings could only be made from fiber portions coursing in the dorsal columns or in the dorsal horn—that is, at distances from the presumed sites of axo-axonic synapses in the ventral horn and intermediate zone. Because of spatial attenuation, the PAD was smaller at the recording site than at axo-axonic synapses. Our experiments showed that despite their small amplitude at the recording site, the PADs still caused reductions of spike amplitudes. This observation suggests that substantial reductions in action potential amplitude may occur near axo-axonic synapses. In order to observe the effects of large depolarizations on incoming action potentials, we injected depolarizing currents through the recording microelectrode. Under these experimental conditions, no shunt occurred, and the sole effects of the depolarizations were observed. In six sciatic nerve fibers (peripheral axonal conduction velocities, 50 to 90 m s−1 ), depolarizations of 0.9 to 11 mV amplitude were elicited by current steps of 1 to 3 nA. The current-induced depolarizations produced reductions of 4 to 21 mV (10 to 45%) in the amplitudes of action potentials evoked by stimulation of the sciatic nerve. On the example of Fig. 7B1 , a 1 nA current step lasting 60 ms produced a 3.7 mV depolarization of the fiber and reduced by 21% the amplitude of the action potential (test spike, arrow) with respect to the control spike recorded before onset of current injection. We verified that no reduction occurred in the test spike when no current was injected. When a 2 nA current (Fig. 7B2 ) was injected, a spike (asterisk) appeared at the onset of a 6.5 mV depolarization because the discharge threshold of the fiber was reached. Remarkably, the amplitude of this

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depolarization-induced spike was lower than the control (see Fig. 3) and the test spike amplitude (arrow) was only 55% of the control spike. Altogether, our experiments showed that, as predicted by our model, (1) the PAD acted primarily by hindering a full regeneration of the spike and (2) the depression of the action potential increased with the PAD amplitude (see Fig. 4B for the theoretical relationship between PAD amplitude and reduction of the spike height).

3.3.

Membrane Current Perturbations Induced by PAD

Our model was used again in order to examine which ionic perturbations are responsible for the depression of action potential amplitude by the PAD. The perturbations of ionic currents by PAD were examined at the node of Ranvier located 315 µm from the synaptic site because, as illustrated in Fig. 5, at shorter distances, perturbations of ionic currents could be due to both PAD and synaptic shunt and it was impossible to dissociate the two effects. At 315 µm from the synapse, no significant shunt effect occurred but a 1.2 mV PAD was present that was responsible for the depression of action potential (see Fig. 5). Though the PAD induced only a 2 mV reduction in action potential amplitude, perturbations were observed in the time course of ionic currents. The net current entering the Ranvier node was first considered—that is, the sum of the different membrane currents (inward sodium, outward potassium, and leak currents) and the axial currents flowing from the neighboring internodal zones. PAD induced small perturbations in the net current during the regeneration of an action potential as demonstrated by subtracting the net current obtained in a control case where the synapse was not activated from the net current entering the compartment in presence of PAD (see Fig. 8, upper trace). Three successive phases could be distinguished. (1) First, an initial positive difference of about 50 µA · cm−2 (upper trace in Fig. 8, phase a), concomitant with the onset of the action potential, indicated that more current was entering the compartment when the PAD was present. This initial transient excess in inward current contributes to the PAD-induced hyperexcitability of the fiber, as detected during electrophysiological experiments (Wall, 1958; see also Schmidt, 1973; Rudomin, 1990). The hyperexcitability results not only from a membrane potential closer to the firing threshold but also from the activation by the PAD of the

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Figure 8. PAD-induced perturbations in net inward current at recording point 2 in Fig. 1. Upper trace: difference between the net inward current (that is, balance between inward sodium, outward potassium, membrane leak current and axoplasmic currents) during and in absence of synaptic activation (Vsyn = −55 mV, gsyn = 50 nS, i.e., same conditions as in Fig. 2A1 ). a, b, and c point to the three successive phases described in the text. Dashed horizontal line: reference level. Bottom trace: control action potential (observed in absence of synaptic activation).

voltage-dependent sodium conductance (see below). (2) Subsequently, a brief large negative difference of 150 µA · cm−2 appeared (Fig. 8, phase b) during the rising phase of the action potential. This deficit in net current was responsible for the reduction of action potential amplitude. (3) Finally, a positive difference of 80 µA · cm−2 , lasting 0.5 ms, appeared during the after-hyperpolarization. It was due to the fact that the membrane potential was returning toward a less hyperpolarized level in presence than in absence of PAD. A similar analysis was performed for individual ionic currents. The PAD-induced perturbations of the inward sodium current (1INa ) are shown in Fig. 9A (bold trace). At rest, the depolarization of the membrane by PAD induced a constant 160 µA · cm−2 deficit in sodium current with respect to the control case. When the afferent action potential reached the Ranvier node, a transient excess of sodium current flew through the membrane at the onset of the action potential (Fig. 9A, hatched area) accounting for most of the net current enhancement. Conversely, during the rising phase of the action potential a smaller amount of sodium current entered the compartment in presence of PAD (Fig. 9A, arrow). This deficit accounted for most of the reduction in the net current. The different time courses of the two gating variables (the activation variable m and the inactivation

variable h) account for the perturbations of the sodium current by PAD (1m and 1h in Fig. 9B). At rest, the presence of PAD very slightly increased m while producing a large decrease of h because the inactivation threshold (−62 mV, see Table 2) was close to the resting level. This enhanced inactivation together with a smaller driving force explained the deficit in sodium current elicited by the PAD at rest. At the onset of the action potential, the activation variable increased more in presence than in absence of PAD: 1m displayed a six-fold increase in less than 0.2 ms (open arrow in Fig. 9B) when the membrane potential reached the activation threshold (−40 mV, see Table 2). However the m variable returned to its control value 0.2 ms after its peak activation. This explains why the sodium current developed faster at the onset of the action potential in presence of PAD and partly accounts for the fiber hyperexcitability. On the other hand, the enhanced inactivation of the sodium current persisted throughout the action potential development and the repolarization phase (see Fig. 9B) because of the slow kinetics of the h variable. This enhanced inactivation was found to be the main cause for the reduction of the action potential amplitude by PAD and thereby indirectly of transmitter release. Figure 9A shows that depolarization of the membrane also induced a constant 170 µA · cm−2 excess in the outward potassium current (1IK ). During the rising phase of the action potential, the magnitude of 1IK further increased due to enhanced activation, contributing to the reduction of spike height. However, while the perturbation of the potassium current induced by the PAD participates in the reduction of the action potential amplitude, it has little effect on the hyperexcitability of the fiber as potassium activation is much slower than sodium activation. 4.

Discussion

The main result of the present study is the demonstration that a large PAD, as may be elicited by coactivation of several axo-axonic synapses, significantly contributes to the reduction of afferent action potentials because membrane depolarization alters the operation of voltage-dependent conductances. Computer simulations showed that (1) at the terminal site, the effect of PAD adds to the shunt effect produced by synaptic conductance; (2) the PAD-induced reduction of action potentials depends on the amplitude of PAD (up to a given limit, see Fig. 4B); (3) the PAD diffuses

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Figure 9. A: PAD-induced perturbations in sodium and potassium currents through the node at recording point 2 in Fig. 1. 1INa (bold line): difference between inward sodium currents during and in absence of synaptic activation (same conditions as in Fig. 8). Hatched area shows the transient excess causing fiber hyperexcitability. Arrow points to the deficit in sodium current responsible for the reduction in peak amplitude of incoming action potentials. 1IK (thin line): difference between potassium currents during and in absence of synaptic activation. Dashed horizontal line: reference level indicating a null 1INa and 1IK . Note that an excess of inward sodium current translates into a positive 1INa , whereas an excess in outward potassium current translates into a negative 1IK . Bottom trace: expanded control action potential. B: PADinduced perturbations of sodium activation and inactivation variables. 1m (bold trace): difference between the values of sodium activation variable during and in absence of synaptic activation. Open arrow: transient enhancement of sodium activation at the onset of action potential. 1h (thin trace): difference between the values of sodium inactivation variable during and in absence of synaptic activation. 1m and 1h are dimensionless variables. Bottom trace: expanded control action potential.

at distances beyond the extent of the shunt (compare b and c in Fig. 5); (4) depolarization by current injection through the axonal membrane also depresses the action potential (Fig. 5e). In vivo experiments, using intraaxonal recordings from group I fibers, confirmed that depolarization, whether induced by activation of neuronal pathways known to mediate presynaptic inhibition or by injection of a depolarizing current through the recording microelectrode (see Fig. 7), also depressed the amplitude of action potentials propagating in the fiber. Altogether these results support the assumption that PAD plays an important role in presynaptic inhibition. On crayfish preparations in vitro, where simultaneous intracellular recordings of a chordotonal afferent and of a postsynaptic motoneuron were possible, it was demonstrated that a reduction in the amplitude of afferent action potentials results in a decrease

of excitatory postsynaptic potentials (Cattaert et al., 1992; see also Hagiwara and Tasaki, 1958; Katz and Miledi, 1967; Llinas et al., 1981; Martin and Ringham, 1975, for an example in vertebrates). Graham and Redman (1994) considered that in vertebrates, presynaptic mechanisms have to lower the amplitude of the action potential down to 90 mV in order to elicit a significant decrease of the postsynaptic potential amplitude. We found that such a reduction could result from a 7 mV PAD. Large PADs (above 7 mV), whose presence was suggested by observations of antidromic action potentials (indicating that the spiking threshold of the fiber was reached, Gossard et al., 1991), could significantly contribute to presynaptic inhibition, by lowering the amplitude of incoming action potential, as demonstrated in this article. This would presumably reduce the transmitter release at terminal or en passant boutons. Additionally, as suggested by Graham and

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Redman (1994), the PAD might also have a more direct effect on the transmitter release by inactivating calcium current. Our computer study allowed assessment of the respective contributions of the shunt and the PAD in presynaptic spike reduction. For instance, the shunt produced when the peak synaptic conductance was 4.7 nS reduced by 5.6 mV the action potential amplitude. When the same synaptic conductance was associated with a 5.3 mV PAD, a further depression of 12.4 mV of spike height occurred. For peak synaptic conductances under 80 nS, the contribution of PAD to spike depression was larger than the contribution of shunt (Fig. 4A) (see also Graham and Redman, 1994). Shunts produced by activation of individual axoaxonic synapses exert their effects over smaller distances than PADs that can diffuse over longer distances (see Fig. 5), and it is also the case for the shunt produced by coactivation of several axo-axonic synapses distributed over an afferent arborization. Collective PAD could thus be the predominant cause for the depression of presynaptic action potentials. This collective effect accounts for the difference between the conclusions of the present study and of Graham and Redman (1994). However, if axo-axonic synapses are located on unexcitable branches (that is, membrane deprived of sodium channels), the PAD cannot elicit any active effect on action potentials and the axo-axonic synapses will act primarily through their shunting effects. A simple analysis of PAD-induced perturbations of ionic currents could be conducted only in a region of the fiber located far enough from axo-axonic synapses to be outside the spatial extent of their shunting actions. Incorporation of unmyelinated portions, boutons or branching points in our model would have made it difficult to find a region of the fiber where action potential size and conduction velocity were not disturbed by other factors than activation of the synapse. An unmyelinated terminal would cause a steep attenuation of the PAD, reducing its spatial extent, and, consequently, the portion of the fiber affected by the PAD beyond the extent of the synaptic shunt. A bouton would locally increase the axon diameter thereby reducing the axonal resistance and affecting the axoplasmic current. A branching point would affect the safety factor for action potential conduction depending on the geometrical branching ratio and thereby the regeneration of the action potential in each of the two daughter branches (Goldstein and Rall, 1974; Parnas and Segev, 1979).

Our analysis showed that the reduction of spike height mainly resulted (1) from an enhanced inactivation of sodium current during the rising phase of the spike and (2) to a lesser extent, from an increased potassium current (see Fig. 9). These effects of PAD are compatible with the well known PAD-induced hyperexcitability (Wall, 1958; see also Schmidt, 1973; Rudomin, 1990). Hyperexcitability is due not only to the fact that less depolarization is needed to reach the firing threshold in presence than in absence of PAD but also to the transient enhancement of sodium current at the onset of the spike that is pointed in this article (see Fig. 9). Altogether, our study suggests that the PAD has two opposite and successive effects on the dynamics of the sodium current: an enhancement of activation that contributes to the fiber hyperexcitability and an enhancement of inactivation that is responsible for the spike height reduction. These two phenomena occur successively because sodium activation is a fast process while inactivation is about 5 to 10 times slower (Hodgkin and Huxley, 1952). The PAD effects we analyzed in this computer study may be generalized to any fibers in which action potentials arise from successive activation and inactivation of a sodium current. This may hold true even when the action potential regeneration does not involve a potassium current as in peripheral myelinated fibers of rabbit sciatic nerve (Chiu et al., 1979). On a version of our model, in which the potassium current was removed and the conductance and reversal potential of the leak current were modified so as to keep the same resting potential and membrane time constant as in the main model, we verified that the effects of the PAD on a purely sodium spike were qualitatively similar to those described in this article (unpublished observation). The depressing action of the PAD is likely to occur in any region of an intraspinal afferent arborization where PAD spreads provided the membrane of this region contains excitable sodium channels. We verified that PAD can exert its action on branched models (see Fig. 6) and on branches including unmyelinated excitable membrane (unpublished observation). Whatever may be the case, our in vivo experiments demonstrated that depolarization prevents the full regeneration of a propagating action potential as expected if the sodium current responsible for spike regeneration was partially inactivated by depolarization. Our hypothesis that PAD plays a major role in presynaptic inhibition rests on the assumption that the spread

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of individual PADs, generated by several coactivated axo-axonic synapses distributed over an intraspinal arborization, may result in the building up of a large PAD. Such a summation requires a weak spatial attenuation of PAD and will be favored by the factors that increase the space and time constants of the collateral branches such as an extensive myelination and a large diameter; it will also depend on the ratio of branch diameters and on the activation pattern of axo-axonic synapses. New modeling work has now to be done in order to (1) analyze how individual PADs sum through the intraspinal arborization of an afferent fiber and (2) explain how a large PAD can develop in some branches while remaining negligible in others. This occurrence is suggested by experiments in which the excitability of two branches of the same group I fiber was simultaneously tested (Eguibar et al., 1994). The authors found that a PAD elicited in one branch by intraspinal microstimulation remained confined to that branch and did not spread to the other. In addition, the same group found that stimulation of cutaneous nerves or of the motor cortex could inhibit almost completely a background PAD in one branch whereas it did not affect the PAD in the other (Eguibar et al., 1997). These experiments suggest that different subpopulations of lastorder interneurons project to the different branches of a particular group I afferent and that the electrotonic structure of the fiber arborization might restrict the spread of the PAD. Such an organization would ensure a differential control by presynaptic inhibition of information flow through different branches of the same afferent fiber. Acknowledgments Financial supports of Ministère de la Recherche et de l’Espace (92 C 0422), DGA-DRET (95062), CNES (95/024) and Association Frangaise Centre las Myopathics (MNM 1996) are gratefully acknowledged. M.-L.M. was a recipient of a DGA-DRET fellowship. References Basser PJ (1993) Cable equation for a myelinated axon derived from its microstructure. Med. Biol. Eng. Comput. 31:S87–S92. Borg-Graham LJ (1991) Modelling the non-linear conductances of excitable membranes. In: H Wheal, J Chad, eds. Cellular and Molecular Neurobiology: A Practical Approach. IRL/Oxford University Press, Oxford. pp. 247–275.

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