Journal of Physiology (1 991), 440, pp. 345-3f6 Writh I1 figures Printed in Great Britain.

345

MEMBRANE PROPERTIES OF EXTERNAL URETHRAL AND EXTERNAL ANAL SPHINCTER MOTONEURONES IN THE CAT

By MITSUYOSHI SASAKI From the Department of Neurophysiology, Institute of Brain Research, School of Medicine, U7niversity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan

(Received 29 October 1990) SUMMARY

1. Intracellular recordings were made from external urethral sphincter (EUS) and external anal sphincter (EAS) motoneurones in the cat spinal cord under pentobarbitone anaesthesia. EUS and EAS motoneurones were located in segments St and 82 in the lateral part of the ventral horn corresponding to column Y of Romanes in the cat or group X of Onuf in man. 2. The axonal conduction velocity of sphincter motoneurones, calculated from the latency of the antidromic action potential and the conduction distance, ranged from 16 to 80 m s-', much slower than that of hindlimb motoneurones. The duration of the spike after-hyperpolarization (AHP) was in a similar range to that of hindlimb motoneurones. The antidromic latency, the duration of the action potential and the duration of the AHP were positively correlated with one another. 3. The input resistance ranged from 2-6 to 9 0 MQ and was positively correlated with the latency of the antidromic spike. The plots of input resistance versus conduction velocity in sphincter motoneurones were distributed around the extrapolated regression line determined for hindlimb motoneurones, indicating that there is a common correlation amongst conduction velocity, input resistance, and size of motoneurones regardless of the muscle type innervated by a motoneurone. 4. The regression line relating AHP duration and input resistance in sphincter motoneurones was quite different from that in hindlimb motoneurones in its slope, indicating that the AHP duration does not depend solely on the size of the motoneurone. 5. The voltage responses to injection of steps of hyperpolarizing current developed a time-dependent depolarizing 'sag' at higher current levels. The delay in onset and the time constant of decay of this depolarizing sag depended upon the peak amplitude of the hyperpolarizing response. The slope resistance in the I-V curve decreased in the hyperpolarizing direction in all neurones examined, indicating the existence of anomalous rectification analogous to the Q current IQ. In some sphincter motoneurones, an increase of slope resistance in the I-V curve was observed when the membrane was further hyperpolarized. 6. The membrane time constant was positively correlated with input resistance, Present address: Department of Shinjuku-ku, Tokyo 160, Japan. N1S 8126

Physiology,

Tokyo Medical College,

6-1-1 Shinjuku,

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suggesting that motoneurones with high input resistance have high specific membrane resistivity. The dendritic-to-soma conductance ratio (p) and electrotonic length of dendrite (L) were estimated according to Rall's model. p was smaller than that of hindlimb motoneurones, suggesting less developed dendritic arborization. L was similar to that of hindlimb motoneurones. 7. No differences were observed, in any of the above characteristics of motoneurones, between EUS and EAS. INTRODUCTION

The external urethral sphincter (EUS) and external anal sphincter (EAS) muscles are composed of striated muscle fibres innervated by the somatic pudendal nerves. Until recently little has been known about the location and physiological properties of spinal motoneurones innervating these muscles. Mannen, Iwata, Toyokura & Nagashima (1977) found that group X of Onuf (1900), called Onuf's nucleus, is preserved during amyotrophic lateral sclerosis (ALS), when other motoneurones degenerate. Because the function of the EUS and EAS is also resistant to ALS, it was suggested that the motoneurones of Onuf's nucleus innervate these muscles. This conclusion has been confirmed in cats and dogs by using retrograde tracer techniques (Sato, Mizuno & Konishi, 1978; Kuzuhara, Kanazawa & Nakanishi, 1980). Mackel (1979) has recorded intracellularly from EUS and EAS motoneurones to investigate segmental and descending control of these muscles. With respect to membrane properties of the motoneurones, he found that the duration of the spike after-hyperpolarization was relatively short (50-100 ms) and was in the range of after-hyperpolarization observed for motoneurones supplying fast-twitch muscles in the hindlimb (Eceles, Eccles & Lundberg, 1958; Kuno, 1959). In contrast, the external sphincter shows a steady tonic discharge in resting conditions (Floyd & Walls, 1953; Kawakami, 1954; Garry, Roberts & Todd, 1959; Taverner & Smiddy, 1959), as would be expected for motoneurones innervating slow-twitch, tonic-type muscles. This apparent discrepancy suggests that the membrane of sphincter motoneurones may have some characteristic properties distinct from those of hindlimb motoneurones. Previous studies have measured various physiological properties of hindlimb motoneurones, such as axonal conduction velocity, duration of the after-hyperpolarization, input resistance, membrane time constant, and current-voltage relation of the membrane. These studies have been thoroughly reviewed by Rall (1977) and Burke (1981). The present paper describes such physiological characteristics in sphincter motoneurones and compares them with those of well-analysed hindlimb motoneurones to elucidate the mechanisms underlying the functional particularity of sphincter motoneurones. METHODS

General procedures Experiments were performed on eighteen adult cats weighing 22-3-2 kg. The animal was anaesthetized with ketamine hydrochloride (Sankyo), 50 mg I.M, followed by pentobarbitone sodium (Abbott), 15 mg kg-' i.P. Additional doses of 3 mg kg-' of pentobarbitone (i.v.) were

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injected every half-hour or hour until the total dose reached 40-50 mg kg-'. Further doses were administered as required. Rectal temperature was maintained at 37-38 °C by an infra-red lamp. Blood pressure of the carotid artery was monitored throughout the experiment. When necessary, a solution of 5 % dextrose in 09 % saline or a diluted solution of Carnigen (Hoechst) was administered (i.v.) to maintain the arterial pressure at above 100 mmHg. The gluteus muscle was removed to expose the pudendal nerve as it branched off the sciatic nerve towards the deep part of the ischiorectal cavity. The branches of the pudendal nerve which innervate the EUS and EAS were dissected free and prepared for antidromic stimulation. Laminectomy was performed at the spinal vertebrae L5-L7. During recording the animals were paralysed with pancronium bromide (Organon Ltd) and artificially ventilated.

Stimulating and recording procedures Bipolar platinum-hook electrodes were used for antidromic stimulation of the pudendal nerve branches innervating the EUS and EAS. A silver plate attached to the back muscles was used as an indifferent electrode. For field-potential analysis, glass micropipettes filled with 2 M-NaCl saturated with Fast Green FCF with resistances of 1-2 MQ were used. Intracellular recordings were made with 3 M-KCI glass microelectrodes with tip diameters less than 1-0 ,um and resistances of 3-5 MQ. EUS and EAS motoneurones were antidromically identified. In three animals, it was difficult to stimulate the EUS and EAS nerves separately due to current spread. In these cases, both EUS and EAS nerves were stimulated together, and thus identified motoneurones were termed sphincter motoneurones not identified as EUS or EAS'. Field potentials were recorded with an AC amplifier (time constant: 0-2 s), and the antidromic spike potential and afterhyperpolarization with a DC amplifier. For intracellular recording and current injection, conventional circuits with a bridge balance (MEZ-8201 and S-9353, Nihon Kohden, Japan) were used. Current step analysis Before current injection, the voltage artifact across the input capacitance was cancelled by adjustment of the capacity compensation control. Electrode resistance was balanced by adjusting the bridge circuit while observing the potential trace with a fast sweep. Three to five superimposed voltage transients were recorded at each different current intensity. Thereafter, the antidromic action potential was again recorded to determine that the neurone had not deteriorated during the test period. After withdrawal of the microelectrode from the cell, a current step was applied in order to measure the balance of the bridge circuit and insure that the electrode possessed no rectifying properties.

Histology At the end of the experiment, the intracellular microelectrode was advanced 2 mm beyond the last recording site and left in place. The animal was perfused with 10% formalin, and the spinal cord was removed and post-fixed. Transverse, 100 ,tm frozen sections were cut. The location of the electrode track for intracellular recording or the dye mark for extracellular field potential recording was determined in thionin-stained serial sections. RESULTS

Location of EUS and EAS motoneurones The location of EUS and EAS motoneurones in the spinal cord was estimated by recording antidromic field potentials evoked by supramaximal (1-1P5 times maximal) stimulation at 5 Hz of the pudendal nerve branches to EUS and EAS muscles respectively. Figure 1B-F shows the distribution of antidromic field potentials in the St ventral horn along five microelectrode tracks indicated in Fig. lA. When an electrode was gradually advanced ventrally, an antidromic response consisting of single or double sharp, spike-like negativities, or fused spikes, appeared at a depth of approximately 1-4 mm from the surface and could be recorded as far as 400 ,um

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ventrally from this point. The mediolateral extension of the field potential was usually confined to less than 400 /um. The area in which antidromic field potentials could be recorded extended from the caudal half of S1 to the caudal end of S2. Antidromic field potentials could not be elicited in 83. The present study deals with A

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Fig. I. Antidromic field potentials in the sacral spinal cord evoked by supramaximal stimulation of the EUS and EAS nerve. A, section through the caudal part of SI segment. Vertical lines show the electrode tracks along which the field potentials were recorded. The distance between the tracks (b-e) is 100 yum and that between e and f is 200 ,tm. The right scale represents the depth from the dorsal surface of track d. The dye mark was made at a depth of 16 mm in track e. The microelectrode was left along a track 01 mm caudal to this plane. These landmarks allowed reconstruction of the direction and depth of the electrode in later histological analysis of tissue sections, assuming 10% shrinkage caused by fixation. B-F, systematic recording of field potentials (B-F) along the tracks b-f in A. Numbers of the left represent the depth in millimetres. In each series, left (A) and right (Ul) arrows indicate the moment of stimulation of EAS and EUS nerve, respectively. Each record consists of superimposition of three to five sweeps at the frequency of 5 Hz.

EUS and EAS motoneurones in SI and S2 segments. The site where the maximal field potentials were recorded was histologically examined by marking with dye, and other recording sites were reconstructed from measurements of electrode depth. By these procedures, the antidromic field potentials were always confirmed to have been recorded in column Y of Romanes (1951), which corresponds to group X of Onuf (1900) in man. The area where antidromic EAS responses were found to be maximal tended to be somewhat medial to the area for maximal antidromic EUS responses (Fig. 1), and the two populations of motoneurones appeared to be lined up in parallel rostrocaudally as suggested also by a retrograde tracing study (Ueyama, Mizuno, Nomura, Konishi, Itoh & Arakawa, 1984). Thus, it was possible to sample throughout a single population by first finding the point of maximal antidromic response, and then moving the electrode rostrally or caudally from there. The latencies of each negative deflection of the double, or in some cases triple, antidromic field potentials ranged widely over 1V0-6-5 ms in spite of the relatively

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short conduction distance (85-105 cm). This wide range of latencies, indicating a spread of axonal conduction velocities, was in agreement with histological observation that this nucleus contains a number of small-sized neurones interspersed with relatively large neurones (Romanes, 1951). D

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Fig. 2. Antidromic potentials (A-C) and AHP (D-F) in three sphincter motoneurones. 'Upper and middle traces are from different EAS motoneurones. and lower traces from a sphincter motoneurone not identified as EUS or EAS (see Methods). Vertical dotted lines indicate the moment of antidromic stimulation. In A-C. arrows indicate the end of the rapid falling phase of the spike. D-F, as A-C, respectively, but recorded with higher gain and slower sweep speed. l)ownward arrows indicate the end of the AHP. Small synaptic activities as in D were observed in about a third of cells. There was no tendency towards short latency cells. They were predominantly depolarizing even just after penetration of cells, suggesting they were mainly excitatory postsynaptic potentials rather than reversed inhibitory postsynaptic potentials.

A ntidromic action potential

Amplitude and latency Figure 2A-C exemplifies the antidromie action potentials recorded intracellularlv from three sphincter motoneurones with short (1H6 ms). medium (2 8 ms), and long (5 0 ms) latencies. The action potential rose abruptly from the resting potential level with a slight inflexion in the rising phase, as seen in other types of motoneurones. The antidromic nature of the spike was inferred from the absence of a slow depolarization before the spike, the invariable latency at threshold-straddling intensity of stimulation, and the ability to follow high-frequency stimulation. The amplitudes of action potentials in Fig. 2A, B and C were 82, 80 and 83 mV, respectively. The upper

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histograms of Fig. 3 show the distribution of spike latencies for all (forty-six EUS and fifty-seven EAS) motoneurones with spike amplitudes of more than 30 mV. The latencies varied between 1-2 and 6-9 ms and covered a range similar to that observed with extracellular spikes (1P0-65 ms, see above). The conduction velocity of the motor axon was estimated by measuring the conduction distance of the peripheral nerve (8-5-10-5 cm) and the latency of the antidromic spike, with an assumption of 0-2 ms for the latency of spike initiation at the stimulated site. The calculated conduction velocity ranged from 16 to 80 m s-'. The present analysis of membrane properties was made on motoneurones whose spike amplitudes were more than 70 mV (twenty-eight motoneurones of lower histograms of Fig. 3 and seven sphincter motoneurones not identified as EUS or EAS). Since the spike latencies of these motoneurones (1-3-5-0 ms) almost covered a range of all motoneurones sampled (Fig. 3), the following data appeared to be representative of the whole population of motoneurones, though with a slight bias towards motoneurones of shorter latencies. No correlation was found between spike amplitude and latency (correlation coefficient (r) = 0-12, P > 0 5). The resting membrane potential was measured in ten successfully penetrated motoneurones (spike amplitudes, 70-99 mV) by comparing the intracellular potential level with that after withdrawal of the microelectrode from the cell. It varied from -60 to -74 mV. The mean resting potential was -68 + 6 mV (mean + S.D.) while the mean amplitude of the action potential was 85+8 mV. When the intracellular spike amplitude was plotted against the resting membrane potential, a clear correlation was obtained (data not shown, r = 0-82, P < 0-005), as has already been shown in other muscle types of motoneurones (Huizar, Kuno & Miyata, 1975; Pinter, Curtis & Hosko, 1983). Duration of the action potential As exemplified in Fig. 2A-C, the duration of the antidromic action potential became longer as the antidromic latency increased. The duration of the action potential (measured from its onset to the termination of its steep decay, arrows in Fig. 2A-C) varied from 10 to 2-6 ms for thirty-five motoneurones. There was a positive correlation between the spike latency and the duration of action potential (r = 0 55, P < 0 001). However, the end of the rapid falling phase of the spike was somewhat ambiguous since it is influenced by the onset of the depolarizing afterpotential which was clearly present in all the cells examined. Thus, we plotted the spike width at half-amplitude against the spike latency (Fig. 4A), and found a tighter correlation between these two parameters (r = 0 71, P < 0 0005). The results indicate that the duration of the action potential is correlated with the antidromic latency. A similar correlation between spike duration and antidromic latency has been found in hindlimb motoneurones (Kuno, 1959) and pyramidal tract neurones (Takahashi, 1965).

Spike after-hyperpolarization (AHP) As in other muscle types of motoneurones, the antidromic action potential of EUS and EAS motoneurones was followed by an AHP (Fig. 2D-F). The duration of the AHP measured from the onset of the spike to the moment when the AHP returned

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to the resting membrane potential level (downward arrows) ranged between 60 and 155 ms. The AHP duration tended to become longer with an increase in the latency of the antidromic spike. Figure 4B shows the relation between the AHP duration and the antidromic latency for twenty-five sphincter motoneurones. There was a clear 8

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positive correlation between these two parameters (r = 085, P < 00005). AHP durations were measured at threshold intensity of nerve stimulation producing the antidromic action potential. Since the duration of the AHP was about the same when spikes were evoked by antidromic stimulation or by a brief depolarizing current pulse (0 2-0 5 ms in duration), it is unlikely that the AHP of the antidromic spike was affected by postsynaptic potentials that could be evoked by the nerve stimulation; the lack of recurrent inhibition in sphincter motoneurones has been shown by Mackel (1979). As exemplified in Fig. 2, the motoneurones with longer AHP duration had longer half-width of the AHP (i.e. the interval from the onset of spike to the time when the AHP returned to its half-amplitude). The half-width of the AHP ranged

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from 35 to 70 ms. A positive correlation was also obtained between the spike latency and the half-width of the AHP (r = 0-67, P < 0 005). The peak amplitude of the AHP ranged from 1P7 to 13-3 mV (mean +s.D., 55 + 37 mV). There was no significant correlation between the spike latency and the peak amplitude of the AHP (r = 0416, P > 0-4). _

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Figure 4C shows the relation between the AHP duration and the spike width at half-amplitude. A positive correlation was obtained between these two parameters (r = 0 60, P < 0 002), as expected from the results shown in Fig. 4A and B. When the AHP duration was plotted against the duration of the action potential (Fig. 4D), positive correlation was also observed (r = 0 61, P < 0 002). Unlike the spike width at half-amplitude, spike amplitude was not correlated with the AHP duration at all

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(r = 0-002, P > 0-5). The results presented above suggest that the AHP duration is influenced by the factors which determine the spike duration, i.e. the intricate interplay of voltage-dependent Na+, Ca2+ and K+ currents.

Input resistance The membrane potential change caused by a weak current pulse (0 5-5 nA) passing through the intracellular microelectrode was recorded (Fig. 5A and B), and the potential shift during the steady state (V) was plotted against the intensity of current (I) (Fig. 5D). The input resistance was estimated by measuring the slope of the linear part of the I-V curve in the hyperpolarizing direction of current injection. This input resistance varied from 2-6 to 9-0 MQ in twenty-two motoneurones (mean+ s.D., 45 + 1-8 MQ). The slope resistance in the depolarizing direction was slightly higher than that in the hyperpolarizing direction (Fig. 5D), but the former could be measured with confidence only in three motoneurones, because a depolarization of significant size was, in most cases, associated with local responses or spike potentials. The slightly lower resistance in the hyperpolarizing direction might be caused by anomalous rectification of the membrane, as described below. Figure 5E shows the relation between the input resistance and the latency of the antidromic spike. As can be seen, the input resistance increased along with the antidromic latency (r = 0 84, P < 0 0005). As expected, the duration of the AHP was also positively correlated with input resistance (r = 0-82, P < 0 0005 (Fig. 5F). Current-voltage (I-V) relationship The membrane potential changes in response to injection of rectangular current pulses of varying strength were examined in eleven motoneurones with action potentials of more than 70 mV (six EUS and five EAS). Figure 6 shows an example of such tests for a EUS motoneurone which had resting and action potentials of -62 and 85 mV, respectively. As shown in Fig. 6A, with weak hyperpolarizing current pulses (1-3 nA) the membrane simply hyperpolarized exponentially to reach a steady level, while with stronger currents a sag developed in the hyperpolarizing response, i.e. the hyperpolarization reached a peak and then declined to a more depolarized steady level in about 40 ms. The I-V curve (Fig. 6B) for the steady-state potential (0) deviates from that for the peak potential ( x ) at about -69 mV, which is the threshold of the sag. Figure 6B also shows a greater decrease in steady-state membrane resistance with stronger hyperpolarization. Plots with a semilogarithmic scale showed that the sag decayed exponentially (Fig. 6 C). Note also in Fig. 6 C that the onset of the depolarizing sag is faster and the slope (time constant) of the decay is shorter as the hyperpolarizing response is larger. The relation between the time constant of the decay and the amplitude of the sag (Fig. 6D) indicated that the decay time constant was a function of the membrane potential. All these properties indicate that the sag was due to the time- and voltagedependent activation of an inward rectifying current which is probably analogous to Q current (IQ, Halliwell & Adams, 1982) or H current (IH' Mayer & Westbrook, 1983). The same results were obtained in all eleven neurones examined. The mean threshold of the appearance of the sag was -737 + 3.3 mV (n = 9). After cessation of current injection, the membrane potential returned to the 12

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resting potential level exponentially with shorter time constants than those of the rising phase of the hyperpolarizing response (Fig. 6A). Four motoneurones showed a slight depolarizing overshoot that cross the resting level transiently. The depolarizing overshoot was always smaller than the sag, which was in contrast with A

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Fig. 5. Input resistance (RN,) of sphincter motoneurones. A and B, upper trace indicates depolarizing or hyperpolarizing step current injected into a motoneurone, and lower trace the response of membrane potential. The amplitude of the antidromic spike of this neurone (not shown) was 90 mV. C, extracellular control. D, I-V relationships of the steady state of the membrane response. *, data from the neurone shown in A and B. 0, from another sphincter motoneurone with a spike height of 98 mV. RN was measured from the slope of the linear portion of the I-V curve with hyperpolarizing current. RNs in these cells were 2-6 MQ (a) and 3-1 MQ (0). E and F, relationships between the latency and RN (E) and between RN and the duration of AHP (F). Symbols are the same as for Fig. 4. the observation in hindlimb motoneurones that the depolarizing overshoot was almost the mirror image of the sag (Ito & Oshima, 1965). Another example of anomalous rectification is seen in Fig. 7B, in which the decreased slope resistance due to anomalous rectification was found to increase beyond -87 mV of steady-state potential (0). Similar further increases in slope resistance were observed in six of eleven motoneurones examined. The threshold of this occurrence was - 90*5+ 6X0 mV (n = 6). Voltage transients around the further increase in slope resistance are illustrated in Fig. 7A. With weak current the time course of decay from the peak of the hyperpolarizing response was fairly smooth (the uppermost trace of lower column), but with strong current the early fast decay

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turned to a slow decay in the later phase (e.g. the fifth trace). The two steps of decay were clearly shown by plotting the potential deviation from the later steady level, semilogarithmically against time after the onset of current (Fig. 7 C). In contrast to the single exponential decay with weak current (@*), the fast exponential decay in the mV

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semilogarithmic plots of the potential deviation from the steady-state level with hyperpolarizing current. Abscissa represents the time after the onset of current and ordinate the potential deviation measured from the later steady-state level (AV, shown in the inset). Intensity of injected current was 5X8 nA (-), 8-3 nA (0), and 14-5 nA (A). D, plot of time constant ofthe decay (T) against peak amplitude of transient measured from the resting potential (Vp). r values were estimated from the slope of the linear part of the voltage transient as exemplified in C. The reciprocal of this slope gives r. The amplitude of the action potential in this neurone was 85 mV.

early phase was followed by a second slow exponential decay as current intensity increased (O and A). The time constants of fast and slow decay determined from the graphical analysis are shown in Fig. 7D. Since the time constant of the early exponential decay and its potential dependency were similar to those of anomalous rectification in motoneurones that showed no further increase in slope resistance (compare Figs 7D and 6D), the later slowing of decay may be interpreted as the interruption of anomalous rectification, probably analogous to the process of inactivation of anomalous rectification. This interruption of anomalous rectification presumably caused the further increase in slope resistance in Fig. 7B. The onset of the interruption of anomalous rectification became faster as the peak amplitude of sag increased, indicating its dependency on membrane potential. Membrane time constant The voltage responses resulting from injection of weak hyperpolarizing current (i.e. those in which inward rectification did not develop) or depolarizing current were analysed to determine the membrane time constant (X0). The differences between the 12-2

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steady-state potential level and successive potential values of the transient response were plotted semilogarithmically against time after the onset of current injection (Fig. 8A). The time constant r0 was estimated by measuring the slope of the later part of potential change and ranged from 25 to 110 ms in sixteen sphincter C

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Fig. 7. Membrane response to injection of current steps into another EUS motoneurone. Same arrangement as in Fig. 6. Note the increase of slope resistance in I-V curve (B) with more than 11 nA of hyperpolarizing current. C, two steps in the decay time course at currents of 13 nA (0) and 14-5 nA (v) and a single exponential decay at 4 nA (@). D, 0 represent the time constant of late slow decay and * represent the time constant of single exponential decay with weak current. * * was obtained for the early fast part of the decay at 13 nA, the time constant being estimated by the slope of the voltage transient. The amplitude of the action potential in this neurone was 90 mV.

motoneurones. Figure 8B shows the relation between the membrane time constant and the chord input resistance of the cell, indicating a clear positive correlation between these two parameters (r = 0-87, P < 00005). When the membrane time constants and chord input resistances measured with depolarizing (0) and hyperpolarizing currents (0) were compared in each cell, those obtained with depolarizing currents were consistently larger than those with hyperpolarizing currents (Fig. 8C).

Electrical properties related to neurone geometry In Fig. 8A, the initial part of the potential change distinctly deviated from the straight line extrapolated from the later part which was used to determine the membrane time constant, T0. This deviation appeared to be related to neurone geometry. Several morphological studies have shown that the dendritic trees can be reduced to the equivalent cylinder (Rall, 1959, 1977) in hindlimb a-motoneurones (Ulfhake & Kellerth, 1981, 1983; however, see Barrett & Crill, 1971, 1974), ymotoneurones (Ulfhake & Cullheim, 1981) and sphincter motoneurones (M. Sasaki,

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unpublished observation). Rall's theoretical neurone model (summarized by Rall, 1977) was applied to the analysis of transient responses to injected current steps. According to this model, the voltage transient, V(t), can be represented as exp (-t/l1) + C2 exp (-t/T2)+ etc.,

V(t) = CO exp (-t/TO) + C A

C

B 12

12 0 0

0 .

.

.

-10 ~~~~~~~~ ~T=11Ms >

O-

*8

.

0c

0 8

* 0

E

0

0

0

1~~~~~~ 10 20 Time (ms)

~~0 0

0

2 4 6 8 0 2 4 6 Chord RN (MQ) Chord RN (MQ) Fig. 8. Estimation of membrane time constant (T0) and relationship between chord input resistance (chord RN) and To. A, the method for estimation of T0. The voltage deviation from the steady-state level (AV, shown in the inset) is plotted semilogarithmically against time after the onset of current step. A continuous straight line fitting the terminal

decay is drawn by eye. The reciprocal of this slope gives T0. B, relationship between chord RN and T0. 0, EUS motoneurones; 0, EAS motoneurones; A, sphincter motoneurone not identified as EUS or EAS. C, changes in chord RN and T0 in four different neurones, estimated by injecting depolarizing (0) and hyperpolarizing (0) currents.

where the longest time constant, To, is the membrane time constant, while the shorter time constants, Tl, T2, etc. depend on neurone geometry and are called the equalizing time constants, with which charge is redistributed through the dendritic membrane capacity. CO, Cl, C2, etc., coefficients; t, time after the onset of current. As compared to determination of these equalizing time constants from the original voltage transient response shown in Fig. 8A, it seemed more advantageous to use the differentiated voltage response expressed as d V/dt =

1(-C.IT) exp -tIT.),

since this procedure accentuates the coefficients of higher-order exponential terms and gives a more reliable estimate of the second- and third-order time constants (Rall, 1969). The time-derivative curve was obtained by drawing a series of tangential lines on an enlarged voltage-transient curve as illustrated in Fig. 9B (slow sweep of voltage transient) and Fig. 9C (fast sweep of the initial transient). Figure 9A shows plots of the derivatives of the voltage transient, dV/dt, on a logarithmic scale against time. The filled circles denote the measured dV/dt values and the continuous straight line represents the best-fit line drawn by eye through the last few of these data points. The reciprocal of the slope of this line indicates the longest time constant, To, which was 6-9 ms for this neurone.

M. SASAKI

358

During the initial 5 ms, the plots deviate considerably from linearity, indicating the presence of faster components with time constants shorter than r0. To obtain these time constants and their coefficients, the standard technique of 'peeling' exponential decays (Rall, 1969) was used, i.e. the deviation of points from the B

C

A

4-

C'a

ro = 6.9 ms 1

0

4 6 12 Time (ms) Fig. 9. Estimation of the membrane time constant and equalizing time constants. A, the slope of the voltage transient (dV/dt) is plotted semilogarithmically (@) against time after the onset of the hyperpolarizing current step (t), and a straight line fitting the terminal part of the decay is drawn by eye. The longest time constant ro represents the membrane time constant. The difference between the values of dV/dt and the extrapolated ro line is replotted (0), and a straight line is drawn in the same manner to obtain the first equalizing time constant, r1. Further peeling is possible in this neurone (A), giving the second equalizing time constant, r2. B and C, traces of the voltage transient curve resulting from an 8 nA hyperpolarizing current step with slow (B) and fast (C) sweep speed. Tangential lines on the slope are drawn at successive times for determination of dV/dt.

straight line was replotted (0). By repeating this procedure, two equalizing time constants were calculated. In this case ri and r2 were 1-2 and 02 ms, respectively. Three time constants (T0, r1 TO2) could be obtained in eleven out of twelve sphincter motoneurones, while two time constants could be obtained in the remaining motoneurone.

Dendritic-to-soma conductance ratio (p) The value for p was estimated with two methods. The first method was that of Brown, Fricke & Perkel (1981), which was based on the voltage transient induced by a hyperpolarizing current step. The value of p was calculated from the equation p

=

(O/Vf) Y(Cn/7n)-

MEMBRANE PROPERTIES OF MOTONEURONES

359

where VJ is the final steady-state potential measured from the resting membrane potential. The second method followed Gorman & Mirolli (1972). For this analysis, ln(T2 dV/dT) was plotted against T, where T (time normalized against TO) = t/T0. B

A 6 2 0

0

A

4

0 0 0 0

2

0

0

0

0

00

0 00 :

1'

A

0

T-

0

2

4 6 RN (MQ)

8

)

10

C

4 6 8 RN (MQ)

2

10

D

2

80

6-

1.5

..0 0 ,0

4-

0

1

-I"

2

O0 T

LL

5 Pi

Fig. 10. A, the relation between input resistance (RN) and dendritic-to-soma conductance ratio (p). B, the relation between RN and electrotonic length of dendrites (L). Symbols in A and B, 0, EUS motoneurones; 0, EAS motoneurones; A, sphincter motoneurone not identified as EUS or EAS. C, semilogarithmic plots of T4 dV/dT against T, where T is time normalized against To (i.e. T = t/TO). The best-fit line is drawn through the plots by eye. The T value at which 1I dV/dt is maximum gives Tmax (Gorman & Mirolli, 1972). D, comparison between p estimated by Gorman and Mirolli's method (P2) and p estimated by the method of Brown et al. (1981) (pl). If p1 equals P2, the plots will fall on the dashed line with the slope of unity. The continuous line denotes the regression line of these plots.

The value of p was determined by finding the time at which the function ln(TI dV/dT) was at the maximum (Tmax) in an experimental transient (Fig. lOC) and by putting the value of Tmax on the graph of p as a function of Tmax (Fig. 1 of Gorman & Mirolli, 1972).

360

M. S5ASAKI

Figure IOA shows the relation between p determined by the first method and the input resistance in eleven sphincter motoneurones. The value of p varied from 1-2 to 5 9 and showed no correlation with the input resistance (r = 0-27, P > 0 4). Values of p determined by the second method (P2) were plotted against those determined by the first method (p1) in Fig. IOD, showing that the former (4 2 + 1P8) was slightly larger than the latter (3 5+ 1P5).

Electrotonic length of dendrites (L) The value for L was obtained from the following equation (Brown et al. 1981):

p+cot (aL)tanh (L) = 0, which was equivalent to eqn (21) of Rall (1969), where = (T0/T1 -1).

L ranged from 1D0 to 1P8 in eleven cells and showed no correlation with the input resistance of motoneurones (r = 0 31, P > 0 3) (Fig. lOB). No significant differences were found statistically in any of the characteristics of motoneurones between EUS and EAS (Student's two-tailed t test, P > 0 1). DISCUSSION

Since extensive analyses have been performed on morphological and physiological properties of hindlimb motoneurones (reviewed by Rall, 1977 and by Burke, 1981), this discussion will be devoted to comparison of the present results with those of hindlimb motoneurones in an attempt to characterize the function of external urethral and external anal sphincters. Motoneurone size, conduction velocity, and input resistance Physiological studies combined with intracellular staining of cat hindlimb motoneurones have shown that the mean diameter of the soma is positively correlated with the conduction velocity of its axon (Cullheim, 1978; Kernell & Zwaagstra, 1981), while the conduction velocity is inversely correlated with the input resistance of the cell (Burke, 1967, 1981). The mean size of neurones in Onuf s nucleus (23,am, Ueyama et al. 1984) is about half the diameter of that of hindlimb motoneurones (58,tm, Cullheim, 1978). In agreement with these anatomical findings, the conduction velocities of sphincter motoneurones, ranging from 16 to 80 m s-', were considerably slower than those of hindlimb motoneurones (70-125 m s-' for triceps surae in the cat, Burke, 1967). To examine whether the correlation between input resistance and conduction velocity in hindlimb motoneurones also holds for external sphincter motoneurones, input resistance versus conduction velocity of sphincter motoneurones was plotted along with similar data obtained for triceps surae motoneurones by Burke (1967) (Fig. 11A). The plots for sphincters were distributed around the extrapolated regression line determined for hindlimb motoneurones. Thus, it seems likely that there is a fixed correlation among the conduction velocity, input resistance, and size of motoneurones, regardless of the

MEMBRANE PROPERTIES OF MOTONEL TRONES

361

muscle type innervated by a motoneurone, across a wide variation in cell size. In other words, the value of conduction velocity or input resistance may be an index of motoneurone size in various muscle types including sphincters. When the relation between membrane time constant (T0) and input resistance (RN) was investigated in various sphincter motoneurones, these parameters were B

A 10

0

8la

40

z

60

80

02

1

1006 -0 0 ii,~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~40~

0.2~4 ~ 20

~

~

~

2

*A

40

60 80 100 50 120 100 150 Conduction velocity (m s-1) Duration of AHP (ms) Fig. II. Relationships between conduction velocity and RN (A) and between duration of AHP and RN (B). A. values for sphincter motoneurones (0) are plotted together with values obtained by Burke (I1967, Fig. I1t) for triceps surae motoneurones (A). The straight line is for triceps surae motoneurones. B, values for sphincter motoneurones (0) are plotted together with values for lumber motoneurones obtained by Gustafsson (1979, Fig. 3F) (A). Conduction velocities of sphincter motoneurones were estimated from latencies of antidromic action potentials and conduction distances, allowing 0-2 ms for initiation spike at the stimulated site.

found to be positively correlated (Fig. 8B). The positive correlation between T0 and RN has also been reported for cat lumbosacral motoneurones (Barrett & Crill, 1974; Gustafsson, 1979). Assuming that the specific membrane capacitance (Cm) is identical in different motoneurones, specific membrane resistance (Rm) would increase with an increase in RN, since T0 = RmCm. Therefore Rm is suggested to be higher in smaller motoneurones. In fact, a recent study on the relation between anatomical membrane surface area and input resistance has revealed that higher input resistance in slow motoneurones cannot be attributed solely to smaller membrane surface area, but is partially due to a 2-3 times higher specific membrane resistance in slow motoneurones than in fast motoneurones (Burke, Dum, Fleshman, Glenn, Lev-Tov, O'Donovan & Pinter, 1982). Duration of AHP and its correlation with motor unXit type Figure 11 B shows a replotting of AHP duration versus input resistance for sphincter motoneurones (same as in Fig. 5F, but the ordinate and abscissa reversed) together with data for lumber motoneurones obtained by Gustafsson (1979). The

362

M. SASAKI

AHP duration is well correlated with input resistance in each group of motoneurones. But the slopes of the regression lines for these two different types of motoneurones are quite different. It should be stressed, however, that the difference of the slope does not just apply to hindlimb versus sphincter muscles but can also apply to flexor versus extensor muscles of hindlimb (Eccles et al. 1958). Their figures (Figs 5-7) showed clearly that the correlation between the conduction time of its axon and the duration of AHP was not fixed amongst hindlimb motoneurones, being different for those innervating extensor and flexor muscles. When values of sphincter motoneurones were plotted on their figures, the slope of the regression line was even less steep than for flexor motoneurones (not shown). These results indicate that the AHP duration has muscle specificity and does not solely depend on the absolute value of the input resistance. In other words, when we compare sphincter motoneurones with limb motoneurones having the same input resistance (hence, probably having the same size), the AHP duration of the former is much shorter than that of the latter. This is in marked contrast to the relation between the conduction velocity and input resistance described above, in which the conduction velocity depended entirely on the input resistance regardless of the type of motoneurone. The duration of the AHP varies with motor unit type; it is shorter on average in motoneurones of fast-twitch muscles (fast fatigue type (FF) and fast fatigue resistant type (FR)) than in motoneurones of slow-twitch muscle (slow type (S)) (Eccles et al. 1958; Burke, 1967, 1981). Mackel (1979) reported that the AHP duration of cat sphincter motoneurones ranged from 50 to 100 ms, which was in the range of AHP durations observed for motoneurones supplying fast-twitch muscle in the hindlimb. In contrast, the present study shows that the AHP duration of sphincter motoneurones can be as long as 160 ms, covering the range of AHP durations for slow as well as fast motoneurones of the hindlimb. This difference may be attributed to different sampling of motoneurones. The EUS and the EAS have long been considered to be tonic muscles mainly from an analysis of electromyogram activity in the cat (Bishop, Garry, Roberts & Todd, 1956; Garry et al. 1959). However, the histochemical study of cat EUS and EAS muscles has revealed that there were three types of muscle fibres, which corresponded to fast fatigue (FF), fast-fatigue resistant (FR) and slow (S) physiological types (Sasaki, 1986; M. Sasaki, unpublished observation). Thus, the wide varation of AHP may represent differentiation of motoneurones into fast and slow types as in the limb motoneurones. Sphincter motoneurones with long antidromic latency had long durations of action potentials and AHPs. Thus it appears that the duration of AHP may be influenced by the factors which determine the spike duration, i.e. Na+, Ca2' and K+ currents. Although the present study does not specify which factor predominates in determining the duration of the action potential, it is suggested that active properties of the motoneuronal membrane such as Na+, Ca2+ and K+ channels may take part in the differentiation of functional properties of motoneurones such as the AHP duration which is closely related to firing rate of motor units (Baldissera & Gustafsson, 1971, 1974).

MEMBRANE PROPERTIES OF MOTONEURONES

363

Non-linear I-V relation of the membrane and its functional significance Since the first demonstration of anomalous rectification in frog striated muscle fibres (Katz, 1949), its existence has been reported for various neurones including those in the mammalian central nervous system (Nelson & Frank, 1967; Halliwell & Adams, 1982; Constanti & Galvan, 1983) and in dorsal root ganglion cells (Mayer & Westbrook, 1983). In cat spinal motoneurones, non-linear membrane properties were first found in some hindlimb motoneurones by Ito & Oshima (1965), and anomalous rectification was confirmed by injecting a short current pulse during the course of longer pulses of either hyperpolarizing or depolarizing currents (Nelson & Frank, 1967). Anomalous rectification observed in sphincter motoneurones in the present study was much more marked than in hindlimb motoneurones. A higher slope resistance in the depolarizing direction than in the hyperpolarizing direction was consistently found in all neurones examined. This non-linearity reflects variability of the membrane time constant. When time constants were measured in the same motoneurone with both depolarizing and hyperpolarizing currents, the time constant measured with depolarizing current was longer and the input resistance was higher, than when measured with hyperpolarizing current (Fig. 8C). Since specific membrane capacitance is expected to be constant regardless of membrane potential level, an increase in time constant with an increase in input resistance may be attributed to an increase in specific membrane resistance (Rm). Assuming for simplification that the non-linear properties described above are uniform over the entire surface of the motoneurone membrane, the increase in Rm in the depolarizing direction should increase the length constant (A) of the dendrite according to the equivalent cylindrical core conductor model (Rall, 1959, 1977), because A = [(Rm/Ri) (d/4)]i, where Ri represents the volume resistivity of the intracellular medium and d is the diameter of the membrane cylinder. Consequently, electrotonic propagation of synaptic potentials from the dendritic region to the soma or initial segment would be less attenuated when the membrane is depolarized, or more attenuated when it is hyperpolarized. It has been reported that sphincter activity recovers from spinal shock earlier than limb activity (Garry et al. 1959; Rossier, Fam, DiBenedetto & Sarkarati, 1980), that sphincter muscle responds to a slight touch to the perineal skin (Floyd & Walls, 1953; Kawakami, 1954; Taverner & Smiddy, 1959), and that discernible sphincter activity was present even during sleep (Floyd & Walls, 1953). This suggests that sphincter motoneurones are highly excitable in response even to weak excitatory inputs. The marked non-linear properties of the sphincter motoneuronal membrane might, at least partly, contribute to these unique functions. That is, when sphincter motoneurones are under reflex and central control by excitatory and inhibitory synaptic inputs, hyperpolarizing effects on the membrane due to inhibitory input would be reduced by anomalous rectification and, hence, the membrane potential would rapidly return to the resting level after cessation of inhibitory input. In contrast, excitatory inputs causing a depolarization would drive the membrane to the range of a higher slope resistance, which would enhance the depolarization in

364

Mk. >SASXAKI

response to succeeding excitatory inputs. In addition, the lack of recurrent inhibition in sphincter motoneurones (Mackel, 1979) would also accentuate the excitability of these neurones. The interruption of the anomalous rectification during strong hyperpolarization (Fig. 7) has been observed in the egg cell membranes (Miyazaki, Takahashi, Tsuda & Yoshii, 1974; Ohmori, 1978), skeletal muscles (Standen & Stanfield, 1979) and dorsal root ganglion cells (Mayer & Westbrook, 1983). The interruption of the anomalous rectification in sphincter motoneurones is probably analogous to the inactivation process of the anomalous rectifier in skeletal muscles and dorsal root ganglion cells. Apart from its mechanism and functional significance, it may also be a characteristic feature that differentiates sphincter motoneurones from other muscle types of motoneurones. Electrical properties related to neuronal geometry The values of dendritie electrotonic length (L) ranged from 1-0 to 1P8 and were similar to those obtained for triceps surae motoneurones, 1P1-25 (Burke & ten Bruggencate, 1971; Rall, 1977). The estimated values of the dendritic-to-soma conductance ratio, p, ranged from 1P2 to 5 9 in sphincter motoneurones. These values were smaller than those for spinal motoneurones which range from 3 to 25 (summarized by Rall, 1977). Studies using intracellular staining are needed to determine how these electrically defined neuronal geometrical parameters can be related to the actual morphology of the neurones (M. Sasaki, in preparation). The author would like to thank Professors Hiroshi Shimazu anid Toshinori Hongo, and Associate Professor Shigeto Sasaki for their constant encouragement and advice throughout this study. Professor Arthur P. Arnold for comments on the manuscript, and MIiss Melissa Jackson for typing the manuscript.

REFERENCES

BALDISSERA, F. & G(TSTAFSSON, B. (197i 1). Regulatioin of repetitive firinig in motonieurones by the afterhyperpolarization conductance. Brain Research 30, 431-434. BALDISSERA, F. & GUSTAFSSON, B. (1974). Firing behaviour of a nleurone model based on the afterhyperpolarization conductance time course. First interval firing. Acta Physiologica Scandinavica 91, 528-544. BARRETT, J. N. & C(RILL, XV. E. (1971). Specific membrane resistivitv of dye-injected cat motoneurons. Brain Research 28, 556-561. BARRETT, J. N. & (CRILL, XT. E. (1974). Specific membrane properties of cat motoneurones. Journal of Physiology 239, 301-324. BisHop, B., GARRY, R. C., ROBERTS, T. D. M1. & TODD, J. K. (1956). Control of the external sphincter of the anus in the cat. Journal of Physiology 134, 229-240. BROWN, T. H., FRICKE, R. A. & PERKEL, D. H. (1981). Passive electrical constants in three classes of hippocampal neurons. Journal of Neurophysiology 46. 812-827. BURKE, R. E. (1967). Motor unit types of cat triceps surae muscle. Journal of Physiology 193, 141-160. BURKE, R. E. (1981). Motor units: anatomy, physiology, and functional organization. In Handbook of Physiology, section 1. The Nervous Sys-tem, vol. II, part I, ed. BROOKS, V. B., pp. 345-422. American Physiological Society, lBethesda, MD, USA.

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BURKE, R. E., DuM, R. P., FLESHMAN, J. WV., GLENN, L. L., LEV-ToV, A., O'DONOVAN, M. J. & PINTER, M. J. (1982). An HRP study of the relation between cell size and motor unit type in cat ankle extensor motoneurons. Journal of Comparative Neurology 209, 17-28. BURKE, R. E. & TEN BRUGGENCATE, G. (1971). Electrotonic characteristics of alpha motoneurones of varying size. Journal of Physiology 212, 1-20. CONSTANTI, A. & GALVAN, M. (1983). Fast inward-rectifying current accounts for anomalous rectification in olfactory cortex neurones. Journal of Physiology 385, 153-178. CULLHEIM, S. (1978). Relations between cell body size, axon diameter and axon conduction velocity of cat sciatic a-motoneurons stained with horseradish peroxidase. Neuroscience Letters 8, 17-20. ECCLES, J. C., ECCLES, R. M. & LUNDBERG, A. (1958). The action potentials of the alpha motoneurones supplying fast and slow muscles. Journal of Physiology 142, 275-291. FLOYD, W. F. & WALLS, E. W. (1953). Electromyography of the sphincter ani externus in man. Journal of Physiology 122, 599-609. GARRY, R. C., ROBERTS, T. D. M. & TODD, J. K. (1959). Reflexes involving the external urethral sphincter in the cat. Journal of Physiology 149, 653-665. GORMAN, A. L. F. & MIROLLI, M. (1972). The passive electrical properties of the membrane of a molluscan neurone. Journal of Physiology 227, 35-49. GUSTAFSSON, B. (1979). Changes in motoneurone electrical properties following axotomy. Journal of Physiology 293, 197-215. HALLIWELL, J. V. & ADAMS, P. R. (1982). Voltage-clamp analysis of muscarinic excitation in hippocampal neurons. Brain Research 250, 71-92. HUIZAR, P., KUSNO, M. & MIYATA, Y. (1975). Electrophysiological properties of spinal motoneurones of normal and dystrophic mice. Journal of Physiology 248, 231-246. ITO, M. & OSHIMA, T. (1965). Electrical behaviour of the motoneurone membrane during intracellularly applied current steps. Journal of Physiology 180, 607-635. KATZ, B. (1949). Les constantes electriques de la membrane du muscle. Archives des Sciences Physiologique,s 3, 285-299. KAWAKAMI, M. (1954). Electro-myographic investigation on the human external sphincter muscle of anus. Japanese Journal of Physiology 4, 196-204. KERNELL, D. & ZWAAGSTRA, B. (1981). Input conductance, axonal conduction velocity and cell size among hindlimb motoneurones of the cat. Brain Research 204, 311-326. KUNO, M. (1959). Excitability following antidromic activation in spinal motoneurones supplying red muscles. Journal of Physiology 149, 374-393. KUZUHARA, S., KANAZAWA, I. & NAKANISHI, T. (1980). Topographical localization of the Onuf7s nuclear neurons innervating the rectal and vesical striated sphincter muscles: a retrograde fluorescent double labeling in cat and dog. Neuroscience Letters 16, 125-130. MACKEL, R. (1979). Segmental and descending control of the external urethral and anal sphincters in the cat. Journal of Physiology 294, 105-122. MANNEN, T., IWATA, M., TOYOKURA, Y. & NAGASHIMA, K. (1977). Preservation of a certain motoneurone group of the sacral cord in amyotrophic lateral sclerosis: its clinical significance. Journal of Neurology, Neurosurgery and Psychiatry 40, 464-469. MAYER, M. L. & WESTBROOK, G. L. (1983). A voltage-clamp analysis of inward (anomalous) rectification in mouse spinal sensory ganglion neurones. Journal of Physiology 340, 19-45. MIYAZAKI, S., TAKAHASHI, K., TSUDA, K. & YosHII, M. (1974). Analysis of non-linearity observed in the current-voltage relation of the tunicate embryo. Journal of Physiology 238, 55-77. NELSON, P. G. & FRANK, K. (1967). Anomalous rectification in cat spinal motoneurons and effect of polarizing currents on excitatory postsynaptic potentials. Journal of Neurophysiology 30, 1097-1113. OHMORI, H. (1978). Inactivation kinetics and steady-state current noise in the anomalous rectifier of tunicate egg cell membranes. Journal of Physiology 281, 77-99. ONUF, B. (1900). On the arrangement and function of the cell groups of the sacral region of the spinal cord in man. Archives of NVeurology and Psychopathology 3, 387-412. PINTER, M. J., CURTIS, R. L. & HOSKO, M. J. (1983). Voltage threshold and excitability among variously sized cat hindlimb motoneurons. Journal of Neurophysiology 50, 644-657. RALL, W. (1959). Branching dendritic trees and motoneuron membrane resistivity. Experimental Neurology 1, 491-527.

366

M. SASAKI

RALL, W. (1969). Time constants and electrotonic length of membrane cylinders and neurons. Biophysical Journal 9, 1483-1508. RALL, W. (1977). Core conductor theory and cable properties of neurons. In Handbook of Physiology, section 1, The lervous System, vol. I, part I, ed. KANDEL, E., pp. 39-97. American Physiological Society, Bethesda, MD, USA. ROMANES, G. J. (1951). The motor cell columns of the lumbo-sacral spinal cord of the cat. Journal of Comparative Neurology 94, 313-364. RossIER, A. B., FAM, B. A., DIBENEDETTO, M. & SARKARATI, AI. (1980). Urethro-vesical fuInctioIn during spinal shock. U.Jrological Research 8, 53-65. SASAKI, M. (1986). Morphological and physiological properties in the external urethral and anial sphincter motoneurons and muscle types of external anal sphincter in the cat. Journal of the Physiological Society of Japan 48, 238. SATO, M., MIZUNO, N. & KONISHI, A. (1978). Localization of motoneurons innervating perineal muscles: a HRP study in cat. Brain Research 140, 149-154. STANDEN, N. B. & STANFIELD, P. R. (1979). Potassium depletion and sodium block of potassium currents under hyperpolarization in frog sartorius muscle. Journal of Physiology 294, 497-520. TAKAHASHI, K. (1965). Slow and fast groups of pyramidal tract, cells and their respective membrane properties. Journal of Neurophysiology 28. 908-924. TAVERNER, D. & SMIDDY, F. G. (1959). An electromyographic study of the normal function of the external anal sphincter and pelvic diaphragm. Diseases of the Colon and Rectum 2, 153-160. UEYAMA, T., MIZUNO, N., NOMURA, S., KONISHI, A.. ITOH, K. & ARAKAWA, H. (1984). Central distribution of afferent and efferent components of the pudendal nerve in cat. Journal of Comparative Neurology 222, 38-46. ULFHAKE, B. & CULLIIEIM, S. (1981). A quantitative light microscopic study of the dendrites of cat spinal y-motoneurons after intracellular staining with horseradish peroxidase. Journal of Comparative Neurology 202, 585-596. ULFHAKE, B. & KELLERTH, J.-O. (1981). A quantitative light microscopic study of the dendrites of cat spinal a-motoneurons after intracellular staining with horseradish peroxidase. Journal of Comparative Neurology 202, 571-583. ULFHAKE, B. & KELLERTH, J.-O. (1983). A quantiative morphological study of HRP-labelled cat a-motoneurones supplying different hindlimb muscles. Brain Research 264, 1-19.