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Membrane conductance course during spike intervals and repetitive firing in cat spinal motoneurones
Brain Research, 76 (1974) 223-233
223
~2~Elsevier ScientificPublishing Company, Amsterdam - Printed in The Netherlands
M E M B R A N E C O N D U C T A N C E C O U R S E D U R I N G SPIKE I N T E R V A L S A N D R E P E T I T I V E F I R I N G IN CAT SPINAL M O T O N E U R O N E S
K. H. MAURITZ*, W. R. SCHLUE**, D. W. RICHTER*** ANDA. C. NAC1MIENTO .~ Physiological Institute, Central Nervous System Research Unit, Saarland University, 665 HomburgSaar (G.F.R.)
(Accepted February 21st, 1974)
SUMMARY The time course of membrane conductance was measured in gastrocnemius motoneurones of spinalised cats during (a) the afterhyperpolarisation (AHP) following a single antidromic spike, and (b) rhythmic firing, elicited by antidromic and intracellular stimulation. In a sample of 26 motoneurones, 18 (69 ~o) showed a conductance decay during A H P which was not a simple exponential function of time. After an initial steep phase, conductance decline was markedly slowed down for a definite time (plateau phase). In the remaining 8 motoneurones (3l ~ ) conductance decay was nearly exponential. Relating the non-exponential conductance curve to the current frequency relation (f-I curve) in the same cell a close correlation was found between the time to the end of the plateau phase and the time of interval shortening leading to the secondary range in the f-I curve. During repetitive firing evoked by antidromic stimulation the plateau phase was progressively smoothed out and conductance during successwe AHPs summated. After the fifth spike, decay was exponential and summation reached a maximum. Conductances did not summate algebraically. Similar results were obtained during rhythmic firing evoked by intracellular stimulation. It is suggested that (1) divergence from a single repolarising conductance declining exponentially with time may be at least one of the factors involved in the shaping of the secondary range in the f-I curve, and (2) the progressive tendency to a simple exponential decline and non-algebraical summation of conductances during a short train of spikes contributes to adaptation.
* Present address: Abt. Physiol. Psychologie,Universit/it Konstanz, Konstanz, G.F.R. ** Present address : Fachbereich Biologie, Universit/it Konstanz, Konstanz, G.F.R. *** Present address: Physiologischeslnstitut der Universitgt Mfinchen, Munich, G,F.R. To whom reprint requests should be sent.
224
K.H. MAURITZet al.
INTRODUCTION
The continuous firing evoked in cat spinal motoneurones by long-lasting injected currents is similar to that triggered by steady excitatory synaptic action 6,10,t4. In such experiments, a plot relating current intensity to discharge frequency (f-I curve) shows two successive straight lines, the primary range, and, following an abrupt transition, the steeper secondary range 7--9,13 ~5. The slopes of both ranges decrease as the number of spikes increases, with eventual abolition of the secondary range 2,14,15. Some recent inquiries into the basis of these findings are available 3,1s,2z,2z. One approach has been the analysis of the course (trajectories) of membrane potential changes between spikes, with descriptions of an initial, slowed rate of change during repolarisation, followed by a linear rise to the next firing level 2',z3. Another line has focused upon the time course of conductance changes between spikes. It has been reported that in some motoneurones conductance decline during the afterhyperpolarisation (AHP)following a single spike is not a simple exponential function of time, this course being interrupted by a plateau phase 3. Suggestions as to mechanisms involved have been put forward in terms of motoneurone models. One of them takes into account the non-exponential time course of conductance and explains adaptation 4. Another, formulated on the basis of voltage clamp equations for peripheral nerve, assumes an essentially exponential declinO6,18,~L The aim of the present work has been an analysis of the conductance changes which take place during the early phase of rhythmic firing. To this end, input membrane conductance was measured as a function of time during (a) the AHP following a single spike, and (b) repetitive firing evoked antidromically, and by intracellular stimulation. An attempt is made to account, at least in part, for the transition leading to the secondary range and for the early adaptation in terms of patterns of conductance change during spike intervals. A preliminary report has been published 2°. METHODS
Low-spinalised adult cats anaesthetised with pentobarbital were used. Some of them were paralysed with gallamine triethiodide and put under artificial respiration. Expired end-tidal CO2 concentration (3-4 %), arterial blood pressure (at least 80-90 mm Hg) and rectal temperature (38 ± 0.5 °C) were continuously monitored. Ringer and plasma expander solutions were given as required. After laminectomy dorsal roots L4 to S1 were sectioned; ventral roots were left in continuity, so as to allow stimulation of peripheral nerves and antidromic identification. The gastrocnemius nerves, the lateral together with the soleus nerve, were routinely stimulated. For intracellular recording and stimulation glass micropipettes with beveled tips 5 and filled with 2 M potassium citrate (DC resistance 2-10 MD~) were used. Their current-voltage characteristics were routinely checked. Data presented in this paper were obtained exclusively with pipettes which were linear within the measurement range. The recording system included a unity gain differential DC amplifier with a negative feedback design, according to principles described elsewhere "4. A bridge
CONDUCTANCE
225
AND REPETITIVE FIRING
circuit allowed intracellular stimulation during recording. The first derivative o f action potentials was obtained at T - - 0.1 or 1.0 msec. F o r assessing c o n d u c t a n c e changes rectangular inward current pulses of 8-12 msec in d u r a t i o n a n d 4-8 n A in a m p l i t u d e were applied, and the voltage d r o p measured (,'lVr and I Vt, Fig. 1C). D u r a t i o n of the current pulses was such t h a t the voltage transient reached 95 ~ o f the steady state value at resting m e m b r a n e resistance. Since the m e m b r a n e time c o n s t a n t 21 in the sample averaged 3.3 msec, a d u r a t i o n o f a b o u t 10 msec was selected. Voltage d r o p s were measured at their maxima, and changes in m e m b r a n e RC neglected. D u r i n g the initial 15 msec o f A H P , however, pulses of 2-5 msec could be applied, on account o f the shorter time constant. The relative conductance changes were expressed as described previously 1. The a m p l i t u d e o f the current pulses did not change the course o f A H P , as routine checks showed. This control was particularly needed in measurements during r h y t h m i c firing induced by intracellular
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Fig. 1. Conductance time course during the A H P alter an antidromic spike. A : conductance measurement at resting potential (l) and at different times after a single antidromic spike (2-5); upper
trace, inward current pulse; lower trace, membrane potential. B: relative conductance changes are plotted logarithmically against the time after the spike onset. The arrow marks the spike interval at the transition from primary to secondary range for this motoneurone (el Fig. 3A). tvl is the time from spike onset to the end of the plateau. The curve was fitted by eye. C: measurements/JV,-, "/Vt and t.
K.H. MAtJRtrZ eta/,
226 lr~
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Fig. 2. Conductance curve during AHP for a motoneurone exhibiting a nearly exponential course after a single antidromic spike. Conductance changes were estimated with inward (circles) and outward (squares) current pulses. Inset: upper trace, current (2 msec); lower trace, membrane potential,
stimulation. In these conditions the interval for the next spike was longer, when the inward current pulse was injected at the end of the interval (cJ~ Fig. 5A and B), i.e., conductance could be measured over longer intervals. The measurements reported here were carried out in 26 gastrocnemius motoneurones, selected from a larger sample, according to the following criteria:minimal recording time of 15 rain at stable resting potentials above --50 mV, spike amplitude and rate of rise of at least 70 mV and 200 V/sec, respectively, and absence of recurrent IPSP. RESULTS
Conductance during the AHP following a single antidromic spike In 18 (69 ~o) of the selected 26 motoneurones, the conductance decrease along the A H P was not a simple exponential function of time, in agreement with previous results 3. Measurements on a cell of this type, as well as the related plot, are shown in Fig. 1. In the remaining 8 cells (31 ~/o), conductance decay was approximately exponential. The curve in Fig. 2 plots measurements on a motoneurone of this group. The curve in Fig. 1B shows that, after a steep initial phase, conductance decay was brought to a halt and remained nearly steady for a time. This plateau ends with the onset of the nearly exponential final segment of the curve. The rate of change of the plateau phase was quantitatively different from cell to cell, that of Fig. 1 being an example of a very slow rate. As for the final part of the curve, it should be pointed out that conductance measurements in this segment tended to be less precise, on account of smaller changes and greater variability. The next step was an attempt to relate the timing of the plateau phase to the transition from primary to secondary range during repetitive firing in the same motoneurone. In Fig. 3A and B, two plots are shown from measurements on the same celt as in Fig. 1. In one plot, Fig. 3A, frequency is plotted as a function of intracellularly
CONDUCTANCE
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AND REPETITIVE FIRING
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Fig. 3. Current-frequency (f-I curve) relation (A) and current-interval curve (B) for the motoneurone in Fig. 1. A : f - I curve for first (circles) and second (squares) spike intervals. B: current exceeding the rheobase plotted logarithmically against the spike interval for first (circles) and second (squares) intervals. The arrow marks the spike interval at the transition from primary to secondary range in A (ttr~.s).
applied current; the second plot, Fig. 3B, relates spike interval and current ~. The time of change from primary to secondary range in this cell, as depicted in Fig. 3A and B, is marked on its conductance curve (Fig. 1B) with an arrow. The time of transition (ttrans) is 16.7 msec, corresponding to a frequency of 60 Hz for the first spike interval (Fig. 3A). The time between spike onset and end of plateau (tvl) is 16 msec (Fig. I B). Also, the time courses of the interval-current (Fig. 3B) and conductance (Fig. 1B) curves were similar for the first interval, as previously reportedL Furthermore, there is also good agreement of the time the plateau emerges from the exponential part of the current-interval curve (in Fig. 3B about 18 msec) with both tvl and ttr~.~. A comparison of ttrans and tvl for all neurones in this group yielded the following results: for tp], the mean and S.D. were 20 ± 4.4 msec (range 14-26 msec); for ttr~,.~, 22 ~- 7.7 msec (range 14-33 msec), for the first interval, at a frequency (f-I curve) of 44.9 + 13.4 Hz. The correlation coefficient was 0.74, and the significance
K.H. MAURFIZ et a[.
228
level P < 0.001. This correspondence of conductance and repetitive firing changes was found in all cells exhibiting a plateau phase in the conductance curve. In the group of 8 cells with nearly exponential conductance curves, 3 displayed f-[ relations without a secondary range. It is possible, however, that measurements in these cells were ended before current intensity reached the required level for firing in the secondary range.
Conductance during repetitive firing evoked by antidromic stimulation Extending the preceding analysis to rhythmic firing, conductance was measured in the wake of antidromic spikes elicited at different frequencies. In the records of Fig. 4B conductance was measured following the last spike in a burst of 3, triggered by a stimulus frequency of 50 Hz. After increasing the burst to 5 spikes, measurements were made during the first, third and fifth AHP, with the results shown in Fig. 4A. The curve for the first AHP has been already described, a plateau being clearly discernible. During the third AHP, however, this phase became less conspicuous, on a background of increased, summated conductance. The change in tv] was f¥om 21 to 25 msec. The curve for the fifth AHP shows, as a prominent feature, a nearly exponential decay. Furthermore, summation reached a maximum at this stage. It should be added that the time constant of the exponential decay for the three series were 20, 25 and 30 msec, respectively. But caution is necessary as to the precision of measurements at this part of the curve (vide supra). A
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Fig. 4. A : time course of conductance change after first (circles), third (squares) and filth (triangles) spikes evoked by antidromic stimulation of 50 Hz. B: sample records from this Cell after a train of 3 spikes. C: conductance time course of another motoneurone after first (circles) and third (squares) antidromic spikes at a stimulus frequency of 25 ttz.
CONDUCTANCE AND REPETITIVE FIRING
229
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Fig. 5. A : conductance time course following the first (circles) and second (squares) spikes elicited by in[racellular stimulation at 14 and 18.5 hA. B: r-I curves of the same cell for the corresponding intervals. The dashed lines mark the two current intensities of A. Conductance measurements in A could be made over intervals longer than those given in B on account of" the presence of" the inward current pulse.
Measuring at a frequency of 25 Hz gave the curves of Fig. 4C, for the first and third intervals. Little change is seen in the plateau phase, and summation is weak.
Conductance during repetitive firing evoked by intracellular stimulation In carrying out these measurements two conditions had to be fulfilled. Firstly, the cell should show a linear current-voltage relationship, so that a control AVr could be reliably measured. This was tested at subthreshold current levels in the resting state; it was possible to check AVr also at just rheobase by timing the measuring pulses so as to precede the first spike. Secondly, conductance measurements during the second spike interval were considered for analysis only when the first interval remained fairly constant (of Methods). Under these conditions, two current intensities were selected, a low one eliciting rhythmic firing in the primary range, and a higher one, for stepping up frequency into the secondary range. A typical measurement is illustrated in Fig. 5A, B. At the outset it can be said that, in analogy to the data obtained with antidromic firing, a low (14 nA Fig. 5A, filled symbols) and a high (18 nA Fig. 5A, open symbols) current intensity yielded conductance curves similar to those plotted for low (Fig. 4C) and high (Fig. 4A) frequencies of antidromic stimulation, respectively.
230
K.H. MAIJRITZ el a/.
A t 14 nA, c o n d u c t a n c e s u m m a t i o n following the second spike was small, a n d the p l a t e a u did not change, tvl r e m a i n i n g nearly c o n s t a n t for the first (26 msec) and the second (28 msec) intervals. The t r a n s i t i o n frequency f r o m p r i m a r y to secondary ranges was 39 Hz, giving a ttrans o f 26 msec, which correlated well with t~)j. T i m e constant, as measured under the qualifications stated above, increased from 14 m s e c for the first interval to 21 msec for the second. A t 18.5 n A a s e c o n d a r y range was o b t a i n e d for the first interval, but not l\)r the second, an a d a p t a t i o n r e p o r t e d to occur in spinalised cats". The c o n d u c t a n c e curve for the first interval was nearly identical to the one plotted at 14 nA. In this connection the a s s u m p t i o n o f a c o n s t a n t p l a t e a u phase at two current intensities is not unreasonable, inasmuch as these m e a s u r e m e n t s could be m a d e over intervals longer than those plotted in Fig. 5B ( @ M e t h o d s ) . As for the second interval, there was a c o n d u c t a n c e increase and a plateau decrease, as in the case o f high frequency a n t i d r o m i c stimulation ( @ Fig. 4A). M e a s u r e m e n t s in two a d d i t i o n a l m o t o n e u r o n e s gave similar results. In a t t e m p t i n g a c o r r e l a t i o n between a b o l i t i o n of the p l a t e a u phase and absence of a s e c o n d a r y range for the second interval at 18.5 nA, it should be stated that, in this case, m e a s u r e m e n t s at higher current intensities were prevented by loss of the c e l l T h u s a s e c o n d a r y range could not be excluded. DISCUSSION T w o questions deserve c o n s i d e r a t i o n : (1) the possible c o n n e c t i o n between p a t t e r n s o f c o n d u c t a n c e curves; and ( 2 ) t h e relation of c o n d u c t a n c e s u m m a t i o n to adaptation. o4:) conductance change
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Fig. 6. Comparison between theoretical conductance course assuming an algebraic summation and measured conductance summation. A: antidromic stimulation. The conductance course for the first interval was taken from the cell in Fig. 4. The same spike frequency as in Fig. 4 and an algebraic conductance summation were assumed and the conductance course was calculated for the third (dashed line) and fifth (dots and dashes) intervals, allowing direct comparison between motoneurone and model conductances. B: intracellular stimulation. The conductance course for the first interval was that of the cell in Fig. 6. The discharge frequency was assumed to be 75 Hz (spike interval without inward current pulse, Fig. 5) for stimulus current ~. 18.5 nA (first interval). The conductance course was calculated for this condition for the second interval (dashed line). The difference between model and motoneurone conductances (dots and dashes) is illustrated.
CONDUCTANCE AND REPETITIVE FIRING
231
It can be regarded as firmly established that, in some motoneurones, conductance decline may diverge from a simple exponential course. On a background of rhythmic firing, the remarkable agreement in 18 motoneurones in the sample between the timing of onset of the secondary range and that of the end of the plateau suggests an association with a plausible functional meaning. Nevertheless, this statement should be brought into context with the fact that in the remaining 8 cells conductance curves were nearly smooth, and that in 5 of them a secondary range could be ascertained. This means that the plateau phase is not a necessary condition for the existence of a secondary range. This contention is supported by the predictions of a model TM, and by results obtained in DSCT neurones, which fire in the secondary range, in spite of the absence of a plateau phase in their A H P conductance decay li. Thus both exponential and non-exponential time courses of conductance may equally well be found in cells firing at secondary range frequencies. The correlation between tl,1 and ttrans reported here, however, suggests that divergence from a single repolarising conductance may be at least one contributing factor for the interval shortening in the secondary range. Obviously much more quantitative work is needed to gauge the functional meaning of both types of conductance curve. Nonetheless it is possible to mention at least two guidelines: (a) at frequencies higher than a primary range, the variation of factors contributing to a shorter interval setting are bound to be more complex; and (b) information as to the influence of supraspinal control is still scanty, and likely to be of importance. For example, it was found in spinalised animals that the secondary range decreased rapidly after a few intervals, and that conductance decline tended to follow a simple exponential pattern 2. The decreasing slope just alluded to signals adaptation. In the present experiments this process set in early in the initial spike train, frequently already after the second interval, in accordance with the report quoted above .). Summation of successive AHPs was advanced as one of the factors leading to adaptation a,~2,17. This suggestion is supported by the present results. Summation clearly stands out in the curves of Figs. 4A and 5A, and correlates well with adaptation in the same cells. Furthermore, within the limits of precision in the measurements (cf. Results), there is a tendency for summation to be larger at the tail of the AHPs. An attempt has been made to account for adaptation in a neurone model in which K ~ conductance changes summate algebraically 4. Calculation of conductance for the motoneurone of Fig. 4 under this assumption yielded the curves of Fig. 6A. Summation after the third and fifth spikes is larger in the motoneurone than in the model, particularly at the tails of the AHPs. Similar calculations for current-elicited spikes based on the first interval in the curve of Fig. 5A gives a summation larger than that actually measured (Fig. 6B). Thus, in both cases a divergence from the model in opposite direction appears, bringing about differences between the firing patterns of motoneurone and model. This is not entirely unexpected, since in another model1% a simple algebraic summation was considered improbable. Further progress along these lines requires quantitative data on the factors contributing to the divergence from a simple exponential time course of conductance.
K.H. MAURITZ et al.
232 ACKNOWLEDGEMENTS
This investigation a n d the p a r ti c i p at i o n o f K . H . M . , D . W . R . and W.R.S. were s u p p o r t ed by the S o n d e r f o r s c h u n g s b e r e i c h 38 ' M e m b r a n f o r s c h u n g ' o f the D e u t s c h e F o r s c h u n g s g e m e i n s c h a f t . S u b m i t t e d by K . H . M . as partial fulfillment o f the requirements for the M . D . degree at the School o f M e d i c i n e o f the S a a r l a n d University. Mrs. M. Eraser, Mrs. H. M o r a t z k i and Mrs. P. R o e d e r p r o v i d e d efficient technical assistance.
REFERENCES 1 BALDISSERA, F., AND GUSTAFSSON, B., Time course and potential dependence of the membrane conductance change during the afterhyperpolarization in the cat's a-motoneurones, Brain Research, 17 (1970) 365-368. 2 BALDISSERA, F., AND GUSTAFSSON, B., Supraspinal control of the discharge evoked by constant current in the alpha-motoneurones, Brain Research, 25 (1971) 642-644. 3 BALDISSERA, F., AND GUSTAFSSON, B., Regulation of repetitive firing in motoneurones by the afterhyperpolarization conductance, Brain Research, 30 (1971) 431-434. 4 BALDISSERA, F., GUSTAFSSON, B., AND PARMIGGIANI, F., Adaptation in a simple neurone model compared to that of spinal motoneurones, Brain Research, 52 (1973) 382-384. 5 BARRETT,J. N., AND GRAUBARD, K., Fluorescent staining of cat motoneurone in vivo with beveled micropipettes, Brain Research, 18 (1970) 565-568. 6 FRANK, K., AND FUORTES, M. G. F., Excitation and conduction, Ann. Rev. Physiol., 23 (1961) 357 386. 7 GRANIT, R., KERNELL, D., AND LAMARgE, Y., Algebraic summation in synaptic activation of motoneurones firing within the 'primary range" to injected currents, J. Physiol. (Lond.), 187 (1966) 379-399. 8 GRAMT,R., KERNELL,D., ANDLAMARRE,Y., Synaptic stimulation superimposed on motoneurones firing in the 'secondary range' to injected current, J. Physiol. (Lond,), 187 (1966) 401-415. 9 GRAMT,R., KERNELL,D., ANO SHORTESS,G. K., Quantitative aspects of repetitive firing of mammalian motoneurones caused by injected currents, J. Physiol. (Lond.), 168 (1963) 911-931. 10 GRAN1T,R., ANn RENKIN,B., Net depolarization and discharge rate of motoneurones, as measured by recurrent inhibition, J. Physiol. (Lond.), 158 (1961) 461-475. 11 GUSTAFSSON,B., LINDSTR~SM,S., AND TAKATA, M., Repetitive firing in dorsal spinocerebellar neurones, Brain Research, 47 (1972) 506-509. 12 ITO,M., ANDOsnlUA, T., Temporal summation of afterhyperpolarization following a motoneurone spike, Nature (Lond.), 195 (1962) 910-911. 13 KERNELL,D., The adaptation and the relation between discharge frequency and current strength of cat tumbosacral motoneurones stimulated by long-lasting injected currents, Acta physiol. scand., 65 (1965) 65--73. 14 KERNELL,D., High frequency repetitive firing of cat lumbosacral motoneurones stimulated by long-lasting injected currents, Actaphysiol. stand., 65 (1965) 74-86. 15 KERNELL D., The limits of firing frequency in cat lumbosacral motoneurones possessing different time course of afterhyperpolarization, Aetaphysiol. scand., 65 (1965) 87-100. 16 KERNELL D., The repetitive impulse discharge of a simple neurone model compared to that of spinal motoneurones, Brain Research, 11 (1968) 685-687. 17 KERNELL,D., The early phase of adaptation in repetitive impulse discharge of cat spinal motoneutones, Brain Research, 41 (1972) 184-186. 18 KERNELL D., AND SJOHOLM, H., Motoneurone model based on voltage clamp equations for peripheral nerve, Actaphysiol. stand., 86 (1972) 546-562. 19 KERNELL D., AND SJ6HOLM, H., Repetitive impulse firing: comparison between neurone models based on 'voltage clamp equations' and spinal motoneurones, Actaphysiol. scand., 87 (1973) 40-56. 20 MAUR1TZ,K. H., SCHLUE, W. R., RICHTER, D. W., ANDNACIMIENTO, A. C., Conductance changes
CONDUCTANCE AND REPETITIVE FIRING
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during the afterhyperpolarization and repetitive firing in cat spinal motoneurones, Pfliigers Arch.
ges. Physiol., 343 (1973) R 73, 21 RALL, W., Time constants and electrotonic length of membrane cylinders and neurones, Biophys. J., 9 (1969) 1483-1508. 22 SCHWIND'r, R. C., Membrane potential trajectories underlying motoneuron rhythmic firing at high rates, J. Neurophysiol., 36 (1973) 434-449. 23 SCHWlYI~'r,P. C., AND CALV1N,W. H., Membrane potential trajectories between spikes underlying motoneurone firing rates, J. Neurophysiol., 35 (1972) 311-325. 24 ST~MeFLI, R., Die doppelte Saccharosetrennwand-Methode zur Messung yon elektrischen Membraneigenschaften mit extrazellulO.ren Elektroden, Helv. physiol. Acta, 21 (1963) 189-204.
223
~2~Elsevier ScientificPublishing Company, Amsterdam - Printed in The Netherlands
M E M B R A N E C O N D U C T A N C E C O U R S E D U R I N G SPIKE I N T E R V A L S A N D R E P E T I T I V E F I R I N G IN CAT SPINAL M O T O N E U R O N E S
K. H. MAURITZ*, W. R. SCHLUE**, D. W. RICHTER*** ANDA. C. NAC1MIENTO .~ Physiological Institute, Central Nervous System Research Unit, Saarland University, 665 HomburgSaar (G.F.R.)
(Accepted February 21st, 1974)
SUMMARY The time course of membrane conductance was measured in gastrocnemius motoneurones of spinalised cats during (a) the afterhyperpolarisation (AHP) following a single antidromic spike, and (b) rhythmic firing, elicited by antidromic and intracellular stimulation. In a sample of 26 motoneurones, 18 (69 ~o) showed a conductance decay during A H P which was not a simple exponential function of time. After an initial steep phase, conductance decline was markedly slowed down for a definite time (plateau phase). In the remaining 8 motoneurones (3l ~ ) conductance decay was nearly exponential. Relating the non-exponential conductance curve to the current frequency relation (f-I curve) in the same cell a close correlation was found between the time to the end of the plateau phase and the time of interval shortening leading to the secondary range in the f-I curve. During repetitive firing evoked by antidromic stimulation the plateau phase was progressively smoothed out and conductance during successwe AHPs summated. After the fifth spike, decay was exponential and summation reached a maximum. Conductances did not summate algebraically. Similar results were obtained during rhythmic firing evoked by intracellular stimulation. It is suggested that (1) divergence from a single repolarising conductance declining exponentially with time may be at least one of the factors involved in the shaping of the secondary range in the f-I curve, and (2) the progressive tendency to a simple exponential decline and non-algebraical summation of conductances during a short train of spikes contributes to adaptation.
* Present address: Abt. Physiol. Psychologie,Universit/it Konstanz, Konstanz, G.F.R. ** Present address : Fachbereich Biologie, Universit/it Konstanz, Konstanz, G.F.R. *** Present address: Physiologischeslnstitut der Universitgt Mfinchen, Munich, G,F.R. To whom reprint requests should be sent.
224
K.H. MAURITZet al.
INTRODUCTION
The continuous firing evoked in cat spinal motoneurones by long-lasting injected currents is similar to that triggered by steady excitatory synaptic action 6,10,t4. In such experiments, a plot relating current intensity to discharge frequency (f-I curve) shows two successive straight lines, the primary range, and, following an abrupt transition, the steeper secondary range 7--9,13 ~5. The slopes of both ranges decrease as the number of spikes increases, with eventual abolition of the secondary range 2,14,15. Some recent inquiries into the basis of these findings are available 3,1s,2z,2z. One approach has been the analysis of the course (trajectories) of membrane potential changes between spikes, with descriptions of an initial, slowed rate of change during repolarisation, followed by a linear rise to the next firing level 2',z3. Another line has focused upon the time course of conductance changes between spikes. It has been reported that in some motoneurones conductance decline during the afterhyperpolarisation (AHP)following a single spike is not a simple exponential function of time, this course being interrupted by a plateau phase 3. Suggestions as to mechanisms involved have been put forward in terms of motoneurone models. One of them takes into account the non-exponential time course of conductance and explains adaptation 4. Another, formulated on the basis of voltage clamp equations for peripheral nerve, assumes an essentially exponential declinO6,18,~L The aim of the present work has been an analysis of the conductance changes which take place during the early phase of rhythmic firing. To this end, input membrane conductance was measured as a function of time during (a) the AHP following a single spike, and (b) repetitive firing evoked antidromically, and by intracellular stimulation. An attempt is made to account, at least in part, for the transition leading to the secondary range and for the early adaptation in terms of patterns of conductance change during spike intervals. A preliminary report has been published 2°. METHODS
Low-spinalised adult cats anaesthetised with pentobarbital were used. Some of them were paralysed with gallamine triethiodide and put under artificial respiration. Expired end-tidal CO2 concentration (3-4 %), arterial blood pressure (at least 80-90 mm Hg) and rectal temperature (38 ± 0.5 °C) were continuously monitored. Ringer and plasma expander solutions were given as required. After laminectomy dorsal roots L4 to S1 were sectioned; ventral roots were left in continuity, so as to allow stimulation of peripheral nerves and antidromic identification. The gastrocnemius nerves, the lateral together with the soleus nerve, were routinely stimulated. For intracellular recording and stimulation glass micropipettes with beveled tips 5 and filled with 2 M potassium citrate (DC resistance 2-10 MD~) were used. Their current-voltage characteristics were routinely checked. Data presented in this paper were obtained exclusively with pipettes which were linear within the measurement range. The recording system included a unity gain differential DC amplifier with a negative feedback design, according to principles described elsewhere "4. A bridge
CONDUCTANCE
225
AND REPETITIVE FIRING
circuit allowed intracellular stimulation during recording. The first derivative o f action potentials was obtained at T - - 0.1 or 1.0 msec. F o r assessing c o n d u c t a n c e changes rectangular inward current pulses of 8-12 msec in d u r a t i o n a n d 4-8 n A in a m p l i t u d e were applied, and the voltage d r o p measured (,'lVr and I Vt, Fig. 1C). D u r a t i o n of the current pulses was such t h a t the voltage transient reached 95 ~ o f the steady state value at resting m e m b r a n e resistance. Since the m e m b r a n e time c o n s t a n t 21 in the sample averaged 3.3 msec, a d u r a t i o n o f a b o u t 10 msec was selected. Voltage d r o p s were measured at their maxima, and changes in m e m b r a n e RC neglected. D u r i n g the initial 15 msec o f A H P , however, pulses of 2-5 msec could be applied, on account o f the shorter time constant. The relative conductance changes were expressed as described previously 1. The a m p l i t u d e o f the current pulses did not change the course o f A H P , as routine checks showed. This control was particularly needed in measurements during r h y t h m i c firing induced by intracellular
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Fig. 1. Conductance time course during the A H P alter an antidromic spike. A : conductance measurement at resting potential (l) and at different times after a single antidromic spike (2-5); upper
trace, inward current pulse; lower trace, membrane potential. B: relative conductance changes are plotted logarithmically against the time after the spike onset. The arrow marks the spike interval at the transition from primary to secondary range for this motoneurone (el Fig. 3A). tvl is the time from spike onset to the end of the plateau. The curve was fitted by eye. C: measurements/JV,-, "/Vt and t.
K.H. MAtJRtrZ eta/,
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Fig. 2. Conductance curve during AHP for a motoneurone exhibiting a nearly exponential course after a single antidromic spike. Conductance changes were estimated with inward (circles) and outward (squares) current pulses. Inset: upper trace, current (2 msec); lower trace, membrane potential,
stimulation. In these conditions the interval for the next spike was longer, when the inward current pulse was injected at the end of the interval (cJ~ Fig. 5A and B), i.e., conductance could be measured over longer intervals. The measurements reported here were carried out in 26 gastrocnemius motoneurones, selected from a larger sample, according to the following criteria:minimal recording time of 15 rain at stable resting potentials above --50 mV, spike amplitude and rate of rise of at least 70 mV and 200 V/sec, respectively, and absence of recurrent IPSP. RESULTS
Conductance during the AHP following a single antidromic spike In 18 (69 ~o) of the selected 26 motoneurones, the conductance decrease along the A H P was not a simple exponential function of time, in agreement with previous results 3. Measurements on a cell of this type, as well as the related plot, are shown in Fig. 1. In the remaining 8 cells (31 ~/o), conductance decay was approximately exponential. The curve in Fig. 2 plots measurements on a motoneurone of this group. The curve in Fig. 1B shows that, after a steep initial phase, conductance decay was brought to a halt and remained nearly steady for a time. This plateau ends with the onset of the nearly exponential final segment of the curve. The rate of change of the plateau phase was quantitatively different from cell to cell, that of Fig. 1 being an example of a very slow rate. As for the final part of the curve, it should be pointed out that conductance measurements in this segment tended to be less precise, on account of smaller changes and greater variability. The next step was an attempt to relate the timing of the plateau phase to the transition from primary to secondary range during repetitive firing in the same motoneurone. In Fig. 3A and B, two plots are shown from measurements on the same celt as in Fig. 1. In one plot, Fig. 3A, frequency is plotted as a function of intracellularly
CONDUCTANCE
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AND REPETITIVE FIRING
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Fig. 3. Current-frequency (f-I curve) relation (A) and current-interval curve (B) for the motoneurone in Fig. 1. A : f - I curve for first (circles) and second (squares) spike intervals. B: current exceeding the rheobase plotted logarithmically against the spike interval for first (circles) and second (squares) intervals. The arrow marks the spike interval at the transition from primary to secondary range in A (ttr~.s).
applied current; the second plot, Fig. 3B, relates spike interval and current ~. The time of change from primary to secondary range in this cell, as depicted in Fig. 3A and B, is marked on its conductance curve (Fig. 1B) with an arrow. The time of transition (ttrans) is 16.7 msec, corresponding to a frequency of 60 Hz for the first spike interval (Fig. 3A). The time between spike onset and end of plateau (tvl) is 16 msec (Fig. I B). Also, the time courses of the interval-current (Fig. 3B) and conductance (Fig. 1B) curves were similar for the first interval, as previously reportedL Furthermore, there is also good agreement of the time the plateau emerges from the exponential part of the current-interval curve (in Fig. 3B about 18 msec) with both tvl and ttr~.~. A comparison of ttrans and tvl for all neurones in this group yielded the following results: for tp], the mean and S.D. were 20 ± 4.4 msec (range 14-26 msec); for ttr~,.~, 22 ~- 7.7 msec (range 14-33 msec), for the first interval, at a frequency (f-I curve) of 44.9 + 13.4 Hz. The correlation coefficient was 0.74, and the significance
K.H. MAURFIZ et a[.
228
level P < 0.001. This correspondence of conductance and repetitive firing changes was found in all cells exhibiting a plateau phase in the conductance curve. In the group of 8 cells with nearly exponential conductance curves, 3 displayed f-[ relations without a secondary range. It is possible, however, that measurements in these cells were ended before current intensity reached the required level for firing in the secondary range.
Conductance during repetitive firing evoked by antidromic stimulation Extending the preceding analysis to rhythmic firing, conductance was measured in the wake of antidromic spikes elicited at different frequencies. In the records of Fig. 4B conductance was measured following the last spike in a burst of 3, triggered by a stimulus frequency of 50 Hz. After increasing the burst to 5 spikes, measurements were made during the first, third and fifth AHP, with the results shown in Fig. 4A. The curve for the first AHP has been already described, a plateau being clearly discernible. During the third AHP, however, this phase became less conspicuous, on a background of increased, summated conductance. The change in tv] was f¥om 21 to 25 msec. The curve for the fifth AHP shows, as a prominent feature, a nearly exponential decay. Furthermore, summation reached a maximum at this stage. It should be added that the time constant of the exponential decay for the three series were 20, 25 and 30 msec, respectively. But caution is necessary as to the precision of measurements at this part of the curve (vide supra). A
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Fig. 4. A : time course of conductance change after first (circles), third (squares) and filth (triangles) spikes evoked by antidromic stimulation of 50 Hz. B: sample records from this Cell after a train of 3 spikes. C: conductance time course of another motoneurone after first (circles) and third (squares) antidromic spikes at a stimulus frequency of 25 ttz.
CONDUCTANCE AND REPETITIVE FIRING
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Fig. 5. A : conductance time course following the first (circles) and second (squares) spikes elicited by in[racellular stimulation at 14 and 18.5 hA. B: r-I curves of the same cell for the corresponding intervals. The dashed lines mark the two current intensities of A. Conductance measurements in A could be made over intervals longer than those given in B on account of" the presence of" the inward current pulse.
Measuring at a frequency of 25 Hz gave the curves of Fig. 4C, for the first and third intervals. Little change is seen in the plateau phase, and summation is weak.
Conductance during repetitive firing evoked by intracellular stimulation In carrying out these measurements two conditions had to be fulfilled. Firstly, the cell should show a linear current-voltage relationship, so that a control AVr could be reliably measured. This was tested at subthreshold current levels in the resting state; it was possible to check AVr also at just rheobase by timing the measuring pulses so as to precede the first spike. Secondly, conductance measurements during the second spike interval were considered for analysis only when the first interval remained fairly constant (of Methods). Under these conditions, two current intensities were selected, a low one eliciting rhythmic firing in the primary range, and a higher one, for stepping up frequency into the secondary range. A typical measurement is illustrated in Fig. 5A, B. At the outset it can be said that, in analogy to the data obtained with antidromic firing, a low (14 nA Fig. 5A, filled symbols) and a high (18 nA Fig. 5A, open symbols) current intensity yielded conductance curves similar to those plotted for low (Fig. 4C) and high (Fig. 4A) frequencies of antidromic stimulation, respectively.
230
K.H. MAIJRITZ el a/.
A t 14 nA, c o n d u c t a n c e s u m m a t i o n following the second spike was small, a n d the p l a t e a u did not change, tvl r e m a i n i n g nearly c o n s t a n t for the first (26 msec) and the second (28 msec) intervals. The t r a n s i t i o n frequency f r o m p r i m a r y to secondary ranges was 39 Hz, giving a ttrans o f 26 msec, which correlated well with t~)j. T i m e constant, as measured under the qualifications stated above, increased from 14 m s e c for the first interval to 21 msec for the second. A t 18.5 n A a s e c o n d a r y range was o b t a i n e d for the first interval, but not l\)r the second, an a d a p t a t i o n r e p o r t e d to occur in spinalised cats". The c o n d u c t a n c e curve for the first interval was nearly identical to the one plotted at 14 nA. In this connection the a s s u m p t i o n o f a c o n s t a n t p l a t e a u phase at two current intensities is not unreasonable, inasmuch as these m e a s u r e m e n t s could be m a d e over intervals longer than those plotted in Fig. 5B ( @ M e t h o d s ) . As for the second interval, there was a c o n d u c t a n c e increase and a plateau decrease, as in the case o f high frequency a n t i d r o m i c stimulation ( @ Fig. 4A). M e a s u r e m e n t s in two a d d i t i o n a l m o t o n e u r o n e s gave similar results. In a t t e m p t i n g a c o r r e l a t i o n between a b o l i t i o n of the p l a t e a u phase and absence of a s e c o n d a r y range for the second interval at 18.5 nA, it should be stated that, in this case, m e a s u r e m e n t s at higher current intensities were prevented by loss of the c e l l T h u s a s e c o n d a r y range could not be excluded. DISCUSSION T w o questions deserve c o n s i d e r a t i o n : (1) the possible c o n n e c t i o n between p a t t e r n s o f c o n d u c t a n c e curves; and ( 2 ) t h e relation of c o n d u c t a n c e s u m m a t i o n to adaptation. o4:) conductance change
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Fig. 6. Comparison between theoretical conductance course assuming an algebraic summation and measured conductance summation. A: antidromic stimulation. The conductance course for the first interval was taken from the cell in Fig. 4. The same spike frequency as in Fig. 4 and an algebraic conductance summation were assumed and the conductance course was calculated for the third (dashed line) and fifth (dots and dashes) intervals, allowing direct comparison between motoneurone and model conductances. B: intracellular stimulation. The conductance course for the first interval was that of the cell in Fig. 6. The discharge frequency was assumed to be 75 Hz (spike interval without inward current pulse, Fig. 5) for stimulus current ~. 18.5 nA (first interval). The conductance course was calculated for this condition for the second interval (dashed line). The difference between model and motoneurone conductances (dots and dashes) is illustrated.
CONDUCTANCE AND REPETITIVE FIRING
231
It can be regarded as firmly established that, in some motoneurones, conductance decline may diverge from a simple exponential course. On a background of rhythmic firing, the remarkable agreement in 18 motoneurones in the sample between the timing of onset of the secondary range and that of the end of the plateau suggests an association with a plausible functional meaning. Nevertheless, this statement should be brought into context with the fact that in the remaining 8 cells conductance curves were nearly smooth, and that in 5 of them a secondary range could be ascertained. This means that the plateau phase is not a necessary condition for the existence of a secondary range. This contention is supported by the predictions of a model TM, and by results obtained in DSCT neurones, which fire in the secondary range, in spite of the absence of a plateau phase in their A H P conductance decay li. Thus both exponential and non-exponential time courses of conductance may equally well be found in cells firing at secondary range frequencies. The correlation between tl,1 and ttrans reported here, however, suggests that divergence from a single repolarising conductance may be at least one contributing factor for the interval shortening in the secondary range. Obviously much more quantitative work is needed to gauge the functional meaning of both types of conductance curve. Nonetheless it is possible to mention at least two guidelines: (a) at frequencies higher than a primary range, the variation of factors contributing to a shorter interval setting are bound to be more complex; and (b) information as to the influence of supraspinal control is still scanty, and likely to be of importance. For example, it was found in spinalised animals that the secondary range decreased rapidly after a few intervals, and that conductance decline tended to follow a simple exponential pattern 2. The decreasing slope just alluded to signals adaptation. In the present experiments this process set in early in the initial spike train, frequently already after the second interval, in accordance with the report quoted above .). Summation of successive AHPs was advanced as one of the factors leading to adaptation a,~2,17. This suggestion is supported by the present results. Summation clearly stands out in the curves of Figs. 4A and 5A, and correlates well with adaptation in the same cells. Furthermore, within the limits of precision in the measurements (cf. Results), there is a tendency for summation to be larger at the tail of the AHPs. An attempt has been made to account for adaptation in a neurone model in which K ~ conductance changes summate algebraically 4. Calculation of conductance for the motoneurone of Fig. 4 under this assumption yielded the curves of Fig. 6A. Summation after the third and fifth spikes is larger in the motoneurone than in the model, particularly at the tails of the AHPs. Similar calculations for current-elicited spikes based on the first interval in the curve of Fig. 5A gives a summation larger than that actually measured (Fig. 6B). Thus, in both cases a divergence from the model in opposite direction appears, bringing about differences between the firing patterns of motoneurone and model. This is not entirely unexpected, since in another model1% a simple algebraic summation was considered improbable. Further progress along these lines requires quantitative data on the factors contributing to the divergence from a simple exponential time course of conductance.
K.H. MAURITZ et al.
232 ACKNOWLEDGEMENTS
This investigation a n d the p a r ti c i p at i o n o f K . H . M . , D . W . R . and W.R.S. were s u p p o r t ed by the S o n d e r f o r s c h u n g s b e r e i c h 38 ' M e m b r a n f o r s c h u n g ' o f the D e u t s c h e F o r s c h u n g s g e m e i n s c h a f t . S u b m i t t e d by K . H . M . as partial fulfillment o f the requirements for the M . D . degree at the School o f M e d i c i n e o f the S a a r l a n d University. Mrs. M. Eraser, Mrs. H. M o r a t z k i and Mrs. P. R o e d e r p r o v i d e d efficient technical assistance.
REFERENCES 1 BALDISSERA, F., AND GUSTAFSSON, B., Time course and potential dependence of the membrane conductance change during the afterhyperpolarization in the cat's a-motoneurones, Brain Research, 17 (1970) 365-368. 2 BALDISSERA, F., AND GUSTAFSSON, B., Supraspinal control of the discharge evoked by constant current in the alpha-motoneurones, Brain Research, 25 (1971) 642-644. 3 BALDISSERA, F., AND GUSTAFSSON, B., Regulation of repetitive firing in motoneurones by the afterhyperpolarization conductance, Brain Research, 30 (1971) 431-434. 4 BALDISSERA, F., GUSTAFSSON, B., AND PARMIGGIANI, F., Adaptation in a simple neurone model compared to that of spinal motoneurones, Brain Research, 52 (1973) 382-384. 5 BARRETT,J. N., AND GRAUBARD, K., Fluorescent staining of cat motoneurone in vivo with beveled micropipettes, Brain Research, 18 (1970) 565-568. 6 FRANK, K., AND FUORTES, M. G. F., Excitation and conduction, Ann. Rev. Physiol., 23 (1961) 357 386. 7 GRANIT, R., KERNELL, D., AND LAMARgE, Y., Algebraic summation in synaptic activation of motoneurones firing within the 'primary range" to injected currents, J. Physiol. (Lond.), 187 (1966) 379-399. 8 GRAMT,R., KERNELL,D., ANDLAMARRE,Y., Synaptic stimulation superimposed on motoneurones firing in the 'secondary range' to injected current, J. Physiol. (Lond,), 187 (1966) 401-415. 9 GRAMT,R., KERNELL,D., ANO SHORTESS,G. K., Quantitative aspects of repetitive firing of mammalian motoneurones caused by injected currents, J. Physiol. (Lond.), 168 (1963) 911-931. 10 GRAN1T,R., ANn RENKIN,B., Net depolarization and discharge rate of motoneurones, as measured by recurrent inhibition, J. Physiol. (Lond.), 158 (1961) 461-475. 11 GUSTAFSSON,B., LINDSTR~SM,S., AND TAKATA, M., Repetitive firing in dorsal spinocerebellar neurones, Brain Research, 47 (1972) 506-509. 12 ITO,M., ANDOsnlUA, T., Temporal summation of afterhyperpolarization following a motoneurone spike, Nature (Lond.), 195 (1962) 910-911. 13 KERNELL,D., The adaptation and the relation between discharge frequency and current strength of cat tumbosacral motoneurones stimulated by long-lasting injected currents, Acta physiol. scand., 65 (1965) 65--73. 14 KERNELL,D., High frequency repetitive firing of cat lumbosacral motoneurones stimulated by long-lasting injected currents, Actaphysiol. stand., 65 (1965) 74-86. 15 KERNELL D., The limits of firing frequency in cat lumbosacral motoneurones possessing different time course of afterhyperpolarization, Aetaphysiol. scand., 65 (1965) 87-100. 16 KERNELL D., The repetitive impulse discharge of a simple neurone model compared to that of spinal motoneurones, Brain Research, 11 (1968) 685-687. 17 KERNELL,D., The early phase of adaptation in repetitive impulse discharge of cat spinal motoneutones, Brain Research, 41 (1972) 184-186. 18 KERNELL D., AND SJOHOLM, H., Motoneurone model based on voltage clamp equations for peripheral nerve, Actaphysiol. stand., 86 (1972) 546-562. 19 KERNELL D., AND SJ6HOLM, H., Repetitive impulse firing: comparison between neurone models based on 'voltage clamp equations' and spinal motoneurones, Actaphysiol. scand., 87 (1973) 40-56. 20 MAUR1TZ,K. H., SCHLUE, W. R., RICHTER, D. W., ANDNACIMIENTO, A. C., Conductance changes
CONDUCTANCE AND REPETITIVE FIRING
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during the afterhyperpolarization and repetitive firing in cat spinal motoneurones, Pfliigers Arch.
ges. Physiol., 343 (1973) R 73, 21 RALL, W., Time constants and electrotonic length of membrane cylinders and neurones, Biophys. J., 9 (1969) 1483-1508. 22 SCHWIND'r, R. C., Membrane potential trajectories underlying motoneuron rhythmic firing at high rates, J. Neurophysiol., 36 (1973) 434-449. 23 SCHWlYI~'r,P. C., AND CALV1N,W. H., Membrane potential trajectories between spikes underlying motoneurone firing rates, J. Neurophysiol., 35 (1972) 311-325. 24 ST~MeFLI, R., Die doppelte Saccharosetrennwand-Methode zur Messung yon elektrischen Membraneigenschaften mit extrazellulO.ren Elektroden, Helv. physiol. Acta, 21 (1963) 189-204.