Brain Research, 84 (1975) 1-22

i

© Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

Review Article

GENERATION OF SPIKE TRAINS IN CNS NEURONS

WILLIAM H. CALVIN

Department of Neurological Surgery, University of Washington School of Medicine, Seattle, Wash. 98195 (U.S.A.) (Accepted October 4th, 1974)

SUMMARY

The membrane potential waveforms to be expected from many asynchronous inputs to CNS neurons are described, along with three modes for repetitive firing through which the input waveforms are converted into spike trains. Area beneath a postsynaptic potential (PSP), rather than PSP peak height, is shown to be an important parameter susceptible to modification. Occasional crossings of threshold produce occasional spikes, but a sustained depolarizing waveform which attempts to hold the membrane potential above threshold elicits rhythmic firing. Firing rate is graded with the amount by which the synaptic depolarizing currents exceed the minimum current for rhythmic firing (approximately rheobase). A systematic sequence of alterations in the membrane potential trajectory between spikes, quite different from those of receptors and invertebrate neurons, may control the firing rate and give rise to sudden changes in the 'gain' of this conversion of depolarizing current into firing rate. The different implications of synaptic location during the occasional spike mode and the rhythmic firing mode are discussed, as is the role of the antidromic invasion of the soma-dendritic region during rhythmic firing. Less frequently, an 'extra spike mode' is seen where depolarizing afterpotentials following a spike themselves cross threshold to elicit an extra spike, which may similarly elicit another extra spike, etc., in a regenerative cycle. The character of the underlying depolarizing afterpotentials (or 'delayed depolarizations') is reviewed, along with theories for their origin from the antidromic invasion of the dendritic tree. The stereotyped burst firing patterns characteristic of the extra spike mode can also be seen in deafferented neurons and neurons studied in chronic syndromes

such as epilepsy and central pain. This raises the question as to whether some disease states may augment extra spike firing, thus multiplying many-fold the response to a normal input.

INTRODUCTION

The most obvious electrical property of a nerve cell is its threshold. If there is insufficient input, there will be no output. The inputs take the form of transient membrane potential changes called postsynaptic potentials (PSPs); the output is usually in the form of action potentials (or 'spikes') which propagate down the axon to eventually generate PSPs in the next cell. The individual inputs are usually not very potent in the central nervous system (CNS), unlike obligatory synapses such as neuromuscular junctions : an individual afferent fiber or interneuron often produces a PSP in the next cell which is smaller than 2 ~ of the voltage change needed to reach threshold2,56,58,62,63,v0. While experimenters often synchronize many inputs to produce a large compound PSP (Fig. 1E) which can cross threshold 9z, this artificial situation provides little physiological insight into how temporal patterns of inputs produce trains of output spikes. This article attempts to elucidate (1) the depolarization waveform to be expected from the summation of many asynchronous input PSP trains, A

B

INPUT~ ] .

extra

.

8pike

mo@e

.

.

.

C

.

rhythmic mode

.

firing

O

.

occasional splke m o d e

Sunlmatlon larg e unit

of

PSf~s

Fig. 1. Schematic drawings of repetitive firing. Lower traces (input) represent membrane potential which would be seen if spike generation were artificially prevented. Upper traces (output) shows spike train generation by these input waveforms. A: regenerative firing mode, where large depolarizing afterpotentials rise through the falling threshold after a spike to set off an extra spike, which may itself set off another extra spike, etc. This firing may outlast the original depolarizing stimulus 28,39. B: rhythmic firing mode, caused by the interaction of the spike's hyperpolarizing afterpotential with the sustained input currents. C: once it exceeds threshold, further increases in the depolarizing current cause linear increments in firing rate. D: input waveforms which only occasionally exceed threshold (at times long compared to the afterpotential durations) cause occasional spikes. E: case where single PSPs are large, individually or cooperatively eliciting spikes. Also illustrative of the artificial situation normally used in most neurophysiological experiments, where many small inputs are artificially synchronized by an electric shock to produce a large compound excitatory postsynaptic potential (EPSP). While the last situation is the usual view of how inputs cooperate to produce spikes, it is an unrepresentative one because most single inputs are very small (less than 2 ~ of the threshold voltage change) and seldom synchronized. Thus, input waveforms such as seen in B and D are more representative than E. See text.

and (2) 3 different modes of repetitive firing (Fig. 1A, B and D) t h r o u g h which input waveforms are transformed into output spike trains. Variations in firing pattern due to cell properties will be emphasized, e.g., rhythmic firing due to m e m b r a n e properties, but not those due to periodic inputs. Some o f the a b n o r m a l n e u r o n spike trains in pathological pain and epilepsy will then be examined.

Summation of input PSPs I f one stretches a muscle, the asynchronous discharge o f m a n y receptors (and subsequently interneurons) produces a barrage o f PSPs in C N S neurons. In these downstream neurons, a sustained depolarization (or hyperpolarization) develops with a ripple atop it reflecting the arrival o f the individual PSPs. The average depolarization shift depends u p o n the size o f each input (actually, the area beneath the PSP), its rate, and its polaritylL Excitatory PSPs (EPSPs) are depolarizing while inhibitory PSPs (IPSPs) tend to hyperpolarize the cell m e m b r a n e away f r o m threshold. We will consider one input at a time to see h o w the temporal s u m m a t i o n process effectively converts an input rate into an average depolarization level. Fig. 2 shows the way in which PSPs temporally summate until a plateau is , ~ ,," .... ~ ',2 ','~ ~ ,'"".~ ,.., ill ll11'1 1~. . . . . . . . . . . . .

v--~

I--"/

PSP rate

temporal summation

~

~

~

slxinpu,s (separately,~

~

~

spatial summation

Fig. 2. Temporal and spatial summation of inputs, using computer simulations of linear summation. The input rate is doubled and tripled to show higher plateau depolarizations developing in temporal summation. Graph at right shows linear relation between PSP rate and average depolarization developed; the slope of this curve is merely the area beneath a single PSP (inset). When input rates are slower (middle), a plateau is not obvious but the average depolarization over I sec is still predicted by the graph. When one sums together the activity in 6 inputs (all firing rhythmically but asynchronously), the resulting sum (bottom) shows a plateau depolarization which can be predicted from the sum of the area × rate products of the 6 individual inputs. The ripple about the plateau corresponds to what is called 'synaptic noise' in CNS'neurons12,17. Adapted from CalvinlL

4

reached where the voltage decays as much after a PSP as it rises upon the next PSP. The mean height of this plateau is proportional to the rate of the PSPs lz, as shown in the graph. If the individual PSPs are smaller, the proportionality constant between plateau level and PSP rate is less: this slope is the area beneath a single PSP. The 'PSPs' illustrated are simulated PSPs lz and assume linear summation of PSPs; the differences between real PSPs and linear theory will be discussed presently. The PSP arrival rates illustrated for temporal summation are rather high; what if PSPs come along more slowly? As seen for 6 inputs with low rates in Fig. 2, a PSP can decay almost to the baseline before another PSP comes along, i.e., no plateau develops. If one averages the membrane potential over a 1-sec period, however, it will be found to accord with the prediction made by multiplying the average PSP arrival rate by the area beneath a single PSP. One may argue that the neuron does not 'see' the average membrane potential, but rather the instantaneous membrane potential. However, the neuron really does not see the individual PSP peak either (because most PSPs are miniscule, e.g., less than 1-2 ~ of the subthreshold swing of the membrane potential). When many inputs are active and superimpose their PSP trains, one sees enough 'spatial' summation to produce steady depolarizations ('spatial' summation is a classical neurophysiological term for what mathematicians call superposition; it need not have geometric implications). Fig. 2 shows 6 inputs firing at low rates, rhythmically but asynchronously; the resulting superposition is shown below. The mean level in spatial summation is merely the sum of the calculated mean depolarizations for each of the 6 inputs. Of course, the arrivals in spatial summation appear irregular and the voltage wanders around randomly 17. The essential features are exactly what one records in a motoneuron upon stretching a muscle (a baseline shift and noise). The same linear theory applies to the summation in the muscle tendons of the twitch tensions of the individual motor units. Imagine that the ordinate in Fig. 2 is tension rather than membrane potential. The 6 inputs are now 6 different motor units, due to 6 motoneurons firing asynchronously; the spatial summation in Fig. 2 shows the muscle tension to be expected if different motor units summate linearly with one another, i.e., if the plot of average tension vs. rates is a straight line, as in Fig. 2. Of course, they may summate nonlinearly for a variety of reasons; indeed, Rack and Westbury 7s have shown that the actual curve is S-shaped. Similarly, for the membrane potential case, facilitation will make individual PSPs bigger at high rates52, 62,67, 74; however, large plateau depolarizations will reduce the distance to the PSP reversal potential, and thus decrease the individual PSP size 6s. Just how much these opposing factors will deviate the depolarization vs. rate curve from a straight line will have to be evaluated in each case. For example, one expects 1A afferent inputs to motoneurons 57 to behave more linearly than corticospinal inputs 74 because of differences in facilitation. The basic relation, however, is average plateau equals rate multiplied by the area beneath the typical unitary response. This plateau in a CNS neuron is analogous to the receptor potential of peripheral receptor neurons.

5 Occasional spike mode

The expected synaptic inputs thus produce a steady depolarization surrounded with noise. Some of these excursions may be big enough to cross threshold and cause a spike; in addition, the average input rates themselves may fluctuate, causing the average depolarization to wander. Fig. 1D illustrates the occasional spike mode where each such threshold crossing causes a spike. This mode is characterized by average depolarization levels less than threshold, the time between successive threshold crossings being long relative to the duration of the afterpotentials following the spike. A special submode is where the compound EPSP of classical neurophysiology (when more than 50 individual PSPs 93 are synchronized to cause a large EPSP) briefly crosses threshold (Fig. 1E). While of great importance in experimental design, such large compound EPSPs are probably seen in nature only when inputs are abnormally synchronized (as when one is struck by lightning or perhaps during sleep spindles or epileptic sharp waves95). The wandering membrane potential of Fig. 1D is undoubtedly a more physiological situation. There are, however, cases when the individual inputs to a CNS neuron are large enough to elicit a spike 1°,59,61. For some second-order sensory relay cells in the dorsal horn of the spinal cord, Brown et al. 1° estimate that more than 100 inputs to such cells are capable of producing an output spike following each input spike. Other second-order sensory cells, e.g., the Clarke's column cells 2v,6l, may have PSPs which are 30 ~ of the size needed to reach threshold. Thus the summation of large PSPs illustrated in Fig. 1E can indeed be a physiological situation in certain cases; it does not, however, provide a good general model for the thousands of other inputs to such cells nor for nearly all inputs to other CNS neurons. Threshold may also wander. Accommodation experiments in motoneurons do imply, however, that threshold remains fairly constant when approached slowly11,13, 79-82. Such threshold 'ceilings' imply that, while spikes may be elicited at lower levels by quick approaches of the membrane potential, there is an upper limit which the dotted threshold line in Fig. 1 represents. The input-output relation of the neuron in this occasional spike mode is difficult to summarize except by the way in which classical neurophysiology has done it: whenever enough inputs increase their firing rates, the membrane potential will cross the accommodating threshold and an output spike will be produced. Trigger zones

It is important to summarize the sequence of events which has been inferred for the spike initiation process. Spikes do not (generally) begin next to the synaptic site; they begin in the initial part of the axon (axon hillock, initial segment, etc.) because the threshold in this 'trigger zone' seems to be much lower than thresholds in the soma and dendrites where the synapses are abundantly located. Thus, synaptic currents spread electrotonically to the trigger zone; spatial summation depends upon the area under the individual PSPs by the time they reach the trigger zone, not their areas at the input sites themselves. The spike begins at the trigger zone, spreading down the axon to be repeated at each gap in the myelin insulation, but also spreading backwards into the soma and dendrites24, 3°. The afterhyperpolarization 24,3° and the

delayed depolarization 4°,71, seen following motoneuron spikes arise from this antidromic invasion; the afterhyperpolarization lasts 50-150 msec, thus taking the membrane potential away from threshold for awhile. It was recognized long ago 25, however, that many spike trains are very regular (rhythmic) and that they are unlikely to arise from the events described above for the occasional spike mode. Experiments in motoneurons, together with similar data from receptors, have elucidated a rhythmic firing mode.

Rhythmic firing mode What if sustained depolarizations from the many asynchronous inputs try to keep the membrane potential above the threshold? Following the first crossing of threshold, the spike afterhyperpolarization will interact with this sustained depolarizing current. As the hyperpolarizing afterpotential wears off, the membrane potential will intersect threshold again. The larger the synaptic depolarizing currents, the sooner one might expect this intersection to occur, i.e., firing rate should increase. Large compound EPSPs may elicit multiple spikes60, 94, but this situation is difficult to analyze. The current clamp technique allows the experimenter to inject currents into the soma of a CNS neuron. They are meant to mimic the steady synaptic depolarizations described earlier. Actual synaptic currents are not only somewhat variable with time, but they have the disadvantage that their magnitude cannot be directly measured once the resulting depolarization exceeds threshold (currents 10 times greater than the minimum values are often needed to fully explore the range of firing rates). Finally, as will be seen presently, it turns out that current is often the appropriate stimulus parameter rather than voltage. For all of these reasons, the standard procedure is to apply current steps to the impaled neuron through the recording microelectrode and study the resulting repetitive firing behavior. This technique has been applied to various CNS neurons4-V,1s,21,~2,26,29,3v,5~,~3, but the most extensive work is on cat spinal motoneurons. In Stockholm in the 1960s, this technique was exploited by Granit et al. aa-aS, 40-49 to explore the repetitive firing behavior of cat spinal motoneurons. A steady depolarizing current just strong enough to evoke a spike (rheobase) will, if continued, often produce a train of spikes. While some motoneurons will stop firing after a few spikes when stimulated with rheobasic currents, only a minor increment in current beyond rheobase is typically needed to produce rhythmic firing for as long as the current step lasts 41. Further increments in current strength will increase the firing rate; indeed, the graph of firing frequency (f) against current (I) often results in a straight line (Figs. 1C and 3F)5,42,s3,as. Thus, a 10 nA increment in current may result in a 10 spike/sec rise in firing rate, whether the step is from 15 to 25 nA or from 45 to 55 nA. The major qualification for saying that the motoneuron converts depolarizing current magnitude into firing rate is the cutoff at low rates: the f-I curve may be linear for current values above the minimum current for rhythmic firing, but the curve suddenly drops down to zero firing rate when the current drops below this minimum. Furthermore, this minimum rhythmic firing rate (e.g., 7-20/sec in spinal

motoneurons) is the reciprocal of the duration of the aflerhyperpolarization 5,43 of that motoneuron (50-150 msec). Above the minimum, the motoneuron seems a rather linear device: it converts current increments into frequency increments. Below the minimum, the occasional spike mode applies, i.e., the voltage threshold itself is the important determinant of firing. Many motoneurons, especially the ones which are somewhat smaller in size 83, exhibit an f-I curve with piecewise linearity. At higher currents the f-I curve suddenly becomes steeper so that a given current increment now raises the firing rate 2-6 times more than it would at lower currents. Fig. 3C shows such an f-1 curve. The initial portion of the f-I curve34,41 is now called the 'primary range'; the steeper portion at higher currents is called the 'secondary range'5,4L Some motoneurons even exhibit another sudden change in the slope of the curve at very high firing rates, called a 'tertiary range 's3. These are not gradual curvatures of the f-I relation, as seen in some other CNS neurons26,37; these are remarkably linear segments, abruptly changing

m

A

cont rol

B

nerve stlm.

~

__IjjjNjjjIj.,,," J ~ I

"~'~'~lH/~lJ//Is

r

t~ 6

AA

~

201

v,

OJ

o

i

hyperpotarlzlng

A

lo

2o 30 ~o

INJECTED

~o

~nA

CURRENT

i, it: IIr,'ll ' 100,

LIIhlll,,;LJ,~,,

80 J

~-

IN,

60

20hA

o.

40

t~

.~2o, I

synaptlc

•

E

f'l tnput

added

o} o 1 NJFCTED

30

40

50 60

70hA

CURRENT

Fig. 3. Effects of sustained synaptic inputs upon rhythmic firing in two (ABC, DEF) cat spinal motoneurons. Peripheral nerves were stimulated at high rates, or appropriate muscles were stretched, to cause sustained depolarizing or hyperpolarizing input; steps of current were then injected into the motoneuron through the recording microelectrode to test the membrane resistance and to elicit rhythmic firing. Comparing A to B, it can be seen that synaptic inputs lowered the input resistance (first panel) and hyperpolarized the membrane. The nerve stimulation began shortly after the beginning of the trace in B (second panel) and many seconds before the resistance measurements were made in B (first panel). A n additional 5 nA of injected current was required to attain control firing rates (lateral shift of f-I curve in C). Sustained depolarizing inputs (not shown) caused less injected current to be required to attain control firing rates (C), suggesting that synaptic inputs produce a constant current (zk 5 nA in these examples) which adds and subtracts with the injected currents to determine the motoneuron firing rate. A similar experiment in another motoneuron (DEF) was done with a mixed synaptic input which, after a transient depolarization, produced no net change in membrane potential. Nonetheless, the synaptic conductance changes substantially reduce the voltage change produced by a 10 nA current step (DE, first panel). It might be expected that this would decrease the efficacy of injected currents for producing rhythmic firing rates, but this is not so. In F, the f-I curve shows no change in slope. Adapted from Schwindt and Calvin 8~.86.

slope. Cortical pyramidal tract neurons also exhibit piecewise linear f-I curves2a, 53. That these steady injected currents mimic the steady synaptic currents can be seen from the experiments in Fig. 3B where a peripheral nerve was stimulated at a high rate and a steady hyperpolarization was obtained (similar results are obtained by stretching muscles). When injected current was superimposed on synaptic current, the firing rate was lower than without the synaptic input34,ss, s6. In fact, the whole f-I curve shifted to the right as if the synaptic input could be overcome by an extra 5 nA of injected current. Thus, one infers that the synaptic current in this instance was the equivalent of - - 5 nA of injected current at both low and high firing rates. Stimulation of other nerves can produce a depolarization at rest (not shown) and a shift in the f-I curve during rhythmic firing (Fig. 3C) which suggests that these synaptic inputs were the equivalent of + 5 nA of current. This leads to a picture which suggests that synaptic currents add and subtract, with the net current being converted into firing rate according to the f-I curve. The PSPs from the individual afferent fibers (and even from the synchronizing nerve stimulations shown in Fig. 3) are quite small; should a large EPSP occur during rhythmic firing, it may force a spike to occur early. Conversely, a large IPSP can delay a rhythmic spikO 2. Such large PSPs are infrequent in most neurons studied, and these f-I curves do not reflect such contingencies.

Sequential steps in spike production In the occasional spike mode, the steps in spike production are simple: current spreads eleetrotonically from a (dendritic) synapse to the (initial segment) trigger zone; if a spike starts at the trigger zone, it spreads simultaneously down the axon and backwards into the soma and dendritesZ4, ~°, as diagrammed in Fig. 4. In the rhythmic firing mode, a rationale for this antidromic invasion of soma and dendrites becomes apparent. The afterhyperpolarization (AHP) arises from the soma-dendritic invasion; the hyperpolarizing currents should spread passively (electrotonically) to the trigger zone, temporarily counteracting the depolarizing synaptic currents1% Somehow, this interaction results in the interval to the next spike being controlled by the depolarizing current strength so that f-I curve is linear. Thus, the first spike generates a 'resetting' aftermath which, as it wears off, allows another rhythmic spike to be generated, and this spatio-temporal sequence repeats over and over (2-3-4-5-2-3-4-5 etc. sequence in Fig. 4). If one examines the time course of the membrane potential between rhythmic spikes, a variety of features is seen. First, there may be a hump-like event several milliseconds after the rhythmic spike called a depolarizing afterpotential or delayed depolarization 16,~9,~°,71. Following the delayed depolarization (DD), the membrane potential drops to a minimum value, reverses direction, and rises rather linearly towards the threshold for the next spike. Describing the sequence as two components, a 'scoop' followed by a 'ramp', accords well with the way in which this membrane potential time course between spikes (the 'trajectory') is observed to change when the firing rate alters. In the primary range of the f-I curve, an increment in current causes the bottom of the scoop to become more elevated, but produces no change

dendrites

Soma

initial

I

PSPs~

I

segment

axon i

/~

I

AP

• ~:~'" ,,;i. i: v~: .:-::.

J.J.

~,.~'.~..~.~;.......:.:.:

4

~

"3", .'.:''."'".:,~::::~.'):'~:;:'~:'C,~.": ' ? ,:(::

DD

..:~

.~'.:.;.:'% . % ~ . " . ' , ' , , , ' , ' " ' ,

~..,

".'. ".'"

5~ " ~

..~..

:-.~,~

A~

....

:

~. . . . . . .

, . . . . .

." ~':':.',.,.,.," ~}:'.!~:..:..:~?!~:-~'v.? :.(~..i:i. "

AHI~~

J TEMPORAL

SEQUENCE

i I

I; Fig. 4. Schematic representation of spatio-temporal sequence of events during repetitive firing whose time course is shown at bottom. Heavy black line represents cell membrane (stippled area is interior of cell). Heavy arrows show sites of active current generators, open arrows show passive spread of these currents. A steady barrage of synaptic inputs is diagrammed as a constant 'EPSP' originating from the dendrites. The current spreads electrotonically and causes IR voltage drops as it exits through the soma (not shown) and initial segment membranes (open arrows). Since the initial segment has a lower threshold than the other regions, spikes (AP) start there when the depolarization is sufficient; the inwards sodium current is shown as 3 black arrows at time 2. In the next instant in time (time 3), the spike spreads down the axon but also backwards into the soma. It will contribute to the depolarizing current spreading electrotonically to the initial segment, but the initial segment is refractory at this time. At time 4, the spike spreads into the dendritic tree, as shown by the single black arrow (DD). This will increase the electrotonic current spreading to the initial segment. Early outwards currents associated with the downstroke of the AP have not been diagrammed. During time 5, a late and prolonged outwards current (AHP) develops in the soma (and perhaps dendrites) and spreads electrotonically to the initial segment, opposing the depolarizing current from the dendrites. The AHP current fades with time, allowing the steady depolarizing current from the dendrites to again force threshold to be crossed in the initial segment (back to time 2 diagram). This sequence 2 - 3 4 - - 5 - 2 - 3 - 4 - 5 - 2 - 3 4 - 5 etc. repeats to give the rhythmic firing mode; the interspike interval shortens as the steady depolarizing current increases. Should the D D contribution during time 4 be large enough at a time when the initial segmenrs threshold had recovered, a spike could be generated during this period, i . e . , 2-3-4-2-3-4. If these D D currents were large enough, the process might even sustain itself without the continuation of the steady depolarizing current (as in the extreme case diagrammed in Fig. 1A). This hypothetical scheme is synthesized from both spinal motoneuron 16,2a,40,71 and crustacean stretch receptor 28,32 data interpretations.

in t h e r a m p p o r t i o n o f t h e t r a j e c t o r y ; t h e rate o f rise t o w a r d s t h r e s h o l d d o e s n o t alterS~-S6. T h u s , t h e i n t e r s p i k e i n t e r v a l (]SI) is s h o r t e n e d b y the r e d u c e d r e p o l a r i z a t i o n e a r l y in t h e ISI, n o t b y a n a l t e r e d r a t e - o f - r i s e o f t h e m e m b r a n e p o t e n t i a l l a t e r in the ISI. W h e n firing rates s l o w f o l l o w i n g a n e w step o f c u r r e n t ( a d a p t a t i o n ) , t h e s c o o p s

10 become deeper with successive spikes to lengthen the ISI and the ramps do not change. When firing rates reach values which signal entry into the secondary range of the f-I curve, the ramp's rate-of-rise does begin to increase, explaining the sudden change in f-I proportionality constant between primary and secondary ranges s3-s6. In cells with a 'tertiary range' at very high firing rates, Schwindt sz has shown that the 'scoop' changes again to control the trajectory alterations. Thus, motoneurons exhibit well-defined alterations in the membrane potential sequence between spikes. These alterations, as well as the piecewise linear f-I curves, are not characteristic of rhythmic firing in invertebrate neurons or in receptors; most examples in the literature show rate-of-rise alterations corresponding to firing rate changes s4. The modified Hodgkin-Huxley equations which are obtained in voltage-clamp experiments on invertebrate somata 20 do, however, suggest additional mechanisms which could control rhythmic firing rates. However, a simple potassium conductance which decays exponentially with time following a rhythmic spike 45 is inadequate to explain the changes in input conductance which are observed during the ISI 6,69,s6.

Thresholds and adequate stimuli The accommodation of threshold in the occasional modeS,54,55, s0-s2 has a counterpart in the rhythmic firing mode. If one probes with a large compound EPSP during the ISI (Fig. 5B), one sees the threshold fall rapidly after a spike, i.e., the relative refractory period is not important at motoneuron firing rates. In fact, the threshold falls well below the level at which the antecedent spike arose. It then rises during most of the ISI when the membrane potential is also rising. In many motoneurons 18, its time course is seen to intersect the time course of the membrane potential at the end of the ISI as one would expect. However, as seen in Fig. 5B, it sometimes seems to ride along immediately atop the membrane potential trajectory for the last portion of the ISI. This conclusion derives from two sources: (a) from the extrapolation of the threshold time course into the voltage trajectory, and (b) because one cannot interpolate even small EPSP during this terminal ramp without immediately eliciting a spike. This anomalous behavior of the threshold means that the history of the membrane potential, as well as its instantaneous value, is often important; this may explain why repetitive firing sometimes fails after a few spikes, as may occur at the low or high end of the f-I curve, in deteriorating cells, or other such 'marginal' situations. The 'adequate stimulus' for a CNS neuron has always been considered to be the voltage change produced by an input. Indeed, if the input resistance of a motoneuron is reduced by the conductance changes from many synaptic inputs, the height of a test monosynaptic EPSP is reduced, its decay time constant is reduced, and the voltage produced by a given subthreshold injected current is reduced 92. Thus, more input is needed to reach threshold. Current (synaptic or injected) is thus not the important parameter; it is the voltage produced by those currents and the resistances they encounter. Thus, voltage change may be considered to be the adequate stimulus in the occasional spike mode, not current change. Is this true in the rhythmic spike mode as

11 A 220mv

Ona lOOms - -

r I ....

tl

f

J B

I

lOma

Fig. 5. Rhythmic firing in a cat spinal motoneuron, showing depolarizing afterpotentials and threshold changes during the interspike interval. A: rhythmic firing to a step of injected current; note the humps after each spike. The hump is elevated after the first rhythmic spike, but humps occur at lower membrane potentials with successive spikes. Note the apparently constant threshold for the rhythmic spikes. B: during the fifth interspike interval, a large compound EPSP was used to explore for the threshold between rhythmic spikes. The usual threshold is marked with an arrow in A and B. Only the rising phase of the exploring EPSP is seen; the interpolated spike and its aftermath have been suppressed for clarity. By the time of the hump, the refractory periods are over and the threshold is actually below ~normal' values (the arrow). The threshold continues to fall but then subsequently rises during the latter part of the interspike interval to eventually intersect the membrane potential trajectory. This intersection would be at the arrow in many motoneurons; in this motoneuron, the threshold curve extrapolates into the membrane potential trajectory several mV below the arrow whereupon even small exploring EPSPs will immediately elicit a spike. This anomalous behavior of threshold is discussed in the text. Adapted from Calvin13.

well? W e have a l r e a d y seen t h a t synaptic c u r r e n t s a d d a n d subtract, t h a t the net currents linearly v a r y the firing rates, etc. W h e n synaptic conductances p r o v i d e shunting p a t h w a y s , one m i g h t expect t h a t the slope o f the f - I curve w o u l d change, b u t this does n o t h a p p e n . It takes m o r e c u r r e n t to r e a c h the t h r e s h o l d for the first spike, b u t r h y t h m i c firing rates are otherwise j u s t w h a t w o u l d be p r e d i c t e d f r o m control f - I curves85, 86. I f the c o n d i t i o n i n g synaptic inputs p r o d u c e a net current, the f - I curve will be shifted by t h a t a m o u n t (Fig. 3C); if excitatory a n d i n h i b i t o r y synaptic currents cancel each o t h e r out, as in Fig. 3F, the curves overlap except for the missing p o i n t s at the b o t t o m o f the curve where the c u r r e n t was insufficient to p r o d u c e a threshold voltage change. The voltage trajectories between spikes are also u n c h a n g e d 85,86. This suggests t h a t c u r r e n t is indeed the a d e q u a t e stimulus in the r h y t h m i c firing m o d e . Thus, n o n - l i n e a r s u m m a t i o n o f inputs can occur in the occasional spike

12 mode due to the synaptic conductance changes, but these effects disappear in the rhythmic firing mode. Synaptic currents would seem to sum linearly. Besides the implications for linear and non-linear summation of inputs, the adequate stimulus also has important implications for the role of synaptic locations in the dendritic tree. While the voltage change produced at a dendritic synapse is often severely attenuated by the time it reaches the soma, much of the synaptic current may reach the soma eventuallyS,9,a6. Thus, synapse location is important if voltage change is the adequate stimulus, but much less important when current is the adequate stimulus.

'Extra spike' mode Perhaps the most poorly understood mode of repetitive firing is the extra spike mode, although it has long been observed in different neuronst3,16,1s,28,a2,39, 55a. Some spikes have depolarizing afterpotentials immediately after the spike. Sometimes these depolarizations seem to rise through the falling threshold after the spike, giving rise to an extra spike. Sometimes this extra spike itself has a depolarizing afterpotential large enough to elicit another extra spike, etc., so that a burst of spikes is seen. This regenerative cycle may be self-limited (as when an extra spike's depolarizing afterpotential is no longer large enough to rise through threshold, as diagrammed in Fig. 1A). What serves as a stimulus for the appearance of the regenerative cycle is unknown; however, this question may be approached by studying the behavior of the underlying depolarizing afterpotentials. The depolarizing afterpotentia14,16,35,40, 71 in motoneurons acquired the descriptive term 'delayed depolarization'; as noted earlier, it is often a hump-like event several milliseconds after a spike (Fig. 5A), but sometimes appears only as a distinctive slowing of the repolarization rate. By direct experiment in lobster stretch receptors zz, and inferentially in motoneurons 7~, the depolarizing afterpotentials are said to arise from the antidromic invasion of the dendritic tree by the spike (Fig. 4). Whether this invasion is active (as shown in Fig. 4, part 4) or passive 89, there would seem to be a substantial source of depolarizing current remaining in the dendrites at the time that the initial segment and soma repolarize. As this current returns to the initial segment, and as the initial segment's resistance recovers, a hump-like depolarization is generated passively in the initial segment (or so the story goes). It has been shown in lobster stretch receptor that this returning current generates extra spikes zz.

Delayed depolarizations When the delayed depolarization is seen only as a slowing in the repolarization rate after the spike, the characteristic hump-like appearance can often be made to appear by changing the driving currents16,zs,40, 71. The hump usually occurs 13 after the rapid downstroke of the spike has carried the membrane potential well below the threshold level (Fig. 5A), but an occasional motoneuron will exhibit a delayed depolarization which is located close to threshold. This elevation of the delayed depolarization sometimes changes with successive spikes in a train; Fig. 6C and D

13

/ jL/V J J s/

A

c

D

J

_J Fig. 6. Large hump-like depolarizing afterpotentials in two cat spinal motoneurons (AB and CD). B and D are enlarged versions of the data in A and C, respectively. Occasionally during rhythmic firing to a sustained depolarizing current, motoneurons will be seen to fire in doublets (A). If one enlarges the record as in B, it is always observed that there are large hump-like depolarizing afterpotentials following the spikes which appear to cross the falling threshold sometimes. Following the extra spike in B, there is no hump so the regenerative cycle is terminated. The hump may change systematically during repetitive firing, as was seen in Fig. 5A and which is well illustrated in C. The first rhythmic spike following a step of depolarizing current lacks a hump. There is a hump after the second rhythmic spike, large and elevated. The elevation of the hump becomes less with each succeeding spike, and it begins to loose its hump-like character. The interspike membrane potential trajectories in C have been enlarged and superimposed in D; note that the hump is missing after the first spike, is large after the second spike, and becomes smaller and less elevated with successive spikes. Calibrations: A (80 mV, 75 msec); B (20 mV, 30 msec); C (10 mV with spikes retouched and off-scale, 50 msec); D (5 mV, 10 msec). Adapted from Calvin and Schwindt 16.

shows the delayed depolarization becoming less elevated following later spikes in a train 16. Some motoneurons13,16 (Fig. 6C) and PT cells 1s,52 omit the hump-like delayed depolarization after the first spike in a train. One m a y summarize delayed depolarizations by saying that some are h u m p like, others s m o o t h ; some are well below threshold, others are elevated: they m a y change with successive spikes in a train; a m o n g the 'adaptation' patterns is the one in which the h u m p is omitted following the first spike o f a rhythmic train. One occasionally sees a spike arising out o f a hump-like delayed depolarization, producing an extra spike with a very short ISI. In the midst of otherwise rhythmic firing, such doublets clearly stand out (Figs. 6A and 7D). These extra spikes m a y themselves have delayed depolarizations following them, but they are often too small to evoke another extra spike (Fig. 6B). W h e n they do, however, one sees a burst o f firing where only a single spike would ordinarily be seen (Fig. 7C). It is apparent, in studying the sequence in Fig. 7B, that the delayed depolarization following the second rhythmic spike has elicited an extra spike, and that the delayed depolarization following this extra spike sometimes (Fig. 7C) elicits another extra spike. Eventually the delayed depolarization is ineffective in eliciting further extra spikes, and the burst ceases. Since delayed depolarizations become smaller with each successive spike in this m o t o n e u r o n (Fig. 7A), the regenerative cycle seems to have been terminated by a self-limiting feature: the failure o f the delayed depolarization to attain threshold.

14

__3

,

gg-

l111[1111!1 w

r l l r w r l l w ~ l l

!

I l l

Fig. 7. Extra spikes arising from depolarizing afterpotentials crossing the falling threshold. Records A, B, and C from a single motoneuron. A: trial where no extra spikes occurred; note large humptype depolarizing afterpotentials starting with second spike but declining with later spikes. Left column shows injected current (upper) and membrane potential response (lower trace). Right column are magnified versions of the early portions of the spike trains in the left column. B : trial in which one extra spike is seen after second rhythmic spike. Note large depolarizing afterpotential following extra spike (arrow). C: two extra spikes are seen following second rhythmic spike. Note smaller depolarizing afterpotential after second extra spike (arrow). Threshold-straddling behavior seen comparing A, B, and C suggest the depolarizing afterpotential causes a self-regenerative cycle to produce burst firing. Adapted from Calvin13. D: response of 'fast'pyramidal tract neuron in cat sensorimotor cortex showing doublet discharges occasionally during a current step. Note triplet starting after an initial rhythmic-type interspike interval (unpublisheJ work of Calvin and Syper#S). Left column calibrations: 20 hA, 20 mV, 50 msec for ABC, 16 nA, 20 mV, 20 msec for D. Right column: 5 mV, 20 msec for ABC, 5 mV, 2 msec for D.

S u m m a t i n g a f t e r h y p e r p o l a r i z a t i o n s 16 or electrogenic p u m p s c o u l d also serve to shut off such regenerative bursts. Calvin a n d Sypert is have recently p e r f o r m e d m a n y o f the m o t o n e u r o n - t y p e repetitive firing experiments on p y r a m i d a l t r a c t n e u r o n s in cat s e n s o r i m o t o r cortex. The extra spike m o d e is quite p r o m i n e n t is in a sizeable percentage o f the 'fast P T cells TM (Fig. 7D), b e h a v i n g m u c h as m o t o n e u r o n s do. The delayed d e p o l a r i z a t i o n s are quite lalge in fast P T cells; the p a t t e r n w h e r e b y the d e l a y e d d e p o l a r i z a t i o n is small after the first r h y t h m i c spike b u t large after succeeding spikes is also seen ls,52.

15

Mode identification Doublet and triplet firing patterns like those seen in Fig. 8 have often been observed with extracellular recording; given that one cannot intracellularly observe the repetitive firing mechanisms at work, is it possible to infer the repetitive firing modes solely from the timing patterns of spikes? Certainly irregular spikes with ISI > 150 msec in a spinal motoneuron would surely suggest the occasional spike mode; very regular spikes with ISI < 150 msec would suggest the rhythmic firing mode; an irregular spike train with a mean ISI of 120 msec would be ambiguous. When may one infer the extra spike ? Delayed depolarizations are often observed to peak within 1-5 m s e c ~,16,27,40,71, SO 1SI in that range are candidates. To attempt to distinguish, between the rhythmic mode and the regenerative mode for ISI < 5 msec, however, one must rely upon spontaneous firing patterns. When one sees an occasional doublet (2 msec ISI) in the midst of otherwise rhythmic firing (100 msec ISI), it seems quite reasonable to infer the regenerative mode occasionally superimposed on the rhythmic mode. Similarly, when one observes doublets (ISI 1-3 msec) recurring quite regularly, as in many records from the dorsal column nuclei (Fig. 8), one again suspects the regenerative mode superimposed upon the rhythmic mode. One may overlay the doublets showing that they are quite stereotyped (dot rasters in Fig. 8). Stereotyped doublets (or triplets) superimposed upon an otherwise rhythmic firing pattern would be very hard to explain by the rhythmic mode alone. While some motoneurons23,38,55a, 90 and fast PT cells is exhibit doublets or bursts, many are seen in cells of the dorsal column nucleil~,31, 50,51. Since the only difference

"r, . . . . . . .

normal

''.

. . . .

t!: : i : :!

one day Six

LI

day l~,

-' ,~IALJL.I._.IJ.,

lJ

.~'l~ld.

I-;-1-1

....

J*~.l.I

-'-: !,...:" '

. I N)rns

.i. i= ,., .

. . •;

Fig. 8. Extracellular recordings of spontaneous firing in cat external cuneate nucleus (ECN). Many normal cells in ECN (and elsewhere in the dorsal column nuclei) exhibit doublet/triplet firing patterns, the short interspike intervals being 1-3 msec. For a given neuron, these doublets may be quite stereotyped, as can be seen (top, right) by making a dot raster display. The first spike of each spontaneous doublet forms the solid-appearing vertical line; the second (and occasional third) spikes are seen to occur 1.2 (and 2.5) msec later. Calibration dots in top row are 1 msec apart. By analogy to motoneuron doublets, one might expect depolarizing afterpotentials to be eliciting extra spikes (Fig. 1A). When the ECN is deafferented via a multilevel dorsal rhizotomy ~°,51,73, all spontaneous activity in the nucleus is silenced for several days. However, by 6 days (and extending many months, at least), a profound hyperactivity is seen in ECN neurons. While some fire rhythmically (smaller spikes in 6-day record), one often sees stereotyped high-frequency burst firing patterns. Dot rasters (bottom, right) are analogous to those seen in the doublets of normal ECN neurons, except that the regenerative cycle would seem to continue for 8 extra spikes rather than one or two. Adapted from Kjerulf, et al. 51.

16 between a doublet and a burst of 8 'extra spikes' would be the shut-off mechanism for the regenerative cycle, one is naturally drawn to examine the firing patterns featuring high-frequency bursts: to what extent may they be explained by the regenerative mechanism (Fig. 1A)? Or are they merely the rhythmic mode, with a large depolarizing wave driving the rhythmic firing mechanism (Fig. 1B)?

Burst firing patterns Firing patterns showing stereotyped high-frequency bursts of spikes are rather rare a5 except where pathology is suspected. If one deafferents (by means of a dorsal rhizotomy) the external cuneate nucleus (ECN) and records days or months later, ECN cells will exhibit a great deal of spontaneous firing5°,51 despite the absence of all of their large synaptic terminals containing round vesiclesTM73. Along with rhythmic firing, one will observe high-frequency burst firing (Fig. 8). Successive bursts, if superimposed, are remarkably stereotyped (this is usually demonstrated with raster displays such as in Fig. 8, right). In fact, the ISI are quite comparable to the ISI seen in the doublets and triplets of normal ECN neurons. Given the strong inference that the extra spike mode is responsible for the doublet/triplet firing patterns of the normal ECN neurons, it is natural to infer that the shutoff mechanism has been altered by the deafferentation (or the accompanying disuse). In other words, the regenerative cycle shuts off after 8 extra spikes (a stereotyped burst) rather than after one spike (doublet). If chronic deafferentation can cause such high-frequency bursting patterns, what else might do so? The exaggeration of the underlying delayed depolarizations by acute anoxiav2, the reports of bursts with muscular paralyzing agents 31, and assorted other reports all suggest that the extra spike mode may be stimulated in a variety of ways, on both an acute and chronic basis. One may also observe decreases in extra spike activity. In motoneurons13,23,3s, extra spikes tend to cease when steady afferent drive is increased (as in the static stretch reflex). This same phenomenon has been seen in normal ECN neurons by Calvin and Loeser14 who increased steady afferent drive and observed that the doublets widened concomitant with the more frequent failure of the extra spike. However, the doublets seen in the fast PT neurons of barbiturate-anesthetized cats ~s are augmented by further increases in the steady driving currents. The best known of the burst firing patterns are those recorded from cortical neurons in an epileptogenic focus3,15,19,95-99. While the bursts from acute epileptogenic foci often seem to be due to a large depolarizing wave 3 of synaptic origin driving the rhythmic mode, chronic epileptogenic loci present a different picture. Both human epileptogenic foci studied during surgery15 and chronic loci produced by injection of alumina gel into monkey cerebral cortex19,95-99, show cells with highly stereotyped burst firing patterns. Like the doublets and bursts in ECN, these epileptic bursts are often quite superimposable and usually have ISI which lengthen slightly during the burst, with the burst terminating before the ISI lengthens beyond 5 reset. Lacking a detailed intracellular study of the repetitive firing modes of epileptic neurons, one has to guess at the modes. For many of the cells, the ISis within the bursts shorten

17 and then lengthen and the bursts are not superimposable; thus, one suspects the rhythmic mode being driven by depolarizing waves (Fig. 1B). But for cells with stereotyped, high-frequency-only bursts, the extra spike mode seems the most likely candidate. One feature of these stereotyped epileptic bursts, which has been especially puzzling since we discovered it 6 years ago, is what we called the 'long-first-interval' burst ~9. It is stereotyped from the second spike onwards in just the manner earlier described; however, the first spike stands out in front of this stereotyped event by varying times. The delayed depolarizations during rhythmic firing of normal cortical neurons can be quite prominent. As in cat spinal motoneurons 13,16, the frequent absence of a hump-like delayed depolarization following the first rhythmic spike of a train (Figs. 6C, 7A and D) was notedlS, 52. Thus, the extra spike mode may start after the first or second rhythmic spike of a normal response of a cortical neuron to a depolarizing wave. This wave need not be large ~8, but only enough to start rhythmic firing at low rates. If the extra spike mode produces extra spikes after the first rhythmic spike, a stereotyped burst should be seen. If the extra spikes start after the second rhythmic spike, as in Fig. 7C and D, a long-first-interval burst should be seen.

Epilepsy and central pain The burst firing patterns recorded in epileptogenic foci were not part of a seizure; they were part of the 'interictal' abnormalities of the epileptogenic focus which seem to go on 24 h a day. Only occasionally do the interictal abnormalities turn into a real seizure; one assumes that the interictal phenomena have involved normal regions of the brain by some sort of recruitment process. Naturally, the highfrequency burst firing patterns of the interictal focus are a good candidate for this recruitment since the temporal summation from such short ISI could produce a potent input to a normal downstream neuron 12. It has been estimated that less than 1% of the inputs to a normal neuron, if such inputs fired in bursts and if the bursts in different inputs came to overlap in time, would be sufficient to produce a depolarizing wave as large as the 'paroxysmal depolarizing shifts' observed in penicillin foci 3, thus causing a burst response via the rhythmic firing mode 16. The central pain diseases (trigeminal neuralgia, anesthesia dolorosa, phantom limb pain, etc.) often act as if they were a seizure in a sensory pathway; indeed, some respond to anticonvulsant drugs. They are often associated with sensory loss, which will produce partial deafferentation of second-order neurons. There are reports that human neurons in affected regions exhibit the high-frequency firing patterns associated with deafferented regions in experimental animals 1,65. To what extent has an alteration in synaptic input enhanced the drive to the rhythmic firing mode, e.g., classical denervation supersensitivity? To what extent is the extra spike mode also stimulated by such diseases? The regenerative cycle described here is not self-starting; a spike elicited by one of the other modes is first required to set off the regenerative cycle. A characteristic of many of the central pain diseases, reminiscent of 'reflex epilepsies '87, is the

18 'trigger area', a region of skin where a stimulus will set off the intense sensation (which may be referred to a different region of the body). Anesthetizing a peripheral nerve will sometimes give temporary relief in central pain states, perhaps because these trigger impulses are blocked. However, when the nerve block wears off, the pain may come back worse than ever. Cutting non-cranial nerves or dorsal roots sometimes exhibits the same temporary relief and subsequent aggravation of the pain 64. One is reminded of automatic gain control circuits, which turn up the gain during a prolonged silence. Judging from the widespread reports of delayed depolarizations in CNS neurons the extra spike mode could be a latent property of many CNS neurons. Anoxia or drugs might acutely stimulate the extra spike mode; on a chronic basis, deafferentation or disuse could also serve as stimuli. This mode magnifies a normal response (many extra spikes following one normal spike); if disuse is indeed an augmenter of the extra spike mode, such an automatic gain control in the repetitive firing mechanisms would have many implications 13 paralleling, but distinct from the classical denervation supersensitivity of postsynaptic receptor sites66, 76 and the fibrillation mechanisms of muscle vS.

Are spikes really necessary? Finally, it should be noted that this review has talked about the cell's output as being mediated by spike trains. For output synapses which are electrically distant from the input sites (and electrical loss with 'distance' depends upon both cable properties and the axonal bifurcation patterns9,36), spikes are surely required to transmit a signal. However, transmitter can also be released by graded depolarizations of an output synapse: the rate of miniature PSPs can be graded with presynaptic terminal depolarization36,vL In a sense, this is perhaps repetitive firing without spikes. an elimination of the middleman where presynaptic depolarization is converted to release rate which is converted into postsynaptic depolarization via temporal summation (Fig. 2). Certainly in the case of dendrodendritic synapses sg, where output sites are next door to input sites, one must consider whether the spike train tells the whole story about the input-output properties of the cell or whether subthreshold depolarizing waves also release transmitter from those output sites which are electrically close. ACKNOWLEDGEMENTS

I wish to thank Dr. Katherine Graubard and numerous other colleagues for their thoughtful suggestions regarding this review; Susan Johnston and Jerrold Maddocks for their technical assistance; and Karen Abelsen and Carla Wood for their assistance with the preparation of the manuscript. Some unpublished data, obtained in collaboration with Dr. George W. Sypert, is included in Fig. 7D. Supported by Research Grants NS 09677 and NS 04053 from the National Institutes of Health,

19 REFERENCES 1 ANDERSON, L. S., BLACK, R. G., ABRAHAM,J., AND WARD, A. A., JR., Neuronal hyperactivity in experimental trigeminal deafferentation, J. Neurosurg., 35 (1971) 444-452. 2 ASANUMA,H., AND ROSI~N,I., Spread of mono- and polysynaptic connections within cat's motor cortex, Exp. Brain Res., 16 (1973) 507-520. 3 AYALA,G. F., DICHTER, M., GUMNIT, R. J., MATSUMOTO,H., AND SPENCER, W. A., Genesis of epileptic interictal spikes. New knowledge of cortical feedback systems suggests a neurophysiological explanation of brief paroxysms, Brain Research, 52 (1973) 1-17. 4 BAKER,R., AND PRECHT, W., Electrophysiological properties of trochlear motoneurons as revealed by 1Vth nerve stimulation, Exp. Brain Res., 14 (1972) 127-157. 5 BALDISSERA,F., AND GUSTAFSSON,B., Supraspinal control of the discharge evoked by constant current in the alpha-motoneurones, Brain Research, 25 (1971) 642-644. 6 BALDISSERA,F., AND GUSTAFSSON,B., Afterhyperpolarization conductance time course in lumbar motoneurones of the cat, Acta physiol, scand., 91 (1974) 512-527. 7 BARMACK,N. H., Saccadic discharges evoked by intracellular stimulation of extraocular motoneurons, J. Neurophysiol., 37 (1974) 395412. 8 BARRETT,J. N,, AND CRILL, W. E., Specific membrane properties of cat motoneurones, J. Physio 1. (Lond.), 239 (1974) 301-324. 9 BARRETT, J. N., AND CRILL, W. E., Influence of dendritic location and membrane properties on the effectiveness of synapses on cat motoneurones, J. Physiol. (Lond.), 239 (1974) 325-345. 10 BROWN, P. B., MORAEE,H., AND TAPPER, D. N., Functional organization of the cat's dorsal horn: spontaneous activity and central cell response to single impulses in single type I fibers, J. Neurophysiol., 36 (1973) 827-839. 11 BURKE, R.E., AND NELSON, P, G., Accommodation to current ramps in motoneurons of fast and slow twitch motor units, bzt. J. Neurosci., 1 (1971) 347-356. 12 CALVIN, W. H., Synaptic potential summation and repetitive firing mechanisms: input output theory for the recruitment of neurons into epileptic bursting firing patterns, Brain Research, 39 (1972) 71-94. 13 CALVIN, W. H., Three modes of repetitive firing and the role of threshold time course between spikes, Brain Research, 69 (1974) 341-346. 14 CALVIN, W. H., AND LOESER, J. D., Stereotyped doublet and burst firing patterns in neurons of normal lateral cuneate nucleus: evidence for a normal substrate for epileptic burst responses?, Electroenceph. clin. Neurophysiol., (1974), Abstract, in press. 15 CALVIN,W. H., OJEMANN,G. A., AND WARD, A. A., JR., Human cortical neurons in epileptogenic foci: comparison of interictal firing patterns to those of ~epileptic' neurons in animals, Electroenceph, clin. Neurophysiol., 34 (1973) 337-351. 16 CALVIN,W. H., ANO SCHW~NDT,P. C., Steps in production of motoneuron spikes during rhythmic firing, J. Neurophysiol., 35 (1972) 297-310. 17 CALVIN, W. H., AND STEVENS, C. F., Synaptic noise and other sources of randomness in motoneuron interspike intervals, J. Neurophysiol., 31 (1968) 574-587. 18 CALVIN, W. H., AND SYPERT, G. W., Cerebral cortex neurons with extra spikes: a normal substrate for epileptic discharges? Brabz Research, 83 (1974) 498-503. 19 CALVIN, W. H., SYPERT, G. W., AND WARD, A. A., JR., Structured timing patterns within bursts from epileptic neurons in undrugged monkey cortex, Exp. Neurol., 21 (1968) 535-549. 20 CONNOR, J. A , AND STEVENS,C. F., Prediction of repetitive firing behaviour from voltage clamp data on an isolated neurone soma, J. Physiol. (Lond.), 213 (1971) 31-53. 21 CREUTZFELDT,O. D., Lux, H. D., AND WATANABE, S., Electrophysiology of cortical nerve cells. In D. P. PURPURA AND M. D. YAHR (Eds.), The Thalamus, Columbia University Press, New York, 1966, pp. 209-235. 22 DALEY, M. L., AND BARMACK, N. H., The current-frequency conversion of extraocular motoneurons, Kybernetik, 15 (1974) 3945. 23 DENSLOW,J. S., Double discharges in human motor units, J. Neurophysiol., 11 (1948) 209-215. 24 ECCLES, J. C., The Physiology of Nerve Cells, The Johns Hopkins Press, Baltimore, Md., 1957. 25 ECCLES,J. C., AND HOEF, H. E., The rhythmic discharge of motoneurones, Pro& roy. Soc. B, 110 (1932) 483-514. 26 EIDE, E., FEDINA,L., JANSEN,J., LUNDBERG,A., AND VYKLICKY,L., Properties of Clarke's column neurones, Acta physiol, scand., 77 (1969) 125-144.

20 27 EIDE, E., FEDINA, L., JANSEN,J., LUNDBERG,A., AND VYKLICKY,L., Unitary components in the activation of Clarke's column neurones, Acta physiol, scand., 77 (1969) 145-158. 28 EYZAGUIRRE,C., AND KUFELER,S. W., Further study of soma, dendrite, and axon excitation in single neurons, J. gen. Physiol., 39 (1955) 121-153. 29 FISCHBACH, G . D . , AND DICHTER, M.A., Electrophysiologic and morphologic properties of neurons in dissociated chick spinal cord cell cultures, Develop. Biol., 37 (1974) 100-116. 30 FUORTES,M. G. F., FRANK, K., ANDBECKER,M. C., Steps in the production ofmotoneuron spikes, J. gen. Physiol., 40 (1957) 735-752. 31 GALINDO,A., KRNJEVIC,K., AND SCHWARTZ,S., Patterns of firing in cuneate neurones and some effects of Flaxedil, Exp. Brain Res., 5 (1968) 87-101. 32 GRAMPP, W., The impulse activity in different parts of the slowly adapting stretch receptor neuron of the lobster, Actaphysiol. scand., 66 Suppl. 262 (1966) 3-36. 33 GRANIT, R., Mechanisms Regulating the Discharge of Motoneurons, The Sherrington Lectures XI, Thomas, Springfield, Ill., 1972, 78 pp. 34 GRANIT, R., KERNELL, D., AND LAMARRE, Y., Algebraical summation in synaptic activation of motoneurones firing within the 'primary range' to injected currents, J. Physiol. (Lond.), 187 (1966) 379-399. 35 GRANIT, R., KERNELL, D., AND SMITH, R. S., Delayed depolarization and the repetitive response to intracellular stimulation of mammalian motoneurones, J. Physiol. (Lond.), 168 (1963) 890-910. 36 GRAUBARD,K., Morphological and Electrotonic Properties of Identified Neurons of the Mollusc, Aplysia californiea, P h . D . Thesis, University of Washington, 1973. 37 GUSTAFSSON,B., LINDSTROM, S., AND TA~ZATA,M., Repetitive firing in dorsal spinocerebellar tract neurones, Brain Research, 47 (1972) 506-509. 38 HOFE, H. E., AND GRANT, R. S., The supernormal period in the recovery cycle of motoneurons, J. Neurophysiol., 7 (1944) 305-322. 39 KANDEL, E.R., AND SPENCER, W.A., Electrophysiology of hippocampal neurons. II. Afterpotentials and repetitive firing, J. Neurophysiol., 24 (1961) 243-259. 40 KERNELL, D., The delayed depolarization in cat and rat motoneurones. In J. C. ECCLES AND J. P. SCHADI~(Eds.), Physiology of Spinal Neurons, Progr. Brain Res., Vol. 12, Elsevier, Amsterdam, 1964, pp. 42-55. 41 KERNELL,D., The adaptation and the relation between discharge frequency and current strength of cat lumbosacral motoneurones stimulated by long-lasting injected currents, Aeta physiol. seand., 65 (1965) 65-73. 42 KERNELL, D., High-frequency repetitive firing of cat lumbosacral motoneurones stimulated by long-lasting injected currents, Aeta physiol, seand., 65 (1965) 74-86. 43 KERNnLL,D., The limits of firing frequency in cat lumbosacral motoneurones possessing different time course of afterhyperpolarization, Aeta physiol, scand., 65 (1965) 87-100. 44 KERNELL, D., Input resistance, electrical excitability and size of ventral horn cells in cat spinal cord, Science, 152 (1966) 1637-1639. 45 KERNELL, D., The repetitive impulse discharge of a simple neurone model compared to that of spinal motoneurones, Brain Research, 11 (1968) 685-687. 46 KERNELL, D., Synaptic conductance changes and the repetitive impulse discharge of spinal motoneurones, Brain Research, 15 (1969) 291-294. 47 KERNELL, D., Effects of synapses of dendrites and soma on the repetitive impulse firing of a compartmental neuron model, Brain Research, 35 (1971) 551-555. 48 KERNELL,D., The early phase of adaptation in repetitive impulse discharges of cat spinal motoneurones, Brain Research, 41 (1972) 184-186. 49 KERNELL,D., AND SJOHOL~, H., Repetitive impulse firing: comparisons between neurone models based on 'voltage clamp equations' and spinal motoneurons, Actaphysiol. seand., 87 (1973) 40-56. 50 KJERULF, T . D . , AND LOESER, J . D . , Neuronal hyperactivity following deafferentation of the lateral cuneate nucleus, Exp. Neurol., 39 (1973) 70 85. 51 KJERULF,T. D., O'NEAL, J. T., CALVIN,W. H., LOESER,J. D., AND WESTRUM,L. E., Deafferentation effects in lateral cuneate nucleus of the cat: correlation of structural alterations with firing pattern changes, Exp. Neurol., 39 (1973) 86-102. 52 KLEE, M. R., Different effects of the membrane potential of motor cortex units after thalamic and reticular stimulation. In D. P. PURPURA AND M. D. YAHR (Eds.), Tile Thalamus, Columbia University Press, New York, N.Y., 1966, pp. 287-322. 53 KOIKE, H., MAYO, N., OKADA, Y., AND OSRIMA, T., Repetitive impulses generated in fast and

21 slow pyramidal tract cells by intracellularly applied current steps, Exp. Brain Res., 11 (1970) 263-281. 54 KOIKE, H., OKADA, Y., ANO OSHIMA, T., Accommodative properties of fast and slow pyramidal tract cells and their modification by different levels of their membrane potential, Exp. Brain Res., 5 (1968) 189-201. 55 KOIKE, H., OKADA, Y., OSHIMA,T., AND TAKAHASHI,K., Accommodative behavior of cat pyramidal tract cells investigated with intracellular injection of currents, Exp. Brain Res,, 5 (1968) 173-188. 55a KUDINA, L. P., Double discharges of human motoneurons, Neurofiziologiya, 6 0974) 152-160. 56 KuNo, M., Quantal components of excitatory synaptic potentials in spinal motoneurones, J. Physiol. (Lond.), 175 (1964) 81-99. 57 KuNo, M., Mechanism of facilitation and depression of the excitatory synaptic potential in spinal motoneurones, J. Physiol. (Lond.), 175 (1964) 100-112. 58 KuNO, M., Quantum aspects of central and ganglionic synaptic transmission in vertebrates, Physiol, Rev., 51 (1971) 647-678. 59 KUNO, M., AND LLIN~S, R., Enhancement of synaptic transmission by dendritic potentials in chromatolysed motoneurones of the cat, J. Physiol. (Lond.), 210 (1970) 807-821. 60 KuNo, M., AND M[YAHARA, J.T., Factors responsible for multiple discharge of neurons in Clarke's column, J. Neurophysiol., 31 (1968) 625-638. 61 KUNO, M., MfJNoz-MARTINEZ, E.J., AND RAND~C, M., Synaptic action on Clarke's column neurones in relation to afferent terminal size, J. Physiol. (Lond.), 228 (1973) 343-360. 62 KUNO, M., ANO WEAKLY, J.N., Facilitation of monosynaptic excitatory synaptic potentials in spinal motoneurones evoked by internuncial impulses, J. Physiol. (Lond.), 224 (1972) 271-286. 63 KtJNo, M., AND WEAKLY,J. N., Quantal components of the inhibitory synaptic potential in spinal motoneurones of the cat, J. Physiol. (Lond.), 224 (1972) 287-303. 64 LOESER, J . D . , Dorsal rhizotomy: indications and results. In J. J. BONICA (Ed.), International Symposium On Pain, Advances in Neurology, 1,'ol. 4, Raven Press, New York, N.Y., 1974, pp.

615-619. 65 LOESER,J. D., WARD, A. A., JR., AND WHITE, L. E., Chronic dcafferentation of human spinal cord neurons, J. Neurosurg., 29 (1968) 48-50. 66 Lt~MO,T., AND ROSENTHAL,J., Control of ACh sensitivity by muscle activity in the rat, J. Physiol. (Lond.), 221 (1972) 493-513. 67 MAGLEBY,K. L., The effect of repetitive stimulation on facilitation of transmitter release at the frog neuromuscular junction, J. Physiol. (Lond.), 234 (1973) 327-352. 68 MARTIN,A. R., A further study of the statistical composition of the end-plate potential, J, Physiol. (Lond.), 130 (1955) 114-122. 69 MAURITZ, K, H., SCHLUE, W. R., RICHTER, D. W., AND NACIMIENTO.A. C., Membrane conductance course during spike intervals and repetitive firing in cat spinal motoneurons, Brain Research, 76 (1974) 223-233. 70 MENDELL,L. M., AND HENNEMAN,E., Terminals of single 1A fibers: location, density, and distribution within a pool of 300 homonymous motoneurons, J. Neurophysiol., 34 0971) 171-187. 71 NELSON, P.G., AND BURKE, R.E., Delayed depolarization in cat spinal motoneurons, Exp. Neurol., 17 (1967) 16-26. 72 NIECr~AJ, A., AND VAN HARREVELD,A., Effect of asphyxia on the delayed depolarization in cat spinal motoneurons, Brain Research, 7 (1968) 463-464. 73 O'NEAL, J. T., AND WESTRUM, L. E., The fine structural synaptic organization of the cat lateral cuneate nucleus. A study of sequential alterations in degeneration, Brain Research, 51 (1973)97-124. 74 PORTER, R., AND MUIR, R. B., The meaning for motoneurones of the temporal pattern of natural activity in pyramidal tract neurones of conscious monkeys, Brain Research, 34 (1971) 127-142. 75 PURVES,D., AND SAKMANN,B., Membrane properties underlying spontaneous activity of denervated muscle fibres, J. Physiol. (Lond.), 239 (1974) 125-153. 76 PURVES,D., AND SAKMANN,B., The effect of contractile activity on fibrillation and extrajunctional acetylcholine-sensitivity in rat muscle maintained in organ culture, J. Physiol. (Lond.), 237 (1974) 157-182. 77 QUASTEL, D. M. J., Excitation-secretion coupling at the mammalian neuromuscular junction. In M. V. L. BENNETT (Ed.), Synaptic Transmission and Neuronal Interaction, Society of General Physiologists Series, Iiol. 28, Raven Press, New York, N.Y., 1974, pp. 23-43. 78 RACK, P. M. H., AND WESTI3URY,D. R., The effects of length and stimulus rate on tension in the isometric cat soleus muscle, J. Physiol. (Lond.), 204 (1969) 443-460.

22 79 RICHTER, D . W . , SCHLUE, W.R., MAURITZ, K. H., AND NACIMIENTO, A.C., Comparison of membrane properties of the cell body and the initial part of the axon of phasic motoneurones in the spinal cord of the cat, Exp. Brahz Res., 21 (1974) 193-206. 80 SCHLUE, W. R., RICHTER, D . W . , MAURITZ, K. H., AND NACIMIENTO,A. C., Responses of cat spinal motoneuron somata and axons to linearly rising currents, J. Neurophysiol., 37 (1974) 303309. 81 SCHLUE,W. R., RICHTER, D. W., MAURITZ,K. H., NACIMIENTO,A. C., Mechanisms of accommodation to linearly rising currents in cat spinal motoneurons, J. Neurophysiol., 37 (1974) 310-315. 82 SCHLUE, W. R., RICHTER, O.W., MAURITZ, K . H . , AND NACIMIENTO, A. C., Accommodation of cat spinal motoneurones to linearly rising currents before and during long-term changes of membrane potential, Brain Research, 76 (1974) 213-221. 83 SCHWI~DT, P. C., Membrane potential trajectories underlying motoneuron rhythmic firing at high rates, J. NeurophysioL, 36 (1973) 434-449. 84 SCrtWINDT, P. C., AND CALVIN, W. H., Membrane-potential trajectories between spikes underlying motoneuron firing rates, J. Neurophysiol., 35 (1972) 311-325. 85 SCHWlNDT,P. C., AND CALVIN,W. H,, Equivalence of synaptic and injected current in determining the membrane potential trajectory during motoneuron rhythmic firing, Brain Research, 59 (1973) 389-394. 86 SCIaWINDT,P. C., AND CALVIN,W. H., Nature of conductances underlying rhythmic firing in cat spinal motoneurons, J. Neurophysiol., 36 (1973) 955-973. 87 SERVlT, F. (Ed.), Reflex Mechanisms in the Genesis of Epilepsy, Elsevier, Amsterdam, 1963. 88 SHAPOVALOV,A. I., AND GRANTYN, A. A., Activity of chromatolysed motor neurones on direct stimulation and transmembrane polarization, Biofizika, 11 (1966) 684-693. 89 SHEPHERD,G. M., The Synaptic Organization of the Braht, Oxford Univ. Press, New York, N.Y,, 1974. 90 SINDERMANN,F., CONRAD, B., JACOBI, H. M., AND PROCHAZKA,V. J., Unusual properties of repetitive fasciculations, Electroenceph. clin. Neurophysiol., 35 (1973) 173-179. 91 TAKAHASHI,K., Slow and fast groups of pyramidal tract cells and their respective membrane properties, J. Neurophysiol., 28 (1965) 908-924. 92 TERZUOLO,C. A., LLIN~,S, R., AND THOMASGREEN, K., Mechanisms of supraspinal actions upon spinal cord activities, Arch. ital. Biol., 103 (1965) 635-651. 93 WEAKLY,J. N., Effect of barbiturates on 'quantal' synaptic transmission in spinal motoneurones, J. Physiol. (Lond.), 204 (1969) 63-77. 94 WILSON,V. J., AND TALBOT,W. H., Pattern of discharge of flexor motoneurons, J. Neurophysiol., 27 (1964) 451-463. 95 WYLER, A. R., Epileptic neurons during sleep and wakefulness, Exp. Neurol., 42 (1974) 593-608. 96 WYLER, A. R., AND FETZ, E. E., Behavioral control of firing patterns of normal and abnormal neurons in chronic epileptic cortex, Exp. Neurol., 42 (1974) 448-464. 97 WYLER, A . R . , FETZ, E.E., AND WARD, A . A . , JR., Spontaneous firing patterns of epileptic neurons in the monkey motor cortex, Exp. Neurol., 40 (1973) 567-585. 98 WYLER, A. R., EETZ, E. E., AND WARD, A. A., JR., Injury-induced long-first-interval bursts in cortical neurons, Exp. Neurol., 41 (1973) 773-776. 9) WYLER, A. R., FETZ, E. E., AND WARD, A. A., JR., Antidromic and orthodromic activation of epileptic neurons in neocortex of awake monkey, Exp. Neurol., 43 (1974) 59-74.