Calvin, W. H. (1980). Normal repetitive firing and its pathophysiology. In: J. Lockard and A. A. Ward, Jr (eds) Epilepsy: A Window to Brain Mechanisms. Raven Press. New York. 97-121.
Copyright 1980 by author and publisher

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William H. Calvin "Normal repetitive firing and its pathophysiology" In: Epilepsy: A Window to Brain Mechanisms (J. Lockard and A. A. Ward, Jr., eds.), Raven Press, New York, pp. 97-121 (1980). Copyright ©1980 by author and publisher.

Normal Repetitive Firing and Its Pathophysiology

William H. Calvin

Department of Neurological Surgery, University of Washington, Seattle, Washington 98195

A neuron communicates over long distances (more than a few millimeters) by generating a train of impulses which propagates down the axon to release a series of prepackaged quanta of neurotransmitter molecules. The rate, or perhaps the patterning, of the impulse train carries the information. One of the hallmarks of an interictal epileptogenic focus is that many of its neurons are observed to cluster their impulses into bursts, with the intervals between impulses being unusually short (several milliseconds). Is the bursting neuron some sort of pacemaker, driving other normal neurons into synchronous activity and thus spreading the trouble? Or is the bursting one observes just one of those recruited neurons, having nothing more wrong with it than an oversized synaptic input? Or perhaps there are no pacemaker neurons; the trouble could be subtly distributed over many neurons, changing the balance of excitation and inhibition so that the whole circuit tends to go into a bursting-type oscillation.

There are many other ways of stating the "epileptic neuron" versus "epileptic aggregate" dichotomy. As presented above, the argument bears a strong resemblance to an argument that has occurred in the more general field of pattern generation: How are actions with alternating activity and silence, such as walking or breathing, generated by groups of neurons?

While there could simply be pacemaker bursting neurons, there could also be a steady level of excitatory drive onto two neurons (or groups of neurons) which mutually inhibit each other (33). When A is firing, it inhibits B into silence. If one allows for inhibition which fatigues (antifacilitation, depression), soon the declining inhibition from A will allow B to begin firing, which will then inhibit A into silence, and so on, back and forth. Hartline (33) has reviewed the emerging data on a number of pattern-generating circuits. Even when there are mutually inhibitory synaptic connections which aid reciprocal bursting, the neurons themselves often have intrinsic bursting properties too. In other words, there are redundant means of enforcing bursting; it is not a matter of cell or circuit bursting but of both cell and circuit. While it would be more convenient for neurophysiologists if nature would use only one bursting mechanism at a time, it would appear that if something is worth doing, it may be done using redundant mechanisms.

In this chapter, the individual neuron is examined for its ability to exaggerate its normal output by overproducing impulses. This emphasis on overproduction at the various stages of computation and data transmission within the individual neuron is not to deny that underproduction (e.g., in inhibitory neurons) could also be important. As in considering the origins of forest fires, one can either emphasize who started the forest fire or consider the factors enhancing the flammability of the forest. Tracing through one of the trees, i.e., the dendritic and axonalarborization of a neuron, is useful for evaluating flammability prospects even if no one neuron is a pacemaker.

THE PROCESSING PATH THROUGH A NEURON

Some neurons are much simpler than the neurons that we examine here. There are spikeless neurons, such as those in the retina, where tonic transmitter release rates are controlled by the size of a graded depolarization. Such neurons are short enough so that electrotonic current spread suffices for communication between the postsynaptic regions, collecting information from upstream neurons, and the presynaptic regions that output the processed result (30,31). Thus the spikeless processing path is particularly simple.

Repetitive firing is the mechanism that allows the postsynaptic and presynaptic regions of the neuron to be separated by more than a few millimeters; transmitter release rate is now controlled by impulse production rate. Firing rates are in turn controlled by synaptic depolarizations, as seen by the spike trigger zone (usually at the initial segment of the axon). Thus impulse trains can be seen as an intermediate coding form, allowing transmitter release rate to remain proportional to the sum of synaptic depolarizing and hyperpolarizing currents. A more detailed comparison of spikeless and spiking modes of operation can be found in Calvin and Graubard (13).

For our purposes, we trace this processing path (Fig. 1), starting with impulse production by the initial segment's interaction with the somadendritic region, following the impulse down the axon through sites where the impulse might be blocked (or additional impulses created), to the transmitter release properties of the axon terminals, and then on to the dendrites of the next neuron to see what processes provide attenuation and augmentation of the synaptic currents driving the impulse production processes of that neuron. At each site, we examine the features capable of overproduction, particularly those relevant to epileptic bursting.

FIG. 1. The processing path from the spike initiation region of one neuron to that of the next neuron in a chain. Repetitive firing mechanisms produce depolarization-to-rate and adaptation features. Extra spikes (as in the double spike in the top record) may occur from reexcitation of the spike initiation region. Spikes may be created or destroyed in midaxon. Synaptic transmission may be sensitive to the history of the spike train; bursts may produce increased transmitter release both during the burst (facilitation) and afterwards (potentiation). Dendritic integration features both temporal summation, giving a conversion of rate back into depolarization levels, and spatial summation with its determination of the E/l ratio and net depolarization. Special combinations of inputs may elicit local dendritic spikes in some neurons.

Depolarization-to-Rate Conversion: Normal Rhythmic Firing from the Trigger Zone

The primary barrier to understanding the input-output conversion produced by the repetitive firing mechanism is the confusion over the nature of the input. Traditional teaching emphasizes the quanta!, exponentially falling shape of the unit synaptic event. It is not often recognized that the unit postsynaptic potential (PSP), from a single impulse in a single presynaptic neuron, is usually very small (a fraction of a millivolt, and thus no more than a few percent of the excursion between rest and the impulse threshold). The common view, where an impulse is initiated by several PSPs standing on the shoulder of one another, is thus misleading. The asynchronous pitter-patter of PSPs bombarding the neuron (think of the motoneuron during a static stretch reflex) does, however, build up a steady depolarization (7,9) analogous to the generator potential of a sensory receptor neuron (see Fig. 5). Experimentally, one usually mimics this steady synaptic depolarization by injecting a step of current through the recording micropipette in the soma of the cell. A family of such steps results in a plot of current versus firing rate (the f-I curve), as in Fig. 2.

FIG. 2. Rhythmic firing in a cat spinal motoneuron, responding to steps of injected current (lower traces) injected through the recording Microelectrode into the neuron's soma, results in this depolarization-to-rate relationship (often called the f-I curv e). Light upper line connects the points representing the initial firing rate (reciprocal of the interval between the first and second spikes of the train). Heavy lower line is the plot of the average firing rate following adaptation. At A, two responses are superimposed; a rheobasic current gives only one spike, but a slightly larger current gives a repetitive response with an interspike interval equal to the duration of the afterhyperpolarization (90 msec) in this neuron. (Reprinted with permission from Federation Proceedings, ref. 10.)

Essentially, there is a dead zone where subthreshold currents produce no response. Rheobasic current usually produces only one impulse, even when the current is maintained; however, increasing the current a little more will usually result in sustained repetitive firing for the duration of the current. The firing rate in this situation is called the minimum rhythmic firing rate: it is usually related to the reciprocal of the duration of the afterhyperpolarization following a single impulse (37). Thus a neuron with a 90-msec afterhyperpolarization will usually jump from O to l l impulses/sec as the current is increased slowly. Further increases in current level raise the firing rate, with a proportionality constant called the sensitivity of the repetitive firing process. This sensitivity is higher for a brief period after a sudden step in the current and then adapts severalfold (Fig. 2).

In many neurons, the depolarization-to-rate curve rises quite linearly; i.e., the sensitivity stays constant. For some cat spinal motoneurons, the curve has two distinct segments (37), with the sensitivity suddenly increasing severalfold at about 30/see; phenomenologically, this change can appear quite suddenly (54,55), although the underlying mechanisms are hardly discontinuous (56). Of particular interest are potassium conductances in the soma (and probably the dendrites) of a type not envisaged in Hodgkin-Huxley descriptions of axons; there are potassium conductances activated by calcium entry (2) and those that inactivate with depolarization (21). The latter property is especially important in generating very long interspike intervals (on the order of seconds) with little jitter (22).

Rhythmic firing does not require these specialized ionic mechanisms; even squid axon will fire rhythmically, although the dynamic range of its f-I curve may be small (58). The trigger zone at the axon initial segment may, by itself, have such axon-like repetitive firing properties. However, the impulse retrogradely invades the somadendritic region at the same time that the newly minted impulse is propagating down the axon. This retrograde invasion activates the specialized currents of the somadendritic region that, in turn, subtract from the synaptic currents and determine the time taken to reach the threshold and initiate the next impulse. It has been hypothesized that the extent of retrograde invasion is important (9,17,62). Certainly, it is likely that fairly extensive retrograde invasion of the dendritic tree occurs in chromatolytic motoneurons (34) because of the excitability evidenced by their orthograde dendritic spikes; their f-I curves lack the sensitivity alterations of normal spinal motoneurons.

Extra Spikes From Normal Trigger Zones: Another Sensitivity-Changing Mechanism

Some motoneurons, while firing a spike with great regularity every 100 msec, may occasionally produce an extra spike only a few milliseconds after a prior spike (Fig. 1, top), despite holding the synaptic and injected current inputs to the motoneuron constant. Lowering the current slightly may cause extra spikes to occur more often, perhaps after almost every rhythmic spike, so that the firing is mostly in doublets. Raising the current sufficiently will eliminate the extra spikes and restore pure rhythmic firing at the appropriate firing rate for that current. Is the doublet a junior-sized version of an epileptic burst? Are there automatic sensitivity controls, augmenting extra spikes if the neuron receives little input? Such questions have led to a comparative survey of repetitive firing and extra spikes in cat spinal motoneurons (8,11,17), in neurons of cat external cuneate nucleus and human dorsal column nuclei (15), in primary vestibular neurons of cat (52), in cat pyramidal tract neurons (PTNs) (18,19), and in crustacean stretch receptor neurons (14,25,29).

Extra spikes are thought to occur by reexcitation near the end of the refractory period of the prior impulse. This requires a source of depolarizing current at the same time as the threshold drops; usually the refractory period lasts until the membrane potential has returned to rest; i.e., there are various wavefronts propagating down the axon, one after the other. The refractory period wavefront never catches up with the impulse waveform. Extra spikes are thought to represent an exception to this rule; it is not a matter of the refractory period wavefront speeding up, but rather of the impulse waveform lasting longer so that its falling phase lags behind.

Perhaps the clearest demonstrations of reexcitation are the theoretical studies on flaring-diameter axons (28) and the experimental investigations of lobster stretch receptor neurons using multiple recording sites (14). In the Goldstein and Rall (28) study, a uniform axon was presumed to change its diameter, flaring 2 to 3 diameters into a larger axon with the same membrane properties. If there was too much flare, conduction from small-to-large axon would fail. Lesser amounts of flare caused the impulse to broaden in duration severalfold at the junction, as the impulse of the small axon was capacitively loaded by the increased surface area of the larger axon. Under these circumstances, one may observe a new impulse propagating backwards from the junction: the long duration of the impulse at the junction reexcited the small axon after its refractory period. Thus, while the original impulse continues forwards, an extra impulse is "reflected" backwards.

Impulses initiated at the initial segment of the axon, or antidromically propagating up the axon, retrogradely invade the somadendritic region. Sometimes this invasion is slowed, as evidenced by a distinct notch developing on the rising phase of the intrasomatic spike (the IS-SD break becomes more prominent). With another recording electrode downstream on the axon, as Calvin and Hartline (14) used with lobster stretch receptors, one may see an extra spike (Fig. 3); evidently, the slowed invasion of the somadendritic region has allowed depolarization there to persist long enough to reexcite the axon at the end of the axon's refractory period. The extra spike cannot itself invade the soma retrogradely as the soma is refractory; thus, for this particular situation, a self-perpetuating cycle cannot start.

There are other reexcitation phenomena not as readily explained by a simple two-compartment interaction. In the typical case, extra spikes are seen to arise from the top of a depolarizing afterpotential, which follows the prior spike. The extra spike may or may not itself retrogradely invade the somadendritic region; if it does, it too may have a depolarizing afterpotential. In some cases, this extra spike's aftermath may trigger still another extra spike. Such bursts of extra spikes have been intracellularly observed in cat spinal motoneurons (8), cat PTNs (18,19), and in various crustacean stretch receptor neurons (25,29); many of the burst discharges of hippocampal pyramidal neurons (59) probably qualify, although their depolarizing afterpotentials are more complex.

The postspike hump, the most prominent form of the depolarizing afterpotential, is probably of dendritic origin. The theory of reexcitation is merely a threecompartment version of the previous story (14). As the impulse propagates retrogradely from the initial segment trigger zone, it should slow down as it invades the dendritic tree. Intradendritic recordings, (e.g., ref. 29), indeed show a delayed beginning of the dendritic impulse and a broader duration (both aspects could arise just from the cable properties of the dendritic tree, even if the spread were passive rather than active). As the axon and soma repolarize, the dendritic spike may lag behind. This source of depolarizing current is important. As the resistance of the soma and axon rise after their spikes, the depolarizing current from the dendrites may cause an increasing I R product, even if the current itself is not rising. This theory for the postspike hump (9,45) contains the necessary ingredients for a self-reexciting process; an extra spike can trigger such a sequence as well as the first spike. This spatial aspect of the depolarizing afterpotential is not its only aspect. The ionic mechanisms may change from axon to soma to dendrite. One reason that the spike of the dendrite has a longer duration may be a slow calcium current (68).

Cat PTNs are much richer in extra spike phenomena than motoneurons, probably because most fast-conducting (> 20 m/see) PTNs have prominent postspike humps (19). More than 25~o of the fast PTNs in the Calvin and Sypert (19) intracellular series also exhibited extra spikes during sustained rhythmic firing driven by a step of injected current (Fig. 4). The extra spikes arose from the top of the postspike hump (as observed from the Microelectrode site, which was probably intrasomatic).

Historical Factors Affecting Extra Spikes

It was noted that motoneurons tend to produce extra spikes only at low rhythmic firing rates; this was also true of primary vestibular neurons (52) and of external cuneate nucleus neurons (15). Many lobster stretch receptor neurons fall into this category; their f-I curves may have a negative sensitivity region where average firing rate falls as current ascends above the extra spiking region. Other lobster stretch receptor neurons, namely those with delayed retrograde invasion (Fig. 3), tend to produce extra spikes only at high firing rates, but this may be secondary to the fatigue aspect in these neurons.

PTNs produce extra spikes from postspike humps only at intermediate and higher rhythmic firing rates, but there is no suggestion of fatigue. Why they differ from most other neurons in this aspect is unknown. The effect of extra spikes on the f-I curve is not always simple. Sometimes, double spike firing patterns may double the sensitivity of the f-I curve; in other cases, the interval between rhythmic spikes is lengthened by an extra spike that produces a compensatory pause. In some cases, f-I curves may appear perfectly compensated as the firing pattern progresses from rhythmic to doublets to triplet bursts with no change in f-I curve sensitivity. PTNs with pronounced bursting tendencies may exhibit extra spikes atop large postspike humps even at minimum rhythmic firing rates.

Many neurons exhibit a tendency to produce shorter interspike intervals at the beginning of a spike train; this adaptation in firing rate seems to have a number of mechanisms in different neurons (see list in ref. 13). About 50% of fast PTNs in the Calvin and Sypert series exhibited a very short interspike interval of the extra spike variety after the first evoked spike, such that extra spikes serve to augment the initial response to a sustained input. Even more interesting is the tendency of other PTNs (11,19) and some motoneurons (8,9,17) to increase the size of the postspike hump with successive spikes of the rhythmic response; thus an extra spike may first occur after the second rhythmic spike of the train. Does the first spike serve to "prime" the postspike hump mechanism so that the second rhythmic spike evokes it?

In a limited series of cells, a single spike (evoked by a very brief pulse of injected current) was located at various times prior to a standard-sized current step evoking a repetitive response. In these cells, the unconditioned response was a spike train with clustered extra spikes following the second rhythmic spike. The conditioning spike shortened the interval between first and second rhythmic spikes; at any conditioning interval shorter than several hundred milliseconds, extra spikes would cluster after the first rhythmic spike rather than the second (11). This conditioning effect, much longer than the duration of the afterhyperpolarization in fast PTNs, suggests that the extra spike mechanism(s) may be primed by antecedent activity.

FIG. 3. Reexcitation of the axon's spike trigger zone results in extra spikes (seen only at the axon recording electrode downstream; lower traces). Slowly increasing current was injected through a double-barreled microelectrode into the soma of this lobster stretch receptor neuron. With moderate heating, the retrograde invasion of the somadendritic region is more susceptible to fatigue, slowing the invasion from the axon trigger zone (note IS-SD notch developing in spike rising phase in some recordings). When the soma spike lasts longer than the axon's refractory period, the axon is reexcited. [From the Calvin and Hartline study (14), reprinted with permission from Federation Proceedings (10).]

Extra Spikes in Pathophysiology: Augmentation of a Normal Mechanism?

The priming phenomenon noted above produces firing patterns with a cluster of extra spikes after the second spike of the response; the first interspike interval varies with the current strength in the usual way, but the following interspike intervals are short and relatively fixed in the extra spike manner. This long first interval (LFI) or stereotyped afterburst pattern was first noted in chronic monkey epileptogenic foci (20) and again in human epileptic neurons (16), suggesting that some epileptic bursts may be clusters of extra spikes.

The short interspike intervals of epileptic bursts are indeed analogous to the typical 2-msec interspike intervals of normal extra spike firing. The priming phenomenon also has analogous features, helping fulfill the original hopes expressed (20) that the structured nature of the LFI burst would place a considerable number of constraints on possible explanations. One interpretation of LFI epileptic bursts would thus be that a moderate-sized synaptic wave sets it off, the first interspike interval being that predicted from the f-l curve, and the afterburst being the extra spikes that tend to appear after the second rhythmic spike. The main problem with this interpretation is that monkey LFI bursts are seen following antidromic stimulation as well (see Wyler and Ward, this volume), something that the cat PTNs did not exhibit. This, together with some unusual properties of the LFI itself (20), keeps the question open as to the origins of the epileptic LFI burst.

Assuming extra spike involvement, the high firing rates in epileptic neurons could be produced by relatively low levels of synaptic input. The high sensitivity of extra spike repetitive firing suggests an alternative concept to the "pacemaker" epileptic neuron. Pacemaker suggests autogenic firing, requiring no synaptic input, but high sensitivity merely says that a small input could give a large output.

FIG. 4. Extra spikes in a cat fast PTN arise from postspike humps, not delayed axon-tosoma invasion, as in Fig. 3. The large postspike humps characteristic of fast PTNs are seen in the bottom trace, evoked by a near-rheobasic current; note that the second spike's hump is much larger than that after the first spike. At intermediate current levels, an extra spike arises from the second spike's hump (middle traces); similar extra spikes are seen intermittently for as long as the current step is maintained. At even higher currents, extra spikes are often seen; indeed, the sensitivity of the f-l curve doubles in this case. Calibration bars: 20 mV 10 nA, 20 msec. [From the Calvin and Sypert (19) study. (Modified from ref. 11; copyright 1976, Raven press).]

As was noted earlier, the sensitivity of the ordinary rhythmic firing process may be controlled by the extent of retrograde invasion, i.e., by the excitability of the dendritic tree. Extra spike production also seems likely to involve dendritic excitability, although the duration of the dendritic spikes and the time course of threshold recovery (8) are other important factors.

One of the major short-term ways of altering the reexcitation phenomena has been anoxia. Niechaj and Van Harreveld (46) found that the motoneurons had increased postspike humps and occasionally extra spikes within minutes after clamping the circulation. There are a variety of drugs affecting crustacean stretch receptor reexcitation-type firing (65).

On a longer time scale, deafferentation is thought to affect reexcitation-type firing. In the cat external cuneate nucleus, neurons can be partially deafferented by extensive dorsal rhizotomies or by dorsal column sections (38). These neurons normally exhibit extra spike firing patterns with stereotyped interspike intervals of 0.8 to 2.0 msec (15). This spontaneous activity is largely secondary to an extensive tonic bombardment from forelimb proprioceptors. When deafferented, the spontaneous activity disappears (38). Within a few days, spontaneous activity returns, although it is no longer driven by forelimb receptors. The 80% of the synapses that are large and contain round vesicles disappear; the 20% that are small, containing flattened vesicles, remain. The extra spike-type short stereotyped interspike intervals are again prominent; in some cases, the burst contains a dozen spikes. The bursts thus have a stereotyped appearance rather like epileptic bursts, except that they never exhibit LFIs. This deafferentation experiment, like others in the dorsal column nuclei (44) and elsewhere, suggests changes in the repetitive firing properties: bursts are seen, despite presumably small (and perhaps inhibitory) synaptic inputs.

Before considering abnormal sites of repetitive spike initiation, one must ask: are extra spikes initiated at the usual trigger zone (e.g., the axon's initial segment) or elsewhere (e.g., perhaps starting in the dendrites and propagating down through the soma to the axon)? So far, studies of trigger zone localization during extra spiking have been limited to crustacean stretch receptor neurons. Extra spikes are initiated in the general vicinity of the normal trigger zone (14,25,29).

For most central nervous system (CNS) neurons, localization studies have been more difficult. Generally, one can say that the trigger zone is downstream from the soma; but one cannot be specific about whether it is at the initial segment, first node, and so on. Yet one can still ask whether the sequence of retrograde invasion of the somadendritic region is the same for normal spikes and for extra spikes. Differentiation of the spike waveforms of fast PTNs shows at least three distinct components; all are the same in normal spikes and in extra spikes (11). This makes it unlikely that the extra spike is beginning in the dendrites and sweeping through the soma, opposite to the sequence of the normal retrogradely invading spikes.

Do Axons Conserve Spikes? The Creation and Destruction of Impulses at Midaxon

It is tempting to think of the axon as a rather uninteresting but reliable conduit for getting impulses from the trigger zone to the presynaptic regions in the axon terminals. In reality, spikes sometimes get lost along the way (48); occasionally, impulses are initiated ectopically, as in neuralgias.

The creation of impulses at midaxon, or at other ectopic sites, is a major problem in neuralgias. Normal dorsal root ganglion (DRG) is, unlike normal dorsal roots or peripheral nerves, tonically mechanosensitive (36). In root or nerve, only quick distortions of an axon are capable of initiating spikes; slower distortions may eventually block conduction without ever having initiated an impulse (36). Yet DRG will initiate spikes tonically for many minutes after laying a light weight atop the exposed DRG; this would appear to provide a physiological basis for the radicular pains of herniated intervertebral discs. Focally injured roots and nerves also develop mechanosensitivity after some days of irritation by chronic suture material; this may play an important role in scarred nerves (such as when radicular pain to leg lifting persists after a decompression).

There appear to be two ectopic impulse initiation processes at work. Reexcitation can occur at the focally demyelinated regions as well as at normal DRG (35). Second, a tonic repetitive firing mechanism develops, capable of producing sustained spike trains whenever tonic depolarizations are present. While one ordinarily thinks of mechanosensitive generator potentials, there may also be chemosensitivity (64). The afterdischarge seen following a priming train of impulses conducted through a focally demyelinated region (35) is suggestive of a generator potential too, perhaps secondary to extracellular potassium accumulation. What is different in the cases exhibiting tonic ectopic spiking (normal DRG, demyelinated axons)?

It is interesting to consider this problem from the standpoint of specializations of the axon for reliable conduction (12). Neural structures have a problem analogous to the impedance matching problem in transmission lines. The active nodes must drive the capacitive and resistive load presented by the yet-silent nodes downstream. When that load changes, as when approaching an axon bifurcation or the unmyelinated terminal area, the requirements on the driving nodes may be substantially increased. One finds nodes more closely spaced in a number of such situations (12). Focal demyelination presents the midaxon with a large capacitive load, and simulations (66) suggest that conduction may often fail unless compensatory steps are taken. Those presumed compensatory steps may have, as a byproduct, effects on impulse initiation (as opposed to replication) by the injured region. Could too much source conductance (too high a sodium channel density, too little potassium conductance or leakage) make impulse origination easier, as well as facilitating impulse conduction in the face of a capacitive load? This is the thesis advanced elsewhere (12); central to it is the presumption that axons specialize not only for conduction but also to avoid initiation, by positioning their source conductance in a middle ground.

From other studies of abnormal repetitive firing, several ionic mechanisms can be mentioned. Lower extracellular cation concentrations may initiate tonic firing (47), perhaps via shifting the activation curve of the sodium conductance (27). Another important factor is the leakage current; the lack of chloride currents in muscle (attributable to either lowered external C1-or to congenitally reduced C1-conductances in myotonic goats) may also convert a faithful follower cell into a cell with afterdischarge (1). In some situations, one may be dealing with sprouting nerves; the sprouts are thought to be mechanosensitive, as is regenerating nerve more generally.

Ectopic Initiation in Epileptic Foci

One of our early postulates to help explain the LFI epileptic burst was that the first spike was initiated ectopically in the axon (20). Subsequent evidence has suggested more promising explanations for the structured bursts, but there is good evidence also for impulses initiated in axon terminals ending within an epileptic focus. Gutnick and Prince (32) showed backfiring from the axon terminals of thalamocortical projection neurons in a penicillin focus, and there has been much subsequent investigation along this line (57). This suggests that antidromic impulses could also help spread the bursting activity via axon reflex from a focus to other nondisrupted areas.

Another exception to the initiation-resistant midaxon property would appear to be axon terminals. Normal axon terminals sometimes initiate impulses, as in the dorsal root reflex (61). For axons in the epileptic focus, the issue becomes one of the strength of the initiating currents (e.g., those associated with the extracellular fields of the EEG spike), the excitability of the axon terminals for single spike initiation (as in the accommodation problem), and the repetitive firing capability of the terminals.

Transmitter Release: Are Bursts Especially Effective?

When impulses are separated by long times, e.g., > 40 msec, the second impulse of a pair may produce a smaller excitatory PSP (EPSP) than the first. For closer spacings, it may be larger. In the la pathway to cat spinal motoneurons (24), the second one may be 15% larger than the first at optimal separations.

There are, however, other synapses with more impressive facilitation properties. The corticospinal pathway onto cervical motoneurons (49) may exhibit substantial facilitation, with the second PSP doubling or tripling in size at optimal spacings; this is also true for the corticorubral pathway (63). The optimal spacing is several milliseconds, much the same interval that extra spikes prefer. This suggests that an epileptic burst might be a rather imperative stimulus to some downstream synapses. There are longer-term effects of bursting stimuli. The best studied is the long-term posttetanic potentiation in hippocampus, where the pathway may remain potentiated for hours, days, and so on.

Another example of the sensitivity of a postsynaptic cell to patterning of the spike train occurs in mammalian muscle. In single motor units of cat gastrocnemius, for example, just one short interspike interval in an otherwise rhythmic train may double the plateau tension produced by the train for seconds thereafter (6).

Spatial and Temporal Summation in Dendrites

Denervation supersensitivity has been one model for hyperexcitable neurons. There is some evidence in various chronic CNS diseases for increased levels of receptors for certain neurotransmitters (3). The ionic channels associated with extrajunctional acetylcholine (ACh) supersensitivity in muscle are also different from junctional channels (53), and one must consider the possibility that chronic epileptogenic foci pathology will include such altered features of the synaptic mechanism.

FIG. 5. Temporal summation of simulated PSPsfor an irregularly firing input (top /efl) and an input with an epileptic bursting firing pattern (top Center) Clustering of spikes into bursts results in peak depolarizations about three times as high as a single PSP. Spatial summation of many asynchronous inputs (bottom left and center) is little different for epileptic bursting inputs than for normal irregular inputs; only when the various bursting inputs are roughly synchronized (bottom rigby is a large depolarizing wave produced. Simulated on a cable model with current injected (hence linear summation) using the methods of Calvin (7) and tape-recorded firing patterns from one normal and two epileptic neurons (20).

An epileptic burst is effective in producing temporal summation of PSPs in the postsynaptic neuron. Figure 5 (top) contrasts the temporal summation expected from an irregular spike train from a normal cortical neuron with that expected from an epileptic bursting neuron. The mean depolarization caused by a single input, assuming small unit PSP sizes so that the driving potential correction may be omitted, is simply the product of the average firing rate and the area beneath the unit PSP (9). The highest peaks of the membrane potential will correspond to the shortest interspike intervals; since the mean depolarization level is attained in the time that it takes a unit PSP to decay (7), epileptic bursts are easily long enough to cause depolarizations which correspond to 500/sec average firing rates. If one averages over a longer time than one burst, e.g., the whole sweep in Fig. 5, the mean depolarization also refers to that rate averaged over that time.

Spatial summation of many irregular inputs (Fig. 5, lower left) gives a mean depolarization which, assuming linear summation, is just the sum of the individual inputs' rate area products. When bursting inputs are not synchronized (Fig. 5, center), the spatial summation gives a sustained noisy depolarization, as in the irregular spatial summation case. When bursting inputs are roughly synchronized (Fig. 5, right), the peaks become much higher, being predictable from the rate area products of the individual inputs using the rates within the bursts. Nonlinear summation effects (facilitation, driving potential decreases) will increase or reduce the net depolarization predicted by the linear summation; however, the point still remains that bursting in inputs producing small PSPs may not be significant until the bursting neurons are synchronized.

The effectiveness of a synaptic input depends not only on the synaptic mechaniss but on its location relative to spike trigger zones or presynaptic regions in the dendrites. This aspect is often quantified by the voltage attenuation between sites in the somadendritic region; but this alone can be misleading. Moving a synaptic input from the proximal to the distal dendrites of a model neuron may cause only minor (10%) changes in the area beneath the EPSP 'recorded' in the soma. The many-fold voltage attenuation between distal dendrites and soma is largely compensated by the increase in the local size of the EPSP when situated on the high input resistance of distal dendritic structures (31). While synaptic loci may not be especially important, in this model, for the initiation of spikes at the initial segment trigger zone, synaptic loci may be important when the relevant variable is the voltage generated within the dendritic tree itself. A presynaptic region in the dendritic tree, as in dendrodendritic synapses, may be more strongly influenced by the local synaptic inputs than by those located more proximally or on another dendrite (31). While dendrodendritic synapses are not common in cerebral cortex, their occurrence in abnormal cortex remains to be determined.

Dendritic Spikes

Large intradendritic voltage may also trigger dendritic spikes. By this term one does not usually imply a propagating spike that travels down through the soma and continues past the normal trigger zone; as noted earlier, dendritic "hot spots" usually provide a booster mechanism for regional synaptic potentials which results in a sharp transient of several millivolts at the soma and initial segment. Whether or not an axon spike is initiated depends on the overall integration of many inputs, as in ordinary synaptic potential summation.

The best examples of orthograde dendritic spikes are from Purkinje cells (41) and from chromatolytic spinal motoneurons where even one impulse in a single afferent fiber may set off a dendritic spike (40). There is evidence that dendritic spikes have substantial calcium components (but see ref. 51), suggesting longer duration in dendrites than soma. This has implications for transmitter release (13) from presynaptic dendrites, for reexcitation possibilities, and for controlling afterhyperpolarization magnitudes via calcium-activated potassium conductances (2). In addition, calcium spikes in dendrites could have a direct effect on transmitter release from presynaptic dendrites, e.g., by local increases in intracellular calcium concentration, as well as by the indirect effect via membrane potential.

Besides their presynaptic effects, bursting firing patterns in the synaptic inputs could have postsynaptic effects too; e.g., Fifkova and Van Harreveld (26) show dendritic spines that swell following tetanic stimulation, although it is not yet known whether this is firing pattern-sensitive or a mass action effect. If there are dendritic spikes, then input bursts might produce enough temporal summation in the finer dendrites to cross threshold for the booster spike phenomena.

EPILEPTIC FOCI: CELL MALFUNCTION OR CIRCUIT PROBLEM?

By tracing through the mechanisms in the axonaland dendritic arborizations of an individual neuron, the trees in the forest have been examined for their flammability prospects. In this section, the circuit aspects are stressed. This takes two forms: the recruitment problem and the unstable circuit problem.

Recruitment by Bursting Neurons

A bursting firing pattern in only one input to a normal neuron should have minimal effects; many such inputs, if they were not synchronized, might produce only a steady background depolarization (Fig. 5). A group of endogenously bursting neurons, if synchronized so that their bursts overlap (not necessarily synchronized spike-for-spike), may recruit other normal neurons to burst along with them by providing a large depolarizing wave of synaptic input which briefly reaches a high level on the f-I curve of that neuron. Given typical values for unit PSP sizes, shapes, and neuron f-I curves, it was calculated that fewer than 1% of the input of a neuron would be required to burst synchronously to evoke a burst response (7). The other inputs could affect the outcome by biasing the synaptic current up or down. The result merely says that turning on such a burst pattern in 1% of the thousands of synaptic inputs could be sufficient to cause bursting. With augmentation from facilitation or dendritic spikes, the number required would decrease; with concomitant inhibitory bursts, more inputs would be required.

Excitatory/Inhibitory Ratios

Converting the numbers of cytologically characterized synaptic endings (e.g., round versus flattened vesicle types) into percentages of types on an individual neuron has been done for the cat spinal motoneuron (39) using Conradi's (23) electron microscope data. Adopting, for illustrative convenience, the round-flat interpretation as excitatory-inhibitory (E/I), one can say that about half of the synaptic endings on the motoneuron are excitatory (the E/I ratios are 40:60 on the soma, grading distally to 60:40 at the dendritic tips). Abnormal development can give rise to considerable alterations in such ratios; for example, Lund and Lund (42) showed that a normal 61:39 ratio changed to 26:74 in the superior colliculus after enucleation at birth. Thus the relative amounts of excitatory and inhibitory synaptic potentials might change with time. Ribak et al. (50) have shown that there is a decrease in GABAergic terminals in monkey epileptic foci. Examples of decreased inhibition exist in other chronic CNS diseases, e.g., the loss of dopaminergic terminals in the striatum in Parkinson's disease (69).

One conclusion is that there may be cases where the flammability cannot be assessed by examining individual trees but only by describing their admixture and specific connectivity. The tendency of a neural circuit to go into oscillation can be described in some simple cases. In clones, the control systems aspects of the fusimotor bias on the stretch reflex can be elucidated, and there are thalamocortical circuits that may exhibit similar oscillatory tendencies. The central questions are likely to be: What determines relative strengths of inputs? Is there an automatic gain control at a synaptic level (e.g., feedback from postto pre-) or at a circuit level (e.g., turning up the level of inhibition to produce synchronizing influences)?

FROM ANTECEDENTS TO ICTAL EVENTS

There are few theories for how a neuron changes its properties to become an epileptic neuron; similarly, there is no comprehensive theory for how an interictal focus evolves to initiate a seizure. In this concluding section, examples are given for both levels of theory. The purpose of this exercise is to demonstrate the need for such theories and what ground they should be expected to cover, not to offer serious answers.

The "Sprouting" Theory

Denervation supersensitivity stands as one of the few fundamental theories for the origin of neuronal hyperactivity in an epileptic focus. Its virtue lies not in its congruence with experimental facts but rather in its attempt to relate the Pathophysiology back to a more fundamental process presumably involved with cellular development and regulation.

While the depopulation of epileptic foci and loss of dendritic spines (67) suggests denervation, depopulation might also give rise to collateral sprouting. This may seem a paradoxical proposal, since the most obvious feature of a focus is the truncated, weathered-looking dendritic tree. Such shapes are also prominent in aged brains; yet careful measurements of terminal apical dendritic branches in aged brain show sprouting (5), presumably collateral sprouting in response to the loss or shrinkage of neighboring neurons.

If sprouting should occur in epileptic foci, what might its physiological consequences be? While there are currently no data on alterations in the physiology of collaterally sprouting neurons, there is information on both regenerating neurons and those undergoing normal developmental stages. In normal development in various cell lines, originally inexcitable neurons first acquire a calcium (Ca) spike, then a mixed sodium-calcium (Na-Ca) spike, and then most parts of the neuron make the final transition to a sodium-only (Na) spike (60). Dendrites (see Schwartzkroin, this volume) and axon terminals may retain mixed Na-Ca spikes. In the regeneration of a severed axon, Meiri et al. (43) show that the cut end first seals; then, perhaps 12 hr later, the Na spike gains a Ca component near the terminal end. This is transient, becoming undetectable with microelectrodes in the main axon after 60 hr; by then the terminal end is bulging out, and obvious sprouting can be seen in later days. Bray and Bunge (4) postulate a role of calcium entry in elongating the growth cone.

This suggestion that collaterally sprouting neurons might have enhanced Ca spikes in their dendritic trees leads one to ask what effect this might have on bursting. The most obvious difference between Na spikes and Ca spikes is their duration, with mixed Na-Ca spikes being intermediate in duration between the fast Na spikes and the slower Ca spikes. Thus the retrograde invasion of the dendritic tree following spike initiation in the initial segment of the axon might be prolonged. Because of the enhanced dendritic excitability that might occur with additional Ca channels, the retrograde dendritic spike might be both longer and larger than in normal neurons (see schematic spikes in Fig. 6).

It is the duration of this retrograde dendritic spike, seen at the soma or initial segment, that creates the postspike hump that intersects the falling threshold and gives rise to extra spikes. Thus an ordinary event initiating a spike might set off a regenerative sequence of many extra spikes.

This theory for how bursting neurons arise begins with cell loss (secondary to anoxia, aging, etc.), postulates collateral sprouting of adjacent dendrites, augmented calcium spikes in those dendrites, an increased duration of retrograde dendritic spikes as a consequence, allowing the initiation of a single spike to give rise to a regenerative burst. Since seizures give rise to continuing degeneration in a focus (see Harris, this volume), the process might be expected to continue in other neurons even if each neuron only went through a brief phase (as in the regenerating axons) of sprouting and augmented Ca spikes.

While its congruence with the experimental facts may not be any more extensive at present than the original denervation supersensitivity theory, the sprouting theory better illustrates the need to specify each of the steps between a more fundamental cellular principle and the end product of the Pathophysiology, in this case the interictal bursting neurons. If the end product is a seizure, the subject is more complicated (circuits of neurons, extracellular ion changes, and so on), but a similar sequence can be proposed to help organize the facts.

The "Epileptic Sequence" Theory

An interictal epileptic focus is sometimes thought of as a localized seizure; considerations of extracellular potassium and calcium alterations arise along with possibilities of spreading depression, depletion of inhibitory transmitter stores, and so forth. Yet the foregoing examination of cell and circuit aspects of bursting suggests that collections of bursting neurons could exist without the more elaborate environmental aspects of seizures; i.e., the focus need not be a "little seizure." Certainly, the areas around a focus, which are recruited into a seizure, undergo a different evolution than the focus itself. In a sense, it is like the distinction between impulse initiation and impulse propagation; although both are impulses, the antecedent of the trigger zone impulse is a summed synaptic potential, while the antecedent of the midaxon impulse is simply another nearby impulse.

FIG. 6. Impulse initiation typically occurs at the beginning of the axon; spikes propagate both forward (filled arrows) and backward (open arrows) into the soma and dendrites. One explanation for the postspike hump seen intrasomatically is that the dendritic spike is of longer duration. Ca spikes seen in dendrites might be augmented during collateral sprouting in response to loss of neighboring neurons, resulting in a larger and longer dendritic spike upon retrograde invasion. This could cause repeated firing of the axon trigger zone in the pattern characteristic of epileptic bursts.

One can propose an epileptic sequence, a set of stages through which a particular patch of cortex evolves before and during a seizure. The items listed below are intentionally simplistic, as the intent here is merely to illustrate the concept of an epileptic sequence rather than to propose a particular one:

( -7) Antecedent causes (anoxia? aging? toxicity?)

( -6) Fundamental cellular mechanism responses (denervation supersensitivity? disuse responses? sprouting?)

( -5) Dendritic excitability changes (augmented Ca spikes?) and prolonged retrograde invasion.

( -4) Reexcitation bursting triggered by normal synaptic inputs.

( -3) A progressive synchronization of previously asynchronous bursting neurons, due to synaptic mechanisms (sleep spindles or recurrent inhibition) or field effects, leading to

( -2) Large synaptic depolarizations in normal neurons, whose depolarizationto-rate mechanism responds with a burst. Enough synchronized neurons could now give rise to a surface BEG spike.

( -1) A decline in the afterinhibition following EEG spikes, perhaps due to inhibitory transmitter depletion or potentiated excitation (E/I ratio increases); increases in extracellular potassium; such declines in repolarization mechanisms could lead to a

(O) Sustained depolarization of many neurons (seizure tonic phase), followed by

(+1) Interactions between pumping mechanisms and synaptic mechanisms to produce the instability of the clonic phase of the seizure.

(+2) Rundown of ionic gradients, depletion of transmitter stores, and their reestablishment during postictal depression.

In the case of an afterdischarge seizure evoked by stimulating contralateral cortex, the local epileptic sequence might start at level--2; if the seizure were spreading from the cortex next door, it might enter the local sequence through both synaptic bombardment and diffusion of extracellular potassium, for example. Drug-induced seizures might start the sequence by reducing inhibition (level --1). Although it would be convenient for experimenters, it is unlikely that the epileptic sequence actually works through a set of mechanisms seriatum; parallel actions and interactions back and forth between levels are more likely.

Whether the paths will turn out to funnel through certain essential levels, e.g., requiring increases in physiological E/I ratios before a seizure can start, remains to be seen. Candidates for the more chronic aspects of epileptogenic cortex are placed nearer the top of the list; yet one could also have a change in E/I ratios occur chronically (on the model of Parkinson's disease), which might bypass earlier levels and have its primary effect at--1. Whether epilepsy is primarily a disorder of a cellular mechanism or of a circuit is still unanswered; given the diversity of the epilepsies, the answer is likely to be both. Unless there turns out to be an essential level in the epileptic sequence which can be disabled by a specific treatment, the understanding and control of epilepsy will depend on the elucidation of how the neuron controls its sensitivity all along the processing path.

ACKNOWLEDGMENTS

Susan M. Johnston provided much assistance. This work was supported by the National Institutes of Health research grants NS 04053 and NS 09677.

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