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Do neurons process information by relative intervals in spike trains?
Neuroscience &BhJbehavioralReviews,Vol. 6, pp. 429--437, 1982. Printed in the U.S.A.
Do Neurons Process Information by Relative Intervals in Spike Trains? W. R. K L E M M * A N D C. J. S H E R R Y Department of Veterinary Anatomy* and Department of Biology Texas A & M University, College Station, TX 77843 R e c e i v e d 5 M a r c h 1982 KLEMM, W. R. AND C. J. SHERRY. Do neurons process htJbrmation by relative intervalsin spike trains? NEUROSCI. BIOBEHAV. REV. 6(4) 429-437, 1982.--We suggest the possibility that neurons process information in terms of the relative duration of clusters of adjacent and successive inter-action potential intervals ("bytes" of intervals). If this concept is plausible, as is supported by research from several laboratories which have specifically addressed this posibility, one should be able to see evidence for such patterning in the published illustrations from studies in which this concept was not considered. We present some of this evidence here, along with some illustrations from the original publications. Byte patterns are evident in these examples, even though they often went unrecognized by authors and readers alike. It is true that interval patterns are not obvious in all published illustrations of spike trains, and we suggest that this can be explained by one or more of the following: (I) some neurons may operate with an interval-pattern code while others do not, (2) a given neuron may use an interval-pattern code only under certain conditions, and (3) even when such a code exists, it may be difficult to detect for identifiable technical reasons. Therefore, we believe that the relative-interval-pattern concept is a valid scientific hypothesis which merits specific testing of its validity and range of applicability. Unit activity
Information processing
Spike train intervals
T H E relative interval coding concept of Sherry and Marczynski [13, 22-23] holds that the relative duration of successive inter-action potential intervals is a means by which "information" can be conveyed in the nervous system. The methodology originated with Sherry's format for calculating transition probabilties for successive intervals, and the methodology has been shown to have very precise descriptive and quantitative value [1, 10, !1,14, 24-28]. The methodology is based on the following steps: (1) measurement and sequential storage of interval durations in computer memory, (2) comparison of each interval in terms of being < , =, or > than its immediately succeeding interval, (3) conversion of the relative relations to corresponding symbols of - , 0, or +, and (4) tally of the sequence of symbols in a matrix, counting in the simplest case, for example, the number of times a given symbol is followed by another ( - by a - , - by a 0, etc.); for the third-order (trigram) matrix the computer counts, for example, how many times a given pair of symbols is followed by another ( - - by a - , - - by a 0, etc.). F o r all possible patterns (9 digrams, 27 trigrams, 81 tetragrams, etc.) the incidence probabilities are calculated by dividing by N (=the number of digrams, trigrams, etc.). To determine if the distribution of such patterns differs from independence, several assumptions must be made. For example, Sherry and Marczynski [22] calculated the theoretical probabilities for the 9 digram patterns, but found that such computations were unwieldy for higher-order patterns. Therefore, they sought the help of Von Foerster and colleagues who proposed that eliminating the 0 case (equal intervals) might circumvent the problem. They suggested that the distribution of + and - patterns was independent of the probability density function [1,19].
C o p y r i g h t © 1982 A N K H 0
However, the incidence of 0-case relations depends on the resolution, which is chosen arbitrarily. Even with a 0.1 msec resolution, some 0 relations still occur, but are not considered by some workers [1] because the incidence is so low. We continue to consider the 0 case and are evaluating the choice of resolution because no empirical data exists to establish the range of interval durations that are considered by the nervous system to be equivalent; theoretical probabilities for symbol sets are determined on the basis of incidence in a shuffled version of the absolute intervals in the spike train being evaluated [31]. A related issue is the choice of a rounding scheme for measured intervals; we round up to the nearest 1 msec, because that is a common procedure for computations in conventional interval histograms and autocorrelation analysis. It is quite possible that more or less resolution is appropriate, but to our knowledge there is no published data that deals with single neuron discharges and addresses this issue. Another theoretical problem is that each interval is used twice in determining relative relationships (it is compared with its predecessor and its immediate successor). Thus, a built-in dependency exists which makes conventional Markovian analysis only approximate. We have, however, performed unbiased Markov analysis on spike intervals which have been classified as " l o n g , " " m e d i u m , " or " s h o r t . " depending on which third of the nonsequential interval histogram includes each given interval; such analysis revealed that true Markovian dependencies exist in the serial ordering, involving as many 5 adjacent intervals [31]. In the case of classical information theory, which we have applied to relative interval patterns [11], this underlying dependency poses much less of a problem, because the
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FIG. 1. EPSP responses in an Aplysia ganglion cell in response to pattern of input spike intervals. Note that even though over-all rate of input stimulation (vertical marks superimposed on EPSPs) remains the same, the EPSPs are larger and exceed the arbitrary threshold (horizontal line) when input spikes are paired ( + - + - . . . ) rather than being equally spaced (000...). From Segundo et al. [20], by permission.
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FIG. 2. Relative interval patterns within the bursts of spikes that are spontaneously produced in a ganglion cell of Aplysia. Note that the first 3 intervals on the left of each burst become progressively shorter, which we describe as + + +. Then there is a variable number of intervals that have approximately the same duration (000...). The last 5 intervals at the right of each burst become progressively longer, ( . . . . . ). From Strumwasser [32], by permission.
probabilities are calculated on the incidence of the symbols, and their groupings. The groupings are treated as equallength entities ("words"), without considering the component symbols, as is the case in generating Markov transition probabilities. Several studies have provided strong evidence that at least some neurons actually use such a coding scheme for information processing. For example, spike trains contain identifiable relative-interval patterns (involving at least as many as 6 adjacent intervals) whose incidence differs from chance levels and which can be altered by drugs to produce statistically significant changes in incidence [10, 11, 22-25, 28-30]. Moreover, the distribution of incidence of the various patterns has been shown to diverge from statistical independence [14, 22, 2%30]. In the hippocampal neruons of cats, statistically significant serial ordering of certain relative interval patterns has been demonstrated during specific behavioral states (quiet wakefulness and REM sleep) while absent in other states (slow-wave sleep) [ 14]. In our laboratory, the spontaneous activity of cerebellar neurons in rats was shown to contain groupings of as many as 6 adjacent intervals whose incidence statistically diverged from independence [30--31]. The absolute time for which this system seemed to have a memory of preceding events was on the order of 36-45 msecs. Also, Markovian dependencies were demonstrated when cerebellar spike-train intervals were evaluated in terms of the serial order of short-, medium-, long-duration intervals (coded as 1, 2, or 3, respectively) [31]. The dependencies involved clusters of intervals of as long as 5 intervals, and this same degree of ordering persisted even when large intravenous doses of alcohol were administered; however, the specific clusters which contributed most to the statistical significance of the serial ordering were generally not the same after alcohol [29]. One interpretation of such results is that these neurons may process
intervals as "clusters" of a given length, and specific "clusters" may be important "information carriers." In a previous review we have summarized a diverse body of literature which suggested that spike train intervals can be serially dependent [12]. We also documented the evidence that classical information theory was an appropriate theoretical context within which to evaluate relative interval coding. Finally, we suggested that the nervous system seems capable of processing spike-train intervals in clusters ("bytes") of adjacent, serially ordered intervals. Such views are not generally accepted, and the literature is dominated by the concept that spikes are randomly generated point processes, with "information" being conveyed solely by the frequency of discharge. Failure of many investigators to detect any other kind of information-carrying property may simply reflect their failure to look for it; indeed, the thesis of this review is that many of these investigators have even published illustrations of spike trains that contained relative interval patterns which often went unrecognized. Interestingly, the original demonstrations of serial ordering were made by workers who did recognize the importance of relative interval relations. The initial milestone, about 30 years ago, seems to have been the work by Wiersma and co-workers who showed that in neuromuscular junction preparations of crustacea, changes in the patterning of nerve stimulation led to remarkable changes in contractions [35]. The next major milestone seems to be the work of Segundo and others [20], who used intraceUular recordings of Aplysia ganglion cells to show that the EPSP and IPSP responses to synaptic inputs were affected by the patterning of input spike intervals, independently of input firing rates. We reproduce here one of their illustrations to show that the patterning effects which they recognized could be stated effectively in our terms of relative interval durations (our method classifies
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each given interval according to whether it is shorter than, longer than, or equal to the duration of the next interval; the relations are expressed symbolically as - , + , 0). Segundo and co-workers [20] showed that when an axon is stimulated with a burst of stimuli at the same frequency, altering the distribution of these intervals drastically alters the degree of postsynaptic response; note from their illustration of this phenomenon (Fig. I) that a stimulus which has mostly equal sized intervals ( 0 0 0 . . ) was less effective in moving the membrane potential toward threshold than was a string of successive + - intervals. In a latter study they showed a special effectiveness of inputs where the intervals were successive + s [21]. Later, in a similar test of patterning of stimuli, Wakabayashi and Kuroda I33,34] reported differential effects of interval pattern, independent of stimulus rate. For example, stimulation of motor neurons in crayfish produced much greater contraction if the stimuli were grouped in clusters of 4, 3, or 2 (in that order of effectiveness), even though the over-all frequency of stimulation was unchanged. RELATIVE INTERVAL PATTERNS IN INVERTEBRATE SPIKE TRAINS Published examples of Aplysia neuronal activity provide very compelling evidence for relative interval patterns. Ganglion cells, for example, tend to fire in bursts which not only have inter-burst interval patterns but also patterns of intervals within each burst. For example, in the recordings by Strumwasser [32] we can see that one burst pattern was a +++00000 ...... (Fig. 2), where the number of 0s may vary. Note that here and elsewhere, we use an arbitrary and approximate definition of the 0 relationship. We assume that there is a narrow range of interval durations where the spikes have, for all practical purposes, the same effect or are "recognized" postsynaptically as equivalent; the exact limits of that range can only be determined empirically. Strumwasser also showed that the patterns in one neuron are often tightly coupled to distinct interval patterns in other
neurons, and if the neurons were bilaterally symmetrical, each contained the same relative interval patterns. The interval between bursts could be artificially fractionated by an imposed hyperpolarization which reset the timing of burst onset. In a display of these effects (Fig. 3), it is seen that bursts on the left contain 3-4 successives +s, followed by 0s, followed in turn by a string of - s . The same effects were shown in another of his illustrations (his Fig. 12, not shown here) when a burst was interrupted by hyperpolarization periods of varying lengths. Also, in Aplysia ganglia, as well as in neurons of Helix, distinct and recurrent patterns in spontaneous spike trains have been published [17] (Fig. 4). Another published example was provided by Bush et al. [2]. Their muscle potential recordings, reflecting activity of underlying single motoneurons, revealed that when the joint proprioceptor in a decapod crustacean limb as stretched, a +--+ response pattern developed in extensor muscle, while a + - + pattern developed in accessory flexor muscle. These patterns were superimposed on an over-all increase in firing rate in the extensor muscle but the firing rate in the other muscle did not change. Tritonia has a group of command neurons in its brain which have a common interval pattern when these neurons initiate swimming [36]. Note in Fig. 5 how the four neurons all share a 0 - - + pattern immediately after the stimulus (arrow). Robertson [18] has acquired some interesting data on spike-train patterns in the motoneurons and interneurons which govern flight movements in locusts. While the exact patterns shown are specific to their conditions of restraint and recording, and may not be the same as occur under natural conditions, they nonetheless show a marked correlation between flight movement and relative-interval patterns in both motoneurons and interneurons (Fig. 6). RELATIVE INTERVAL PATFERNS IN VERTEBRATE SPIKE TRAINS Some fundamental studies on the role of temporal rela-
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FIG. 4. Rhythmic interval patterns as seen in intraceilular recordings in a Helix neuron (a) and in the Aplysia RI5 neuron (b). The Helix neuron has a repetitive pattern that begins with one + followed by a string of 0s, followed in turn by . . . . . The Aplysia neuron has a +, followed by a string of 0s, followed by - - - . Note the similarity of the Aplysia pattern in this study with that from the study referenced in Figs. 2 and 3. From Ristanovic and Pasic II7], by permission.
FIG. 5. Interval patterns of four command neurons in the brain of Tritonia. Immediately after a stimulus (arrow) which initiates swimming, all 4 neurons show the same pattern of 0 - - + . From Willows et al. [36], by permission.
tions in spike genesis in mammalian synapses were reported by Calvin [3]. In the mammalian CNS a single synaptic input spike usually generates a PSP that is less than 2% of the voltage change needed to reach threshold for postsynaptic spike generation (literature reviewed in [3]). Clearly, the temporal relations of input spikes, and the decay constant for the postsynaptic membrane, determine whether or not enough PSP summation occurs to reach threshold (or in the case of inhibition, to move membrane potential away from
threshold). While most workers believe that spike frequency is the determinant of this summation, it should be evident that patterning of intervals between (and among) input spikes affects the interaction of PSP development and decay which collectively govern the relative position of membrane potential and discharge threshold. In short, both frequency and interval pattern of spikes govern temporal summation. In the illustration of this point, Calvin and Sypert [4] have shown records of intracellularly obtained responses of sensorimotor cortical neurons of cats during imposed steps of depolarizing current. These neurons show steady repetitive firing patterns, and the relative interval pattern changes accordingly as magnitude of applied current is increased (Fig. 7). Another published example of relative interval patterns can be seen in the retinal ganglion cell discharges which Fitzhugh [8] recorded during stimulation of the eye with brief flashes of light. The responses to repeated 1-sec flashes consistently included a distinct - + interval pattern (his Fig. I); if zero is defined "loosely," then the pattern also has several 0s preceding the - + . Another example is found in the neurons of cutaneous mechanoreceptors in the cat. During a 10 Hz vibrational stimulus there was a pattern of 0 - - +, which changed to a string of 0s during 1200 Hz stimulation [9] (Fig. 8). Mountcastle and co-workers [15] reported rhythmic interval patterns from recordings of postcentral gyrus neurons of unanesthetized monkeys in response to 40 Hz sine-wave stimulation of the palmar surface of the hand. Even though the records are not concantenated and are presented in raster fashion, one illustration of spike train replicas shows a clear change in pattern with increasing intensity of stimulation. At low intensity there is a predominance of + - + and + - - + patterns. At intermediate frequencies a trend develops toward a predominance of + - + , and, at the largest intensity used, there is a marked presence of repeated + - + sequences (Fig. 9). Recordings from other, quickly adapting neurons revealed that one neuron had a pattern dominated by an irregu-
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lar s e q u e n c e o f + and - at low intensity, but progressively d e v e l o p e d a pattern where there were m a n y successive 0s. In another illustration (their Fig. 17), two cortical neurons which r e c e i v e d Pacinian first-order afferents showed a marked change in interval pattern as stimulus intensity increased. F o r e x a m p l e , one neuron (shown on the left of their figure) (Fig. 10) had a p r e d o m i n a n c e of + - + patterns at low stimulus intensity (2 micron depression), but at 9 microns of stimulus there w e r e many equally spaced intervals ( 0 0 0 . . . ) . The o t h e r neuron had many - + + patterns at low stimulus intensity (3 microns), but that changed to a predominance of --+ at high intensity (12 microns). A n o t h e r e x a m p l e of patterns in mammalian r e c e p t o r neurons has been reported by C r o w e and Matthews [7].
Sinusoidal stretching of cat muscle created a bursting pattern in the fusimotor fibers; note in the left portion of Fig. 1 I, the train at the top shows an initial pattern of + 0 0 0 - - each time the muscle was stretched and the bottom trace shows the same pattern e x c e p t that 1 or 2 more 0s are in the string. When the g a m m a fibers were electrically stimulated at 100 H z (during the bars in the photo), the fusimotor response changed to + + , followed by a string o f 0s, and ending in ---; the bottom trace shows a change to + + , followed by a continuous string of 0s. There are some well known mammalian i n t e r v a l p a t t e r n s which have been recognized and described, but not couched in the - + 0 terminology. F o r example, epileptic neurons in both m o n k e y and humans often fire in patterns I5]. In such
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b u r s t s , the first interval is long a n d the o t h e r 2 - 8 intervals are a p p r o x i m a t e l y of equal d u r a t i o n ; i.e., the p a t t e r n is +000 .... A n o t h e r e x a m p l e is with cells in the diagonal band of Broca, m a n y o f w h i c h fire a s t r e a m o f relatively c o n s t a n t intervals ( 0 0 0 . . . ) during alert w a k e f u l n e s s (see 1161 and its Fig. 11); this p a t t e r n b r e a k s up into a m u c h more r a n d o m a p p e a r i n g train d u r i n g s l o w - w a v e sleep. N o t e h o w this parallels the i n t e r v a l - p a t t e r n distribution c h a n g e s r e p o r t e d in the earlier m e n t i o n e d s t u d y o f h i p p o c a m p a l cells [14]. CONCLUSIONS
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While these e x a m p l e s o f interval p a t t e r n s m a y seem s o m e w h a t striking we m u s t a d m i t t h a t o b v i o u s p a t t e r n s are not p r e s e n t in all the p u b l i s h e d illustrations w h i c h we examined in the literature s e a r c h for this report. H o w t h e n do we explain the i n c o n s i s t e n c y ? T h r e e possibilities c o m e to mind, and they are not m u t u a l l y exclusive: 1. S o m e n e u r o n s m a y o p e r a t e o n a n i n t e r v a l - p a t t e r n code while o t h e r s do not. Different n e u r o n s h a v e different " i n f o r m a t i o n carrying d e m a n d s " m a d e upon t h e m . Highero r d e r n e u r o n s , w h i c h r e c e i v e a vast a r r a y of t e m p o r a l and spatial inputs, m a y be t h e m o s t likely to rely on interval coding b e c a u s e it has infinitely m o r e c a r r y i n g capacity t h a n simple firing rate, w h i c h m a y b e quite a d e q u a t e for simple r e c e p t o r s .
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2. A given neuron uses an interval pattern code only under certain conditions. The information carrying requirements could certainly be expected to vary with physiological state. Note for example that in one of our examples, relative-interval serial ordering was evident during alert states but absent during sleep. 3. Finally, even when an interval-pattern mode of operation exists, its identification may not always be self-evident. There are two basic reasons why such coding could be obscured, yet still present: (a) the definition of what constitutes equal intervals may not be precise. For a given postsynaptic output, input spike intervals may vary considerably, yet still be "regarded"
as functionally equivalent by the postsynaptic neuron. Thus spike intervals which an observor may think are + or - may in fact be 0, as far as the nervous system is concerned. To confound the problem, the nervous system may "change its definition of 0" under different physiological conditions in which various modulating influences adjust and bias the responsiveness of postsynaptic neurons. (b) The interval-pattern coding may be stochastic, as is true for most time series types of data [6]. For a stochastic time series, the future is only partly dependent on past events; that is, future values have a probability distribution which is conditioned by a knowledge of past values. In the context of interval patterns, the Markovian dependencies and the divergences from statistical independence which have been demonstrated by many workers for long spike trains would not be evident over a very short segment of data. Thus, even though such interval dependency exists, one normally would not know it without establishing the probability distribution for the various interval patterns. We would therefore conclude that the clear demonstration of such interval patterns in short data segments, as we have shown here, is very compelling evidence for intervalpattern coding, at least in certain neurons under certain conditions. This motivates us to continue our study of such possibilities in various neuronal systems, despite the fact that identifying the "'neural code" in a given system will not be easy and may often be impossible.
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REFERENCES 1. Brudno, S. and T. J. Marczynski. Temporal patterns, their distribution and redundancy in trains of spontaneous neuronal spike intervals of the feline hippocampus studied with a nonparametric technique. Brain Res. 125: 65-89, 1977. 2. Bush, B. M. H., J. P. Vedel and F. Clarac. Intersegmental reflex actions from a joint sensory organ (CB) to a muscle receptor (MCO) in decapod crustacean limbs. J. exp. Biol. 73: 47-63, 1978.
3. Calvin, W. H. Generation of spike trains in CNS neurons. Brain Res. 84: 1-22, 1975. 4. Calvin, W. H. and G. W. Sypert. Fast and slow pyramidal tract neurons; an intraceUular analysis of their contrasting repetitive properties in the cat. J. Neurophysiol. 39" 420--434, 1976. 5. Calvin, W. H., G. W. Sypert and A. A. Ward, Jr. Structured timing patterns within bursts from epileptic neurons in undrugged monkey cortex. Expl Neuro/. 21: 535-549, 1968. 6. Chatfield, C. The Analysis o f Time Series: Theory and Practice. London: Chapman and Hall, 1975. 7. Crowe, A. and P. B. C. Matthews. Further studies of static and dynamic fusimotor fibres. J. Physiol• 174: 132-151, 1964. 8. Fitzhugh, R. The statistical detection of threshold signals in the retina, J. gen. Physiol. 40: 925-948, 1957. 9. Gottschaldt, K.-M. and C. Vahle-Hinz. Merkel cell receptors: structure and transducer function. Science 214: 183--186, 1981. 10. Klemm, W. R., C. J. Sherry and J. A. Mikeska. Serial-order analysis of spike trains: ethanol effects on cerebellar neurons, with and without penicillamine. Prog. Neuropsychopharmac. 4: 137-143, 1980. 11. Klemm, W. R. and C. J. Sherry. Entropy measures of signal in the presence of noise: evidence for " b y t e " versus " b i t " processing in the nervous system. Experientia 37: 55-58, 1981a. 12. Klemm, W. R. and C. J. Sherry. Serial ordering in spike trains: what's it "'trying to tell us"?Int. J. Neurosci. 14: 15-33, 1981b. 13. Marczynski, T. J. and C. J. Sherry. A new analysis of increasing and decreasing neuronal spike intervals treated as self-adjusting sets of ratios• Brain Res. 35: 533-538, 1971. 14. Marczynski, T. J., L. L. Burns and G. T. Marczynski. Neuronal firing patterns in the feline hippocampus during sleep and wakefulness. Braht Res. 185: 139-160, 1980.
15. Mountcastle, V. B., W. H. Talbot, H. Sakata and J. Hyvarinen. Cortical neuronal mechanisms in flutter-vibration studied in unanesthetized monkeys. Neuronal periodicity and frequency discrimination. J. Neurophysiol. 32: 452--484, 1969. 16. Ranck, J. B., Jr. Behavioral correlates and firing repertoires of neurons in septal nuclei in unrestrained cats. In: The Septal Nuclei. edited by J. F. DeFrance. New York: Plenum Press, 1976, pp. 423-462. 17. Ristanovic, D. and M. Pasic. The application of an averaging method to intermittently modified and endogenously generated spike activities of neurons in mollusc ganglia, Biol. Cyhernet. 17: 65-70, 1975. 18. Robertson, R. M., K. G. Pearson and H. Reichert. Flight interneurons in the Locust and the origin of insect wings. Sciemc 217:177-179 1982. 19. Saxena, K., H. Von Foerster and D.-Wolf~-Two theorems-regarding interpike interval histograms. In: The Bioh,gical ('omputer Laboratory Report No. 722. University of Illinois at Urbana, 1971/1972, pp. 127-141• 20. Segundo, J. P., G. P. Moore, L. J. Stensaas and T. H. Bullock. Sensitivity of neurones in Aplysia to temporal pattern of arriving impulses. J. exp. Biol. 40: 643--667, 1963. 21. Segundo, J. P., D. H. Perkel and G. P. Moore. Spike probability in neurons: influence of temporal structure in the train of synaptic events. Kybernetik 3" 67-82, 1966. 22. Sherry, C. J. and T. J. Marczynski. A new analysis of neuronal interspike intervals based on inequality tests. Int. J. Neurosc'i. 3: 259-270, 1972. 23. Sherry, C. J., T. J. Marczynski and S. Brudno. A technique that discloses complex (sequential) multiphasic patterns in trains of increasing or decreasing neuronal interspike intervals• Life Sci. 11: 441--448, 1972. 24. Sherry, C. J. and W. R. Klemm. The statistical relationship between the "'entropy" of a neuronal signal and its variability. Int. J. Neurosci. l l : 109-113, 1980. 25. Sherry, C. J. and W. R. Klemm. An information coding system that seems to be independent of noise and variability. Brain Res. Bull. 5: 297-300, 1980.
I N T E R V A L P A T T E R N S IN S P I K E T R A I N S 26. Sherry, C. J. and W. R. Klemm. Entropy correlations with ethanol-induced changes in specified patterns of nerve impulses: evidence for "'byte" processing in the nervous system. Prog. Neuropsychopharmac. 4: 261-267, 1980. 27. Sherry, C. J. and W. R. Klemm. Serial-order analysis of spike trains: ethanol effects on cerebellar neurons, with and without penicillamine. Prog. Neuropsychopharmac. 4: 137-143, 1980. 28. Sherry, C. J. and W. R. Klemm. Entropy as an index of the informational state of neurons. Int. J. Neurosci. 15: 171-178, 1981. 29. Sherry, C. J. and W. R. Klemm. Failure of large doses of ethanol to eliminate Markovian serial dependencies in neuronal spike train intervals. Int. J. Neurosci.. in press, 1982. 30. Sherry, C. J. and W. R. Klemm. Divergence from statistical independence in specified clusters of adjacent spike train intervals before and after drug-induced state changes. Int. J. Neurosci., in press, 1982. 31. Sherry, C. J., D. L. Barrow and W. R. Klemm. Serial dependencies and Markov properties of neuronal interspike intervals from rat cerebellum. Brain Res. Bull. 8: 163-169. 1982.
437 32. Strumwasser, F. Types of information stored in single neurons, In: Invertebrate Nervous Systems, edited by C. A. G. Wiersma. Chicago: University of Chicago Press, 1967, pp. 291-319. 33. Wakabayashi, T. and T. Kuroda. Responses of crayfish muscle preparations to nerve stimulation with various patterns of impulse sequence. Effects of intermittent, intercalated and adaptational types of impulse sequence. Tohoku J. exp. Med. 121: 207-218, 1977. 34. Wakabayashi, T. and T. Kuroda. Effect of stimulation with impulse trains of various patterns, including adaptational type, on frog's nerve-muscle and spinal reflex preparations. Tohoku J. exp. Med. 121: 219--229, 1977. 35. Wiersma, C. A. G. and R. T. Adams. The influence of nerve impulse sequence on the contractions of different crustacean muscles. Physiol. comp. oecol. 2: 20-33, 1950. 36. Willows, A. O. D., D. A. Dorsett and G. Hoyle. The neuronal basis of behavior in Tritonia. III. Neuronal mechanisms of a fixed action pattern. J. Neurobiol. 4: 255-285, 1973.
Do Neurons Process Information by Relative Intervals in Spike Trains? W. R. K L E M M * A N D C. J. S H E R R Y Department of Veterinary Anatomy* and Department of Biology Texas A & M University, College Station, TX 77843 R e c e i v e d 5 M a r c h 1982 KLEMM, W. R. AND C. J. SHERRY. Do neurons process htJbrmation by relative intervalsin spike trains? NEUROSCI. BIOBEHAV. REV. 6(4) 429-437, 1982.--We suggest the possibility that neurons process information in terms of the relative duration of clusters of adjacent and successive inter-action potential intervals ("bytes" of intervals). If this concept is plausible, as is supported by research from several laboratories which have specifically addressed this posibility, one should be able to see evidence for such patterning in the published illustrations from studies in which this concept was not considered. We present some of this evidence here, along with some illustrations from the original publications. Byte patterns are evident in these examples, even though they often went unrecognized by authors and readers alike. It is true that interval patterns are not obvious in all published illustrations of spike trains, and we suggest that this can be explained by one or more of the following: (I) some neurons may operate with an interval-pattern code while others do not, (2) a given neuron may use an interval-pattern code only under certain conditions, and (3) even when such a code exists, it may be difficult to detect for identifiable technical reasons. Therefore, we believe that the relative-interval-pattern concept is a valid scientific hypothesis which merits specific testing of its validity and range of applicability. Unit activity
Information processing
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T H E relative interval coding concept of Sherry and Marczynski [13, 22-23] holds that the relative duration of successive inter-action potential intervals is a means by which "information" can be conveyed in the nervous system. The methodology originated with Sherry's format for calculating transition probabilties for successive intervals, and the methodology has been shown to have very precise descriptive and quantitative value [1, 10, !1,14, 24-28]. The methodology is based on the following steps: (1) measurement and sequential storage of interval durations in computer memory, (2) comparison of each interval in terms of being < , =, or > than its immediately succeeding interval, (3) conversion of the relative relations to corresponding symbols of - , 0, or +, and (4) tally of the sequence of symbols in a matrix, counting in the simplest case, for example, the number of times a given symbol is followed by another ( - by a - , - by a 0, etc.); for the third-order (trigram) matrix the computer counts, for example, how many times a given pair of symbols is followed by another ( - - by a - , - - by a 0, etc.). F o r all possible patterns (9 digrams, 27 trigrams, 81 tetragrams, etc.) the incidence probabilities are calculated by dividing by N (=the number of digrams, trigrams, etc.). To determine if the distribution of such patterns differs from independence, several assumptions must be made. For example, Sherry and Marczynski [22] calculated the theoretical probabilities for the 9 digram patterns, but found that such computations were unwieldy for higher-order patterns. Therefore, they sought the help of Von Foerster and colleagues who proposed that eliminating the 0 case (equal intervals) might circumvent the problem. They suggested that the distribution of + and - patterns was independent of the probability density function [1,19].
C o p y r i g h t © 1982 A N K H 0
However, the incidence of 0-case relations depends on the resolution, which is chosen arbitrarily. Even with a 0.1 msec resolution, some 0 relations still occur, but are not considered by some workers [1] because the incidence is so low. We continue to consider the 0 case and are evaluating the choice of resolution because no empirical data exists to establish the range of interval durations that are considered by the nervous system to be equivalent; theoretical probabilities for symbol sets are determined on the basis of incidence in a shuffled version of the absolute intervals in the spike train being evaluated [31]. A related issue is the choice of a rounding scheme for measured intervals; we round up to the nearest 1 msec, because that is a common procedure for computations in conventional interval histograms and autocorrelation analysis. It is quite possible that more or less resolution is appropriate, but to our knowledge there is no published data that deals with single neuron discharges and addresses this issue. Another theoretical problem is that each interval is used twice in determining relative relationships (it is compared with its predecessor and its immediate successor). Thus, a built-in dependency exists which makes conventional Markovian analysis only approximate. We have, however, performed unbiased Markov analysis on spike intervals which have been classified as " l o n g , " " m e d i u m , " or " s h o r t . " depending on which third of the nonsequential interval histogram includes each given interval; such analysis revealed that true Markovian dependencies exist in the serial ordering, involving as many 5 adjacent intervals [31]. In the case of classical information theory, which we have applied to relative interval patterns [11], this underlying dependency poses much less of a problem, because the
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probabilities are calculated on the incidence of the symbols, and their groupings. The groupings are treated as equallength entities ("words"), without considering the component symbols, as is the case in generating Markov transition probabilities. Several studies have provided strong evidence that at least some neurons actually use such a coding scheme for information processing. For example, spike trains contain identifiable relative-interval patterns (involving at least as many as 6 adjacent intervals) whose incidence differs from chance levels and which can be altered by drugs to produce statistically significant changes in incidence [10, 11, 22-25, 28-30]. Moreover, the distribution of incidence of the various patterns has been shown to diverge from statistical independence [14, 22, 2%30]. In the hippocampal neruons of cats, statistically significant serial ordering of certain relative interval patterns has been demonstrated during specific behavioral states (quiet wakefulness and REM sleep) while absent in other states (slow-wave sleep) [ 14]. In our laboratory, the spontaneous activity of cerebellar neurons in rats was shown to contain groupings of as many as 6 adjacent intervals whose incidence statistically diverged from independence [30--31]. The absolute time for which this system seemed to have a memory of preceding events was on the order of 36-45 msecs. Also, Markovian dependencies were demonstrated when cerebellar spike-train intervals were evaluated in terms of the serial order of short-, medium-, long-duration intervals (coded as 1, 2, or 3, respectively) [31]. The dependencies involved clusters of intervals of as long as 5 intervals, and this same degree of ordering persisted even when large intravenous doses of alcohol were administered; however, the specific clusters which contributed most to the statistical significance of the serial ordering were generally not the same after alcohol [29]. One interpretation of such results is that these neurons may process
intervals as "clusters" of a given length, and specific "clusters" may be important "information carriers." In a previous review we have summarized a diverse body of literature which suggested that spike train intervals can be serially dependent [12]. We also documented the evidence that classical information theory was an appropriate theoretical context within which to evaluate relative interval coding. Finally, we suggested that the nervous system seems capable of processing spike-train intervals in clusters ("bytes") of adjacent, serially ordered intervals. Such views are not generally accepted, and the literature is dominated by the concept that spikes are randomly generated point processes, with "information" being conveyed solely by the frequency of discharge. Failure of many investigators to detect any other kind of information-carrying property may simply reflect their failure to look for it; indeed, the thesis of this review is that many of these investigators have even published illustrations of spike trains that contained relative interval patterns which often went unrecognized. Interestingly, the original demonstrations of serial ordering were made by workers who did recognize the importance of relative interval relations. The initial milestone, about 30 years ago, seems to have been the work by Wiersma and co-workers who showed that in neuromuscular junction preparations of crustacea, changes in the patterning of nerve stimulation led to remarkable changes in contractions [35]. The next major milestone seems to be the work of Segundo and others [20], who used intraceUular recordings of Aplysia ganglion cells to show that the EPSP and IPSP responses to synaptic inputs were affected by the patterning of input spike intervals, independently of input firing rates. We reproduce here one of their illustrations to show that the patterning effects which they recognized could be stated effectively in our terms of relative interval durations (our method classifies
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each given interval according to whether it is shorter than, longer than, or equal to the duration of the next interval; the relations are expressed symbolically as - , + , 0). Segundo and co-workers [20] showed that when an axon is stimulated with a burst of stimuli at the same frequency, altering the distribution of these intervals drastically alters the degree of postsynaptic response; note from their illustration of this phenomenon (Fig. I) that a stimulus which has mostly equal sized intervals ( 0 0 0 . . ) was less effective in moving the membrane potential toward threshold than was a string of successive + - intervals. In a latter study they showed a special effectiveness of inputs where the intervals were successive + s [21]. Later, in a similar test of patterning of stimuli, Wakabayashi and Kuroda I33,34] reported differential effects of interval pattern, independent of stimulus rate. For example, stimulation of motor neurons in crayfish produced much greater contraction if the stimuli were grouped in clusters of 4, 3, or 2 (in that order of effectiveness), even though the over-all frequency of stimulation was unchanged. RELATIVE INTERVAL PATTERNS IN INVERTEBRATE SPIKE TRAINS Published examples of Aplysia neuronal activity provide very compelling evidence for relative interval patterns. Ganglion cells, for example, tend to fire in bursts which not only have inter-burst interval patterns but also patterns of intervals within each burst. For example, in the recordings by Strumwasser [32] we can see that one burst pattern was a +++00000 ...... (Fig. 2), where the number of 0s may vary. Note that here and elsewhere, we use an arbitrary and approximate definition of the 0 relationship. We assume that there is a narrow range of interval durations where the spikes have, for all practical purposes, the same effect or are "recognized" postsynaptically as equivalent; the exact limits of that range can only be determined empirically. Strumwasser also showed that the patterns in one neuron are often tightly coupled to distinct interval patterns in other
neurons, and if the neurons were bilaterally symmetrical, each contained the same relative interval patterns. The interval between bursts could be artificially fractionated by an imposed hyperpolarization which reset the timing of burst onset. In a display of these effects (Fig. 3), it is seen that bursts on the left contain 3-4 successives +s, followed by 0s, followed in turn by a string of - s . The same effects were shown in another of his illustrations (his Fig. 12, not shown here) when a burst was interrupted by hyperpolarization periods of varying lengths. Also, in Aplysia ganglia, as well as in neurons of Helix, distinct and recurrent patterns in spontaneous spike trains have been published [17] (Fig. 4). Another published example was provided by Bush et al. [2]. Their muscle potential recordings, reflecting activity of underlying single motoneurons, revealed that when the joint proprioceptor in a decapod crustacean limb as stretched, a +--+ response pattern developed in extensor muscle, while a + - + pattern developed in accessory flexor muscle. These patterns were superimposed on an over-all increase in firing rate in the extensor muscle but the firing rate in the other muscle did not change. Tritonia has a group of command neurons in its brain which have a common interval pattern when these neurons initiate swimming [36]. Note in Fig. 5 how the four neurons all share a 0 - - + pattern immediately after the stimulus (arrow). Robertson [18] has acquired some interesting data on spike-train patterns in the motoneurons and interneurons which govern flight movements in locusts. While the exact patterns shown are specific to their conditions of restraint and recording, and may not be the same as occur under natural conditions, they nonetheless show a marked correlation between flight movement and relative-interval patterns in both motoneurons and interneurons (Fig. 6). RELATIVE INTERVAL PATFERNS IN VERTEBRATE SPIKE TRAINS Some fundamental studies on the role of temporal rela-
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FIG. 5. Interval patterns of four command neurons in the brain of Tritonia. Immediately after a stimulus (arrow) which initiates swimming, all 4 neurons show the same pattern of 0 - - + . From Willows et al. [36], by permission.
tions in spike genesis in mammalian synapses were reported by Calvin [3]. In the mammalian CNS a single synaptic input spike usually generates a PSP that is less than 2% of the voltage change needed to reach threshold for postsynaptic spike generation (literature reviewed in [3]). Clearly, the temporal relations of input spikes, and the decay constant for the postsynaptic membrane, determine whether or not enough PSP summation occurs to reach threshold (or in the case of inhibition, to move membrane potential away from
threshold). While most workers believe that spike frequency is the determinant of this summation, it should be evident that patterning of intervals between (and among) input spikes affects the interaction of PSP development and decay which collectively govern the relative position of membrane potential and discharge threshold. In short, both frequency and interval pattern of spikes govern temporal summation. In the illustration of this point, Calvin and Sypert [4] have shown records of intracellularly obtained responses of sensorimotor cortical neurons of cats during imposed steps of depolarizing current. These neurons show steady repetitive firing patterns, and the relative interval pattern changes accordingly as magnitude of applied current is increased (Fig. 7). Another published example of relative interval patterns can be seen in the retinal ganglion cell discharges which Fitzhugh [8] recorded during stimulation of the eye with brief flashes of light. The responses to repeated 1-sec flashes consistently included a distinct - + interval pattern (his Fig. I); if zero is defined "loosely," then the pattern also has several 0s preceding the - + . Another example is found in the neurons of cutaneous mechanoreceptors in the cat. During a 10 Hz vibrational stimulus there was a pattern of 0 - - +, which changed to a string of 0s during 1200 Hz stimulation [9] (Fig. 8). Mountcastle and co-workers [15] reported rhythmic interval patterns from recordings of postcentral gyrus neurons of unanesthetized monkeys in response to 40 Hz sine-wave stimulation of the palmar surface of the hand. Even though the records are not concantenated and are presented in raster fashion, one illustration of spike train replicas shows a clear change in pattern with increasing intensity of stimulation. At low intensity there is a predominance of + - + and + - - + patterns. At intermediate frequencies a trend develops toward a predominance of + - + , and, at the largest intensity used, there is a marked presence of repeated + - + sequences (Fig. 9). Recordings from other, quickly adapting neurons revealed that one neuron had a pattern dominated by an irregu-
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lar s e q u e n c e o f + and - at low intensity, but progressively d e v e l o p e d a pattern where there were m a n y successive 0s. In another illustration (their Fig. 17), two cortical neurons which r e c e i v e d Pacinian first-order afferents showed a marked change in interval pattern as stimulus intensity increased. F o r e x a m p l e , one neuron (shown on the left of their figure) (Fig. 10) had a p r e d o m i n a n c e of + - + patterns at low stimulus intensity (2 micron depression), but at 9 microns of stimulus there w e r e many equally spaced intervals ( 0 0 0 . . . ) . The o t h e r neuron had many - + + patterns at low stimulus intensity (3 microns), but that changed to a predominance of --+ at high intensity (12 microns). A n o t h e r e x a m p l e of patterns in mammalian r e c e p t o r neurons has been reported by C r o w e and Matthews [7].
Sinusoidal stretching of cat muscle created a bursting pattern in the fusimotor fibers; note in the left portion of Fig. 1 I, the train at the top shows an initial pattern of + 0 0 0 - - each time the muscle was stretched and the bottom trace shows the same pattern e x c e p t that 1 or 2 more 0s are in the string. When the g a m m a fibers were electrically stimulated at 100 H z (during the bars in the photo), the fusimotor response changed to + + , followed by a string o f 0s, and ending in ---; the bottom trace shows a change to + + , followed by a continuous string of 0s. There are some well known mammalian i n t e r v a l p a t t e r n s which have been recognized and described, but not couched in the - + 0 terminology. F o r example, epileptic neurons in both m o n k e y and humans often fire in patterns I5]. In such
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FIG. 7. Relative interval patterns from cortical neurons of cats in response to applied depolarizing currents. Note how the patterns change with changes in applied current. With neuron A, 6 nA of current produces a - followed by a string of 0s. At 8 nA, there is a + - and then a string of 0s. At 9.5 there is + - - + - + - +, and then a string of 0s that contain an occasional doublet ( + - ) . At 11 nA, there is a + 0 0 - followed by a string of + - + - + - . With neuron B, 13 nA produces - - - , and then a string of 0s. At 17 nA there is + - - 0 0 followed by 0s. At 23 nA there is rapid onset of a doublet mode (+ - + - ) and at 33 nA the initial doublet mode converts to a triplet mode of + 0 - . With neuron C', 12 nA causes + - + - doublet patterns. At 13.6 nA there is alternate doublet/triplet firing. At 15 nA the triplet mode contains some quadruplet patterns ( + 0 0 - ) and at 19 nA there are quadruplet and higher-order patterns (+0000-). From Calvin and Sypert [4], by permission.
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While these e x a m p l e s o f interval p a t t e r n s m a y seem s o m e w h a t striking we m u s t a d m i t t h a t o b v i o u s p a t t e r n s are not p r e s e n t in all the p u b l i s h e d illustrations w h i c h we examined in the literature s e a r c h for this report. H o w t h e n do we explain the i n c o n s i s t e n c y ? T h r e e possibilities c o m e to mind, and they are not m u t u a l l y exclusive: 1. S o m e n e u r o n s m a y o p e r a t e o n a n i n t e r v a l - p a t t e r n code while o t h e r s do not. Different n e u r o n s h a v e different " i n f o r m a t i o n carrying d e m a n d s " m a d e upon t h e m . Highero r d e r n e u r o n s , w h i c h r e c e i v e a vast a r r a y of t e m p o r a l and spatial inputs, m a y be t h e m o s t likely to rely on interval coding b e c a u s e it has infinitely m o r e c a r r y i n g capacity t h a n simple firing rate, w h i c h m a y b e quite a d e q u a t e for simple r e c e p t o r s .
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2. A given neuron uses an interval pattern code only under certain conditions. The information carrying requirements could certainly be expected to vary with physiological state. Note for example that in one of our examples, relative-interval serial ordering was evident during alert states but absent during sleep. 3. Finally, even when an interval-pattern mode of operation exists, its identification may not always be self-evident. There are two basic reasons why such coding could be obscured, yet still present: (a) the definition of what constitutes equal intervals may not be precise. For a given postsynaptic output, input spike intervals may vary considerably, yet still be "regarded"
as functionally equivalent by the postsynaptic neuron. Thus spike intervals which an observor may think are + or - may in fact be 0, as far as the nervous system is concerned. To confound the problem, the nervous system may "change its definition of 0" under different physiological conditions in which various modulating influences adjust and bias the responsiveness of postsynaptic neurons. (b) The interval-pattern coding may be stochastic, as is true for most time series types of data [6]. For a stochastic time series, the future is only partly dependent on past events; that is, future values have a probability distribution which is conditioned by a knowledge of past values. In the context of interval patterns, the Markovian dependencies and the divergences from statistical independence which have been demonstrated by many workers for long spike trains would not be evident over a very short segment of data. Thus, even though such interval dependency exists, one normally would not know it without establishing the probability distribution for the various interval patterns. We would therefore conclude that the clear demonstration of such interval patterns in short data segments, as we have shown here, is very compelling evidence for intervalpattern coding, at least in certain neurons under certain conditions. This motivates us to continue our study of such possibilities in various neuronal systems, despite the fact that identifying the "'neural code" in a given system will not be easy and may often be impossible.
436
KLEMM AND SHERRY
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