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Slow rhythms and correlations in spike trains from midbrain neurons
EXPERIMENTAL
NEUROLOGY
Slow Rhythms
R. J.
MACGREGOR,
47, 581-598
(1975)
and Correlations in Spike from Midbrain Neurons S.
W.
MILLER,
AND
P.
M.
Trains
GROVES
Drpartnkent of E,tgi,keering Dcsigfk and Economic Eznluation De/uwtlrkekkt of Psykology, University of Colorado, Bofklder, Colorado 80302 Rcccived
Decewkber
1
and
16. 1974
This paper describes auto-and cross-correlation histograms from single and simultaneously recorded spike trains in 57 neurons and 32 pairs of neurons in and around the reticular formation region in the midbrain of the rat. Firing patterns in most of these cells are random although some cells exhibit marked slow rhythms in firing, and closer inspection reveals the occurrence of slow rhythms which in many cells are partially masked by the more vigorous random activity. Sixteen percent of cells are markedly rhythmic in firing, 53% are moderately or marginally rhythmic, and 32% show no slow rhythms. At least three and at most six of nine neuron pairs recorded with single electrodes show short latency correlations in firing. At least two and at most five of 23 pairs recorded with separate electrodes show short latency correlations in firing. The occurrence of short latency correlations in firing between cell pairs is associated with the occurrence of rhythmicities in the firing patterns of the cells. Neuron pairs recorded with single electrodes exhibit broad rhythmic correlations which are in phase, while pairs recorded with separate electrodes exhibit broad rhythmic correlations which are out of phase. These observations suggest but do not necessarily imply the existence of slow rhythmic oscillations which propagate through midbrain tissue and engage to various degrees many of the constituent neurons. 1 This work has been supported by National Science Foundation Grant Number GB-33687 and National Institute of Neurological Diseases and Stroke Number 1 R01 NS10781-01 to R. J. MacGregor, and National Institute of Mental Health Grant Number MH-19515 and Research Scientist Development Award K0.2 MH70706 to P. M. Groves. We thank the Council on Research and Creative Work of the University of Colorado for an award enabling the purchase of a solid state amplitude discriminator for this work. We also thank D. H. Perkel for providing the package of programs PEDRO for neuronal spike train analysis, W. Tatton for helping us obtain the amplitude discriminator, and Christina Cronkite and Aurelie Snyder for skilled technical assistance. Finally we thank D. E. Bailey for making the CLIPR computing facilities available for part of these analyses. 581 Copyright 0 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.
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INTRODUCTION An important element in the understanding of the dynamics of neuron pools consists of the building up of experimentally based pictures of ongoing firing patterns in constituent network neurons in various states of activity. Moore, Perkel, and Gerstein (10) have pointed out that statistical measures of spike train activity can be used to glean considerably more information concerning network structure than is typically obtainable by visual inspection of such records or, indeed, by any other known means. More specifically, by building up an assessment of firing patterns in broad collections of individual cells and of interrelations in firing in pairs and groups of simultaneously recorded cells, one can develop an overview of the functional architecture of a neuronal network with which any proposed theory must be consistent. In this paper we present results based on cross-correlation histograms obtained from pairs of simultaneously recorded neurons of the midbrain (mostly in the mesencephalic reticular formation) of the unanesthetized and artificially respired rat. The main finding is the existence of a pervasive slow rhythmicity which seems to be associated with the occurrence of fast correlations in firing in cell pairs and which seems to have a spatial distribution. Several earlier studies on firing patterns in reticular neurons of cats have been presented. Amassian and Waller (1) reported that several pairs of reticular neurons recorded simultaneously in unanesthetized paralyzed cats with separate electrodes were independent in their spontaneous activity. Manohar, Noda, and Adey (11) f ound many cells in chronically prepared cats which change their rate and pattern according to the state of wakefulness or sleep. Activity in arousal is generally more regular than in REM sleep which is characterized as more random, and neuronal activity in slow sleep is intermediate between these two patterns. These authors also found many units whose firing patterns and rates did not change with state of sleep or wakefulness. Some 10% of the units fired rather regularly and might be considered as noisy pacemakers with intervals between 15 and 80 msec. Cross-correlation histograms obtained from seven pairs of neurons recorded in each case with a single microelectrode showed no striking relationships. Skvaril, Radil-Weiss, Bohdanecky, and Syka (17) reported that neurons from unanesthetized curarized rats and cats tend to exhibit exponential interval histograms if firing rates are low and symetrical interval histograms if firing rates are high. Interval histograms from a given unit may change form as the unit changes firing rate. Nakahama, Ishii, and Kamamoto (14), reporting on spike trains from unanesthetized paralyzed cats, showed that midbrain reticular neurons exhibit a Markov dependency to the fourth order. In a previous publication describing autocorrelation histograms from neurons in the mesencephalic
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reticular formation of unanesthetized, paralyzed rats (9), we described various rhythmic and pacemaker-like patterns ; a pervasive slow rhythmicity was manifested to various degrees in some 55% of cells and an elevated probability of firing extending about 500 msec after the occurrence of a spike. The statistical techniques used here have been developed and discussed primarily by Perkel, Moore, Gerstein, Segundo and various colleagues (2, 3, 10, 12, 13, and 1.5). METHODS Neuronal activity was recorded extracellularly utilizing one or two glass coated tungsten microelectrodes in 26 adult, male albino rats. Subjects were first anesthetized by ether inhalation and placed in a stereotaxic instrument. The skull was exposed and a hole drilled over the reticular formation target area. The areas in and surrounding the surgical incision and in contact with the hollow, blunt ear bars were infiltrated thoroughly with procaine hydrochloride (Novacain) by subcutaneous injections on each side of the wound and local application to all cut edges and the portion of the external auditory meatus touching the ear bars. In addition, an anesthetic ointment was applied to the external auditory meatus and commercial eyedrops (Visine) were applied to prevent cornea1 drying. Application of local anesthetic was continued at 30-45 min intervals until the experiment was terminated. Ether anesthesia was discontinued following these surgical preparations and the animal was paralyzed with tubocurarine chloride and artificially respired at 70-75 cycles/min by means of a Harvard Instruments Rodent Respirator attached to a rubber cone fitted snugly over the snout. Heart rate, typically 360-420 beats/min, and body temperature, maintained between 36-37.5 C, were monitored continuously to ensure stable physiological conditions of the paralyzed animals (5). In addition, electrocorticographic activity was checked periodically to ensure the absence of slow waves. Based upon these observations, and the presence of alterations in heart rate produced by sensory stimulation of the animal, indicative of orienting responses, the records presented here are presumed to reflect the waking state. The duration of experimental recordings were typically 5-30 min with a total duration of 2-3 hr for a single animal. Typically, three to six electrode penetrations were made in each animal. The data described here were obtained from 26 animals. Single unit activity was recorded and amplified by conventional techniques and stored on magnetic tape for subsequent analysis. A signal-to-noise criterion of 3: 1 or greater was used for all unit recordings. Attempts were made, when possible, to isolate more than a single spike train with any given electrode. Placements of electrode tips were determined by placing a small d-c lesion at the tip
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of the electrode and subsequent histological analysis. The locations determined by these methods are provided in the figures of all correlations presented in this paper. Additional details of experimental methods have been reported (4, 9). The spontaneous activity from this preparation as preserved on magnetic tape was played back on a Sony TC-640 stereo tape deck and screened on an oscilloscope. The spike trains were extracted from simultaneous records obtained in each of two extracellular electrodes several hundred microns apart. Often it was possible to discriminate the activity of two cells from a single electrode so that in several cases we observed simultaneously recorded triplets of cells and in one case a simultaneously recorded quadruplet of cells. A detailed report of firing properties and correlations between cells within groups was constructed on the basis of visual screening of the trains. The raw data were converted into time series of identical spikes amenable for statistical analysis with the help of a solid state amplitude discriminator designed especially for this purpose (18). The data were retained for statistical analysis only when individual units were clearly discriminable from background signals. In all cases great care was taken that the signal amplitudes remained constant throughout the length of the recording. For electrode tracings which contained only one discriminable unit, a signal-to-noise criterion of three was required. For the few cases where two units were discriminated from a single electrode tracing, this criterion was relaxed to about 1.5 for the smaller unit. These latter cases were processed independently twice to double-check the procedure. A representative sample illustrating our technique of spike separation for two units from a single electrode is shown in Fig. 1. Part A of Fig. 1 shows an electrode tracing containing two discriminable units of constant but different amplitudes. Part B shows the corresponding output trains as determined by the amplitude discriminator. In all such cases we double checked the discriminator output vs the data signal particularly during bursting activity by repeated sampling on a 4-channel storage oscilloscope. Only those sections of data which appeared homogenous and stationary upon visual inspection were accepted for quantitative analysis. A few sample tests showed no significant changes in statistical measures within the sections. The output signals from the amplitude discriminator were then supplied to a Sony TC-277-4 four-channel tape deck. Analog to digital conversion was affected on a hybrid computer system and the corresponding sets of spike times preserved on digital tape. These data and a general purpose program for statistical analysis of neuronal spike trains were stored on a general purpose dual CDC 6400 computer system. Processing of the data was performed at a Tektronix T-4010 interactive graphics terminal. In most cases three autocorrelation histograms and one interspike interval
FIG. 1. Extracellular record photographed from tape recorded neuronal activity from a single electrode in B. Output of the spike discriminator. The upper record indicates discrimination of the smaller action potentials, cates discriminator output for the larger of the spike trains. Each snapshot includes a time span of 1 sec.
the reticular the lower
formation. record indi-
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GROVES
histogram were obtained for each single unit, and three cross-correlation histograms were obtained for each pair of units. The correlograms usually used bin sizes of 0.001, 0.01, and 0.1 set, and ranges of 150 bins, whereas the interspike interval histogram used a range of 2.5 times the mean firing interval. Finally, the four channel tapes were screened audially on a quadraphonic sound system and a detailed report constructed on the basis of this screening. The results of the statistical analyses were then compared with and interpreted within the framework of both the visual and auditory screening reports. RESULTS Our single unit results were obtained from a total of 57 cells. Crosscorrelation analyses were obtained from 22 groups of simultaneously recorded spike trains. We used at most two electrodes, but in some cases two cells were discriminated from a single electrode tracing. Our data consist of five pairs from a single electrode only, and 17 other groups involving two separate electrodes. These comprise one set of four simultaneously recorded spike trains, three sets of three simultaneously recorded spike trains, and 18 casesof pairs of spike trains. Recordings were obtained from a total of 32 pairs of cells. Nine of the pairs are from single electrodes, and 23 pairs are from separate electrodes. Single Unit Firing Patterns. The first impression one has is that reticular firing patterns are for the most part random. Interspike interval histograms are approximately exponential and visual inspection of records reveals an unremarkable randomness consistent with a Poisson process. Firing rates range from l/set to more than lOO/sec with many firing between 1 and lO/sec and most firing at about 15-25/set. A few scattered cells exhibit noticeable slow rhythmicities in firing. In a typical group of about 13 cells, for example, 11 would exhibit unremarkable random patterns, while one would exhibit pacemaker activity firing a single spike with clock-like regularity with period of about 0.64 set, and another single unit would exhibit marked bursts of activity recurring rhythmically every 1.3 sec. The pacemaker units have firing rates of from ld/sec while the bursting cells have firing rates of 4--43/set with an average of about 20/set. On closer inspection, however, it becomes clear that many of the randomly firing cells contain an underlying slow rhythmicity at about the same interval as that of the pacemaker and bursting cells. These rhythms are not easily (and often not at all) discernable on visual or auditory screening of the records. However, auto-correlation histograms show clear although low level rhythmicities in about two-thirds of the randomly firing cells. We have categorized the slow rhythmic character of our 57 reticular cells into four main groups : pacemaker (P), marked rhythmicity (M),
MIDBRAIN
FIG. ‘La. Autocorrelation
FIG. 2b. Autocorrelation
histogram
histogram
587
UNITS
from
from
representative
representative
pacemaker
markedly
cell.
rhythmic
cell.
588
MACGREGOR,
MILLER
AND
GROVES Cell
3610
-
2,372
events
204%B(T)
FIG.
2c. Autocorrelation
FIG. 2d. Autocorrelation
histogram
from
histogram
representative
from
representative
moderately
arhythmic
rhythmic
cell.
cell.
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moderate or marginal rhythmicity (m), and no rhythmicity (n). Four of 57 or 7% are pacemakers (regular intervals of 0.64, 0.64, 0.585, and 0.625 set) ; five or 9% exhibit marked rhythmicities (these had periods of 0.64, 0.64, 1.28, 1.76, and 1.88 set) ; 30 or 53% show moderate or marginal rhythms ; and 18 or 32% have no slow rhythms. A representative example of each of these four classesof units is shown in Fig. 2. Short Latency Correlations in Firing. Cross-correlation histograms using 1 msec bin size and 150 msec range reveal a general paucity of correlated firing. The general impression is that particular synaptic pathways between midbrain neurons and from afferent fibers to neurons which are prepotent and repeatedly successfulin eliciting postsynaptic action potentials are at a minimum. However, there do indeed exist some correlations in firing in pairs of reticular cells and there seemsto be a tendency for these correlations to be associatedwith the occurrence of rhythmicities in cells. More precisely, of the 32 pairs of cells for which we constructed crosscorrelation histograms, two exhibit very strong and short latency correlations in firing. These are shown in Figs. 3 and 4. Both these casesmust reflect shared excitation since the peak in the cross-correlation histogram straddles the zero reference line. Three of the cross-correlation histograms show definite but weaker correlations in firing. Two of these are shown in Fig. 5. In all three of these casesthe peak is lessthan 7 msecwide and occurs on one or the other side of the zero reference. Thus, these casesmight reflect either a synaptic connection between the recorded cells or an excitatory input shared by both of them. Six of the cross-correlation histograms exhibit very weak or marginal peaks. In these casesit is not possible to ascertain whether or not a real synaptic connection or shared input is being reflected by the data. A representative example of this class of crosscorrelation is shown in Fig. 6. These correlations have peaks that are only one, two or three bins wide or only marginally above the noise level. Finally, short latency correlation histograms for 21 pairs of cells clearly show the absenceof any significant correlation in firing. Thus, at least 5 of 32 pairs or 16%, and at most 11 of 32 or 34% of cell pairs show evidence of short latency correlation in firing. By the same token at least 66% and perhaps as many as 84% of cell pairs show an absenceof correlated firing. In these data, correlated firing is more likely to occur between cell pairs recorded with a single electrode than between cell pairs recorded with separate electrodes. Thus, of nine pairs of cells recorded with single electrodes, two exhibit strong broad correlations evidencing shared input, one exhibits a clear but weaker correlation, three exhibit marginal relations, and three exhibit no correlation in firing. Of 23 pairs recorded with separate electrodes, none exhibit strong broad correlations in firing, two exhibit clear but weaker correlations, three exhibit weaker and marginal relations and 18 exhibit no correlation in firing.
590
FIG.
(markedly
MACGREGOR,
3a.
Crosscorrelation rhythmic).
MILLER
histogram
AND
for
Cells
GROVES
29-l
(Pacemaker)
2) P:
2048 Btl)
PO.1
FIG.
3b. Autocorrelation
histogram
for Cell
29-2.
and
B-2
MIDBRAIN
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64 B(T) 1
0 -.09 FIG.
ginally
0
4a. Crosscorrelation rhythmic).
FIG.
histogram
4b. Autocorrelation
for
Cells
.094 (SEC) 38-1
histogram
(Pacemaker)
for Cell
3&l.
and
38-2
(mar-
592
MACGREGOR,
FIG.
MILLER
4c. Autocorrelation
AND
GROVES
histogram for Cell 38-2.
The data suggest that the occurrence of short latency correlations in firing between cell pairs is associatedwith the occurrence of rhythmicities in the firing patterns of the cells, although the nature of that association is difficult to delineate precisely. Generally the tendency to exhibit a rhythmicity goes hand in hand with the tendency of the cell to correlate in firing with other cells. The more pronounced the rhythmicity the more prominent the correlation. Of the two pairs that exhibit strong, broad correlations reflecting shared excitation, both involve a pacemaker (P-M and P-m) ; of the three pairs that exhibit clear but weaker correlations, two contain a pacemaker or markedly rhythmic cell (P-n, m-M, m-n) : of the six pairs that exhibit weaker and marginal correlations, two include a pacemaker or markedly rhythmic cell (P-n, M-n, 3 of m-m, n-m) ; finally, of the 21 pairs that show no correlation, five contain pacemaker or markedly rhythmic cells (2 P-n, 3 of M-n, 16 of various combinations of n and m). Thus, of eleven cell pairs which contain at least one pacemaker or markedly rhythmic cell, two have strong broad correlations, two have clear but weaker correlations, two have weak but marginal correlations, and five show no correlations. A total of four of 11 to six of 11 such pairs show correlations. On the other hand, of 21 pairs which do not contain pacemakers or markedly rhythmic cells (that is, which contain only m or n cells) no pairs exhibit strong correlations, one exhibits clear but weaker correla-
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! Di -a FIG.
5a. Crosscorrelation
histogram
for Cells
31-1 and 30.
FIG.
5b. Crosscorrelation
histogram
for
36-1
Cells
and 36-2.
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MACGREGOR,
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MILLER
AND
GROVES
6. Crosscorrelation histogram for Cells l-l and l-2.
tions, four exhibit weaker and marginal correlations, and 16 exhibit That is, one to four of 21 such pairs exhibit clearly no correlations. correlations. This information can be separated for pairs obtained from single electrodes as compared to those that came from separate electrodes as follows. For cell pairs recorded with single electrodes, cell pairs containing at least one pacemaker or markedly rhythmic cell exhibit two strong broad connections, zero clear but weaker connection, zero marginal connections and zero no correlations. Cell pairs containing only moderate or marginally rhythmic cells and nonrhythmic cells recorded with single electrodes exhibit zero strong connections, one pair with clear but weaker correlations, three pairs with marginal correlations, and three pairs with no correlation. On the other hand for cell pairs recorded with separate electrodes, cell pairs containing at least one pacemaker or markedly rhythmic cell exhibit no strong correlations, two clear but weaker correlations, two marginal correlations, and five no correlations. Cell pairs recorded with separate electrodes and containing only nonrhythmic and moderate or marginally rhythmic cells exhibit zero pairs with strong correlations, zero pairs with clear but weaker correlations, one pair with marginal correlations, and 13 pairs with no correlations. Four of the five strong and clear-but-weaker correlations we found are exhibited by pairs at least one member of which is a pacemaker or markedly
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rhythmic cell whereas only nine of the 32 pairs involve P or M cells. On the other hand, 20 of the 27 pairs which exhibit clearly no correlation or marginal correlation are obtained from pairs which have only marginal rhythmic or nonrhythmic cells whereas 23 of the 32 pairs involve only m or n cells. It is particularly noteworthy that the only two strong correlations we found in 32 pairs occurred between pacemakers and nearby cells, and, moreover, that these two pacemakers were the only two pacemakers which we were able to record simultaneously with other units. Broad Rkythic Correlations in Cell Pairs. The rhythmicities of these cells have a spatial distribution in the sensethat neighboring cells exhibit slow rhythmicities which are in phase,whereas distant cells exhibit rhythmicities which are out of phase to various degrees. These conclusions are based on cross-correlation histograms with bin widths of 40 msec and ranges of 6 sec. Sixteen of our 32 celf pairs are comprised of pacemaker cells, markedly rhythmic cells, or marginally rhythmic cells. Of six such pairs recorded from a single electrode and therefore presumably relatively close together, five exhibit slow rhythmic waves with zero lag in the crosscorrelation histograms. A representative sample is shown in Fig. 7. Of ten cell pairs which were recorded with separate electrodes and, therefore, further apart as verified by subsequent histological analysis, eight exhibit slow rhythmic waves with a non-zero phase lag in the cross-correlation
FIG.
7. Slow rhythmic
correlation
between two cells recorded with
one electrode.
596
FIG.
MACGREGOR,
8. SIow
rhythmic
correlation
MILLER
between
two
AND
cells
GROVES
recorded
with
separate
electrodes.
histogram. A representative example is shown in Fig. 8. In our data three cell pairs are exceptions to the rule that local pairs exhibit zero lag and separate pairs exhibit nonzero lag. Each one of these pairs involves a single unit (unit 49-2) which is peculiar. If this particular unit were 180 degrees reversed in phase then all six of our local pairs would exhibit zero lag and all ten of our pairs from separate electrodes would exhibit nonzero lag. DISCUSSION The main fiindings in this work are : (i) There exist pervasive slow rhythmicities often partially masked behind random firing in spike trains of midbrain neurons. (ii) The tendency for a midbrain neuron to exhibit correlations in firing with other midbrain neurons seems to increase with the degree of rhythmicity apparent in the cell. (iii) Neighboring cells tend to exhibit in-phase broad rhythmic correlations, whereas cells separated by hundreds of microns tend to exhibit out of phase broad rhythmic correlations. A noteable feature of these slow rhythms is that the most prominent intervals seem to be integer multiples of a common base interval of 0.64 sec. One of our two most marked pacemakers has a firing interval of this value, while the other pacemaker, although also clearly firing at this interval,
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tends quite often to skip two firings. This results in a very prominent peak at 1.92 set in the auto-correlation histogram for this unit as seen in Fig. 4 (unit 38-1). Many of the slower rhythms in marked or moderate/marginal cells occur with intervals of about 1.3, 1.9, and 2.5 set, with 1.3 set by far the most common. In earlier studies, Holmes and Houchin have described prominent slow waves with 1.5-2.0 set periods in the spike trains of cortical neurons of anesthetized rats (6, 7). Moreover, they found that neuron pairs in the cortex exhibited slow rhythmic correlations with the same period which were in phase if the neuron pairs were in the same coronal section and out of phase otherwise. They suggested that their data are consistent with a travelling wave propagating at 5-10 cm/set anterior to posterior. The degrees of both the rhythmicities and cross-correlations increased with depth of anesthesia. Holmes and Houchin suggest that these phenomena may be due to either groups of impulses from some subcortical structure bombarding the cortex or to a spread of activity within the cortex. The fact that previous investigators of the reticular formation have not remarked on the pervasive rhythmicity we have described, may reflect a species difference in that most previous investgations have been performed on cats. Also, we should note that pilot studies on a small number of anesthetized rats in our laboratory provided a very markedly reduced occurrence of slow rhythms although these did occur in this preparation in the absence of artificial respiration. The rhythm may relate to the animals’ respiration, but if this is so it is a subtle relationship and not so simple as one might suppose. For example, the rhythmic firing intervals do not correspond to the period of the respirator. A tentative picture consistent with these data is that local regions in midbrain sometimes exhibit synchronized firing activity upon which any other afferent activation is superimposed. Slightly distal regions, however, would be out of phase with each other. This situation could reflect either the propagation of a slow wave through the midbrain or the existence of separate subsystems of cells each tending to fire synchronously within itself but remaining not necessarily synchronized with other systems (8, 16). If this picture is generally valid there are some exceptions in that some local neuron pairs are out of phase and some distal cell pairs are in phase. For example, one pair of cells including a markedly rhythmic cell and a moderate or marginally rhythmic cell obtained from separate electrodes, exhibited broad out of phase relationships consistent with the generalization but also exhibited weak but clear short latency correlations in firing. Another unit (unit 49-2) was out of phase with a local neighboring cell but in phase with two distal cells recorded with the same electrode. This cell did not exhibit short latency correlations with any of the other three. One might speculate that the hypothetical wave advances in a not totally
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homogeneous fashion extending isolated branches of synchronizing influence into as yet uninvaded regions or alternatively that separate functionally synchronized subsystems might interpenetrate anatomically. REFERENCES 1. AMASSIAN, V. E., and H. J. WALLER. 1958. Spatiotemporal patterns of activity in individual reticular neurons. In “Reticular Formation of the Brain,” R. H. Jasper et al. [Eds.]. Little Brown, Boston. 69-108. 2. BRYANT, JR., H. L., A. R. MARCOS, and J. P. SEGUNM). 1973. Correlations of neuronal spike discharges produced by monosynaptic connections and by common inputs, J. Neuro~hysiol. 36 : 205-225. 3. GERSTEIN, L., and D. H. PERKEL. 1972. Mutual temporal relationships among neuronal spike trains, Statistical techniques for display and analysis, Biophys, J. 12 : 453-473. 4. GROVES, P. M., S. W. MILLER, M. V. PARKER, and G. REBEC. 1973. Organization by sensory modality in the reticular formation of the rat. Brain Res. 54: 207-224. ,5. 6. 7.
8. 9.
10. 11. 12. 13. 14. 15. 16. 17.
18.
GUYTON, A. C. 1947. Measurement of the respiratory volumes of laboratory animals, Amer. J. Physiol. 150 : 70-77. HOLMES, O., and J: HOUCHIN. 1966. Units in the cerebral cortex of the anaesthetized rat and the correlations between their discharges, J. Physiol. 187 : 651-671. HOLMES, O., and J. HOUCHIN. 1967. Analysis of the activity of one type of spontaneously discharging unit in the cortex cerebri of the anaesthetized rat, J. Physiol. 193: 173-186. MACGREGOR, R. J. 1972. A model for reticular-like networks: Ladder nets, recruitment fuses, and sustained responses, Bra& Res. 41 : 345-363. MACGREGOR, R. J., R. PRIETO-DIAZ, S. W. MILLER, and P. M. GROVES. 1973. Statistical properties of neurons in the rat mesencephalic reticular formation, Brain Res. 64 : 167-187. MACGREGOR, R. J., and E. R. LEWIS. 1975. Neural Modeling. Plenum Press, New York. (To be published, See discussion). MANOHAR, S., H. NODA, and W. R. ADEY. 1972. Behavior mesencephalic reticular neurons in sleep and wakefulness, E.@. Neural. 34: 140-157. MOORE, G. P., D. H. PERKEL, and J. P. SEGUNDO. 1%6. Statistical analysis and functional interpretation of neuronal spike data, Am. Rev. Physiol. 28: 493-522. MOORE, G. P., J. P. SEGUNDO, D. H. PERKEL, and H. LEVITAN. 1970. Statistical signs of synaptic interaction in neurons Biophys. J. 10: 876-900. NAKAHAMA, H., N. ISHII, and M. YAMAMOTO. 1972. Markov process of maintained impulse activity in central single neurons, Kybernetik 11: 61-72. PERKEL, D. H., G. L. GERSTEIN, and G. P. MOORE. 1967. Neuronal spike trains and stochastic point processes (I and II), Biophys. J. 7, 391-440. SCHEIBEL, M. E., and A. B. SCHEIBEL. 1958. Structural substrates for integrative patterns in the brain stem reticular core, pp. 31-56. In “Reticular Formation of the Brain.” H. H. Jasper et al. [Eds.]. Little, Brown, Boston. SKVARIL, J., T. RADIL-WEISS, 2. BOHDANECKY, and J. SYKA. 1971. Spontaneous discharge patterns of mesencephalic neurons: interval histogram and mean interval relationship, Kybernetik 9: 11-15. STRONG, D., W. TATTON, and D. CRAPPER. 1971. Solid-state amplitude discriminator for neural units. IEEE Trans. Bio-Med. Eng. BME-18: 237-240.
NEUROLOGY
Slow Rhythms
R. J.
MACGREGOR,
47, 581-598
(1975)
and Correlations in Spike from Midbrain Neurons S.
W.
MILLER,
AND
P.
M.
Trains
GROVES
Drpartnkent of E,tgi,keering Dcsigfk and Economic Eznluation De/uwtlrkekkt of Psykology, University of Colorado, Bofklder, Colorado 80302 Rcccived
Decewkber
1
and
16. 1974
This paper describes auto-and cross-correlation histograms from single and simultaneously recorded spike trains in 57 neurons and 32 pairs of neurons in and around the reticular formation region in the midbrain of the rat. Firing patterns in most of these cells are random although some cells exhibit marked slow rhythms in firing, and closer inspection reveals the occurrence of slow rhythms which in many cells are partially masked by the more vigorous random activity. Sixteen percent of cells are markedly rhythmic in firing, 53% are moderately or marginally rhythmic, and 32% show no slow rhythms. At least three and at most six of nine neuron pairs recorded with single electrodes show short latency correlations in firing. At least two and at most five of 23 pairs recorded with separate electrodes show short latency correlations in firing. The occurrence of short latency correlations in firing between cell pairs is associated with the occurrence of rhythmicities in the firing patterns of the cells. Neuron pairs recorded with single electrodes exhibit broad rhythmic correlations which are in phase, while pairs recorded with separate electrodes exhibit broad rhythmic correlations which are out of phase. These observations suggest but do not necessarily imply the existence of slow rhythmic oscillations which propagate through midbrain tissue and engage to various degrees many of the constituent neurons. 1 This work has been supported by National Science Foundation Grant Number GB-33687 and National Institute of Neurological Diseases and Stroke Number 1 R01 NS10781-01 to R. J. MacGregor, and National Institute of Mental Health Grant Number MH-19515 and Research Scientist Development Award K0.2 MH70706 to P. M. Groves. We thank the Council on Research and Creative Work of the University of Colorado for an award enabling the purchase of a solid state amplitude discriminator for this work. We also thank D. H. Perkel for providing the package of programs PEDRO for neuronal spike train analysis, W. Tatton for helping us obtain the amplitude discriminator, and Christina Cronkite and Aurelie Snyder for skilled technical assistance. Finally we thank D. E. Bailey for making the CLIPR computing facilities available for part of these analyses. 581 Copyright 0 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.
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MACGREGOR,
MILLER
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INTRODUCTION An important element in the understanding of the dynamics of neuron pools consists of the building up of experimentally based pictures of ongoing firing patterns in constituent network neurons in various states of activity. Moore, Perkel, and Gerstein (10) have pointed out that statistical measures of spike train activity can be used to glean considerably more information concerning network structure than is typically obtainable by visual inspection of such records or, indeed, by any other known means. More specifically, by building up an assessment of firing patterns in broad collections of individual cells and of interrelations in firing in pairs and groups of simultaneously recorded cells, one can develop an overview of the functional architecture of a neuronal network with which any proposed theory must be consistent. In this paper we present results based on cross-correlation histograms obtained from pairs of simultaneously recorded neurons of the midbrain (mostly in the mesencephalic reticular formation) of the unanesthetized and artificially respired rat. The main finding is the existence of a pervasive slow rhythmicity which seems to be associated with the occurrence of fast correlations in firing in cell pairs and which seems to have a spatial distribution. Several earlier studies on firing patterns in reticular neurons of cats have been presented. Amassian and Waller (1) reported that several pairs of reticular neurons recorded simultaneously in unanesthetized paralyzed cats with separate electrodes were independent in their spontaneous activity. Manohar, Noda, and Adey (11) f ound many cells in chronically prepared cats which change their rate and pattern according to the state of wakefulness or sleep. Activity in arousal is generally more regular than in REM sleep which is characterized as more random, and neuronal activity in slow sleep is intermediate between these two patterns. These authors also found many units whose firing patterns and rates did not change with state of sleep or wakefulness. Some 10% of the units fired rather regularly and might be considered as noisy pacemakers with intervals between 15 and 80 msec. Cross-correlation histograms obtained from seven pairs of neurons recorded in each case with a single microelectrode showed no striking relationships. Skvaril, Radil-Weiss, Bohdanecky, and Syka (17) reported that neurons from unanesthetized curarized rats and cats tend to exhibit exponential interval histograms if firing rates are low and symetrical interval histograms if firing rates are high. Interval histograms from a given unit may change form as the unit changes firing rate. Nakahama, Ishii, and Kamamoto (14), reporting on spike trains from unanesthetized paralyzed cats, showed that midbrain reticular neurons exhibit a Markov dependency to the fourth order. In a previous publication describing autocorrelation histograms from neurons in the mesencephalic
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reticular formation of unanesthetized, paralyzed rats (9), we described various rhythmic and pacemaker-like patterns ; a pervasive slow rhythmicity was manifested to various degrees in some 55% of cells and an elevated probability of firing extending about 500 msec after the occurrence of a spike. The statistical techniques used here have been developed and discussed primarily by Perkel, Moore, Gerstein, Segundo and various colleagues (2, 3, 10, 12, 13, and 1.5). METHODS Neuronal activity was recorded extracellularly utilizing one or two glass coated tungsten microelectrodes in 26 adult, male albino rats. Subjects were first anesthetized by ether inhalation and placed in a stereotaxic instrument. The skull was exposed and a hole drilled over the reticular formation target area. The areas in and surrounding the surgical incision and in contact with the hollow, blunt ear bars were infiltrated thoroughly with procaine hydrochloride (Novacain) by subcutaneous injections on each side of the wound and local application to all cut edges and the portion of the external auditory meatus touching the ear bars. In addition, an anesthetic ointment was applied to the external auditory meatus and commercial eyedrops (Visine) were applied to prevent cornea1 drying. Application of local anesthetic was continued at 30-45 min intervals until the experiment was terminated. Ether anesthesia was discontinued following these surgical preparations and the animal was paralyzed with tubocurarine chloride and artificially respired at 70-75 cycles/min by means of a Harvard Instruments Rodent Respirator attached to a rubber cone fitted snugly over the snout. Heart rate, typically 360-420 beats/min, and body temperature, maintained between 36-37.5 C, were monitored continuously to ensure stable physiological conditions of the paralyzed animals (5). In addition, electrocorticographic activity was checked periodically to ensure the absence of slow waves. Based upon these observations, and the presence of alterations in heart rate produced by sensory stimulation of the animal, indicative of orienting responses, the records presented here are presumed to reflect the waking state. The duration of experimental recordings were typically 5-30 min with a total duration of 2-3 hr for a single animal. Typically, three to six electrode penetrations were made in each animal. The data described here were obtained from 26 animals. Single unit activity was recorded and amplified by conventional techniques and stored on magnetic tape for subsequent analysis. A signal-to-noise criterion of 3: 1 or greater was used for all unit recordings. Attempts were made, when possible, to isolate more than a single spike train with any given electrode. Placements of electrode tips were determined by placing a small d-c lesion at the tip
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of the electrode and subsequent histological analysis. The locations determined by these methods are provided in the figures of all correlations presented in this paper. Additional details of experimental methods have been reported (4, 9). The spontaneous activity from this preparation as preserved on magnetic tape was played back on a Sony TC-640 stereo tape deck and screened on an oscilloscope. The spike trains were extracted from simultaneous records obtained in each of two extracellular electrodes several hundred microns apart. Often it was possible to discriminate the activity of two cells from a single electrode so that in several cases we observed simultaneously recorded triplets of cells and in one case a simultaneously recorded quadruplet of cells. A detailed report of firing properties and correlations between cells within groups was constructed on the basis of visual screening of the trains. The raw data were converted into time series of identical spikes amenable for statistical analysis with the help of a solid state amplitude discriminator designed especially for this purpose (18). The data were retained for statistical analysis only when individual units were clearly discriminable from background signals. In all cases great care was taken that the signal amplitudes remained constant throughout the length of the recording. For electrode tracings which contained only one discriminable unit, a signal-to-noise criterion of three was required. For the few cases where two units were discriminated from a single electrode tracing, this criterion was relaxed to about 1.5 for the smaller unit. These latter cases were processed independently twice to double-check the procedure. A representative sample illustrating our technique of spike separation for two units from a single electrode is shown in Fig. 1. Part A of Fig. 1 shows an electrode tracing containing two discriminable units of constant but different amplitudes. Part B shows the corresponding output trains as determined by the amplitude discriminator. In all such cases we double checked the discriminator output vs the data signal particularly during bursting activity by repeated sampling on a 4-channel storage oscilloscope. Only those sections of data which appeared homogenous and stationary upon visual inspection were accepted for quantitative analysis. A few sample tests showed no significant changes in statistical measures within the sections. The output signals from the amplitude discriminator were then supplied to a Sony TC-277-4 four-channel tape deck. Analog to digital conversion was affected on a hybrid computer system and the corresponding sets of spike times preserved on digital tape. These data and a general purpose program for statistical analysis of neuronal spike trains were stored on a general purpose dual CDC 6400 computer system. Processing of the data was performed at a Tektronix T-4010 interactive graphics terminal. In most cases three autocorrelation histograms and one interspike interval
FIG. 1. Extracellular record photographed from tape recorded neuronal activity from a single electrode in B. Output of the spike discriminator. The upper record indicates discrimination of the smaller action potentials, cates discriminator output for the larger of the spike trains. Each snapshot includes a time span of 1 sec.
the reticular the lower
formation. record indi-
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histogram were obtained for each single unit, and three cross-correlation histograms were obtained for each pair of units. The correlograms usually used bin sizes of 0.001, 0.01, and 0.1 set, and ranges of 150 bins, whereas the interspike interval histogram used a range of 2.5 times the mean firing interval. Finally, the four channel tapes were screened audially on a quadraphonic sound system and a detailed report constructed on the basis of this screening. The results of the statistical analyses were then compared with and interpreted within the framework of both the visual and auditory screening reports. RESULTS Our single unit results were obtained from a total of 57 cells. Crosscorrelation analyses were obtained from 22 groups of simultaneously recorded spike trains. We used at most two electrodes, but in some cases two cells were discriminated from a single electrode tracing. Our data consist of five pairs from a single electrode only, and 17 other groups involving two separate electrodes. These comprise one set of four simultaneously recorded spike trains, three sets of three simultaneously recorded spike trains, and 18 casesof pairs of spike trains. Recordings were obtained from a total of 32 pairs of cells. Nine of the pairs are from single electrodes, and 23 pairs are from separate electrodes. Single Unit Firing Patterns. The first impression one has is that reticular firing patterns are for the most part random. Interspike interval histograms are approximately exponential and visual inspection of records reveals an unremarkable randomness consistent with a Poisson process. Firing rates range from l/set to more than lOO/sec with many firing between 1 and lO/sec and most firing at about 15-25/set. A few scattered cells exhibit noticeable slow rhythmicities in firing. In a typical group of about 13 cells, for example, 11 would exhibit unremarkable random patterns, while one would exhibit pacemaker activity firing a single spike with clock-like regularity with period of about 0.64 set, and another single unit would exhibit marked bursts of activity recurring rhythmically every 1.3 sec. The pacemaker units have firing rates of from ld/sec while the bursting cells have firing rates of 4--43/set with an average of about 20/set. On closer inspection, however, it becomes clear that many of the randomly firing cells contain an underlying slow rhythmicity at about the same interval as that of the pacemaker and bursting cells. These rhythms are not easily (and often not at all) discernable on visual or auditory screening of the records. However, auto-correlation histograms show clear although low level rhythmicities in about two-thirds of the randomly firing cells. We have categorized the slow rhythmic character of our 57 reticular cells into four main groups : pacemaker (P), marked rhythmicity (M),
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FIG. ‘La. Autocorrelation
FIG. 2b. Autocorrelation
histogram
histogram
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FIG. 2d. Autocorrelation
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cell.
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moderate or marginal rhythmicity (m), and no rhythmicity (n). Four of 57 or 7% are pacemakers (regular intervals of 0.64, 0.64, 0.585, and 0.625 set) ; five or 9% exhibit marked rhythmicities (these had periods of 0.64, 0.64, 1.28, 1.76, and 1.88 set) ; 30 or 53% show moderate or marginal rhythms ; and 18 or 32% have no slow rhythms. A representative example of each of these four classesof units is shown in Fig. 2. Short Latency Correlations in Firing. Cross-correlation histograms using 1 msec bin size and 150 msec range reveal a general paucity of correlated firing. The general impression is that particular synaptic pathways between midbrain neurons and from afferent fibers to neurons which are prepotent and repeatedly successfulin eliciting postsynaptic action potentials are at a minimum. However, there do indeed exist some correlations in firing in pairs of reticular cells and there seemsto be a tendency for these correlations to be associatedwith the occurrence of rhythmicities in cells. More precisely, of the 32 pairs of cells for which we constructed crosscorrelation histograms, two exhibit very strong and short latency correlations in firing. These are shown in Figs. 3 and 4. Both these casesmust reflect shared excitation since the peak in the cross-correlation histogram straddles the zero reference line. Three of the cross-correlation histograms show definite but weaker correlations in firing. Two of these are shown in Fig. 5. In all three of these casesthe peak is lessthan 7 msecwide and occurs on one or the other side of the zero reference. Thus, these casesmight reflect either a synaptic connection between the recorded cells or an excitatory input shared by both of them. Six of the cross-correlation histograms exhibit very weak or marginal peaks. In these casesit is not possible to ascertain whether or not a real synaptic connection or shared input is being reflected by the data. A representative example of this class of crosscorrelation is shown in Fig. 6. These correlations have peaks that are only one, two or three bins wide or only marginally above the noise level. Finally, short latency correlation histograms for 21 pairs of cells clearly show the absenceof any significant correlation in firing. Thus, at least 5 of 32 pairs or 16%, and at most 11 of 32 or 34% of cell pairs show evidence of short latency correlation in firing. By the same token at least 66% and perhaps as many as 84% of cell pairs show an absenceof correlated firing. In these data, correlated firing is more likely to occur between cell pairs recorded with a single electrode than between cell pairs recorded with separate electrodes. Thus, of nine pairs of cells recorded with single electrodes, two exhibit strong broad correlations evidencing shared input, one exhibits a clear but weaker correlation, three exhibit marginal relations, and three exhibit no correlation in firing. Of 23 pairs recorded with separate electrodes, none exhibit strong broad correlations in firing, two exhibit clear but weaker correlations, three exhibit weaker and marginal relations and 18 exhibit no correlation in firing.
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Crosscorrelation rhythmic).
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The data suggest that the occurrence of short latency correlations in firing between cell pairs is associatedwith the occurrence of rhythmicities in the firing patterns of the cells, although the nature of that association is difficult to delineate precisely. Generally the tendency to exhibit a rhythmicity goes hand in hand with the tendency of the cell to correlate in firing with other cells. The more pronounced the rhythmicity the more prominent the correlation. Of the two pairs that exhibit strong, broad correlations reflecting shared excitation, both involve a pacemaker (P-M and P-m) ; of the three pairs that exhibit clear but weaker correlations, two contain a pacemaker or markedly rhythmic cell (P-n, m-M, m-n) : of the six pairs that exhibit weaker and marginal correlations, two include a pacemaker or markedly rhythmic cell (P-n, M-n, 3 of m-m, n-m) ; finally, of the 21 pairs that show no correlation, five contain pacemaker or markedly rhythmic cells (2 P-n, 3 of M-n, 16 of various combinations of n and m). Thus, of eleven cell pairs which contain at least one pacemaker or markedly rhythmic cell, two have strong broad correlations, two have clear but weaker correlations, two have weak but marginal correlations, and five show no correlations. A total of four of 11 to six of 11 such pairs show correlations. On the other hand, of 21 pairs which do not contain pacemakers or markedly rhythmic cells (that is, which contain only m or n cells) no pairs exhibit strong correlations, one exhibits clear but weaker correla-
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6. Crosscorrelation histogram for Cells l-l and l-2.
tions, four exhibit weaker and marginal correlations, and 16 exhibit That is, one to four of 21 such pairs exhibit clearly no correlations. correlations. This information can be separated for pairs obtained from single electrodes as compared to those that came from separate electrodes as follows. For cell pairs recorded with single electrodes, cell pairs containing at least one pacemaker or markedly rhythmic cell exhibit two strong broad connections, zero clear but weaker connection, zero marginal connections and zero no correlations. Cell pairs containing only moderate or marginally rhythmic cells and nonrhythmic cells recorded with single electrodes exhibit zero strong connections, one pair with clear but weaker correlations, three pairs with marginal correlations, and three pairs with no correlation. On the other hand for cell pairs recorded with separate electrodes, cell pairs containing at least one pacemaker or markedly rhythmic cell exhibit no strong correlations, two clear but weaker correlations, two marginal correlations, and five no correlations. Cell pairs recorded with separate electrodes and containing only nonrhythmic and moderate or marginally rhythmic cells exhibit zero pairs with strong correlations, zero pairs with clear but weaker correlations, one pair with marginal correlations, and 13 pairs with no correlations. Four of the five strong and clear-but-weaker correlations we found are exhibited by pairs at least one member of which is a pacemaker or markedly
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rhythmic cell whereas only nine of the 32 pairs involve P or M cells. On the other hand, 20 of the 27 pairs which exhibit clearly no correlation or marginal correlation are obtained from pairs which have only marginal rhythmic or nonrhythmic cells whereas 23 of the 32 pairs involve only m or n cells. It is particularly noteworthy that the only two strong correlations we found in 32 pairs occurred between pacemakers and nearby cells, and, moreover, that these two pacemakers were the only two pacemakers which we were able to record simultaneously with other units. Broad Rkythic Correlations in Cell Pairs. The rhythmicities of these cells have a spatial distribution in the sensethat neighboring cells exhibit slow rhythmicities which are in phase,whereas distant cells exhibit rhythmicities which are out of phase to various degrees. These conclusions are based on cross-correlation histograms with bin widths of 40 msec and ranges of 6 sec. Sixteen of our 32 celf pairs are comprised of pacemaker cells, markedly rhythmic cells, or marginally rhythmic cells. Of six such pairs recorded from a single electrode and therefore presumably relatively close together, five exhibit slow rhythmic waves with zero lag in the crosscorrelation histograms. A representative sample is shown in Fig. 7. Of ten cell pairs which were recorded with separate electrodes and, therefore, further apart as verified by subsequent histological analysis, eight exhibit slow rhythmic waves with a non-zero phase lag in the cross-correlation
FIG.
7. Slow rhythmic
correlation
between two cells recorded with
one electrode.
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8. SIow
rhythmic
correlation
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histogram. A representative example is shown in Fig. 8. In our data three cell pairs are exceptions to the rule that local pairs exhibit zero lag and separate pairs exhibit nonzero lag. Each one of these pairs involves a single unit (unit 49-2) which is peculiar. If this particular unit were 180 degrees reversed in phase then all six of our local pairs would exhibit zero lag and all ten of our pairs from separate electrodes would exhibit nonzero lag. DISCUSSION The main fiindings in this work are : (i) There exist pervasive slow rhythmicities often partially masked behind random firing in spike trains of midbrain neurons. (ii) The tendency for a midbrain neuron to exhibit correlations in firing with other midbrain neurons seems to increase with the degree of rhythmicity apparent in the cell. (iii) Neighboring cells tend to exhibit in-phase broad rhythmic correlations, whereas cells separated by hundreds of microns tend to exhibit out of phase broad rhythmic correlations. A noteable feature of these slow rhythms is that the most prominent intervals seem to be integer multiples of a common base interval of 0.64 sec. One of our two most marked pacemakers has a firing interval of this value, while the other pacemaker, although also clearly firing at this interval,
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tends quite often to skip two firings. This results in a very prominent peak at 1.92 set in the auto-correlation histogram for this unit as seen in Fig. 4 (unit 38-1). Many of the slower rhythms in marked or moderate/marginal cells occur with intervals of about 1.3, 1.9, and 2.5 set, with 1.3 set by far the most common. In earlier studies, Holmes and Houchin have described prominent slow waves with 1.5-2.0 set periods in the spike trains of cortical neurons of anesthetized rats (6, 7). Moreover, they found that neuron pairs in the cortex exhibited slow rhythmic correlations with the same period which were in phase if the neuron pairs were in the same coronal section and out of phase otherwise. They suggested that their data are consistent with a travelling wave propagating at 5-10 cm/set anterior to posterior. The degrees of both the rhythmicities and cross-correlations increased with depth of anesthesia. Holmes and Houchin suggest that these phenomena may be due to either groups of impulses from some subcortical structure bombarding the cortex or to a spread of activity within the cortex. The fact that previous investigators of the reticular formation have not remarked on the pervasive rhythmicity we have described, may reflect a species difference in that most previous investgations have been performed on cats. Also, we should note that pilot studies on a small number of anesthetized rats in our laboratory provided a very markedly reduced occurrence of slow rhythms although these did occur in this preparation in the absence of artificial respiration. The rhythm may relate to the animals’ respiration, but if this is so it is a subtle relationship and not so simple as one might suppose. For example, the rhythmic firing intervals do not correspond to the period of the respirator. A tentative picture consistent with these data is that local regions in midbrain sometimes exhibit synchronized firing activity upon which any other afferent activation is superimposed. Slightly distal regions, however, would be out of phase with each other. This situation could reflect either the propagation of a slow wave through the midbrain or the existence of separate subsystems of cells each tending to fire synchronously within itself but remaining not necessarily synchronized with other systems (8, 16). If this picture is generally valid there are some exceptions in that some local neuron pairs are out of phase and some distal cell pairs are in phase. For example, one pair of cells including a markedly rhythmic cell and a moderate or marginally rhythmic cell obtained from separate electrodes, exhibited broad out of phase relationships consistent with the generalization but also exhibited weak but clear short latency correlations in firing. Another unit (unit 49-2) was out of phase with a local neighboring cell but in phase with two distal cells recorded with the same electrode. This cell did not exhibit short latency correlations with any of the other three. One might speculate that the hypothetical wave advances in a not totally
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homogeneous fashion extending isolated branches of synchronizing influence into as yet uninvaded regions or alternatively that separate functionally synchronized subsystems might interpenetrate anatomically. REFERENCES 1. AMASSIAN, V. E., and H. J. WALLER. 1958. Spatiotemporal patterns of activity in individual reticular neurons. In “Reticular Formation of the Brain,” R. H. Jasper et al. [Eds.]. Little Brown, Boston. 69-108. 2. BRYANT, JR., H. L., A. R. MARCOS, and J. P. SEGUNM). 1973. Correlations of neuronal spike discharges produced by monosynaptic connections and by common inputs, J. Neuro~hysiol. 36 : 205-225. 3. GERSTEIN, L., and D. H. PERKEL. 1972. Mutual temporal relationships among neuronal spike trains, Statistical techniques for display and analysis, Biophys, J. 12 : 453-473. 4. GROVES, P. M., S. W. MILLER, M. V. PARKER, and G. REBEC. 1973. Organization by sensory modality in the reticular formation of the rat. Brain Res. 54: 207-224. ,5. 6. 7.
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GUYTON, A. C. 1947. Measurement of the respiratory volumes of laboratory animals, Amer. J. Physiol. 150 : 70-77. HOLMES, O., and J: HOUCHIN. 1966. Units in the cerebral cortex of the anaesthetized rat and the correlations between their discharges, J. Physiol. 187 : 651-671. HOLMES, O., and J. HOUCHIN. 1967. Analysis of the activity of one type of spontaneously discharging unit in the cortex cerebri of the anaesthetized rat, J. Physiol. 193: 173-186. MACGREGOR, R. J. 1972. A model for reticular-like networks: Ladder nets, recruitment fuses, and sustained responses, Bra& Res. 41 : 345-363. MACGREGOR, R. J., R. PRIETO-DIAZ, S. W. MILLER, and P. M. GROVES. 1973. Statistical properties of neurons in the rat mesencephalic reticular formation, Brain Res. 64 : 167-187. MACGREGOR, R. J., and E. R. LEWIS. 1975. Neural Modeling. Plenum Press, New York. (To be published, See discussion). MANOHAR, S., H. NODA, and W. R. ADEY. 1972. Behavior mesencephalic reticular neurons in sleep and wakefulness, E.@. Neural. 34: 140-157. MOORE, G. P., D. H. PERKEL, and J. P. SEGUNDO. 1%6. Statistical analysis and functional interpretation of neuronal spike data, Am. Rev. Physiol. 28: 493-522. MOORE, G. P., J. P. SEGUNDO, D. H. PERKEL, and H. LEVITAN. 1970. Statistical signs of synaptic interaction in neurons Biophys. J. 10: 876-900. NAKAHAMA, H., N. ISHII, and M. YAMAMOTO. 1972. Markov process of maintained impulse activity in central single neurons, Kybernetik 11: 61-72. PERKEL, D. H., G. L. GERSTEIN, and G. P. MOORE. 1967. Neuronal spike trains and stochastic point processes (I and II), Biophys. J. 7, 391-440. SCHEIBEL, M. E., and A. B. SCHEIBEL. 1958. Structural substrates for integrative patterns in the brain stem reticular core, pp. 31-56. In “Reticular Formation of the Brain.” H. H. Jasper et al. [Eds.]. Little, Brown, Boston. SKVARIL, J., T. RADIL-WEISS, 2. BOHDANECKY, and J. SYKA. 1971. Spontaneous discharge patterns of mesencephalic neurons: interval histogram and mean interval relationship, Kybernetik 9: 11-15. STRONG, D., W. TATTON, and D. CRAPPER. 1971. Solid-state amplitude discriminator for neural units. IEEE Trans. Bio-Med. Eng. BME-18: 237-240.