1Department of Physiology and Biophysics and 2Neuroscience Program, University of South Florida Health Sciences Center, Tampa, Florida 33612-4799
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ABSTRACT |
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Chang, E. Y., K. F. Morris, R. Shannon, and B. G. Lindsey. Repeated Sequences of Interspike Intervals in Baroresponsive Respiratory Related Neuronal Assemblies of the Cat Brain Stem. J. Neurophysiol. 84: 1136-1148, 2000. Many neurons exhibit spontaneous activity in the absence of any specific experimental perturbation. Patterns of distributed synchrony embedded in such activity have been detected in the brain stem, suggesting that it represents more than "baseline" firing rates subject only to being regulated up or down. This work tested the hypothesis that nonrandom sequences of impulses recur in baroresponsive respiratory-related brain stem neurons that are elements of correlational neuronal assemblies. In 15 Dial-urethan anesthetized vagotomized adult cats, neuronal impulses were monitored with microelectrode arrays in the ventral respiratory group, nucleus tractus solitarius, and medullary raphe nuclei. Efferent phrenic nerve activity was recorded. Spike trains were analyzed with cycle-triggered histograms and tested for respiratory-modulated firing rates. Baroreceptors were stimulated by unilateral pressure changes in the carotid sinus or occlusion of the descending aorta; changes in firing rates were assessed with peristimulus time and cumulative sum histograms. Cross-correlation analysis was used to test for nonrandom temporal relationships between spike trains. Favored patterns of interspike interval sequences were detected in 31 of 58 single spike trains; 18 of the neurons with significant sequences also had short-time scale correlations with other simultaneously recorded cells. The number of distributed patterns exceeded that expected under the null hypothesis in 12 of 14 data sets composed of 4-11 simultaneously recorded spike trains. The data support the hypothesis that baroresponsive brain stem neurons operate in transiently configured coordinated assemblies and suggest that single neuron patterns may be fragments of distributed impulse sequences. The results further encourage the search for coding functions of spike patterns in the respiratory network.
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INTRODUCTION |
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Many brain stem neurons exhibit
"spontaneous" activity in the absence of any specific experimental
perturbation (Barman and Gebber 1992; Mason
1997
). Neurons with these properties include baroresponsive
cells, and neurons that, while functionally associated with the
respiratory network as indicated by correlation analysis, may have
little or no respiratory modulation of their individual firing rates
(Li et al. 1999
; Lindsey et al. 1992b
,
1998
). Patterns of distributed synchrony embedded in
such "background" activity have been detected, suggesting that it
represents more than the baseline firing rates of brain stem neurons
subject only to up or down rate modulation (Lindsey et al.
1997
).
There is also a growing body of evidence for repeated sequences of
interspike intervals not detected by traditional measures of firing
rate (Abeles et al. 1993; Dayhoff and Gerstein
1983b
; Ku and Wang 1991
; Lestienne and
Strehler 1987
; Prut et al. 1998
; Villa et
al. 1999
). This advance followed the development of appropriate tools (Abeles and Gerstein 1988
; Dayhoff and
Gerstein 1983a
; Frostig et al. 1990
;
Tetko and Villa 1997
), and together with the synchrony data, motivated the present work. The initial aim was to test the
hypothesis that nonrandom sequences of impulses recur in
cardiorespiratory-related brain stem neurons that are elements of
correlational neuronal assemblies. The detection of such "favored"
patterns in single brain stem neurons led to a search for patterns of
impulses distributed among multiple spike trains. The presence of such
patterns would provide additional evidence for cooperation among
baroresponsive respiratory-related neurons proposed to have roles in
the regulation of breathing (Arata et al. 2000
;
Lindsey et al. 1998
). Preliminary accounts of these
results have been published (Chang et al. 1995
; Lindsey et al. 1995
).
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METHODS |
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Many of the materials and methods have been described in detail
elsewhere (Lindsey et al. 1998). All experiments were
performed under protocols approved by the University of South
Florida's Animal Care and Use Committee. Data were obtained from 15 adult cats of either sex (2.0-5.7 kg). Animals were initially
anesthetized with sodium thiopental (22.0 mg
kg
1 iv); anesthesia was
maintained with Dial-urethan (allobarbital; Ciba, 60.0 mg
kg
1; urethan, 240 mg
kg
1). Blood pressure and
respiration were monitored continuously. Animals were given additional
Dial-urethan if there was an increase in blood pressure or respiration
in response to periodic noxious stimuli (toe pinch). Animals received
dexamethasone (2.0 mg/kg) and atropine (0.5 mg
kg
1). Arterial blood
pressure, PO2, PCO2, pH,
[HCO3
] and end-tidal
CO2 were monitored and maintained within normal limits. Core body temperature was maintained at 38.0 ± 0.5°C.
The vago-sympathetic nerve trunks were isolated within the neck between
1 and 4 cm caudal to the carotid sinus and sectioned to eliminate vagal
afferent feedback from lung receptors. The influence of aortic
baroreceptors via the vagus nerve was also eliminated. The left
C5 phrenic rootlet was isolated, desheathed and
cut for subsequent recording. Animals were paralyzed with a bolus of
gallamine triethiodide (2.2 mg
kg1) followed by constant
infusion (0.4 mg · kg
1 · h
1) to reduce brain stem
movements. An occipital craniotomy was performed, and the caudal
portion of the cerebellum was aspirated to expose the brain stem. In
most experiments, a unilateral or bilateral thoracotomy further reduced
brain stem movements. These animals were ventilated with 100%
O2 to counteract the hypoxia due to
ventilation-perfusion mismatching that may occur in such preparations.
The functional residual capacity of the lungs was maintained within
normal range by adjustment of the end expiratory pressure.
Periodically, the upper airways were suctioned and the lungs were
hyperinflated. At the end of the experiments, cats were overdosed with
pentobarbital sodium and perfused intracardially with 0.9% NaCl,
followed by 10% neutral-buffered Formalin solution. Brain stem
sections were prepared for histological examination to verify the
placement of electrodes.
Neuron recording
Neuronal impulses were monitored extracellularly with planar
arrays of six to eight individual tungsten microelectrodes (3-5 M)
placed concurrently in two to four of five sampled domains; boundaries
of stereotaxic coordinates were as previously reported (Lindsey
et al. 1998
; Morris et al. 1996
). Individual
neurons were labeled with a number and abbreviations that denoted the site at which their spike trains were recorded: RM, rostral midline in
the region of n. raphe magnus; CM, caudal midline in the region of
nucleus raphe obscurus; CV, caudal ventrolateral medulla; RV, rostral
ventrolateral medulla; and N, nucleus tractus solitarius or NTS.
Signals were amplified, filtered (100-5,000 Hz band-pass), and
recorded on either two or three 16-channel FM instrumentation recorders
together with phrenic nerve activity, a stimulus marker, systemic blood
pressure, and, in some experiments, carotid blood pressure. Common
synchronization pulses (5 Hz) were recorded on each tape.
Stimulus protocols
Signals were recorded for at least 15 min prior to the onset of baroreceptor stimulation by occlusion of the descending aorta with an embolectomy catheter or by unilateral injection of arterial blood into the carotid sinus through a catheter connected to a pressure transducer following occlusion of the lingual and common carotid arteries. Series of three to six inflations, each having a duration of approximately 30 s, were applied during each recording. Trials were separated by 3- to 5-min intervals to allow a return to baseline values.
Data entry and analysis
Single neuron action potentials and synchronized timing pulses
from each tape were converted to transistor-transistor logic (TTL)
pulses and entered into a laboratory computer. Multiunit phrenic nerve
activity was amplified and fed into a resistor-capacitor "leaky"
integrator with a time constant of 200 ms. The resulting analog signal
and those corresponding to systemic blood pressure, carotid blood
pressure, and a stimulus marker were digitized with 12-bit precision at
20 Hz. Data files were merged and first analyzed as detailed elsewhere
(Lindsey et al. 1998). The times of onset of the
inspiratory and expiratory phases were derived from the phrenic nerve
signal and inserted into each data file. Two previously described
statistical methods were used to decide whether each neuron had a
respiratory-modulated firing rate (Morris et al. 1996
;
Orem and Dick 1983
).
Changes in the peak amplitude of integrated phrenic motoneuron activity
and respiratory phase durations associated with baroreceptor stimulation were assessed from measures of integrated efferent phrenic
nerve activity. A change was considered significant when measurements
departed more than 2 SD from the average value of at least 10 consecutive preceding control cycles (Lindsey et al. 1998). Spike trains were evaluated for responses to
baroreceptor stimulation with peristimulus time histogram and
cumulative sum histograms (Davey et al. 1986
). An
additional method was used to evaluate spike trains for firing rate
changes in respiratory cycles during baroreceptor stimulation. The null
hypothesis was that peak and average firing rates were not different
from control. To reject the null hypothesis, these parameters, averaged
over at least three stimulus trials, had to be significantly different from the mean of control cycles just preceding each of the stimuli (P < 0.05, Student's t-test).
Cycle-triggered histograms were used to classify neurons with significant respiratory modulation as inspiratory (I) or expiratory (E) neurons according to the phase during which they were more active. Neurons with peak firing rates in the first half of the phase were categorized as decrementing (DEC) neurons. Neurons with peak firing rates in the second half of the phase were classified as augmenting (AUG) neurons. Phase spanning neurons were classified first by the phase with peak average activity and then by the phase transition of greater activity, e.g., I-EI. Respiratory-modulated neurons with patterns not easily classified were denoted as "Others" (OTH). Neurons that were not respiratory modulated were designated NRM. Cardiac cycle-triggered histograms were calculated in some experiments.
Cross-correlograms were calculated for each pair of simultaneously
recorded spike trains and evaluated for significant features (Perkel et al. 1967b). A detectability index (DI, equal
to the ratio of the maximum amplitude of departure from background, D, to the background, divided by the standard deviation of the correlogram noise) was used to test significance (Aertsen and Gerstein
1985
). Values >2 were considered significant. If this
criterion was met, the D/background ratio was used as an indicator of
the visibility or strength, S, of the correlation.
All spike trains were screened with autocorrelograms (Perkel et
al. 1967a) to aid interpretation of cross-correlograms
(Moore et al. 1970
) and to ensure that none of the data
sets analyzed had a degree of autocorrelation suggestive of rapid
variations in firing rates that could result in an underestimation of
the numbers of expected patterns (see Abeles and Gerstein
1988
).
Detection of favored patterns in single spike trains
Favored patterns in the spike trains of single neurons were
detected with two methods developed by Dayhoff and Gerstein
(1983a). In the quantized Monte Carlo method, all interspike
intervals were first converted to integer values. A minimum temporal
resolution or bin value was defined for each run, and each interval was
assigned an integer value based on the minimum bin value. For example, if the minimum bin value was 2.0 ms, then intervals >0.0 ms and <2.0
ms were assigned the value "1," intervals
2.0 ms and <4.0 were
set to "2," etc. Repeated sequences of interspike intervals or
"words" with little temporal jitter from one occurrence to the next
are more likely to be detected using small bin values. Words with more
temporal variability from one occurrence to the next are better
detected using larger bin values. Because one has no a priori knowledge
of what type of words, if any, will be found, various bin values should
be used. In this study, at least five different temporal resolutions
were used in sequential pattern searches of each spike train; values of
2.0, 4.0, 8.0, 16.0, and 32.0 ms, or 2.5, 5.0, 10.0, 25.0, and 50.0 ms,
were used most frequently.
Each spike train was searched for all excessively recurring sequences
of "quantized" interspike intervals consisting of from 2 to 10 intervals. The original quantized spike train was searched; all words
occurring two or more times were tallied. The quantized interspike
intervals were then randomly shuffled, and the shuffled train was
searched for recurring words. This process was repeated 99 times. The
numbers of occurrences of words of each length detected two or more
times in the original train were then compared with the numbers of
words of each length occurring two or more times in all the shuffled
trains. If words of a particular length and repetition value had a
greater frequency of occurrence in the original train than in any of
the shuffled trains, the null hypothesis that they were all generated
by a random process was rejected. Small numbers of patterns that
exceeded the maximum shuffled count value by one were not reported as
significant to reduce the likelihood of type I errors (false positives)
as recommended by Dayhoff and Gerstein (1983b).
Two types of significant results could be detected. 1) If a word of a particular length had a particular number of occurrences, and no such words were detected in any of the randomly shuffled trains, then the occurrences of this word were considered statistically significant. The actual interspike sequences could then be listed with a utility program. 2) A nonrandom process would also be indicated if multiple sets of words of a particular length and particular number of occurrences were detected in the original train and fewer sets of such words (but at least one) were in the shuffled trains. However, in this case simply listing the sets of words would not indicate which sets were generated by a nonrandom process: some sets had a higher than chance probability of having been generated by a random process. The template matching method can be used in searches for specific nonrandom sequences.
The template match algorithm used requires that a specific sequence of interspike intervals in milliseconds be defined together with a "wobble" factor that determined the amount of temporal jitter or noise allowed for each interval in the sequence. For example, if a wobble factor of 3.0 ms is used, then the interval between each spike in the sequence and the first spike in the sequence can vary by ±1.5 ms inclusively and be counted as a matching interval. The program also permits the user to allow up to two extra or missing spikes in a sequence and still have a word match the template, if all the remaining intervals fall within the template's wobble time windows. The "extra" and "missing" spike options can be used separately or together in a search; neither option was used in this study.
The template matching method was used to search a spike train for multiple occurrences of a specific sequence of interspike intervals and then to search 99 shuffled versions of the same train for the same word. If the number of occurrences in the original train was greater than the maximum found in all shuffled trains, then the word pattern was reported to recur excessively.
In this work, the template method was used to search the spike train
for sequences that were similar to a excessively recurring quantized
patterns detected by the Monte Carlo method and to evaluate them for
significance. As discussed in Dayhoff and Gerstein
(1983a), the quantized Monte Carlo and template matching
methods are complementary. The two methods treat pattern variability
differently. Consequently, a pattern detected with one method may not
be detected with the other.
Detection of favored patterns in multiple spike trains
The method of Abeles and Gerstein (1988) was used
to search for repeated patterns of action potential sequences
distributed among several simultaneously recorded spike trains. The
relative times of the spikes within each iteration of the pattern had
to be exactly the same; however, events within and between patterns were allowed. The number of spikes that constituted the pattern defined
its "complexity." Patterns of either 4 or 5 spikes that fit within
a 500-ms time window and occurred at least twice were counted. The
total number of patterns of each complexity were compared with 99%
significance levels derived from the ad hoc probability calculation
described in the APPENDIX of Abeles and Gerstein
(1988)
. Observed numbers of patterns with a particular spike
sequence order were also evaluated for significance with calculated
99% confidence limits.
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RESULTS |
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The spike trains evaluated in this work were drawn from a database
containing information on 707 neurons collected during experiments done
in collaboration with A. Arata and Y. M. Hernandez; changes in
average firing rates of these neurons during pressure stimulation of
baroreceptors and results of correlational analyses have been reported
(Arata et al. 2000; Lindsey et al. 1998
).
In this parent database, 385 of 387 (>99%) medullary raphe neurons had firing probabilities greater than zero throughout the respiratory cycle; 168 of 320 (52%) of the ventrolateral medullary neurons were also classified as "tonic."
A subset of the tonic neurons represented in the database were
evaluated in the present study on interspike interval patterns in
baroresponsive neurons. The aim was to search for repeating impulse
sequences that could potentially influence pattern-sensitive synaptic
mechanisms (Erulkar 1983; Segundo et al.
1963
; Wiersma and Adams 1950
; Zucker
1999
), or, when distributed among several neurons, indicate
transient configurations of functional assemblies. Such patterns could
be "subtle" and not necessarily appear as firing rate changes
locked to a particular phase of the respiratory or cardiac cycle.
Neurons with tonic firing patterns were targeted because such
neurons may have potential modulatory actions on motor and premotor neurons and other cells functionally antecedent to them (Lindsey et al. 1998; Morris et al. 1996
). Some of the
spike trains were selected because of their short-time scale
correlations with those of other simultaneously recorded neurons. Such
properties aid placement of neurons in functional contexts. Recordings
with well-isolated single neuron spike waveforms were analyzed.
Commonly used methods that sort two or more different waveforms in
recordings either from conventional electrodes or tetrodes may
"miss" spikes because of waveform overlap or otherwise distort
timing relationships (e.g., Quirk and Wilson 1999
), and
thereby contribute to type I and type II errors in pattern searches.
Patterns in single spike trains
Figure 1A shows one favored pattern, represented in a sequence detected with a quantization value of 25.0 ms. The Monte Carlo search report (Fig. 1B) that included this pattern lists the numbers of patterns or "words" of a particular length that occurred K or more times. The third column (Count) gives the number of different patterns detected, each of the particular length and frequency of occurrence indicated in the first and second columns, respectively. For example, the highlighted row indicates that seven different patterns, each with five intervals, occurred at least four times. The null hypothesis was that the seven different patterns were not more than expected by chance in a spike train with the same interspike intervals, but with those intervals randomly shuffled. To test the hypothesis, the pattern search was repeated in 100 shuffled data sets. Five patterns of the same class were detected, leading to rejection of the null hypothesis.
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As noted in METHODS, if no patterns of length five and four iterations had been detected in the shuffled trains, then all of the listed patterns would have been considered significant. Because this condition was not true for this case, the list of the original seven patterns shown in Fig. 1C does not indicate which patterns can be considered nonrandom under the Monte Carlo test. The template method was used to search for specific interspike interval sequences that occurred more than expected under the null hypothesis.
This template method is illustrated in Fig. 2. The top trace shows a simulated template spike sequence. Another sequence with similar interspike intervals is considered a match if the spikes fall within the specified time windows indicated by the shaded regions (e.g., 2nd trace). This procedure allows for some wobble in the times of occurrence. In the present work, the wobble was ±1/2 the quantization bin value. The method also allows matches if the sequence includes an extra or missing spike. This option was not used in this study. One hundred shuffled trains that retained one copy of the template were also examined. If each had fewer matches than the original data, then the template was considered significant.
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One of the interspike intervals sequences in the quantized pattern
4-3-6-4-3 (Fig. 1C) was used as a template. The times when matches to the template were detected are shown in Fig.
3A. The top trace
shows a firing rate histogram of spontaneous activity in a raphe
obscurus neuron that responded to baroreceptor stimulation with an
increase in firing rate (not shown). The bottom trace shows
when the matching sequences occurred. The 16 matches exceeded the
number expected under the null hypothesis. The thicker lines indicate
close or overlapping occurrences of the favored pattern. Two of the
words that included an overlapping region are detailed in Fig.
3B. Note that the second sequence had a different quantized value because of the allowed wobble. The possibility of several occurrences of a pattern having overlapping fragments that are elements
of a larger pattern was recognized by Dayhoff and Gerstein (1983a). Another example is described below and shown in Fig. 5.
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Favored patterns of interspike interval sequences were detected in 31 of 58 spike trains recorded in 12 cats. Table 1 is a summary of the evaluated properties of the screened neurons. Unless otherwise noted, the reported patterns were detected in spike train data samples recorded during control conditions prior to baroreceptor stimulation protocols.
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Each train was searched for patterns after intervals were transformed to a sequence of integers that were multiples of at least five different minimum quantization bin values. For a particular quantization bin value, the algorithms searched for all patterns composed of 2-10 interspike intervals. The length of the longest significant sequence found in each of 31 spike trains with detected favored patterns ranged from 2 to 10 intervals (Fig. 4).
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Ten examples of quantized interspike interval patterns detected in seven different animals are detailed in Table 2. Both the binwidths (temporal resolution) of the listed quantized patterns and the shortest interspike intervals found with the template matching method are included to give an indication of the absolute time scale of the patterns. The template matching method was used to identify specific sequences.
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All words of a particular length and repetition value were reported as significant when there were no occurrences in any of the shuffled data sets of words with those values. One such sequence is shown in Table 2, fourth row from the bottom. Template matching revealed that this sequence recurred three times as overlapping fragments of a longer word composed of 30 interspike intervals (Fig. 5A). This sequence and a second (underlined regions of the firing rate histogram) were found during periods when blood pressure was elevated (Fig. 5B). The inset shows spike times on an expanded time scale for a segment of the data that included the long word. The interspike intervals of the detected sequence were relatively uniform as compared with more variable firing rates in other portions of the spike train. This pattern was detected in a data sample selected from a larger set of spike train data after a search with the same parameters failed to detect favored patterns in data acquired before baroreceptor stimulation. The perturbations of blood pressure were sufficient to reduce significantly the amplitude of integrated phrenic motoneuron activity (Fig. 5B, arrows, bottom trace).
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The results suggest that favored patterns were not simply a consequence of firing rate changes locked to the respiratory cycle or cardiac cycles. Significant sequences were detected in nine single neurons with no respiratory modulation of their rates; the firing rates of seven changed during baroreceptor stimulation. Repeating patterns were not detected in nine other neurons with respiratory modulated firing rates, including five baroresponsive cells. Cardiac cycle-triggered histograms calculated for four of the neurons represented in Table 2 (bottom 4 rows) are shown in Fig. 6, together with first-order interspike intervals and autocorrelograms. The interval between the peaks in the cardiac cycle-triggered histogram of the neuron represented in Fig. 6C was 310 ms. The interspike intervals of the favored pattern for this neuron (Table 2, row 8), or of two other neurons from the same animal (Table 2, row 2), were not simple multiples or fractions of that inter-peak interval. The other three spike trains represented in Fig. 6 had no obvious modulation of their average firing rate that was time locked to the cardiac cycle. One neuron did have a regular periodic discharge; the primary peak in the first-order interspike interval histogram included events ranging from 40 to 95 ms, with the peak at 57.5 ms (Fig. 6D). The intervals represented in the quantized favored pattern 3-3-2-2-3-3 for this neuron shown in Table 2 (bottom row) were within this range. This number of occurrences of this pattern with slightly longer intervals separated by slightly shorter intervals was greater than expected by chance.
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Impulses in 18 of the 31 neurons with detected favored patterns were correlated on a short-time scale with other simultaneously recorded spike trains. Examples of primary correlogram features indicative of paucisynaptic interactions are shown in Fig. 7, A-C. Correlogram features, respiratory-related discharge patterns, and firing rate changes during baroreceptor stimulation are graphically enumerated in labeled circles that represent neurons (Fig. 7, D-L). Circles with wider borders correspond to neurons with detected favored patterns.
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Patterns in multiple spike trains
Our implementations of the pattern detection algorithms were
tested with searches for "known" patterns inserted into independent spike trains generated with the network simulation program SYSTM11 (MacGregor 1987). Figure
8A shows an example of the
data used in the validation process for the detection of patterns
distributed among several spike trains. The top panel
displays the firing times of 10 simulated neurons. The three arrows
indicate the times at which copies of the distributed pattern were
inserted into 5 of the 10 spike trains. The panel in the bottom
left of Fig. 8A details one copy of the pattern; each
of the five spikes that constituted the pattern was successively
inserted into one of five trains: 3, 2, 1, 5, and
7, as indicated by the arrows. Spike trains were re-ordered
in this panel to show the order of insertion. The search report for the
example of the validation process indicated detection of the added
sequences (Fig. 8B). The number of patterns that repeated
three times for complexity 4 and 5 were greater than the number expected under the null hypothesis at the 99% confidence limit.
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The ad hoc method can determine whether the total number of distributed patterns is greater than expected under the null hypothesis. Unlike the single neuron pattern methods, it does not, in general, allow identification of specific individual patterns as significant. However, when the number of patterns is small, the method can identify particular subsets of patterns as significant, e.g., those composed of a given order of occurrence based on neuronal identities. In Fig. 8, the numbers of detected sequences that repeated a significant number of times matched the number inserted. Five different patterns of complexity 4 each occurred three times. These patterns represented the five possible combinations of complexity 4 for the one inserted pattern of complexity 5. For example, if the pattern A-B-C-D-E (representing a sequence of 5 spikes in 5 different neurons) were inserted three times, then each of the following patterns would also have three occurrences: A-B-C-D, A-B-C-E, A-B-D-E, A-C-D-E, and B-C-D-E. A utility program confirmed that the pattern of complexity 5, which occurred three times, matched the times of the inserted patterns.
Data sets composed of 4-11 spike trains recorded simultaneously during
control periods were screened for repeated patterns of interspike
interval sequences. The search window was set to detect patterns with a
total time span of 500 ms. Patterns could include more than one spike
from the same neuron. The minimum complexity was set to 4. Because of
the computational expense of the ad hoc method, the maximum complexity
was set to 5. Prior to searches for distributed patterns, all spike
trains were screened with autocorrelograms. Firing rate histograms
(Fig. 9A) and autocorrelograms (Fig. 9B) from one set of neurons (Table
3, group 7) are illustrated. None of the data sets analyzed had a degree of autocorrelation suggestive of rapid variations in firing rates or bursts that could
result in an underestimation of the numbers of expected patterns (see
Fig. 1B in Abeles and Gerstein 1988
). Neither
did any of the neurons have a periodic firing pattern such as that shown in Fig. 6D.
|
|
The number of patterns composed of 4 or 5 spikes exceed the number expected under the null hypothesis (99% confidence limits) in 12 of 14 data sets from 10 animals (Table 3). An example of a search report for one sample (group 2, Table 3) is shown in Fig. 10A. For complexities 4 and 5, the numbers of patterns that occurred twice exceeded the values expected for independent spike trains. The temporal resolution for all searches was set to either 0.5 or 1.0 ms because the objective was to screen for relatively precise iterations of temporal patterns. However, time bin resolutions up to 4.0 ms were also used to scan one data set (Table 3, group 10b). With these less stringent match criteria, patterns that repeated up to four times were detected (Fig. 10B).
|
When significant numbers of patterns were detected in a set of spike trains, the next step was to count the occurrences of specific sequences of spikes that fit within the selected time window. To identify subsets of the patterns that were most likely to be nonrandom, the observed number of patterns with a particular spike order was compared against the calculated number that defined the 99% confidence limit. All 12 of the data sets with more spatiotemporal patterns than expected under the null hypothesis included significant subsets of spike sequences distributed among spike trains recorded at 2 or more sites (Table 3). For example, a search of the data set represented in Fig. 10A and Table 3, group 2, detected 80 distinct patterns with spike order 1-1-2-4 that occurred twice. One specific sequence of two spikes in neuron 1 followed by spikes in neurons 2 and 4 is represented in Fig. 11A.
|
Spike trains in this data set were also evaluated with the Monte Carlo and template matching methods for the detection of patterns in single neurons as described in the preceding section of RESULTS. For example, the distributed pattern sequence 1-1-2-4 (Fig. 11A) detected with the ad hoc method included a fragment of a significant template pattern in neuron 1 (boxed area around spike code 1 in Fig. 10A). The template and matching patterns are shown in Fig. 11B. Overall, data from six of seven animals screened for both single and multi-neuron patterns had favored sequences in single spike trains and significant subcategories of distributed patterns that included intervals in those impulse trains.
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DISCUSSION |
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The results of this study confirmed the hypothesis that nonrandom
sequences of interspike intervals recur in baroresponsive respiratory-related neurons. Search algorithms detected both single neuron patterns and sequences distributed among several spike trains
recorded in parallel at multiple sites implicated in respiratory control, thereby extending an earlier report of favored patterns in
single brain stem neurons (Ku and Wang 1991).
Furthermore, the data demonstrated the occurrence of patterns in
neurons that were elements of correlated functional groups and
suggested that some single neuron patterns may have been fragments of
distributed impulse sequences. Together with our previous findings of
distributed patterns of synchrony (Lindsey et al. 1997
),
the present sequence data supplement a large body of evidence, based on
several other methods, for nonrandom timing relationships among
respiratory-related brain stem neurons (Lindsey et al.
2000
; Utikal 1997
) and the hypothesis that those
neurons operate in transiently configured assemblies (Arata et
al. 2000
).
The patterns detected in this study could represent "markers" or
fragments of markers of a network repeatedly engaged in similar operations. The possibility of larger patterns identified from overlapping words was predicted by Dayhoff and Gerstein
(1983a), who suggested that such patterns could
reflect, for example, a second iteration of a process that starts
before the previous one is completed.
Some patterns were composed of relatively regular interspike intervals,
a property of some types of brain stem neurons recorded in vivo (e.g.,
Barman and Gebber 1992; Mason 1997
).
Regular patterns could also reflect moments when the firing rate limit
of the neuron is transiently constrained by refractoriness, although
this cannot be the sole explanation, given the variations in rate
apparent at other times in spike trains with such patterns (e.g., Fig. 5).
Another possibility is that the detected spike patterns represent
"signatures" of neuronal relationships. For example, a circuit that
promotes synchrony by recurrent inhibition (Fig.
12) could contribute to the generation
of regular intervals in individual spike trains and distributed firing
patterns and correlations such as those reported here and elsewhere
(Lindsey et al. 1992a, 1994
). Spike
timing relationships in multiple channels also have potential
"coding" properties (reviewed in Fetz 1997
).
|
This work focused on the detection of relatively precise temporal patterns. The extra and missing spike options of the template method were not used in this study. Searches for both single neuron patterns and distributed patterns always included small bin resolutions of 0.5-2.0 ms. Searches were not exhaustive. Selected quantization bin values used to screen each spike train were small subsets of possible values, and, because of the computational expense, the range of successive interspike intervals screened for patterns was limited. The failure to detect favored sequences of interspike intervals should not be construed as evidence that patterns did not exist.
The results of supplementary screening with "coarser" temporal
resolutions did indicate the presence of more variable patterns. Previous work unmasked overlapping subsets of neurons represented in
different patterns of distributed synchrony when the template resolution was changed (Lindsey et al. 1997). That
earlier observation suggested that multiple information streams are
conveyed concurrently by fluctuations in the synchrony of ongoing activity.
We emphasize that the potential "information content" in the
relative firing times of single and multiple neurons must be evaluated
with caution. The influence of action potentials may change as a
function of many variables, including history-dependent mechanisms that
influence transmitter release and postsynaptic actions (Erulkar
1983; Segundo et al. 1963
; Zucker
1999
), branch point filtering of spike sequences in axons
(Baranes-Shahrabany et al. 1984
), and concurrent
activities in parallel channels (Lindsey and Brown
1982
). In this regard, multi-array recording technologies offer
an efficient approach for simultaneously monitoring many neurons
subject to shared stimulus, history, and state-dependent conditions.
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ACKNOWLEDGMENTS |
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The authors thank J. Gilliland, C. Orsini, and T. Krepel for excellent technical assistance.
This work was supported by National Institute of Neurological Disorders and Stroke Grant NS-19814.
Present address of E. Y. Chang: Baylor College of Medicine, Houston, TX 77030.
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FOOTNOTES |
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Address for reprint requests: B. G. Lindsey, Dept. of Physiology and Biophysics, University of South Florida Health Sciences Center, 12901 Bruce B. Downs Blvd., Tampa, FL 33612-4799 (E-mail: blindsey{at}hsc.usf.edu).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 18 January 2000; accepted in final form 16 May 2000.
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REFERENCES |
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