The Journal of Neurophysiology Vol. 78 No. 3 September 1997, pp. 1714-1719
Copyright ©1997 by the American Physiological Society

RAPID COMMUNICATION

Repeated Patterns of Distributed Synchrony in Neuronal Assemblies

B. G. Lindsey, K. F. Morris, R. Shannon, and G. L. Gerstein

Department of Physiology and Biophysics and Neuroscience Program, University of South Florida Health Sciences Center, Tampa, Florida 33612; and Department of Neuroscience, School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104

	ABSTRACT

Abstract Introduction Methods Results Discussion References

Lindsey, B. G., K. F. Morris, R. Shannon, and G. L. Gerstein. Repeated patterns of distributed synchrony in neuronal assemblies. J. Neurophysiol. 78: 1714-1719, 1997. Models of brain function predict that the recurrence of a process or state will be reflected in repeated patterns of correlated activity. Previous work on medullary raphe assembly dynamics revealed transient changes inimpulse synchrony. This study tested the hypothesis that these variations in synchrony include distributed nonrandom patterns of association. Spike trains were recorded simultaneously in the ventrolateral medulla, n. raphe obscurus, and n. raphe magnus of four anesthetized (Dial), vagotomized, paralyzed, and artificially ventilated adult cats. The "gravitational" representation of spike trains was used to detect moments of impulse synchrony in neuronal assemblies visualized as variations in the aggregation velocities of particles corresponding to each neuron. Template matching algorithms were developed to identify excessively repeating patterns of particle condensation rates. Repeating patterns weredetected in each animal. The reiterated patterns represented anemergent property not apparent in either corresponding firing rate histograms or conventional gravity representations. Overlapping subsets of neurons represented in different patterns were unmasked when the template resolution was changed. The results demonstrate repeated transient network configurations defined by the tightness and duration of synchrony in different combinations of neurons and suggest that multiple information streams are conveyed concurrently by fluctuations in the synchrony of on-going activity.

	INTRODUCTION

Abstract Introduction Methods Results Discussion References

Theories of sensory processing, motor control, and memory retrieval propose that systems of neurons engaged in such tasks encode information in transient distributed synchrony (Arbib 1995). Patterns of coordinated activity may recur if similar operations are repeated (Abeles and Gerstein 1988; Dayhoff and Gerstein 1983; Frostig et al. 1990; Mainen and Sejnowski 1995). In a previous study on medullary raphe assembly dynamics, we noted transient changes in impulse synchrony apparently unrelated to monitored physiological variables (Lindsey et al. 1992b). We conjectured that these fluctuations in synchrony included nonrandom patterns of associations predicted under the hypothesis that raphe assemblies operate as an equilibrium seeking system in the regulation of cardiorespiratory function and have roles in the induction and expression of respiratory memory (Lindsey et al. 1992a; Millhorn 1982; Morris et al. 1996a,b). Preliminary accounts have been presented (Lindsey and Gerstein 1996; Lindsey et al. 1996).

	METHODS

Abstract Introduction Methods Results Discussion References

Data acquisition

Materials and methods have been described in detail (Lindsey et al. 1994; Morris et al. 1996a). All experiments were performed under protocols approved by the University of South Florida's Animal Care and Use Committee. Four adult cats of either sex initially were anesthetized with thiopental sodium (22.0 mg/kg iv). Anesthesia was maintained with Dial-urethane (allobarbital; Ciba; 60.0 mg/kg; urethane, 240 mg/kg). Blood pressure and respiration were monitored continuously. Animals were given additional Dial-urethane 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). Arterial blood pressure, pH, PO₂, PCO₂, and [HCO_3] and end-tidal CO₂ were monitored and maintained within normal limits. Core body temperature was maintained at 38.0 ± 0.5°C. Animals were ventilated, vagotomized, and paralyzed to reduce brain stem movements with a bolus of gallamine triethiodide (2.2 mg/kg) followed by constant infusion (0.4 mg·kg¹·h¹). Multiple single neuron spike trains were recorded extracellularly in the medullary raphe nuclei and ventrolateral medulla with planar arrays of tungsten microelectrodes. Some data samples were recorded during a change in blood pressure produced by inflation of an embolectomy catheter in the descending aorta. 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 and examined.

Data analysis

Correlational neuronal assemblies were first identified with the gravity method, which provides a conceptual framework for the analysis and representation of groups of simultaneously monitored neurons and their dynamic associations (Gerstein andAertsen 1985; Gerstein et al. 1985; Lindsey et al. 1989, 1992a,b; Strangman 1997). Each of N neurons is represented as a particle in N space. Each particle is initially equidistant from all other particles and has a time varying charge that is a filtered version of its spike activity. The charged particles exert forces on each other and move as though in a viscous fluid. The trajectories of particle aggregation may indicate interesting temporal modulation of neuronal timing relationships that would be lost in a summary or averaging procedure, such as ordinary cross-correlation analysis.

Each particle travels at terminal velocity, which is proportional to the product of its charge, the propulsive force generated by all other particles (a vector quantity), and a user-defined coefficient that represents the reciprocal of viscosity, i.e., particle mobility. (See equation 8 in Gerstein et al. 1985 and equation 5 in Gerstein and Aertsen 1985.) The sign of the propulsive force was set to cause attraction if the particles simultaneously had a high charge (i.e., if the neurons they represented were firing in close temporal contiguity), as would be the case with a shared input or excitatory interactions. Aggregation indicated nonrandom spike train timing relationships in a time range set by the time constant of the charge decay parameter used in the computation.

Two procedures ensured that transient increases in short-time scale synchrony, not changes in firing rate, were responsible for the significant particle aggregation patterns. First, the charge decay constants used were short compared with interspike intervals; second, the charge corresponding to a sliding window of local firing rate was subtracted from each raw charge function, thus creating an effective charge function with approximately zero mean charge.

The variable that determined particle mobility was adjusted to prevent close approaches. Gravity particle condensation profiles were generated to detect recurring transient assembly configurations. Successive elements in each row of a two-dimensional array contained the aggregation velocity of each pair of particles during an interval represented by the column. The velocities in each column served, in turn, as a template that was compared with all other columns for a match. Velocity values were nulled if the particle pair never exhibited significant aggregation or if they were less than a nulling threshold of either 3.25 or 10% of the maximum velocity detected in the data set. These values were selected to filter out arbitrarily small fluctuations in aggregation velocity. Significant patterns were detected in all animals with each threshold value.

Each data set was analyzed at three different temporal resolutions defined by the number of consecutive plotted time steps used to calculate each particle aggregation velocity vector. Thus each temporal resolution was associated with a different number of template columns. Seven different match criteria based on velocity thresholds, ranging from a noisy match to a nearly perfect duplication were used in each search and tested for significance. 1) More than 80% of the nonnulled velocities in the template column matched in the target column; a 90% cut-off was used in most pattern searches. 2) Criterion 1 met and >75% of the matched pairs had velocities within a range of ±25% of the corresponding template velocities. 3) Criterion 1 met and the percentage of extra nonnulled velocities in the target column was <5% of the total pairs in the group evaluated. 4) Criterion 2 and 3 met. 5) More than 99% of the nonnulled velocities in the template column matched in the target column and the percentage of extra nonnulled velocities in the target column was <5% of the total pairs in the group evaluated. 6) More than 99% of the nonnulled velocities in the template column matched in the target column and there were no extra nonnulled velocities in the target column. 7) More than 99% of the nonnulled velocities in the template column matched in the target column, there were no extra nonnulled velocities in the target column, and >75% of the matched pairs had velocities within a range of ±25% of the corresponding template velocities. A column had to have at least two velocities to be used as a template. A template could match under more than one criterion.

The null hypothesis was that the number of repeating patterns found when a particular template column was compared with the other columns was not greater than expected by chance. We constructed 100 pair-wise shuffled condensation profile sets and searched them for the maximum number of matching columns. This provided a Monte Carlo type estimate of the number of recurrences of a given pattern expected by chance (P < 0.01) in identical distributions of condensation rates associated at random. The null hypothesis was rejected if the maximum number of matches for a particular column was greater than the Monte Carlo estimate.

	RESULTS

Abstract Introduction Methods Results Discussion References

Correlational assemblies were first identified in four animals by screening simultaneously monitored neurons with the gravity method. Data from one sample, displayed in eight firing rate histograms (Fig. 1A), were collected during a perturbation of blood pressure. Several particles in the gravitational representation aggregated as illustrated in the animated projections of particle trajectories (Fig. 1B). Labeled circles in the last frame of the movie show final particle positions; trails can be followed back to initial positions in the projected space. Because of information loss in such projections from the N space, the distance between each pair of particles always was plotted as a function of time and evaluated for significance (Fig. 1C). The heavy black line (I) in the particle distance as a function of time (PDFT) graph defines the aggregation of particles 1 and 4. The light black lines indicate the minimum, maximum and mean distances between particles 1 and 4 at each time step in 100 different data sets. The original correlations were obliterated in each data set by shifting and rotating spike times by different amounts. These minimum and maximum lines provide a Monte Carlo estimate of significance for aggregation caused by short-term correlation, as compared with aggregation attributable to all other factors (e.g., "random movements" due to incomplete correction for zero mean charge) (see Lindsey et al. 1992a). The null hypothesis was that significant aggregation did not occur; it was rejected for all periods in the data when the interparticle distance trajectory fell below the minimum line. Each horizontal bar in Fig. 1D is a graphical summary of the times when the corresponding pair of particles was significantly close. The gray row (I) corresponds to the labeled line plotted in Fig. 1C. Screening for aggregation velocities and pattern properties was limited to particles that met the aggregation significance test and therefore represented members of putative neuronal assemblies.

View larger version (34K): [in this window] [in a new window]   FIG. 1. A: firing rate histograms for 8 simultaneously recorded spike trains with blood pressure and integrated efferent phrenic nerve activity to indicate phases of respiratory cycle. Rate calibration corresponds to highest bins. Neurons 1-3 and 5-8 were monitored in nucleus raphe magnus; cell 4 was recorded in ventrolateral medulla. B: final frame of an animated projection of the particle trajectories from the N space to a plane for the spike data in A. Labeled circles show final particle positions; trails can be followed to initial positions of particles shown as colored rectangles. Calculation parameters: acceptor and effector charge decays forward; decay time constant 10.0 ms. Numbers of spikes in sample are 1: 686; 2: 85; 3: 135; 4: 674; 5: 170; 6: 851; 7: 100; and 8: 186. C:  (I) is particle distance as a function of time (PDFT) plot for particles 1 and 4. Initially each particle was equidistant (100 arbitrary units) from all other particles. Top and bottom define maximum and minimum distances between particles in 100 shifted control data sets at each time step. Thus probability that aggregation of particles 1 and 4 was due to random coincident spikes was <0.01. Middle  indicates mean particle distance at each time step for the 100 control calculations. D:  in each row indicate if and when distance between each pair of particles was less than expected by chance (P < 0.01). Row corresponding to the PDFT plot in C is labeled (I).

The graph of all particle pair distances revealed transient moments of synchrony among several neurons; these appeared as coincident steps or jumps in corresponding plots (e.g.,  in Fig. 2A). Data for neurons 4 and 1 are plotted in black (J) for comparison with Fig. 1C. A template matching algorithm was developed to determine whether combinations of neurons exhibited such recurring moments of impulse synchrony or near synchrony more frequently than would be expected by chance. We initially chose a time bin equal to the minimum plotted interval in the PDFT graph, or multiples thereof, over which to calculate an average aggregation velocity for the particle pairs. The results are shown in the particle condensation profile (Fig. 2B) where each row shows the aggregation velocities of a particular pair during consecutive time intervals. Each column allows comparison of aggregation velocities of all particle pairs at a particular time. The values in each column served in turn as a template, illustrated in a tutorial figure (Fig. 2C), that was compared with other columns for a match. The value for a pair was set to zero in the absence of net movement of pair elements toward each other during an interval or if the velocity was below a nulling threshold. One of two such threshold values (METHODS) was used in each pattern search to remove small velocities from further consideration. The seven different match criteria based on velocity thresholds were tested concurrently. A significant pattern was recorded if the number of matches detected for some template column in the original data set exceeded the number found for that same template in 100 data sets, each of which had different randomly shuffled rows of pair condensation velocities.

View larger version (45K): [in this window] [in a new window]   FIG. 2. A: PDFT graph of aggregation of all constituent pairs in group represented in Fig. 1B. Condensation of pair 4,1 is plotted in black (J); other pairs exhibited concurrent moments of high velocity aggregation (e.g., ). B: gravity particle condensation profile derived from PDFT data in A. Successive elements in each row of this 2-dimensional array are shaded to represent the relative aggregation velocities of each pair of particles during an interval (812 ms) represented by the particular column. , correspond to times similarly labeled in A. C: cartoon to illustrate the template matching method used to detect repeated assembly configurations: the set of velocity values in each column served in turn as a template that was compared to all other columns for a match. A pattern was recorded if the number of matches detected for each template column in original data set was greater than the maximum number of matches found between the same template and results derived from 100 pair-wise shuffled condensation profiles. D: illustration of how an individual condensation profile column may be represented in compact form as a set of vectors with a common origin. The direction of each vector in a plane identifies the neuron pair represented; vector length indicates the aggregation velocity of corresponding particles.

Assemblies from each animal exhibited transient configurations of constituent neurons. To detect patterns of distributed synchrony with different durations, all data sets were searched with the temporal resolution set to different multiples of the smallest plotted gravity step time. One to three consecutive plotted time steps were used to calculate each particle pair aggregation velocity. Single-step durations ranged from 119 to 546 ms (average: 289 ± 127 ms;mean ± SD). Two-step durations ranged from 239 to 1,129 ms (average: 578 ± 254 ms). Three-step durations ranged from 358 to 1,693 ms (average: 867 ± 380 ms). This procedure also reduced the possibility that repeated patterns would remain undetected because of the sampling frequency. Significant numbers of repeated patterns were detected in samples of seven or eight simultaneously recorded neurons from each animal for each time resolution used (Table 1). In three of four animals, patterns were detected with each of the seven criteria. For the numbers of neurons analyzed in this work, criteria 4 and 7 were similarly stringent and required the closest matches. No significant matches were found in one animal with criterion 7. The reiterated patterns represented an emergent property that was not apparent in either corresponding firing rate histograms or the conventional gravity representations.

Particle aggregation patterns that recurred with a frequency greater than that of any of the shifted data sets were displayed as sets of vectors, each with a common origin and at the time of occurrence as illustrated in Fig. 2D. Vector length indicated the aggregation velocity; vector direction served solely to identify the neuron pair represented. The sets of vectors are termed "spark" patterns because of their transient appearance in animations of successive planes through time. Repeated sparks indicative of recurring transient assembly configurations are illustrated in Fig. 3. These examples were derived from the data illustrated in the previous figures. The two sparks in Fig. 3A were detected when velocities were calculated during 1.218-s intervals (3 plotted time steps) and matched according to criterion 7. In this sample, no other patterns repeated significantly under criteria 4-7 at this temporal resolution. The blood pressure trace and integrated efferent phrenic nerve activity in Fig. 1A were plotted again on the side panel. Time is represented along the z axis in these spark plots. The rear panel of the plot shows a phase plane of the smoothed integrated phrenic signal (x axis) against its first derivative (y axis). This particular spark pattern was confined to an interval with control blood pressure (side panel) and to the early expiratory phase of the respiratory cycle (m, rear panel).

View larger version (38K): [in this window] [in a new window]   FIG. 3. A: spark plots display repeated particle condensation profiles indicative of transient neuronal assembly configurations. Data were derived from the results illustrated in Figs. 1 and 2. The sparks matched according to criterion 7. Blood pressure and integrated efferent phrenic nerve signals in Fig. 1A are plotted on side panel. Time is represented along z axis. The phase plane on the rear panel is a plot of the smoothed integrated phrenic signal (x axis) against its first derivative (y axis). The early expiratory phases of 2 respiratory cycles during which the spark patterns occurred are indicated by black segments in the phase plane (m). The following particle-pair aggregation velocities, calculated during a 1.218-s interval, were represented in the first spark: 4, 1: 1.47; 4, 2: 0.52; 4, 3: 0.61; 6, 4: 1.18; 7, 4: 0.58. Corresponding values in the second spark were: 2.25, 0.51, 0.70, 1.07, 0.55. B: another spark pattern repeated only during the interval with elevated blood pressure; it was confined to the inspiratory phases of 2 respiratory cycles (arrow in phase plane). These patterns matched by criterion 3. Pair aggregation velocities in the first spark, calculated during 0.812-s intervals, were 3, 1: 0.31; 4, 1: 0.89; 4, 2: 0.36; 5, 1: 0.34; 6, 1: 1.19; 6, 4: 0.78; 6, 5: 0.73. Corresponding values in the second spark were: 3, 1: 0.52; 4, 1: 2.65; 4, 2: 0.14; 5, 1: 0.29; 6, 1: 0.98; 6, 4: 2.36; 6, 5: absent.

A second spark pattern repeated (criterion 3) exclusively during the period of altered baroreceptor stimulation (Fig. 3B). This second pattern was detected when velocities were calculated during 0.812-s intervals (2 plotted time steps); it was confined to the inspiratory phase of the respiratory cycle (m, rear panel). No other patterns repeated significantly under criteria 3-7 at this temporal resolution. The spike rates of all eight neurons during respiratory cycles concurrent with the increase in blood pressure were not significantly different from control cycles (t-test, n1 = n2 =15, P > 0.05).

	DISCUSSION

Abstract Introduction Methods Results Discussion References

The gravity method previously demonstrated that medullary raphe neurons with no respiratory modulation of their individual firing rates collectively exhibited respiratory phase-dependent synchrony (Lindsey et al. 1992b). Those results suggested the hypothesis that rate and synchrony codes are transmitted in the impulse traffic of raphe assemblies. In this work, different spark patterns that repeated more frequently than expected by chance were unmasked in the same time series when the interval duration used to calculate each velocity was changed. These data demonstrate repeated transient network configurations defined by the tightness and duration of synchrony in different combinations of neurons and suggest that multiple information streams are conveyed concurrently by fluctuations in the synchrony of on-going activity. The metabolic efficiency of such synchrony coding, as compared with firing rate modulation, remains to be determined.

Searches for recurring patterns of coordinated activity were always confined to elements of correlational assemblies. Spark patterns detected without such prior screening may be of interest in their own right. The less stringent match criteria allow for the possibility that velocities of different particles representing independent neurons may increase at particular moments because of spikes coincident with the concurrent activity of neurons in the identified assemblies.

This work extends earlier efforts to assess the functional consequences of coincident and near-coincident spikes in concurrently active parallel channels (Gerstein 1970; Stevens and Gerstein 1976; Lindsey 1982; Murthy and Fetz 1994). The constellations of gravity particles defined by repeating spark patterns may represent moments when a (partially represented) set of neurons reads, stores, or transmits information encoded by distributed synchrony. In some contexts, it may be useful to consider these moments discrete events, bearing in mind that each spark is an abstraction of many parallel processes. Approaches such as spark triggered averaging of physiological measurements can link transient assembly configurations to changes in behavior or state.

The spark plot inherits the advantages of the gravity method and offers, in compact form, the information needed to reconstruct the net movements of particles in the gravity N space. The method is scaleable with respect to the number of neurons represented and the temporal resolution of each spark interval. Computation time for the initial gravity calculations scales as the cube of the number of neurons represented. The core pattern detection algorithm scales as the number of template columns squared times the number of neuron pairs. Time for the various Monte-Carlo significance tests increases in direct proportion to the number of iterations required. With current data acquisition technology and typical workstation performance, analysis of 100 simultaneously recorded neurons can be achieved readily. Real-time visualization is currently not practical in most laboratories. However, multiprocessor computers and other optimizations should permit at least initial screening for patterns during experiments.

Other data sets, such as alternate representations of the gravity N space or synchronized video, may be projected on to the back panel of the spark animation sequence. The algorithms can incorporate readily other match criteria and can be extended to identify recurring patterns of patterns or hyperpatterns of spatiotemporal activity. Spark sequences then would serve as the template for "visualization" of sequential fluctuations of spatiotemporal patterns of synchrony as implied, for example, in holographic memory models (Pribram 1971).

	ACKNOWLEDGEMENTS

  The authors thank J. Gilliland, C. Orsini, T. Krepel, R. McGowan, and X. Li for technical assistance.

  This work was supported by National Institute of Neurological Disorders and Stroke Grant NS-19814.

	FOOTNOTES

  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.

  Received 17 April 1997; accepted in final form 4 June 1997.

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