Two enhancements of the gravity algorithm for multiple spike train analysis

Carotid chemoreceptors tune breathing via multipath routing: reticular chain and loop operations supported by parallel spike train correlations

We tested the hypothesis that carotid chemoreceptors tune breathing through parallel circuit paths that target distinct elements of an inspiratory neuron chain in the ventral respiratory column (VRC). Microelectrode arrays were used to monitor neuronal spike trains simultaneously in the VRC, peri-nucleus tractus solitarius (p-NTS)-medial medulla, the dorsal parafacial region of the lateral tegmental field (FTL-pF), and medullary raphe nuclei together with phrenic nerve activity during selective stimulation of carotid chemoreceptors or transient hypoxia in 19 decerebrate, neuromuscularly blocked, and artificially ventilated cats. Of 994 neurons tested, 56% had a significant change in firing rate. A total of 33,422 cell pairs were evaluated for signs of functional interaction; 63% of chemoresponsive neurons were elements of at least one pair with correlational signatures indicative of paucisynaptic relationships. We detected evidence for postinspiratory neuron inhibition of rostral VRC I-Driver (pre-Bötzinger) neurons, an interaction predicted to modulate breathing frequency, and for reciprocal excitation between chemoresponsive p-NTS neurons and more downstream VRC inspiratory neurons for control of breathing depth. Chemoresponsive pericolumnar tonic expiratory neurons, proposed to amplify inspiratory drive by disinhibition, were correlationally linked to afferent and efferent "chains" of chemoresponsive neurons extending to all monitored regions. The chains included coordinated clusters of chemoresponsive FTL-pF neurons with functional links to widespread medullary sites involved in the control of breathing. The results support long-standing concepts on brain stem network architecture and a circuit model for peripheral chemoreceptor modulation of breathing with multiple circuit loops and chains tuned by tegmental field neurons with quasi-periodic discharge patterns. NEW & NOTEWORTHY We tested the long-standing hypothesis that carotid chemoreceptors tune the frequency and depth of breathing through parallel circuit operations targeting the ventral respiratory column. Responses to stimulation of the chemoreceptors and identified functional connectivity support differential tuning of inspiratory neuron burst duration and firing rate and a model of brain stem network architecture incorporating tonic expiratory "hub" neurons regulated by convergent neuronal chains and loops through rostral lateral tegmental field neurons with quasi-periodic discharge patterns.

Functional connectivity in raphé-pontomedullary circuits supports active suppression of breathing during hypocapnic apnea

Hyperventilation is a common feature of disordered breathing. Apnea ensues if CO2 drive is sufficiently reduced. We tested the hypothesis that medullary raphé, ventral respiratory column (VRC), and pontine neurons have functional connectivity and persistent or evoked activities appropriate for roles in the suppression of drive and rhythm during hyperventilation and apnea. Phrenic nerve activity, arterial blood pressure, end-tidal CO2, and other parameters were monitored in 10 decerebrate, vagotomized, neuromuscularly-blocked, and artificially ventilated cats. Multielectrode arrays recorded spiking activity of 649 neurons. Loss and return of rhythmic activity during passive hyperventilation to apnea were identified with the S-transform. Diverse fluctuating activity patterns were recorded in the raphé-pontomedullary respiratory network during the transition to hypocapnic apnea. The firing rates of 160 neurons increased during apnea; the rates of 241 others decreased or stopped. VRC inspiratory neurons were usually the last to cease firing or lose rhythmic activity during the transition to apnea. Mayer wave-related oscillations (0.04-0.1 Hz) in firing rate were also disrupted during apnea. Four-hundred neurons (62%) were elements of pairs with at least one hyperventilation-responsive neuron and a correlational signature of interaction identified by cross-correlation or gravitational clustering. Our results support a model with distinct groups of chemoresponsive raphé neurons contributing to hypocapnic apnea through parallel processes that incorporate disfacilitation and active inhibition of inspiratory motor drive by expiratory neurons. During apnea, carotid chemoreceptors can evoke rhythm reemergence and an inspiratory shift in the balance of reciprocal inhibition via suppression of ongoing tonic expiratory neuron activity.

Peripheral chemoreceptors tune inspiratory drive via tonic expiratory neuron hubs in the medullary ventral respiratory column network

Models of brain stem ventral respiratory column (VRC) circuits typically emphasize populations of neurons, each active during a particular phase of the respiratory cycle. We have proposed that "tonic" pericolumnar expiratory (t-E) neurons tune breathing during baroreceptor-evoked reductions and central chemoreceptor-evoked enhancements of inspiratory (I) drive. The aims of this study were to further characterize the coordinated activity of t-E neurons and test the hypothesis that peripheral chemoreceptors also modulate drive via inhibition of t-E neurons and disinhibition of their inspiratory neuron targets. Spike trains of 828 VRC neurons were acquired by multielectrode arrays along with phrenic nerve signals from 22 decerebrate, vagotomized, neuromuscularly blocked, artificially ventilated adult cats. Forty-eight of 191 t-E neurons fired synchronously with another t-E neuron as indicated by cross-correlogram central peaks; 32 of the 39 synchronous pairs were elements of groups with mutual pairwise correlations. Gravitational clustering identified fluctuations in t-E neuron synchrony. A network model supported the prediction that inhibitory populations with spike synchrony reduce target neuron firing probabilities, resulting in offset or central correlogram troughs. In five animals, stimulation of carotid chemoreceptors evoked changes in the firing rates of 179 of 240 neurons. Thirty-two neuron pairs had correlogram troughs consistent with convergent and divergent t-E inhibition of I cells and disinhibitory enhancement of drive. Four of 10 t-E neurons that responded to sequential stimulation of peripheral and central chemoreceptors triggered 25 cross-correlograms with offset features. The results support the hypothesis that multiple afferent systems dynamically tune inspiratory drive in part via coordinated t-E neurons.

Algorithms for the analysis of ensemble neural spiking activity using simultaneous-event multivariate point-process models

Understanding how ensembles of neurons represent and transmit information in the patterns of their joint spiking activity is a fundamental question in computational neuroscience. At present, analyses of spiking activity from neuronal ensembles are limited because multivariate point process (MPP) models cannot represent simultaneous occurrences of spike events at an arbitrarily small time resolution. Solo recently reported a simultaneous-event multivariate point process (SEMPP) model to correct this key limitation. In this paper, we show how Solo's discrete-time formulation of the SEMPP model can be efficiently fit to ensemble neural spiking activity using a multinomial generalized linear model (mGLM). Unlike existing approximate procedures for fitting the discrete-time SEMPP model, the mGLM is an exact algorithm. The MPP time-rescaling theorem can be used to assess model goodness-of-fit. We also derive a new marked point-process (MkPP) representation of the SEMPP model that leads to new thinning and time-rescaling algorithms for simulating an SEMPP stochastic process. These algorithms are much simpler than multivariate extensions of algorithms for simulating a univariate point process, and could not be arrived at without the MkPP representation. We illustrate the versatility of the SEMPP model by analyzing neural spiking activity from pairs of simultaneously-recorded rat thalamic neurons stimulated by periodic whisker deflections, and by simulating SEMPP data. In the data analysis example, the SEMPP model demonstrates that whisker motion significantly modulates simultaneous spiking activity at the 1 ms time scale and that the stimulus effect is more than one order of magnitude greater for simultaneous activity compared with non-simultaneous activity. Together, the mGLM, the MPP time-rescaling theorem and the MkPP representation of the SEMPP model offer a theoretically sound, practical tool for measuring joint spiking propensity in a neuronal ensemble.

Analysis and modeling of ensemble recordings from respiratory pre-motor neurons indicate changes in functional network architecture after acute hypoxia

We have combined neurophysiologic recording, statistical analysis, and computational modeling to investigate the dynamics of the respiratory network in the brainstem. Using a multielectrode array, we recorded ensembles of respiratory neurons in perfused in situ rat preparations that produce spontaneous breathing patterns, focusing on inspiratory pre-motor neurons. We compared firing rates and neuronal synchronization among these neurons before and after a brief hypoxic stimulus. We observed a significant decrease in the number of spikes after stimulation, in part due to a transient slowing of the respiratory pattern. However, the median interspike interval did not change, suggesting that the firing threshold of the neurons was not affected but rather the synaptic input was. A bootstrap analysis of synchrony between spike trains revealed that both before and after brief hypoxia, up to 45% (but typically less than 5%) of coincident spikes across neuronal pairs was not explained by chance. Most likely, this synchrony resulted from common synaptic input to the pre-motor population, an example of stochastic synchronization. After brief hypoxia most pairs were less synchronized, although some were more, suggesting that the respiratory network was transiently “rewired” after the stimulus. To investigate this hypothesis, we created a simple computational model with feed-forward divergent connections along the inspiratory pathway. Assuming that (1) the number of divergent projections was not the same for all presynaptic cells, but rather spanned a wide range and (2) that the stimulus increased inhibition at the top of the network; this model reproduced the reduction in firing rate and bootstrap-corrected synchrony subsequent to hypoxic stimulation observed in our experimental data.

Causal pattern recovery from neural spike train data using the Snap Shot Score

We present a new approach to learning directed information flow networks from multi-channel spike train data. A novel scoring function, the Snap Shot Score, is used to assess potential networks with respect to their quality of causal explanation for the data. Additionally, we suggest a generic concept of plausibility in order to assess network learning techniques under partial observability conditions. Examples demonstrate the assessment of networks with the Snap Shot Score, and neural network simulations show its performance in complex situations with partial observability. We discuss the application of the new score to real data and indicate how it can be modified to suit other neural data types.

Functional clustering algorithm for the analysis of dynamic network data

We formulate a technique for the detection of functional clusters in discrete event data. The advantage of this algorithm is that no prior knowledge of the number of functional groups is needed, as our procedure progressively combines data traces and derives the optimal clustering cutoff in a simple and intuitive manner through the use of surrogate data sets. In order to demonstrate the power of this algorithm to detect changes in network dynamics and connectivity, we apply it to both simulated neural spike train data and real neural data obtained from the mouse hippocampus during exploration and slow-wave sleep. Using the simulated data, we show that our algorithm performs better than existing methods. In the experimental data, we observe state-dependent clustering patterns consistent with known neurophysiological processes involved in memory consolidation.

Maximum decoding abilities of temporal patterns and synchronized firings: application to auditory neurons responding to click trains and amplitude modulated white noise

Simultaneous recordings of an increasing number of neurons have recently become available, but few methods have been proposed to handle this activity. Here, we extract and investigate all the possible temporal neural activity patterns based on synchronized firings of neurons recorded on multiple electrodes, or based on bursts of single-electrode activity in cat primary auditory cortex. We apply this to responses to periodic click trains or sinusoïdal amplitude modulated noise by obtaining for each pattern its temporal modulation transfer function. An algorithm that maximizes the mutual information between all patterns and stimuli subsequently leads to the identification of patterns that optimally decode modulation frequency (MF). We show that stimulus information contained in multi-electrode synchronized firing is not redundant with single-electrode firings and leads to improved efficiency of MF decoding. We also show that the combined use of firing rate and temporal codes leads to a better discrimination of the MF.

Identifying functional connectivity in large-scale neural ensemble recordings: a multiscale data mining approach

Identifying functional connectivity between neuronal elements is an essential first step toward understanding how the brain orchestrates information processing at the single-cell and population levels to carry out biological computations. This letter suggests a new approach to identify functional connectivity between neuronal elements from their simultaneously recorded spike trains. In particular, we identify clusters of neurons that exhibit functional interdependency over variable spatial and temporal patterns of interaction. We represent neurons as objects in a graph and connect them using arbitrarily defined similarity measures calculated across multiple timescales. We then use a probabilistic spectral clustering algorithm to cluster the neurons in the graph by solving a minimum graph cut optimization problem. Using point process theory to model population activity, we demonstrate the robustness of the approach in tracking a broad spectrum of neuronal interaction, from synchrony to rate co-modulation, by systematically varying the length of the firing history interval and the strength of the connecting synapses that govern the discharge pattern of each neuron. We also demonstrate how activity-dependent plasticity can be tracked and quantified in multiple network topologies built to mimic distinct behavioral contexts. We compare the performance to classical approaches to illustrate the substantial gain in performance.

Functional connectivity in the pontomedullary respiratory network

Current models propose that a neuronal network in the ventrolateral medulla generates the basic respiratory rhythm and that this ventrolateral respiratory column (VRC) is profoundly influenced by the neurons of the pontine respiratory group (PRG). However, functional connectivity among PRG and VRC neurons is poorly understood. This study addressed four model-based hypotheses: 1) the respiratory modulation of PRG neuron populations reflects paucisynaptic actions of multiple VRC populations; 2) functional connections among PRG neurons shape and coordinate their respiratory-modulated activities; 3) the PRG acts on multiple VRC populations, contributing to phase-switching; and 4) neurons with no respiratory modulation located in close proximity to the VRC and PRG have widely distributed actions on respiratory-modulated cells. Two arrays of microelectrodes with individual depth adjustment were used to record sets of spike trains from a total of 145 PRG and 282 VRC neurons in 10 decerebrate, vagotomized, neuromuscularly blocked, ventilated cats. Data were evaluated for respiratory modulation with respect to efferent phrenic motoneuron activity and short-timescale correlations indicative of paucisynaptic functional connectivity using cross-correlation analysis and the "gravity" method. Correlogram features were found for 109 (3%) of the 3,218 pairs composed of a PRG and a VRC neuron, 126 (12%) of the 1,043 PRG-PRG pairs, and 319 (7%) of the 4,340 VRC-VRC neuron pairs evaluated. Correlation linkage maps generated for the data support our four motivating hypotheses and suggest network mechanisms for proposed modulatory functions of the PRG.

Identification and clustering of event patterns from in vivo multiphoton optical recordings of neuronal ensembles

In vivo multiphoton fluorescence microscopy allows imaging of cellular structures in brain tissue to depths of hundreds of micrometers and, when combined with the use of activity-dependent indicator dyes, opens the possibility of observing intact, functioning neural circuitry. We have developed tools for analyzing in vivo multiphoton data sets to identify responding structures and events in single cells as well as patterns of activity within the neural ensemble. Data were analyzed from populations of cerebellar Purkinje cell dendrites, which generate calcium-based complex action potentials. For image segmentation, active dendrites were identified using a correlation-based method to group covarying pixels. Firing events were extracted from dendritic fluorescence signals with a 95% detection rate and an 8% false-positive rate. Because an event that begins in one movie frame is sometimes not detected until the next frame, detection delays were compensated using a likelihood-based correction procedure. To identify groups of dendrites that tended to fire synchronously, a k-means-based procedure was developed to analyze pairwise correlations across the population. Because repeated runs of k-means often generated dissimilar clusterings, the runs were combined to determine a consensus cluster number and composition. This procedure, termed meta-k-means, gave clusterings as good as individual runs of k-means, was independent of random initial seeding, and allowed the exclusion of outliers. Our methods should be generally useful for analyzing multicellular activity recordings in a variety of brain structures.

Gravity transform for input conditioning in brain machine interfaces

Gravity transform measures cooperative neural activity being utilized for the analysis of neural assemblies. In this paper we verify the applicability of the gravity transform to specify components of neural assemblies, which could be combined, leading ultimately to a reduction of the input dimensionality in brain-machine interface models. Our analysis was performed on data collected from rats performing a lever pressing task. We compare the results from the gravity transform analysis with the assignment obtained through a sensitivity analysis applied on a linear optimal filter.

Repetition rates of specific interval patterns in single spike train reflect excitation level of specific receptor types, shown by high-speed favored-pattern detection method

Interval patterns in single spike train, e.g. "favored patterns (FPs, the FP is a sequence of successive intervals of action potentials that occur more often than what is reasonably expected at random.)", may represent neural codes containing information. The present study developed a "high-speed FP-detection method" which could qualitatively and quantitatively analyze FPs. By using this method, single spike trains of nucleus paraventricularis (NPV) and rostral ventrolateral medulla (RVL) having different firing patterns, being involved in regulation of arterial pressure, and controlled by different transmitters, were chosen for analysis.

RESULTS

(1) Corticotropin releasing factor, substance P and agonists of alpha-, beta- and M-receptor microinjected into these brain areas, respectively, induced dominant change of specific FP. Repetition rates of specific FPs reflect excitation level of specific receptor types. It shows that chemical codes (different transmitters with their receptor types or subtypes) are transformed into electrical codes (different FPs). (2) When alpha-, beta- and M-receptors of RVL neurons were activated simultaneously by intrinsic excitatory transmitters released due to activation of input pathway, only repetition rate of the specific FP that represented the predominant activity of the receptor type (alpha-adrenergic receptor) markedly increased. The activities of other receptor types (beta- and M-receptors) were masked. (3) Intrinsic inhibitory transmitters (GABA, beta-endorphin) in the RVL all decreased specific FP repetition rate of dominant receptor type. These results may provide a new way to further explore how information in the CNS is conveyed and processed.

Properties of Correlated Neural Activity Clusters in Cat Auditory Cortex Resemble Those of Neural Assemblies

Spiking activity was recorded from cat auditory cortex using multi-electrode arrays. Cross-correlograms were calculated for spikes recorded on separate microelectrodes. The pair-wise cross-correlation matrix was constructed for the peak values of the correlograms. Hierarchical clustering was performed on the cross-correlation matrix for six stimulus conditions. These were silence, three multi-tone stimulus ensembles with different spectral densities, low-pass amplitude-modulated noise, and Poisson-distributed click trains that each lasted 15 min. The resulting neuron clusters reflect patches in cortex of up to several mm2 in size that expand and contract in response to different stimuli. Cluster positions and size were very similar for spontaneous activity and multi-tone stimulus-evoked activity but differed between those conditions and the noise and click stimuli. Cluster size was significantly larger in posterior auditory field (PAF) compared with primary auditory cortex (AI), whereas the fraction of common spikes (within a 10-ms window) across all electrode activity participating in a cluster was significantly higher in AI compared with PAF. Clusters crossed area boundaries in <5% of the cases were simultaneous recording were made in AI and PAF. Clusters are therefore similar to but not synonymous with the traditional view of neural assemblies. Common-spike spectrotemporal receptive fields (STRFs) were obtained for common-spike activity and all-spike activity within a cluster. Common-spike STRFs had higher signal-to-noise ratio than all-spike STRFs and showed generally spectral and temporal sharpening. The coincident and noncoincident output of the clusters could potentially act in parallel and may serve different modes of stimulus coding.