Detecting neural assemblies in calcium imaging data

CalciSeg: A versatile approach for unsupervised segmentation of calcium imaging data

Recent advances in calcium imaging, including the development of fast and sensitive genetically encoded indicators, high-resolution camera chips for wide-field imaging, and resonant scanning mirrors in laser scanning microscopy, have notably improved the temporal and spatial resolution of functional imaging analysis. Nonetheless, the variability of imaging approaches and brain structures challenges the development of versatile and reliable segmentation methods. Standard techniques, such as manual selection of regions of interest or machine learning solutions, often fall short due to either user bias, non-transferability among systems, or computational demand. To overcome these issues, we developed CalciSeg, a data-driven and reproducible approach for unsupervised functional calcium imaging data segmentation. CalciSeg addresses the challenges associated with brain structure variability and user bias by offering a computationally efficient solution for automatic image segmentation based on two parameters: regions' size limits and number of refinement iterations. We evaluated CalciSeg efficacy on datasets of varied complexity, different insect species (locusts, bees, and cockroaches), and imaging systems (wide-field, confocal, and multiphoton), showing the robustness and generality of our approach. Finally, the user-friendly nature and the open-source availability of CalciSeg facilitate the integration of this algorithm into existing analysis pipelines.

Aberrant cortical activity, functional connectivity, and neural assembly architecture after photothrombotic stroke in mice

Despite substantial progress in mapping the trajectory of network plasticity resulting from focal ischemic stroke, the extent and nature of changes in neuronal excitability and activity within the peri-infarct cortex of mice remains poorly defined. Most of the available data have been acquired from anesthetized animals, acute tissue slices, or infer changes in excitability from immunoassays on extracted tissue, and thus may not reflect cortical activity dynamics in the intact cortex of an awake animal. Here, in vivo two-photon calcium imaging in awake, behaving mice was used to longitudinally track cortical activity, network functional connectivity, and neural assembly architecture for 2 months following photothrombotic stroke targeting the forelimb somatosensory cortex. Sensorimotor recovery was tracked over the weeks following stroke, allowing us to relate network changes to behavior. Our data revealed spatially restricted but long-lasting alterations in somatosensory neural network function and connectivity. Specifically, we demonstrate significant and long-lasting disruptions in neural assembly architecture concurrent with a deficit in functional connectivity between individual neurons. Reductions in neuronal spiking in peri-infarct cortex were transient but predictive of impairment in skilled locomotion measured in the tapered beam task. Notably, altered neural networks were highly localized, with assembly architecture and neural connectivity relatively unaltered a short distance from the peri-infarct cortex, even in regions within 'remapped' forelimb functional representations identified using mesoscale imaging with anaesthetized preparations 8 weeks after stroke. Thus, using longitudinal two-photon microscopy in awake animals, these data show a complex spatiotemporal relationship between peri-infarct neuronal network function and behavioral recovery. Moreover, the data highlight an apparent disconnect between dramatic functional remapping identified using strong sensory stimulation in anaesthetized mice compared to more subtle and spatially restricted changes in individual neuron and local network function in awake mice during stroke recovery.

Stimulus encoding by specific inactivation of cortical neurons

Neuronal ensembles are groups of neurons with correlated activity associated with sensory, motor, and behavioral functions. To explore how ensembles encode information, we investigated responses of visual cortical neurons in awake mice using volumetric two-photon calcium imaging during visual stimulation. We identified neuronal ensembles employing an unsupervised model-free algorithm and, besides neurons activated by the visual stimulus (termed "onsemble"), we also find neurons that are specifically inactivated (termed "offsemble"). Offsemble neurons showed faster calcium decay during stimuli, suggesting selective inhibition. In response to visual stimuli, each ensemble (onsemble+offsemble) exhibited small trial-to-trial variability, high orientation selectivity, and superior predictive accuracy for visual stimulus orientation, surpassing the sum of individual neuron activity. Thus, the combined selective activation and inactivation of cortical neurons enhances visual encoding as an emergent and distributed neural code.

A computational model to uncover the biophysical underpinnings of neural firing heterogeneity in dissociated hippocampal cultures

Calcium (Ca2+ ) imaging reveals a variety of correlated firing in cultures of dissociated hippocampal neurons, pinpointing the non-synaptic paracrine release of glutamate as a possible mediator for such firing patterns, although the biophysical underpinnings remain unknown. An intriguing possibility is that extracellular glutamate could bind metabotropic receptors linked with inositol trisphosphate (IP3 ) mediated release of Ca2+ from the endoplasmic reticulum of individual neurons, thereby modulating neural activity in combination with sarco/endoplasmic reticulum Ca2+ transport ATPase (SERCA) and voltage-gated Ca2+ channels (VGCC). However, the possibility that such release may occur in different neuronal compartments and can be inherently stochastic poses challenges in the characterization of such interplay between various Ca2+ channels. Here we deploy biophysical modeling in association with Monte Carlo parameter sampling to characterize such interplay and successfully predict experimentally observed Ca2+ patterns. The results show that the neurotransmitter level at the plasma membrane is the extrinsic source of heterogeneity in somatic Ca2+ transients. Our analysis, in particular, identifies the origin of such heterogeneity to an intrinsic differentiation of hippocampal neurons in terms of multiple cellular properties pertaining to intracellular Ca2+ signaling, such as VGCC, IP3 receptor, and SERCA expression. In the future, the biophysical model and parameter estimation approach used in this study can be upgraded to predict the response of a system of interconnected neurons.

Generalization of generative model for neuronal ensemble inference method

Various brain functions that are necessary to maintain life activities materialize through the interaction of countless neurons. Therefore, it is important to analyze functional neuronal network. To elucidate the mechanism of brain function, many studies are being actively conducted on functional neuronal ensemble and hub, including all areas of neuroscience. In addition, recent study suggests that the existence of functional neuronal ensembles and hubs contributes to the efficiency of information processing. For these reasons, there is a demand for methods to infer functional neuronal ensembles from neuronal activity data, and methods based on Bayesian inference have been proposed. However, there is a problem in modeling the activity in Bayesian inference. The features of each neuron's activity have non-stationarity depending on physiological experimental conditions. As a result, the assumption of stationarity in Bayesian inference model impedes inference, which leads to destabilization of inference results and degradation of inference accuracy. In this study, we extend the range of the variable for expressing the neuronal state, and generalize the likelihood of the model for extended variables. By comparing with the previous study, our model can express the neuronal state in larger space. This generalization without restriction of the binary input enables us to perform soft clustering and apply the method to non-stationary neuroactivity data. In addition, for the effectiveness of the method, we apply the developed method to multiple synthetic fluorescence data generated from the electrical potential data in leaky integrated-and-fire model.

Structure and function in artificial, zebrafish and human neural networks

Network science provides a set of tools for the characterization of the structure and functional behavior of complex systems. Yet a major problem is to quantify how the structural domain is related to the dynamical one. In other words, how the diversity of dynamical states of a system can be predicted from the static network structure? Or the reverse problem: starting from a set of signals derived from experimental recordings, how can one discover the network connections or the causal relations behind the observed dynamics? Despite the advances achieved over the last two decades, many challenges remain concerning the study of the structure-dynamics interplay of complex systems. In neuroscience, progress is typically constrained by the low spatio-temporal resolution of experiments and by the lack of a universal inferring framework for empirical systems. To address these issues, applications of network science and artificial intelligence to neural data have been rapidly growing. In this article, we review important recent applications of methods from those fields to the study of the interplay between structure and functional dynamics of human and zebrafish brain. We cover the selection of topological features for the characterization of brain networks, inference of functional connections, dynamical modeling, and close with applications to both the human and zebrafish brain. This review is intended to neuroscientists who want to become acquainted with techniques from network science, as well as to researchers from the latter field who are interested in exploring novel application scenarios in neuroscience.

Recurrent network interactions explain tectal response variability and experience-dependent behavior

Response variability is an essential and universal feature of sensory processing and behavior. It arises from fluctuations in the internal state of the brain, which modulate how sensory information is represented and transformed to guide behavioral actions. In part, brain state is shaped by recent network activity, fed back through recurrent connections to modulate neuronal excitability. However, the degree to which these interactions influence response variability and the spatial and temporal scales across which they operate, are poorly understood. Here, we combined population recordings and modeling to gain insights into how neuronal activity modulates network state and thereby impacts visually evoked activity and behavior. First, we performed cellular-resolution calcium imaging of the optic tectum to monitor ongoing activity, the pattern of which is both a cause and consequence of changes in network state. We developed a minimal network model incorporating fast, short range, recurrent excitation and long-lasting, activity-dependent suppression that reproduced a hallmark property of tectal activity - intermittent bursting. We next used the model to estimate the excitability state of tectal neurons based on recent activity history and found that this explained a portion of the trial-to-trial variability in visually evoked responses, as well as spatially selective response adaptation. Moreover, these dynamics also predicted behavioral trends such as selective habituation of visually evoked prey-catching. Overall, we demonstrate that a simple recurrent interaction motif can be used to estimate the effect of activity upon the incidental state of a neural network and account for experience-dependent effects on sensory encoding and visually guided behavior.

fmr1 Mutation Alters the Early Development of Sensory Coding and Hunting and Social Behaviors in Larval Zebrafish

Autism spectrum disorders (ASDs) are developmental in origin; however, little is known about how they affect the early development of behavior and sensory coding. The most common inherited form of autism is Fragile X syndrome (FXS), caused by a mutation in FMR1 Mutation of fmr1 in zebrafish causes anxiety-like behavior, hyperactivity, and hypersensitivity in auditory and visual processing. Here, we show that zebrafish fmr1-/- mutant larvae of either sex also display changes in hunting behavior, tectal coding, and social interaction. During hunting, they were less successful at catching prey and displayed altered behavioral sequences. In the tectum, representations of prey-like stimuli were more diffuse and had higher dimensionality. In a social behavioral assay, they spent more time observing a conspecific but responded more slowly to social cues. However, when given a choice of rearing environment fmr1-/- larvae preferred one with reduced visual stimulation, and rearing them in this environment reduced genotype-specific effects on tectal excitability. Together, these results shed new light on how fmr1-/- changes the early development of neural systems and behavior in a vertebrate.SIGNIFICANCE STATEMENT Autism spectrum disorders (ASDs) are caused by changes in early neural development. Animal models of ASDs offer the opportunity to study these developmental processes in greater detail than in humans. Here, we found that a zebrafish mutant for a gene which in humans causes one type of ASD showed early alterations in hunting behavior, social behavior, and how visual stimuli are represented in the brain. However, we also found that mutant fish preferred reduced visual stimulation, and rearing them in this environment reduced alterations in neural activity patterns. These results suggest interesting new directions for using zebrafish as a model to study the development of brain and behavior in ASDs, and how the impact of ASDs could potentially be reduced.

A Novel Mechanism for T1R-Independent Taste Responses to Concentrated Sugars

Recent findings from our laboratory demonstrated that the rostral nucleus of the solitary tract (rNST) retains some responsiveness to sugars in double-knock-out mice lacking either the T1R1+T1R3 (KO1+3) or T1R2+T1R3 (KO2+3) taste receptor heterodimers. Here, we extended these findings in the parabrachial nucleus (PBN) of male and female KO1+3 mice using warm stimuli to optimize sugar responses and employing additional concentrations and pharmacological agents to probe mechanisms. PBN T1R-independent sugar responses, including those to concentrated glucose, were more evident than in rNST. Similar to the NST, there were no "sugar-best" neurons in KO1+3 mice. Nevertheless, 1000 mm glucose activated nearly 55% of PBN neurons, with responses usually occurring in neurons that also displayed acid and amiloride-insensitive NaCl responses. In wild-type (WT) mice, concentrated sugars activated the same electrolyte-sensitive neurons but also "sugar-best" cells. Regardless of genotype, phlorizin, an inhibitor of the sodium-glucose co-transporter (SGLT), a component of a hypothesized alternate glucose-sensing mechanism, did not diminish responses to 1000 mm glucose. The efficacy of concentrated sugars for driving neurons broadly responsive to electrolytes implied an origin from Type III taste bud cells. To test this, we used the carbonic anhydrase (CA) inhibitor dorzolamide (DRZ), previously shown to inhibit amiloride-insensitive sodium responses arising from Type III taste bud cells. Dorzolamide had no effect on sugar-elicited responses in WT sugar-best PBN neurons but strongly suppressed them in WT and KO1+3 electrolyte-generalist neurons. These findings suggest a novel T1R-independent mechanism for hyperosmotic sugars, involving a CA-dependent mechanism in Type III taste bud cells.SIGNIFICANCE STATEMENT Since the discovery of Tas1r receptors for sugars and artificial sweeteners, evidence has accrued that mice lacking these receptors maintain some behavioral, physiological, and neural responsiveness to sugars. But the substrate(s) has remained elusive. Here, we recorded from parabrachial nucleus (PBN) taste neurons and identified T1R-independent responses to hyperosmotic sugars dependent on carbonic anhydrase (CA) and occurring primarily in neurons broadly responsive to NaCl and acid, implying an origin from Type III taste bud cells. The effectiveness of different sugars in driving these T1R-independent responses did not correlate with their efficacy in driving licking, suggesting they evoke a nonsweet sensation. Nevertheless, these salient responses are likely to comprise an adequate cue for learned preferences that occur in the absence of T1R receptors.

To be and not to be: wide-field Ca2+ imaging reveals neocortical functional segmentation combines stability and flexibility

The stability and flexibility of the functional parcellation of the cerebral cortex is fundamental to how familiar and novel information is both represented and stored. We leveraged new advances in Ca2+ sensors and microscopy to understand the dynamics of functional segmentation in the dorsal cerebral cortex. We performed wide-field Ca2+ imaging in head-fixed mice and used spatial independent component analysis (ICA) to identify independent spatial sources of Ca2+ fluorescence. The imaging data were evaluated over multiple timescales and discrete behaviors including resting, walking, and grooming. When evaluated over the entire dataset, a set of template independent components (ICs) were identified that were common across behaviors. Template ICs were present across a range of timescales, from days to 30 seconds, although with lower occurrence probability at shorter timescales, highlighting the stability of the functional segmentation. Importantly, unique ICs emerged at the shorter duration timescales that could act to transiently refine the cortical network. When data were evaluated by behavior, both common and behavior-specific ICs emerged. Each behavior is composed of unique combinations of common and behavior-specific ICs. These observations suggest that cerebral cortical functional segmentation exhibits considerable spatial stability over time and behaviors while retaining the flexibility for task-dependent reorganization.

Neural assemblies uncovered by generative modeling explain whole-brain activity statistics and reflect structural connectivity

Patterns of endogenous activity in the brain reflect a stochastic exploration of the neuronal state space that is constrained by the underlying assembly organization of neurons. Yet, it remains to be shown that this interplay between neurons and their assembly dynamics indeed suffices to generate whole-brain data statistics. Here, we recorded the activity from ∼40,000 neurons simultaneously in zebrafish larvae, and show that a data-driven generative model of neuron-assembly interactions can accurately reproduce the mean activity and pairwise correlation statistics of their spontaneous activity. This model, the compositional Restricted Boltzmann Machine (cRBM), unveils ∼200 neural assemblies, which compose neurophysiological circuits and whose various combinations form successive brain states. We then performed in silico perturbation experiments to determine the interregional functional connectivity, which is conserved across individual animals and correlates well with structural connectivity. Our results showcase how cRBMs can capture the coarse-grained organization of the zebrafish brain. Notably, this generative model can readily be deployed to parse neural data obtained by other large-scale recording techniques.

Data management strategy for a collaborative research center

The importance of effective research data management (RDM) strategies to support the generation of Findable, Accessible, Interoperable, and Reusable (FAIR) neuroscience data grows with each advance in data acquisition techniques and research methods. To maximize the impact of diverse research strategies, multidisciplinary, large-scale neuroscience research consortia face a number of unsolved challenges in RDM. While open science principles are largely accepted, it is practically difficult for researchers to prioritize RDM over other pressing demands. The implementation of a coherent, executable RDM plan for consortia spanning animal, human, and clinical studies is becoming increasingly challenging. Here, we present an RDM strategy implemented for the Heidelberg Collaborative Research Consortium. Our consortium combines basic and clinical research in diverse populations (animals and humans) and produces highly heterogeneous and multimodal research data (e.g., neurophysiology, neuroimaging, genetics, behavior). We present a concrete strategy for initiating early-stage RDM and FAIR data generation for large-scale collaborative research consortia, with a focus on sustainable solutions that incentivize incremental RDM while respecting research-specific requirements.

Conceptual framework for neuronal ensemble identification and manipulation related to behavior using calcium imaging

Significance: The identification and manipulation of spatially identified neuronal ensembles with optical methods have been recently used to prove the causal link between neuronal ensemble activity and learned behaviors. However, the standardization of a conceptual framework to identify and manipulate neuronal ensembles from calcium imaging recordings is still lacking. Aim: We propose a conceptual framework for the identification and manipulation of neuronal ensembles using simultaneous calcium imaging and two-photon optogenetics in behaving mice. Approach: We review the computational approaches that have been used to identify and manipulate neuronal ensembles with single cell resolution during behavior in different brain regions using all-optical methods. Results: We proposed three steps as a conceptual framework that could be applied to calcium imaging recordings to identify and manipulate neuronal ensembles in behaving mice: (1) transformation of calcium transients into binary arrays; (2) identification of neuronal ensembles as similar population vectors; and (3) targeting of neuronal ensemble members that significantly impact behavioral performance. Conclusions: The use of simultaneous two-photon calcium imaging and two-photon optogenetics allowed for the experimental demonstration of the causal relation of population activity and learned behaviors. The standardization of analytical tools to identify and manipulate neuronal ensembles could accelerate interventional experiments aiming to reprogram the brain in normal and pathological conditions.

From calcium imaging to graph topology

Systems neuroscience is facing an ever-growing mountain of data. Recent advances in protein engineering and microscopy have together led to a paradigm shift in neuroscience; using fluorescence, we can now image the activity of every neuron through the whole brain of behaving animals. Even in larger organisms, the number of neurons that we can record simultaneously is increasing exponentially with time. This increase in the dimensionality of the data is being met with an explosion of computational and mathematical methods, each using disparate terminology, distinct approaches, and diverse mathematical concepts. Here we collect, organize, and explain multiple data analysis techniques that have been, or could be, applied to whole-brain imaging, using larval zebrafish as an example model. We begin with methods such as linear regression that are designed to detect relations between two variables. Next, we progress through network science and applied topological methods, which focus on the patterns of relations among many variables. Finally, we highlight the potential of generative models that could provide testable hypotheses on wiring rules and network progression through time, or disease progression. While we use examples of imaging from larval zebrafish, these approaches are suitable for any population-scale neural network modeling, and indeed, to applications beyond systems neuroscience. Computational approaches from network science and applied topology are not limited to larval zebrafish, or even to systems neuroscience, and we therefore conclude with a discussion of how such methods can be applied to diverse problems across the biological sciences.

Long-term development of dynamic changes in neurovascular coupling after acute temporal lobe epilepsy

Epilepsy is an abnormal brain state that may be induced by synchronous neuronal activation and also abnormalities in energy metabolism or the oxygen supply vascular system. Neurovascular coupling (NVC), the relationship between neuron, capillary, and penetrating artery, remains unexplored on a fine-scale with respect to the pathology process after acute temporal lobe epilepsy (TLE). Here we use two-photon microscopy (TPM) to provide high temporal-spatial resolution imaging to identify changes in NVC during spontaneous and electro-stimulated (ES) states in awake mice. Implantation of a long-term craniotomy window allowed TPM recording of the pathological development after the acute Kainic Acid temporal lobe epilepsy model. Our results provide direct evidence that the capillary and penetrating artery are not correlated to rhythmic neuronal activity during acute epilepsy. During the CSD period, NVC shows a strong correlation. We demonstrate that NVC exhibits nonlinear dynamics after status epilepticus. Furthermore, the vascular correlation to neuronal signals in spontaneous and ES states shows dynamic changes which correlate to the evolution after acute TLE. Understanding NVC in all TLE stages, from the acute through the TLE pathological development, may provide new therapeutic pathways.

Brain-wide visual habituation networks in wild type and fmr1 zebrafish

Habituation is a form of learning during which animals stop responding to repetitive stimuli, and deficits in habituation are characteristic of several psychiatric disorders. Due to technical challenges, the brain-wide networks mediating habituation are poorly understood. Here we report brain-wide calcium imaging during larval zebrafish habituation to repeated visual looming stimuli. We show that different functional categories of loom-sensitive neurons are located in characteristic locations throughout the brain, and that both the functional properties of their networks and the resulting behavior can be modulated by stimulus saliency and timing. Using graph theory, we identify a visual circuit that habituates minimally, a moderately habituating midbrain population proposed to mediate the sensorimotor transformation, and downstream circuit elements responsible for higher order representations and the delivery of behavior. Zebrafish larvae carrying a mutation in the fmr1 gene have a systematic shift toward sustained premotor activity in this network, and show slower behavioral habituation.

Neuronal Graphs: A Graph Theory Primer for Microscopic, Functional Networks of Neurons Recorded by Calcium Imaging

Connected networks are a fundamental structure of neurobiology. Understanding these networks will help us elucidate the neural mechanisms of computation. Mathematically speaking these networks are "graphs"-structures containing objects that are connected. In neuroscience, the objects could be regions of the brain, e.g., fMRI data, or be individual neurons, e.g., calcium imaging with fluorescence microscopy. The formal study of graphs, graph theory, can provide neuroscientists with a large bank of algorithms for exploring networks. Graph theory has already been applied in a variety of ways to fMRI data but, more recently, has begun to be applied at the scales of neurons, e.g., from functional calcium imaging. In this primer we explain the basics of graph theory and relate them to features of microscopic functional networks of neurons from calcium imaging-neuronal graphs. We explore recent examples of graph theory applied to calcium imaging and we highlight some areas where researchers new to the field could go awry.

Spontaneous and evoked activity patterns diverge over development

The immature brain is highly spontaneously active. Over development this activity must be integrated with emerging patterns of stimulus-evoked activity, but little is known about how this occurs. Here we investigated this question by recording spontaneous and evoked neural activity in the larval zebrafish tectum from 4 to 15 days post-fertilisation. Correlations within spontaneous and evoked activity epochs were comparable over development, and their neural assemblies refined in similar ways. However, both the similarity between evoked and spontaneous assemblies, and also the geometric distance between spontaneous and evoked patterns, decreased over development. At all stages of development, evoked activity was of higher dimension than spontaneous activity. Thus, spontaneous and evoked activity do not converge over development in this system, and these results do not support the hypothesis that spontaneous activity evolves to form a Bayesian prior for evoked activity.

A method for high-content functional imaging of intracellular calcium responses in gelatin-immobilized non-adherent cells

Functional imaging of the intracellular calcium concentration [Ca²⁺]_i using fluorescent indicators is a powerful and frequently applied method for assessing various biological questions in vitro, including ion channel function and intracellular signaling in homeostasis and disease. In functional [Ca²⁺]_i imaging experiments, the fluorescence intensity of single cells is typically recorded during application of a chemical stimulus, i.e. by exchange of modified extracellular media, exposure to drugs and/or ligands. The concomitant mechanical perturbation caused by the perfusion of different solution during experimentation severely hinders calcium imaging in non-adherent cells, including peripheral immune cells, as cells in suspension are dislocated by turbulent flow during chemical stimulation. The quantitative analysis, involving time-courses of intracellular fluorescence signal changes, necessitates cells to remain at the same position throughout the experiment. To prevent dislocation of cells during solution exchange, and to enable imaging as well as analysis of Ca²⁺ responses in immune cells, a gelatin-based method for immobilization of non-adherent cells was developed. Gelatin has been a long-serving material for cell immobilization, e.g. in 3D bio-printing of cells and has thus, also been employed in the context of this study. To demonstrate the applicability of the established method for functional Ca²⁺ imaging in gelatin-immobilized suspension cells, a proof-of-concept study was conducted using human peripheral blood model cell lines (Jurkat/T-lymphocytes and THP-1/monocytes), Ca²⁺ indicators (Fluo-4 and Fura-2) and two different fluorescence microscopy rigs. The data presented that the established methodology is applicable for studying Ca²⁺ signaling by in vitro high-content functional imaging of [Ca²⁺]_i in suspension cells, including but not restricted to human immune cells.

Neural circuit reorganisation after spinal cord injury in zebrafish

Spinal cord injuries disrupt signalling from the brain leading to loss of limb, locomotion, sexual and bladder function, usually irreversible in humans. In zebrafish, recovery of function occurs in a few days for larvae or a few weeks for adults due to regrowth of axons and de novo neurogenesis. Together with its genetic amenability and optical clarity, this makes zebrafish a powerful animal model to study circuit reorganisation after spinal cord injuries. With the fast evolution of techniques, we can forecast significative improvements of our knowledge of the mechanisms leading to successful or failed recovery of spinal cord function. We review here the present knowledge on the subject, the new technological approaches and we propose future directions of research.

Bayesian inference of neuronal assemblies

In many areas of the brain, both spontaneous and stimulus-evoked activity can manifest as synchronous activation of neuronal assemblies. The characterization of assembly structure and dynamics provides important insights into how brain computations are distributed across neural networks. The proliferation of experimental techniques for recording the activity of neuronal assemblies calls for a comprehensive statistical method to describe, analyze and characterize these high dimensional datasets. The performance of existing methods for defining assemblies is sensitive to noise and stochasticity in neuronal firing patterns and assembly heterogeneity. To address these problems, we introduce a generative hierarchical model of synchronous activity to describe the organization of neurons into assemblies. Unlike existing methods, our analysis provides a simultaneous estimation of assembly composition, dynamics and within-assembly statistical features, such as the levels of activity, noise and assembly synchrony. We have used our method to characterize population activity throughout the tectum of larval zebrafish, allowing us to make statistical inference on the spatiotemporal organization of tectal assemblies, their composition and the logic of their interactions. We have also applied our method to functional imaging and neuropixels recordings from the mouse, allowing us to relate the activity of identified assemblies to specific behaviours such as running or changes in pupil diameter.