Spike-train communities: finding groups of similar spike trains

An unbiased method to partition diverse neuronal responses into functional ensembles reveals interpretable population dynamics during innate social behavior

In neuroscience, understanding how single-neuron firing contributes to distributed neural ensembles is crucial. Traditional methods of analysis have been limited to descriptions of whole population activity, or, when analyzing individual neurons, criteria for response categorization varied significantly across experiments. Current methods lack scalability for large datasets, fail to capture temporal changes and rely on parametric assumptions. There's a need for a robust, scalable, and non-parametric functional clustering approach to capture interpretable dynamics. To address this challenge, we developed a model-based, statistical framework for unsupervised clustering of multiple time series datasets that exhibit nonlinear dynamics into an a-priori-unknown number of parameterized ensembles called Functional Encoding Units (FEUs). FEU outperforms existing techniques in accuracy and benchmark scores. Here, we apply this FEU formalism to single-unit recordings collected during social behaviors in rodents and primates and demonstrate its hypothesis-generating and testing capacities. This novel pipeline serves as an analytic bridge, translating neural ensemble codes across model systems.

In vivo ephaptic coupling allows memory network formation

It is increasingly clear that memories are distributed across multiple brain areas. Such "engram complexes" are important features of memory formation and consolidation. Here, we test the hypothesis that engram complexes are formed in part by bioelectric fields that sculpt and guide the neural activity and tie together the areas that participate in engram complexes. Like the conductor of an orchestra, the fields influence each musician or neuron and orchestrate the output, the symphony. Our results use the theory of synergetics, machine learning, and data from a spatial delayed saccade task and provide evidence for in vivo ephaptic coupling in memory representations.

Spikebench: An open benchmark for spike train time-series classification

Modern well-performing approaches to neural decoding are based on machine learning models such as decision tree ensembles and deep neural networks. The wide range of algorithms that can be utilized to learn from neural spike trains, which are essentially time-series data, results in the need for diverse and challenging benchmarks for neural decoding, similar to the ones in the fields of computer vision and natural language processing. In this work, we propose a spike train classification benchmark, based on open-access neural activity datasets and consisting of several learning tasks such as stimulus type classification, animal's behavioral state prediction, and neuron type identification. We demonstrate that an approach based on hand-crafted time-series feature engineering establishes a strong baseline performing on par with state-of-the-art deep learning-based models for neural decoding. We release the code allowing to reproduce the reported results.

Beyond dimension reduction: Stable electric fields emerge from and allow representational drift

It is known that the exact neurons maintaining a given memory (the neural ensemble) change from trial to trial. This raises the question of how the brain achieves stability in the face of this representational drift. Here, we demonstrate that this stability emerges at the level of the electric fields that arise from neural activity. We show that electric fields carry information about working memory content. The electric fields, in turn, can act as "guard rails" that funnel higher dimensional variable neural activity along stable lower dimensional routes. We obtained the latent space associated with each memory. We then confirmed the stability of the electric field by mapping the latent space to different cortical patches (that comprise a neural ensemble) and reconstructing information flow between patches. Stable electric fields can allow latent states to be transferred between brain areas, in accord with modern engram theory.

To deconvolve, or not to deconvolve: Inferences of neuronal activities using calcium imaging data

BACKGROUND

With the increasing popularity of calcium imaging in neuroscience research, choosing the right methods to analyze calcium imaging data is critical to address various scientific questions. Unlike spike trains measured using electrodes, fluorescence intensity traces provide an indirect and noisy measurement of the underlying neuronal activities. The observed calcium traces are either analyzed directly or deconvolved to spike trains to infer neuronal activities. When both approaches are applicable, it is unclear whether deconvolving calcium traces is a necessary step.

METHODS

In this article, we compare the performance of using calcium traces or their deconvolved spike trains for three common analyses: clustering, principal component analysis (PCA), and population decoding.

RESULTS

We found that (1) the two approaches lead to diverging results; (2) estimated spike trains, when smoothed or binned appropriately, usually lead to satisfactory performances, such as more accurate estimation of cluster membership; (3) although estimate spike train produce results more similar to true spike data than trace data, we found that the PCA results from trace data might better reflect the underlying neuronal ensembles (clusters); and (4) for both approaches, decobability can be improved by using denoising or smoothing methods.

COMPARISON WITH EXISTING METHODS

Our simulations and applications to real data suggest that estimated spike data outperform trace data in cluster analysis and give comparable results for population decoding. In addition, the decobability of estimated spike data can be slightly better than that of calcium trace data with appropriate filtering / smoothing methods.

CONCLUSION

We conclude that spike detection might be a useful pre-processing step for certain problems such as clustering; however, the continuous nature of calcium imaging data provides a natural smoothness that might be helpful for problems such as dimensional reduction.

Single-cell and ensemble activity of lumbar intermediate and ventral horn interneurons in the spinal air-stepping cat

We explored the relationship between population interneuronal network activation and motor output in the adult, in vivo, air-stepping, spinal cat. By simultaneously measuring the activity of large numbers of spinal interneurons, we explored ensembles of coherently firing interneurons and their relation to motor output. In addition, the networks were analyzed in relation to their spatial distribution along the lumbar enlargement for evidence of localized groups driving particular phases of the locomotor step cycle. We simultaneously recorded hindlimb EMG activity during stepping and extracellular signals from 128 channels across two polytrodes inserted within lamina V-VII of two separate lumbar segments. Results indicated that spinal interneurons participate in one of two ensembles that are highly correlated with the flexor or the extensor muscle bursts during stepping. Interestingly, less than half of the isolated single units were significantly unimodally tuned during the step cycle whereas >97% of the single units of the ensembles were significantly correlated with muscle activity. These results show the importance of population scale analysis in neural studies of behavior as there is a much greater correlation between muscle activity and ensemble firing than between muscle activity and individual neurons. Finally, we show that there is no correlation between interneurons' rostrocaudal locations within the lumbar enlargement and their preferred phase of firing or ensemble participation. These findings indicate that spinal interneurons of lamina V-VII encoding for different phases of the locomotor cycle are spread throughout the lumbar enlargement in the adult spinal cord.NEW & NOTEWORTHY We report on the ensemble organization of interneuronal activity in the spinal cord during locomotor movements and show that lumbar intermediate zone interneurons organize in two groups related to the two major phases of walking: stance and swing. Ensemble organization is also shown to better correlate with muscular output than single-cell activity, although ensemble membership does not appear to be somatotopically organized within the spinal cord.

Scalable and accurate method for neuronal ensemble detection in spiking neural networks

We propose a novel, scalable, and accurate method for detecting neuronal ensembles from a population of spiking neurons. Our approach offers a simple yet powerful tool to study ensemble activity. It relies on clustering synchronous population activity (population vectors), allows the participation of neurons in different ensembles, has few parameters to tune and is computationally efficient. To validate the performance and generality of our method, we generated synthetic data, where we found that our method accurately detects neuronal ensembles for a wide range of simulation parameters. We found that our method outperforms current alternative methodologies. We used spike trains of retinal ganglion cells obtained from multi-electrode array recordings under a simple ON-OFF light stimulus to test our method. We found a consistent stimuli-evoked ensemble activity intermingled with spontaneously active ensembles and irregular activity. Our results suggest that the early visual system activity could be organized in distinguishable functional ensembles. We provide a Graphic User Interface, which facilitates the use of our method by the scientific community.

Spectral estimation for detecting low-dimensional structure in networks using arbitrary null models

Discovering low-dimensional structure in real-world networks requires a suitable null model that defines the absence of meaningful structure. Here we introduce a spectral approach for detecting a network’s low-dimensional structure, and the nodes that participate in it, using any null model. We use generative models to estimate the expected eigenvalue distribution under a specified null model, and then detect where the data network’s eigenspectra exceed the estimated bounds. On synthetic networks, this spectral estimation approach cleanly detects transitions between random and community structure, recovers the number and membership of communities, and removes noise nodes. On real networks spectral estimation finds either a significant fraction of noise nodes or no departure from a null model, in stark contrast to traditional community detection methods. Across all analyses, we find the choice of null model can strongly alter conclusions about the presence of network structure. Our spectral estimation approach is therefore a promising basis for detecting low-dimensional structure in real-world networks, or lack thereof.

Non-backtracking walks reveal compartments in sparse chromatin interaction networks

Chromatin communities stabilized by protein machinery play essential role in gene regulation and refine global polymeric folding of the chromatin fiber. However, treatment of these communities in the framework of the classical network theory (stochastic block model, SBM) does not take into account intrinsic linear connectivity of the chromatin loci. Here we propose the polymer block model, paving the way for community detection in polymer networks. On the basis of this new model we modify the non-backtracking flow operator and suggest the first protocol for annotation of compartmental domains in sparse single cell Hi-C matrices. In particular, we prove that our approach corresponds to the maximum entropy principle. The benchmark analyses demonstrates that the spectrum of the polymer non-backtracking operator resolves the true compartmental structure up to the theoretical detectability threshold, while all commonly used operators fail above it. We test various operators on real data and conclude that the sizes of the non-backtracking single cell domains are most close to the sizes of compartments from the population data. Moreover, the found domains clearly segregate in the gene density and correlate with the population compartmental mask, corroborating biological significance of our annotation of the chromatin compartmental domains in single cells Hi-C matrices.

Spike-field Granger causality for hybrid neural data analysis

Neurotechnological innovations allow for simultaneous recording at various scales, ranging from spiking activity of individual neurons to large neural populations’ local field potentials (LFPs). This capability necessitates developing multiscale analysis of spike-field activity. A joint analysis of the hybrid neural data is crucial for bridging the scales between single neurons and local networks. Granger causality is a fundamental measure to evaluate directional influences among neural signals. However, it is mainly limited to inferring causal influence between the same type of signals—either LFPs or spike trains—and not well developed between two different signal types. Here we propose a model-free, nonparametric spike-field Granger causality measure for hybrid data analysis. Our measure is distinct from existing methods in that we use “binless” spikes (precise spike timing) rather than “binned” spikes (spike counts within small consecutive time windows). The latter clearly distort the information in the mixed analysis of spikes and LFP. Therefore, our spectral estimate of spike trains is directly applied to the neural point process itself, i.e., sequences of spike times rather than spike counts. Our measure is validated by an extensive set of simulated data. When the measure is applied to LFPs and spiking activity simultaneously recorded from visual areas V1 and V4 of monkeys performing a contour detection task, we are able to confirm computationally the long-standing experimental finding of the input-output relationship between LFPs and spikes. Importantly, we demonstrate that spike-field Granger causality can be used to reveal the modulatory effects that are inaccessible by traditional methods, such that spike→LFP Granger causality is modulated by the behavioral task, whereas LFP→spike Granger causality is mainly related to the average synaptic input.

NEW & NOTEWORTHY It is a pressing question to study the directional interactions between local field potential (LFP) and spiking activity. In this report, we propose a model-free, nonparametric spike-field Granger causality measure that can be used to reveal directional influences between spikes and LFPs. This new measure is crucial for bridging the scales between single neurons and neural networks; hence it represents an important step to explicate how the brain orchestrates information processing.

Fast and exact search for the partition with minimal information loss

In analysis of multi-component complex systems, such as neural systems, identifying groups of units that share similar functionality will aid understanding of the underlying structures of the system. To find such a grouping, it is useful to evaluate to what extent the units of the system are separable. Separability or inseparability can be evaluated by quantifying how much information would be lost if the system were partitioned into subsystems, and the interactions between the subsystems were hypothetically removed. A system of two independent subsystems are completely separable without any loss of information while a system of strongly interacted subsystems cannot be separated without a large loss of information. Among all the possible partitions of a system, the partition that minimizes the loss of information, called the Minimum Information Partition (MIP), can be considered as the optimal partition for characterizing the underlying structures of the system. Although the MIP would reveal novel characteristics of the neural system, an exhaustive search for the MIP is numerically intractable due to the combinatorial explosion of possible partitions. Here, we propose a computationally efficient search to precisely identify the MIP among all possible partitions by exploiting the submodularity of the measure of information loss, when the measure of information loss is submodular. Submodularity is a mathematical property of set functions which is analogous to convexity in continuous functions. Mutual information is one such submodular information loss function, and is a natural choice for measuring the degree of statistical dependence between paired sets of random variables. By using mutual information as a loss function, we show that the search for MIP can be performed in a practical order of computational time for a reasonably large system (N = 100 ∼ 1000). We also demonstrate that MIP search allows for the detection of underlying global structures in a network of nonlinear oscillators.

Uncovering Neuronal Networks Defined by Consistent Between-Neuron Spike Timing from Neuronal Spike Recordings

It is widely assumed that distributed neuronal networks are fundamental to the functioning of the brain. Consistent spike timing between neurons is thought to be one of the key principles for the formation of these networks. This can involve synchronous spiking or spiking with time delays, forming spike sequences when the order of spiking is consistent. Finding networks defined by their sequence of time-shifted spikes, denoted here as spike timing networks, is a tremendous challenge. As neurons can participate in multiple spike sequences at multiple between-spike time delays, the possible complexity of networks is prohibitively large. We present a novel approach that is capable of (1) extracting spike timing networks regardless of their sequence complexity, and (2) that describes their spiking sequences with high temporal precision. We achieve this by decomposing frequency-transformed neuronal spiking into separate networks, characterizing each network’s spike sequence by a time delay per neuron, forming a spike sequence timeline. These networks provide a detailed template for an investigation of the experimental relevance of their spike sequences. Using simulated spike timing networks, we show network extraction is robust to spiking noise, spike timing jitter, and partial occurrences of the involved spike sequences. Using rat multineuron recordings, we demonstrate the approach is capable of revealing real spike timing networks with sub-millisecond temporal precision. By uncovering spike timing networks, the prevalence, structure, and function of complex spike sequences can be investigated in greater detail, allowing us to gain a better understanding of their role in neuronal functioning.

Neuronal Assemblies Evidence Distributed Interactions within a Tactile Discrimination Task in Rats

Accumulating evidence suggests that neural interactions are distributed and relate to animal behavior, but many open questions remain. The neural assembly hypothesis, formulated by Hebb, states that synchronously active single neurons may transiently organize into functional neural circuits-neuronal assemblies (NAs)-and that would constitute the fundamental unit of information processing in the brain. However, the formation, vanishing, and temporal evolution of NAs are not fully understood. In particular, characterizing NAs in multiple brain regions over the course of behavioral tasks is relevant to assess the highly distributed nature of brain processing. In the context of NA characterization, active tactile discrimination tasks with rats are elucidative because they engage several cortical areas in the processing of information that are otherwise masked in passive or anesthetized scenarios. In this work, we investigate the dynamic formation of NAs within and among four different cortical regions in long-range fronto-parieto-occipital networks (primary somatosensory, primary visual, prefrontal, and posterior parietal cortices), simultaneously recorded from seven rats engaged in an active tactile discrimination task. Our results first confirm that task-related neuronal firing rate dynamics in all four regions is significantly modulated. Notably, a support vector machine decoder reveals that neural populations contain more information about the tactile stimulus than the majority of single neurons alone. Then, over the course of the task, we identify the emergence and vanishing of NAs whose participating neurons are shown to contain more information about animal behavior than randomly chosen neurons. Taken together, our results further support the role of multiple and distributed neurons as the functional unit of information processing in the brain (NA hypothesis) and their link to active animal behavior.

Dynamical networks: Finding, measuring, and tracking neural population activity using network science

Systems neuroscience is in a headlong rush to record from as many neurons at the same time as possible. As the brain computes and codes using neuron populations, it is hoped these data will uncover the fundamentals of neural computation. But with hundreds, thousands, or more simultaneously recorded neurons come the inescapable problems of visualizing, describing, and quantifying their interactions. Here I argue that network science provides a set of scalable, analytical tools that already solve these problems. By treating neurons as nodes and their interactions as links, a single network can visualize and describe an arbitrarily large recording. I show that with this description we can quantify the effects of manipulating a neural circuit, track changes in population dynamics over time, and quantitatively define theoretical concepts of neural populations such as cell assemblies. Using network science as a core part of analyzing population recordings will thus provide both qualitative and quantitative advances to our understanding of neural computation.

Motion contrast in primary visual cortex: a direct comparison of single neuron and population encoding

Features from outside the classical receptive field (CRF) can modulate the stimulus-driven activity of single cells in the primary visual cortex. This modulation, mediated by horizontal and feedback networks, has been extensively described as a variation of firing rate and is considered the basis of processing features as, for example, motion contrast. However, surround influences have also been identified in pairwise spiking or local field coherence. Yet, evidence about co-existence and integration of different neural signatures remains elusive. To compare multiple signatures, we recorded spiking and LFP activity evoked by stimuli exhibiting a motion contrast in the CRFs surround in anesthetized cat primary visual cortex. We chose natural-like scenes over gratings to avoid predominance of simple visual features, which could be easily represented by a rate code. We analyzed firing rates and phase-locking to low-gamma frequency in single cells and neuronal assemblies. Motion contrast was reflected in all measures but in semi-independent populations. Whereas activation of assemblies accompanied single neuron rates, their phase relations were modulated differently. Interestingly, only assembly phase relations mirrored the direction of movement of the surround and were selectively affected by thermal deactivation of visual interhemispheric connections. We argue that motion contrast can be reflected in complementary and superimposed neuronal signatures that can represent different surround features in independent neuronal populations.

Emergent cortical circuit dynamics contain dense, interwoven ensembles of spike sequences

Temporal codes are theoretically powerful encoding schemes, but their precise form in the neocortex remains unknown in part because of the large number of possible codes and the difficulty in disambiguating informative spikes from statistical noise. A biologically plausible and computationally powerful temporal coding scheme is the Hebbian assembly phase sequence (APS), which predicts reliable propagation of spikes between functionally related assemblies of neurons. Here, we sought to measure the inherent capacity of neocortical networks to produce reliable sequences of spikes, as would be predicted by an APS code. To record microcircuit activity, the scale at which computation is implemented, we used two-photon calcium imaging to densely sample spontaneous activity in murine neocortical networks ex vivo. We show that the population spike histogram is sufficient to produce a spatiotemporal progression of activity across the population. To more comprehensively evaluate the capacity for sequential spiking that cannot be explained by the overall population spiking, we identify statistically significant spike sequences. We found a large repertoire of sequence spikes that collectively comprise the majority of spiking in the circuit. Sequences manifest probabilistically and share neuron membership, resulting in unique ensembles of interwoven sequences characterizing individual spatiotemporal progressions of activity. Distillation of population dynamics into its constituent sequences provides a way to capture trial-to-trial variability and may prove to be a powerful decoding substrate in vivo. Informed by these data, we suggest that the Hebbian APS be reformulated as interwoven sequences with flexible assembly membership due to shared overlapping neurons.NEW & NOTEWORTHY Neocortical computation occurs largely within microcircuits comprised of individual neurons and their connections within small volumes (<500 μm³). We found evidence for a long-postulated temporal code, the Hebbian assembly phase sequence, by identifying repeated and co-occurring sequences of spikes. Variance in population activity across trials was explained in part by the ensemble of active sequences. The presence of interwoven sequences suggests that neuronal assembly structure can be variable and is determined by previous activity.

Fast wide-volume functional imaging of engineered in vitro brain tissues

The need for in vitro models that mimic the human brain to replace animal testing and allow high-throughput screening has driven scientists to develop new tools that reproduce tissue-like features on a chip. Three-dimensional (3D) in vitro cultures are emerging as an unmatched platform that preserves the complexity of cell-to-cell connections within a tissue, improves cell survival, and boosts neuronal differentiation. In this context, new and flexible imaging approaches are required to monitor the functional states of 3D networks. Herein, we propose an experimental model based on 3D neuronal networks in an alginate hydrogel, a tunable wide-volume imaging approach, and an efficient denoising algorithm to resolve, down to single cell resolution, the 3D activity of hundreds of neurons expressing the calcium sensor GCaMP6s. Furthermore, we implemented a 3D co-culture system mimicking the contiguous interfaces of distinct brain tissues such as the cortical-hippocampal interface. The analysis of the network activity of single and layered neuronal co-cultures revealed cell-type-specific activities and an organization of neuronal subpopulations that changed in the two culture configurations. Overall, our experimental platform represents a simple, powerful and cost-effective platform for developing and monitoring living 3D layered brain tissue on chip structures with high resolution and high throughput.

A spiral attractor network drives rhythmic locomotion

The joint activity of neural populations is high dimensional and complex. One strategy for reaching a tractable understanding of circuit function is to seek the simplest dynamical system that can account for the population activity. By imaging Aplysia's pedal ganglion during fictive locomotion, here we show that its population-wide activity arises from a low-dimensional spiral attractor. Evoking locomotion moved the population into a low-dimensional, periodic, decaying orbit - a spiral - in which it behaved as a true attractor, converging to the same orbit when evoked, and returning to that orbit after transient perturbation. We found the same attractor in every preparation, and could predict motor output directly from its orbit, yet individual neurons' participation changed across consecutive locomotion bouts. From these results, we propose that only the low-dimensional dynamics for movement control, and not the high-dimensional population activity, are consistent within and between nervous systems.

An integrated calcium imaging processing toolbox for the analysis of neuronal population dynamics

The development of new imaging and optogenetics techniques to study the dynamics of large neuronal circuits is generating datasets of unprecedented volume and complexity, demanding the development of appropriate analysis tools. We present a comprehensive computational workflow for the analysis of neuronal population calcium dynamics. The toolbox includes newly developed algorithms and interactive tools for image pre-processing and segmentation, estimation of significant single-neuron single-trial signals, mapping event-related neuronal responses, detection of activity-correlated neuronal clusters, exploration of population dynamics, and analysis of clusters' features against surrogate control datasets. The modules are integrated in a modular and versatile processing pipeline, adaptable to different needs. The clustering module is capable of detecting flexible, dynamically activated neuronal assemblies, consistent with the distributed population coding of the brain. We demonstrate the suitability of the toolbox for a variety of calcium imaging datasets. The toolbox open-source code, a step-by-step tutorial and a case study dataset are available at https://github.com/zebrain-lab/Toolbox-Romano-et-al.

Cell assemblies at multiple time scales with arbitrary lag constellations

Hebb's idea of a cell assembly as the fundamental unit of neural information processing has dominated neuroscience like no other theoretical concept within the past 60 years. A range of different physiological phenomena, from precisely synchronized spiking to broadly simultaneous rate increases, has been subsumed under this term. Yet progress in this area is hampered by the lack of statistical tools that would enable to extract assemblies with arbitrary constellations of time lags, and at multiple temporal scales, partly due to the severe computational burden. Here we present such a unifying methodological and conceptual framework which detects assembly structure at many different time scales, levels of precision, and with arbitrary internal organization. Applying this methodology to multiple single unit recordings from various cortical areas, we find that there is no universal cortical coding scheme, but that assembly structure and precision significantly depends on the brain area recorded and ongoing task demands.

DOI:http://dx.doi.org/10.7554/eLife.19428.001

Spatially Compact Neural Clusters in the Dorsal Striatum Encode Locomotion Relevant Information

An influential striatal model postulates that neural activities in the striatal direct and indirect pathways promote and inhibit movement, respectively. Normal behavior requires coordinated activity in the direct pathway to facilitate intended locomotion and indirect pathway to inhibit unwanted locomotion. In this striatal model, neuronal population activity is assumed to encode locomotion relevant information. Here, we propose a novel encoding mechanism for the dorsal striatum. We identified spatially compact neural clusters in both the direct and indirect pathways. Detailed characterization revealed similar cluster organization between the direct and indirect pathways, and cluster activities from both pathways were correlated with mouse locomotion velocities. Using machine-learning algorithms, cluster activities could be used to decode locomotion relevant behavioral states and locomotion velocity. We propose that neural clusters in the dorsal striatum encode locomotion relevant information and that coordinated activities of direct and indirect pathway neural clusters are required for normal striatal controlled behavior. VIDEO ABSTRACT.

Cell Assembly Dynamics of Sparsely-Connected Inhibitory Networks: A Simple Model for the Collective Activity of Striatal Projection Neurons

Striatal projection neurons form a sparsely-connected inhibitory network, and this arrangement may be essential for the appropriate temporal organization of behavior. Here we show that a simplified, sparse inhibitory network of Leaky-Integrate-and-Fire neurons can reproduce some key features of striatal population activity, as observed in brain slices. In particular we develop a new metric to determine the conditions under which sparse inhibitory networks form anti-correlated cell assemblies with time-varying activity of individual cells. We find that under these conditions the network displays an input-specific sequence of cell assembly switching, that effectively discriminates similar inputs. Our results support the proposal that GABAergic connections between striatal projection neurons allow stimulus-selective, temporally-extended sequential activation of cell assemblies. Furthermore, we help to show how altered intrastriatal GABAergic signaling may produce aberrant network-level information processing in disorders such as Parkinson's and Huntington's diseases.

Functional Clusters, Hubs, and Communities in the Cortical Microconnectome

Although relationships between networks of different scales have been observed in macroscopic brain studies, relationships between structures of different scales in networks of neurons are unknown. To address this, we recorded from up to 500 neurons simultaneously from slice cultures of rodent somatosensory cortex. We then measured directed effective networks with transfer entropy, previously validated in simulated cortical networks. These effective networks enabled us to evaluate distinctive nonrandom structures of connectivity at 2 different scales. We have 4 main findings. First, at the scale of 3-6 neurons (clusters), we found that high numbers of connections occurred significantly more often than expected by chance. Second, the distribution of the number of connections per neuron (degree distribution) had a long tail, indicating that the network contained distinctively high-degree neurons, or hubs. Third, at the scale of tens to hundreds of neurons, we typically found 2-3 significantly large communities. Finally, we demonstrated that communities were relatively more robust than clusters against shuffling of connections. We conclude the microconnectome of the cortex has specific organization at different scales, as revealed by differences in robustness. We suggest that this information will help us to understand how the microconnectome is robust against damage.

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective, communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires the know-how of all the methodological steps of the pipeline that manipulate the input brain signals and extract the functional network properties. On the other hand, knowledge of the neural phenomenon under study is required to perform physiologically relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes.

Modular deconstruction reveals the dynamical and physical building blocks of a locomotion motor program

The neural substrates of motor programs are only well understood for small, dedicated circuits. Here we investigate how a motor program is constructed within a large network. We imaged populations of neurons in the Aplysia pedal ganglion during execution of a locomotion motor program. We found that the program was built from a very small number of dynamical building blocks, including both neural ensembles and low-dimensional rotational dynamics. These map onto physically discrete regions of the ganglion, so that the motor program has a corresponding modular organization in both dynamical and physical space. Using this dynamic map, we identify the population potentially implementing the rhythmic pattern generator and find that its activity physically traces a looped trajectory, recapitulating its low-dimensional rotational dynamics. Our results suggest that, even in simple invertebrates, neural motor programs are implemented by large, distributed networks containing multiple dynamical systems.

Finding communities in sparse networks

Spectral algorithms based on matrix representations of networks are often used to detect communities, but classic spectral methods based on the adjacency matrix and its variants fail in sparse networks. New spectral methods based on non-backtracking random walks have recently been introduced that successfully detect communities in many sparse networks. However, the spectrum of non-backtracking random walks ignores hanging trees in networks that can contain information about their community structure. We introduce the reluctant backtracking operators that explicitly account for hanging trees as they admit a small probability of returning to the immediately previous node, unlike the non-backtracking operators that forbid an immediate return. We show that the reluctant backtracking operators can detect communities in certain sparse networks where the non-backtracking operators cannot, while performing comparably on benchmark stochastic block model networks and real world networks. We also show that the spectrum of the reluctant backtracking operator approximately optimises the standard modularity function. Interestingly, for this family of non- and reluctant-backtracking operators the main determinant of performance on real-world networks is whether or not they are normalised to conserve probability at each node.

Monitoring Spiking Activity of Many Individual Neurons in Invertebrate Ganglia

Optical recording with fast voltage sensitive dyes makes it possible, in suitable preparations, to simultaneously monitor the action potentials of large numbers of individual neurons. Here we describe methods for doing this, including considerations of different dyes and imaging systems, methods for correlating the optical signals with their source neurons, procedures for getting good signals, and the use of Independent Component Analysis for spike-sorting raw optical data into single neuron traces. These combined tools represent a powerful approach for large-scale recording of neural networks with high temporal and spatial resolution.

Recent developments in VSD imaging of small neuronal networks

Voltage-sensitive dye (VSD) imaging is a powerful technique that can provide, in single experiments, a large-scale view of network activity unobtainable with traditional sharp electrode recording methods. Here we review recent work using VSDs to study small networks and highlight several results from this approach. Topics covered include circuit mapping, network multifunctionality, the network basis of decision making, and the presence of variably participating neurons in networks. Analytical tools being developed and applied to large-scale VSD imaging data sets are discussed, and the future prospects for this exciting field are considered.

Revealing cell assemblies at multiple levels of granularity

BACKGROUND

Current neuronal monitoring techniques, such as calcium imaging and multi-electrode arrays, enable recordings of spiking activity from hundreds of neurons simultaneously. Of primary importance in systems neuroscience is the identification of cell assemblies: groups of neurons that cooperate in some form within the recorded population.

NEW METHOD

We introduce a simple, integrated framework for the detection of cell-assemblies from spiking data without a priori assumptions about the size or number of groups present. We define a biophysically-inspired measure to extract a directed functional connectivity matrix between both excitatory and inhibitory neurons based on their spiking history. The resulting network representation is analyzed using the Markov Stability framework, a graph theoretical method for community detection across scales, to reveal groups of neurons that are significantly related in the recorded time-series at different levels of granularity.

RESULTS AND COMPARISON WITH EXISTING METHODS

Using synthetic spike-trains, including simulated data from leaky-integrate-and-fire networks, our method is able to identify important patterns in the data such as hierarchical structure that are missed by other standard methods. We further apply the method to experimental data from retinal ganglion cells of mouse and salamander, in which we identify cell-groups that correspond to known functional types, and to hippocampal recordings from rats exploring a linear track, where we detect place cells with high fidelity.

CONCLUSIONS

We present a versatile method to detect neural assemblies in spiking data applicable across a spectrum of relevant scales that contributes to understanding spatio-temporal information gathered from systems neuroscience experiments.

Early hypersynchrony in juvenile PINK1(-)/(-) motor cortex is rescued by antidromic stimulation

In Parkinson’s disease (PD), cortical networks show enhanced synchronized activity but whether this precedes motor signs is unknown. We investigated this question in PINK1⁻/⁻ mice, a genetic rodent model of the PARK6 variant of familial PD which shows impaired spontaneous locomotion at 16 months. We used two-photon calcium imaging and whole-cell patch clamp in slices from juvenile (P14–P21) wild-type or PINK1⁻/⁻ mice. We designed a horizontal tilted cortico-subthalamic slice where the only connection between cortex and subthalamic nucleus (STN) is the hyperdirect cortico-subthalamic pathway. We report excessive correlation and synchronization in PINK1⁻/⁻ M1 cortical networks 15 months before motor impairment. The percentage of correlated pairs of neurons and their strength of correlation were higher in the PINK1⁻/⁻ M1 than in the wild type network and the synchronized network events involved a higher percentage of neurons. Both features were independent of thalamo-cortical pathways, insensitive to chronic levodopa treatment of pups, but totally reversed by antidromic invasion of M1 pyramidal neurons by axonal spikes evoked by high frequency stimulation (HFS) of the STN. Our study describes an early excess of synchronization in the PINK1⁻/⁻ cortex and suggests a potential role of antidromic activation of cortical interneurons in network desynchronization. Such backward effect on interneurons activity may be of importance for HFS-induced network desynchronization.

Statistical evaluation of synchronous spike patterns extracted by frequent item set mining

We recently proposed frequent itemset mining (FIM) as a method to perform an optimized search for patterns of synchronous spikes (item sets) in massively parallel spike trains. This search outputs the occurrence count (support) of individual patterns that are not trivially explained by the counts of any superset (closed frequent item sets). The number of patterns found by FIM makes direct statistical tests infeasible due to severe multiple testing. To overcome this issue, we proposed to test the significance not of individual patterns, but instead of their signatures, defined as the pairs of pattern size z and support c. Here, we derive in detail a statistical test for the significance of the signatures under the null hypothesis of full independence (pattern spectrum filtering, PSF) by means of surrogate data. As a result, injected spike patterns that mimic assembly activity are well detected, yielding a low false negative rate. However, this approach is prone to additionally classify patterns resulting from chance overlap of real assembly activity and background spiking as significant. These patterns represent false positives with respect to the null hypothesis of having one assembly of given signature embedded in otherwise independent spiking activity. We propose the additional method of pattern set reduction (PSR) to remove these false positives by conditional filtering. By employing stochastic simulations of parallel spike trains with correlated activity in form of injected spike synchrony in subsets of the neurons, we demonstrate for a range of parameter settings that the analysis scheme composed of FIM, PSF and PSR allows to reliably detect active assemblies in massively parallel spike trains.

Hemodynamic and electrophysiological spontaneous low-frequency oscillations in the cortex: directional influences revealed by Granger causality

We used a combined electrophysiological/hemodynamic system to examine low-frequency oscillations (LFOs) in spontaneous neuronal activities (spike trains and local field potentials) and hemodynamic signals (cerebral blood flow) recorded from the anesthetized rat somatosensory and visual cortices. The laser Doppler flowmetry (LDF) probe was tilted slightly to approach the area in which a microelectrode array (MEA) was implanted for simultaneous recordings. Spike trains (STs) were converted into continuous-time rate functions (CRFs) using the ST instantaneous firing rates. LFOs were detected for all three of the components using the multi-taper method (MTM). The frequencies of these LFOs ranged from 0.052 to 0.167 Hz (mean±SD, 0.10±0.026 Hz) for cerebral blood flow (CBF), from 0.027 to 0.26 Hz (mean±SD, 0.12±0.041 Hz) for the CRFs of the STs and from 0.04 to 0.19 Hz (mean±SD, 0.11±0.035 Hz) for local field potentials (LFPs). We evaluated the Granger causal relationships of spontaneous LFOs among CBF, LFPs and CRFs using Granger causality (GC) analysis. Significant Granger causal relationships were observed from LFPs to CBF, from STs to CBF and from LFPs to STs at approximately 0.1 Hz. The present results indicate that spontaneous LFOs exist not only in hemodynamic components but also in neuronal activities of the rat cortex. To the best of our knowledge, the present study is the first to identify Granger causal influences among CBF, LFPs and STs and show that spontaneous LFOs carry important Granger causal influences from neural activities to hemodynamic signals.

Population-wide distributions of neural activity during perceptual decision-making

Cortical activity involves large populations of neurons, even when it is limited to functionally coherent areas. Electrophysiological recordings, on the other hand, involve comparatively small neural ensembles, even when modern-day techniques are used. Here we review results which have started to fill the gap between these two scales of inquiry, by shedding light on the statistical distributions of activity in large populations of cells. We put our main focus on data recorded in awake animals that perform simple decision-making tasks and consider statistical distributions of activity throughout cortex, across sensory, associative, and motor areas. We transversally review the complexity of these distributions, from distributions of firing rates and metrics of spike-train structure, through distributions of tuning to stimuli or actions and of choice signals, and finally the dynamical evolution of neural population activity and the distributions of (pairwise) neural interactions. This approach reveals shared patterns of statistical organization across cortex, including: (i) long-tailed distributions of activity, where quasi-silence seems to be the rule for a majority of neurons; that are barely distinguishable between spontaneous and active states; (ii) distributions of tuning parameters for sensory (and motor) variables, which show an extensive extrapolation and fragmentation of their representations in the periphery; and (iii) population-wide dynamics that reveal rotations of internal representations over time, whose traces can be found both in stimulus-driven and internally generated activity. We discuss how these insights are leading us away from the notion of discrete classes of cells, and are acting as powerful constraints on theories and models of cortical organization and population coding.

Aggregate input-output models of neuronal populations

An extraordinary amount of electrophysiological data has been collected from various brain nuclei to help us understand how neural activity in one region influences another region. In this paper, we exploit the point process modeling (PPM) framework and describe a method for constructing aggregate input-output (IO) stochastic models that predict spiking activity of a population of neurons in the "output" region as a function of the spiking activity of a population of neurons in the "input" region. We first build PPMs of each output neuron as a function of all input neurons, and then cluster the output neurons using the model parameters. Output neurons that lie within the same cluster have the same functional dependence on the input neurons. We first applied our method to simulated data, and successfully uncovered the predetermined relationship between the two regions. We then applied our method to experimental data to understand the input-output relationship between motor cortical neurons and 1) somatosensory and 2) premotor cortical neurons during a behavioral task. Our aggregate IO models highlighted interesting physiological dependences including relative effects of inhibition/excitation from input neurons and extrinsic factors on output neurons.

Input dependent cell assembly dynamics in a model of the striatal medium spiny neuron network

The striatal medium spiny neuron (MSN) network is sparsely connected with fairly weak GABAergic collaterals receiving an excitatory glutamatergic cortical projection. Peri-stimulus time histograms (PSTH) of MSN population response investigated in various experimental studies display strong firing rate modulations distributed throughout behavioral task epochs. In previous work we have shown by numerical simulation that sparse random networks of inhibitory spiking neurons with characteristics appropriate for UP state MSNs form cell assemblies which fire together coherently in sequences on long behaviorally relevant timescales when the network receives a fixed pattern of constant input excitation. Here we first extend that model to the case where cortical excitation is composed of many independent noisy Poisson processes and demonstrate that cell assembly dynamics is still observed when the input is sufficiently weak. However if cortical excitation strength is increased more regularly firing and completely quiescent cells are found, which depend on the cortical stimulation. Subsequently we further extend previous work to consider what happens when the excitatory input varies as it would when the animal is engaged in behavior. We investigate how sudden switches in excitation interact with network generated patterned activity. We show that sequences of cell assembly activations can be locked to the excitatory input sequence and outline the range of parameters where this behavior is shown. Model cell population PSTH display both stimulus and temporal specificity, with large population firing rate modulations locked to elapsed time from task events. Thus the random network can generate a large diversity of temporally evolving stimulus dependent responses even though the input is fixed between switches. We suggest the MSN network is well suited to the generation of such slow coherent task dependent response which could be utilized by the animal in behavior.

Identifying neuron communities during a reach and grasp task using an unsupervised clustering analysis

Recent advances in brain-machine interfaces (BMIs) have allowed for high density recordings using microelectrode arrays. However, these large datasets present a challenge in how to practically identify features of interest and discard non-task-related neurons. Thus, we apply a previously reported unsupervised clustering analysis to neural data acquired from a non-human primate as it performed a center-out reach-and-grasp task. Although neurons were recorded from multiple arrays across motor and premotor areas, neurons were found to cluster into only two groups which differ by their mean firing rate. No spatial distribution of neurons was evident in different groups, either across arrays or at different depths. Using a Kalman filter to decode arm, hand, and finger kinematics, we find that using neurons from only one of the groups resulted in higher decoding accuracy (r=0.73) than using randomly selected neurons (r=0.68). This suggests that the proposed method can be used to prune the input space and identify an optimal population of neurons for BMI tasks.

Onset of Pup Locomotion Coincides with Loss of NR2C/D-Mediated Cortico-Striatal EPSCs and Dampening of Striatal Network Immature Activity

Adult motor coordination requires strong coincident cortical excitatory input to hyperpolarized medium spiny neurons (MSNs), the dominant neuronal population of the striatum. However, cortical and subcortical neurons generate during development large ongoing patterns required for activity-dependent construction of networks. This raises the question of whether immature MSNs have adult features from early stages or whether they generate immature patterns that are timely silenced to enable locomotion. Using a wide range of techniques including dynamic two-photon imaging, whole cell or single-channel patch clamp recording in slices from Nkx2.1-GFP mice, we now report a silencing of MSNs that timely coincides with locomotion. At embryonic stage (as early as E16) and during early postnatal days, genetically identified MSNs have a depolarized resting membrane potential, a high input resistance and lack both inward rectifying (IK_IR) and early slowly inactivating (I_D) potassium currents. They generate intrinsic voltage-gated clustered calcium activity without synaptic components. From postnatal days 5–7, the striatal network transiently generates synapse-driven giant depolarizing potentials when activation of cortical inputs evokes long lasting EPSCs in MSNs. Both are mediated by NR2C/D-receptors. These immature features are abruptly replaced by adult ones before P10: MSNs express IK_IR and I_D and generate short lasting, time-locked cortico-striatal AMPA/NMDA EPSCs with no NR2C/D component. This shift parallels the onset of quadruped motion by the pup. Therefore, MSNs generate immature patterns that are timely shut off to enable the coordination of motor programs.

Functional properties of striatal fast-spiking interneurons

Striatal fast-spiking interneurons (FSIs) have a major influence over behavioral output, and a deficit in these cells has been observed in dystonia and Tourette syndrome. FSIs receive cortical input, are coupled together by gap junctions, and make perisomatic GABAergic synapses onto many nearby projection neurons. Despite being critical components of striatal microcircuits, until recently little was known about FSI activity in behaving animals. Striatal FSIs are near-continuously active in awake rodents, but even neighboring FSIs show uncorrelated activity most of the time. A coordinated "pulse" of increased FSI firing occurs throughout striatum when rats initiate one chosen action while suppressing a highly trained alternative. This pulse coincides with a drop in globus pallidus population activity, suggesting that pallidostriatal disinhibition may have a important role in timing or coordinating action execution. In addition to changes in firing rate, FSIs show behavior-linked modulation of spike timing. The variability of inter-spike intervals decreases markedly following instruction cues, and FSIs also participate in fast striatal oscillations that are linked to rewarding events and dopaminergic drugs. These studies have revealed novel and unexpected properties of FSIs, that should help inform new models of striatal information processing in both normal and aberrant conditions.

Neuronal assembly detection and cell membership specification by principal component analysis

In 1949, Donald Hebb postulated that assemblies of synchronously activated neurons are the elementary units of information processing in the brain. Despite being one of the most influential theories in neuroscience, Hebb's cell assembly hypothesis only started to become testable in the past two decades due to technological advances. However, while the technology for the simultaneous recording of large neuronal populations undergoes fast development, there is still a paucity of analytical methods that can properly detect and track the activity of cell assemblies. Here we describe a principal component-based method that is able to (1) identify all cell assemblies present in the neuronal population investigated, (2) determine the number of neurons involved in ensemble activity, (3) specify the precise identity of the neurons pertaining to each cell assembly, and (4) unravel the time course of the individual activity of multiple assemblies. Application of the method to multielectrode recordings of awake and behaving rats revealed that assemblies detected in the cerebral cortex and hippocampus typically contain overlapping neurons. The results indicate that the PCA method presented here is able to properly detect, track and specify neuronal assemblies, irrespective of overlapping membership.