Unsupervised clustering of temporal patterns in high-dimensional neuronal ensembles using a novel dissimilarity measure

Beyond correlation: optimal transport metrics for characterizing representational stability and remapping in neurons encoding spatial memory

Introduction

Spatial representations in the entorhinal cortex (EC) and hippocampus (HPC) are fundamental to cognitive functions like navigation and memory. These representations, embodied in spatial field maps, dynamically remap in response to environmental changes. However, current methods, such as Pearson's correlation coefficient, struggle to capture the complexity of these remapping events, especially when fields do not overlap, or transformations are non-linear. This limitation hinders our understanding and quantification of remapping, a key aspect of spatial memory function.

Methods

We propose a family of metrics based on the Earth Mover's Distance (EMD) as a versatile framework for characterizing remapping.

Results

The EMD provides a granular, noise-resistant, and rate-robust description of remapping. This approach enables the identification of specific cell types and the characterization of remapping in various scenarios, including disease models. Furthermore, the EMD's properties can be manipulated to identify spatially tuned cell types and to explore remapping as it relates to alternate information forms such as spatiotemporal coding.

Discussion

We present a feasible, lightweight approach that complements traditional methods. Our findings underscore the potential of the EMD as a powerful tool for enhancing our understanding of remapping in the brain and its implications for spatial navigation, memory studies and beyond.

SpikeShip: A method for fast, unsupervised discovery of high-dimensional neural spiking patterns

Neural coding and memory formation depend on temporal spiking sequences that span high-dimensional neural ensembles. The unsupervised discovery and characterization of these spiking sequences requires a suitable dissimilarity measure to spiking patterns, which can then be used for clustering and decoding. Here, we present a new dissimilarity measure based on optimal transport theory called SpikeShip, which compares multi-neuron spiking patterns based on all the relative spike-timing relationships among neurons. SpikeShip computes the optimal transport cost to make all the relative spike-timing relationships (across neurons) identical between two spiking patterns. We show that this transport cost can be decomposed into a temporal rigid translation term, which captures global latency shifts, and a vector of neuron-specific transport flows, which reflect inter-neuronal spike timing differences. SpikeShip can be effectively computed for high-dimensional neuronal ensembles, has a low (linear) computational cost that has the same order as the spike count, and is sensitive to higher-order correlations. Furthermore, SpikeShip is binless, can handle any form of spike time distributions, is not affected by firing rate fluctuations, can detect patterns with a low signal-to-noise ratio, and can be effectively combined with a sliding window approach. We compare the advantages and differences between SpikeShip and other measures like SPIKE and Victor-Purpura distance. We applied SpikeShip to large-scale Neuropixel recordings during spontaneous activity and visual encoding. We show that high-dimensional spiking sequences detected via SpikeShip reliably distinguish between different natural images and different behavioral states. These spiking sequences carried complementary information to conventional firing rate codes. SpikeShip opens new avenues for studying neural coding and memory consolidation by rapid and unsupervised detection of temporal spiking patterns in high-dimensional neural ensembles.

How our understanding of memory replay evolves

Memory reactivations and replay, widely reported in the hippocampus and cortex across species, have been implicated in memory consolidation, planning, and spatial and skill learning. Technological advances in electrophysiology, calcium imaging, and human neuroimaging techniques have enabled neuroscientists to measure large-scale neural activity with increasing spatiotemporal resolution and have provided opportunities for developing robust analytic methods to identify memory replay. In this article, we first review a large body of historically important and representative memory replay studies from the animal and human literature. We then discuss our current understanding of memory replay functions in learning, planning, and memory consolidation and further discuss the progress in computational modeling that has contributed to these improvements. Next, we review past and present analytic methods for replay analyses and discuss their limitations and challenges. Finally, looking ahead, we discuss some promising analytic methods for detecting nonstereotypical, behaviorally nondecodable structures from large-scale neural recordings. We argue that seamless integration of multisite recordings, real-time replay decoding, and closed-loop manipulation experiments will be essential for delineating the role of memory replay in a wide range of cognitive and motor functions.

Improved visualization of high-dimensional data using the distance-of-distance transformation

Dimensionality reduction tools like t-SNE and UMAP are widely used for high-dimensional data analysis. For instance, these tools are applied in biology to describe spiking patterns of neuronal populations or the genetic profiles of different cell types. Here, we show that when data include noise points that are randomly scattered within a high-dimensional space, a "scattering noise problem" occurs in the low-dimensional embedding where noise points overlap with the cluster points. We show that a simple transformation of the original distance matrix by computing a distance between neighbor distances alleviates this problem and identifies the noise points as a separate cluster. We apply this technique to high-dimensional neuronal spike sequences, as well as the representations of natural images by convolutional neural network units, and find an improvement in the constructed low-dimensional embedding. Thus, we present an improved dimensionality reduction technique for high-dimensional data containing noise points.

The Hybrid Drive: a chronic implant device combining tetrode arrays with silicon probes for layer-resolved ensemble electrophysiology in freely moving mice

Objective. Understanding the function of brain cortices requires simultaneous investigation at multiple spatial and temporal scales and to link neural activity to an animal's behavior. A major challenge is to measure within- and across-layer information in actively behaving animals, in particular in mice that have become a major species in neuroscience due to an extensive genetic toolkit. Here we describe the Hybrid Drive, a new chronic implant for mice that combines tetrode arrays to record within-layer information with silicon probes to simultaneously measure across-layer information.Approach. The design of our device combines up to 14 tetrodes and 2 silicon probes, that can be arranged in custom arrays to generate unique areas-specific (and multi-area) layouts.Main Results. We show that large numbers of neurons and layer-resolved local field potentials can be recorded from the same brain region across weeks without loss in electrophysiological signal quality. The drive's lightweight structure (~3.5 g) leaves animal behavior largely unchanged, compared to other tetrode drives, during a variety of experimental paradigms. We demonstrate how the data collected with the Hybrid Drive allow state-of-the-art analysis in a series of experiments linking the spiking activity of CA1 pyramidal layer neurons to the oscillatory activity across hippocampal layers.Significance. Our new device fits a gap in the existing technology and increases the range and precision of questions that can be addressed about neural computations in freely behaving mice.

Hidden Hypergraphs, Error-Correcting Codes, and Critical Learning in Hopfield Networks

In 1943, McCulloch and Pitts introduced a discrete recurrent neural network as a model for computation in brains. The work inspired breakthroughs such as the first computer design and the theory of finite automata. We focus on learning in Hopfield networks, a special case with symmetric weights and fixed-point attractor dynamics. Specifically, we explore minimum energy flow (MEF) as a scalable convex objective for determining network parameters. We catalog various properties of MEF, such as biological plausibility, and then compare to classical approaches in the theory of learning. Trained Hopfield networks can perform unsupervised clustering and define novel error-correcting coding schemes. They also efficiently find hidden structures (cliques) in graph theory. We extend this known connection from graphs to hypergraphs and discover n-node networks with robust storage of 2Ω(n1-ϵ) memories for any ϵ>0. In the case of graphs, we also determine a critical ratio of training samples at which networks generalize completely.

A Model of the Early Visual System Based on Parallel Spike-Sequence Detection, Showing Orientation Selectivity

Simple Summary

A computational model of primates’ early visual processing, showing orientation selectivity, is presented. The system importantly integrates two key elements: (1) a neuromorphic spike-decoding structure that considerably resembles the circuitry between layers IV and II/III of the primary visual cortex, both in topology and operation; (2) the plasticity of intrinsic excitability, to embed recent findings about the operation of the same area. The model is proposed as a tool for the analysis and reproduction of the orientation selectivity phenomenon, whose underlying neuronal-level computational mechanisms are today the subject of intense scrutiny. In response to rotated Gabor patches the model is able to exhibit realistic orientation tuning curves and to reproduce responses similar to those found in neurophysiological recordings from the primary visual cortex obtained under the same task, considering different stages of the network. This demonstrates its aptness to capture the mechanisms underlying the evoked response in the primary visual cortex. Our tool is available online, and can be expanded to other experiments using a dedicated software library developed by the authors, to elucidate the computational mechanisms underlying orientation selectivity.

Abstract

Since the first half of the twentieth century, numerous studies have been conducted on how the visual cortex encodes basic image features. One of the hallmarks of basic feature extraction is the phenomenon of orientation selectivity, of which the underlying neuronal-level computational mechanisms remain partially unclear despite being intensively investigated. In this work we present a reduced visual system model (RVSM) of the first level of scene analysis, involving the retina, the lateral geniculate nucleus and the primary visual cortex (V1), showing orientation selectivity. The detection core of the RVSM is the neuromorphic spike-decoding structure MNSD, which is able to learn and recognize parallel spike sequences and considerably resembles the neuronal microcircuits of V1 in both topology and operation. This structure is equipped with plasticity of intrinsic excitability to embed recent findings about V1 operation. The RVSM, which embeds 81 groups of MNSD arranged in 4 oriented columns, is tested using sets of rotated Gabor patches as input. Finally, synthetic visual evoked activity generated by the RVSM is compared with real neurophysiological signal from V1 area: (1) postsynaptic activity of human subjects obtained by magnetoencephalography and (2) spiking activity of macaques obtained by multi-tetrode arrays. The system is implemented using the NEST simulator. The results attest to a good level of resemblance between the model response and real neurophysiological recordings. As the RVSM is available online, and the model parameters can be customized by the user, we propose it as a tool to elucidate the computational mechanisms underlying orientation selectivity.

Formalizing planning and information search in naturalistic decision-making

Decisions made by mammals and birds are often temporally extended. They require planning and sampling of decision-relevant information. Our understanding of such decision-making remains in its infancy compared with simpler, forced-choice paradigms. However, recent advances in algorithms supporting planning and information search provide a lens through which we can explain neural and behavioral data in these tasks. We review these advances to obtain a clearer understanding for why planning and curiosity originated in certain species but not others; how activity in the medial temporal lobe, prefrontal and cingulate cortices may support these behaviors; and how planning and information search may complement each other as means to improve future action selection.

Do not waste your electrodes-principles of optimal electrode geometry for spike sorting

Objective. This study examines how the geometrical arrangement of electrodes influences spike sorting efficiency, and attempts to formalise principles for the design of electrode systems enabling optimal spike sorting performance.Approach. The clustering performance of KlustaKwik, a popular toolbox, was evaluated using semi-artificial multi-channel data, generated from a library of real spike waveforms recorded in the CA1 region of mouse Hippocampusin vivo.Main results. Based on spike sorting results under various channel configurations and signal levels, a simple model was established to describe the efficiency of different electrode geometries. Model parameters can be inferred from existing spike waveform recordings, which allowed quantifying both the cooperative effect between channels and the noise dependence of clustering performance.Significance. Based on the model, analytical and numerical results can be derived for the optimal spacing and arrangement of electrodes for one- and two-dimensional electrode systems, targeting specific brain areas.

Point process models for sequence detection in high-dimensional neural spike trains

Sparse sequences of neural spikes are posited to underlie aspects of working memory [1], motor production [2], and learning [3, 4]. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience [5-7]. Promising recent work [4, 8] utilized a convolutive nonnegative matrix factorization model [9] to tackle this challenge. However, this model requires spike times to be discretized, utilizes a sub-optimal least-squares criterion, and does not provide uncertainty estimates for model predictions or estimated parameters. We address each of these shortcomings by developing a point process model that characterizes fine-scale sequences at the level of individual spikes and represents sequence occurrences as a small number of marked events in continuous time. This ultra-sparse representation of sequence events opens new possibilities for spike train modeling. For example, we introduce learnable time warping parameters to model sequences of varying duration, which have been experimentally observed in neural circuits [10]. We demonstrate these advantages on experimental recordings from songbird higher vocal center and rodent hippocampus.

Entorhinal-retrosplenial circuits for allocentric-egocentric transformation of boundary coding

Spatial navigation requires landmark coding from two perspectives, relying on viewpoint-invariant and self-referenced representations. The brain encodes information within each reference frame but their interactions and functional dependency remains unclear. Here we investigate the relationship between neurons in the rat's retrosplenial cortex (RSC) and entorhinal cortex (MEC) that increase firing near boundaries of space. Border cells in RSC specifically encode walls, but not objects, and are sensitive to the animal's direction to nearby borders. These egocentric representations are generated independent of visual or whisker sensation but are affected by inputs from MEC that contains allocentric spatial cells. Pharmaco- and optogenetic inhibition of MEC led to a disruption of border coding in RSC, but not vice versa, indicating allocentric-to-egocentric transformation. Finally, RSC border cells fire prospective to the animal's next motion, unlike those in MEC, revealing the MEC-RSC pathway as an extended border coding circuit that implements coordinate transformation to guide navigation behavior.

On the methods for reactivation and replay analysis

A major task in the history of neurophysiology has been to relate patterns of neural activity to ongoing external stimuli. More recently, this approach has branched out to relating current neural activity patterns to external stimuli or experiences that occurred in the past or future. Here, we aim to review the large body of methodological approaches used towards this goal, and to assess the assumptions each makes with reference to the statistics of neural data that are commonly observed. These methods primarily fall into two categories, those that quantify zero-lag relationships without examining temporal evolution, termed reactivation, and those that quantify the temporal structure of changing activity patterns, termed replay. However, no two studies use the exact same approach, which prevents an unbiased comparison between findings. These observations should instead be validated by multiple and, if possible, previously established tests. This will help the community to speak a common language and will eventually provide tools to study, more generally, the organization of neuronal patterns in the brain. This article is part of the Theo Murphy meeting issue 'Memory reactivation: replaying events past, present and future'.

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.

SpikeDeeptector: a deep-learning based method for detection of neural spiking activity

OBJECTIVE

In electrophysiology, microelectrodes are the primary source for recording neural data (single unit activity). These microelectrodes can be implanted individually or in the form of arrays containing dozens to hundreds of channels. Recordings of some channels contain neural activity, which are often contaminated with noise. Another fraction of channels does not record any neural data, but only noise. By noise, we mean physiological activities unrelated to spiking, including technical artifacts and neural activities of neurons that are too far away from the electrode to be usefully processed. For further analysis, an automatic identification and continuous tracking of channels containing neural data is of great significance for many applications, e.g. automated selection of neural channels during online and offline spike sorting. Automated spike detection and sorting is also critical for online decoding in brain-computer interface (BCI) applications, in which only simple threshold crossing events are often considered for feature extraction. To our knowledge, there is no method that can universally and automatically identify channels containing neural data. In this study, we aim to identify and track channels containing neural data from implanted electrodes, automatically and more importantly universally. By universally, we mean across different recording technologies, different subjects and different brain areas.

APPROACH

We propose a novel algorithm based on a new way of feature vector extraction and a deep learning method, which we call SpikeDeeptector. SpikeDeeptector considers a batch of waveforms to construct a single feature vector and enables contextual learning. The feature vectors are then fed to a deep learning method, which learns contextualized, temporal and spatial patterns, and classifies them as channels containing neural spike data or only noise.

MAIN RESULTS

We trained the model of SpikeDeeptector on data recorded from a single tetraplegic patient with two Utah arrays implanted in different areas of the brain. The trained model was then evaluated on data collected from six epileptic patients implanted with depth electrodes, unseen data from the tetraplegic patient and data from another tetraplegic patient implanted with two Utah arrays. The cumulative evaluation accuracy was 97.20% on 1.56 million hand labeled test inputs.

SIGNIFICANCE

The results demonstrate that SpikeDeeptector generalizes not only to the new data, but also to different brain areas, subjects, and electrode types not used for training.

CLINICAL TRIAL REGISTRATION NUMBER

The clinical trial registration number for patients implanted with the Utah array is NCT01849822. For the epilepsy patients, approval from the local ethics committee at the Ruhr-University Bochum, Germany, was obtained prior to implantation.

Unsupervised identification of states from voltage recordings of neural networks

BACKGROUND

Modern techniques for multi-neuronal recording produce large amounts of data. There is no automatic procedure for the identification of states in recurrent voltage patterns.

NEW METHOD

We propose NetSAP (Network States And Pathways), a data-driven analysis method that is able to recognize multi-neuron voltage patterns (states). To capture the subtle differences between snapshots in voltage recordings, NetSAP infers the underlying functional neural network in a time-resolved manner with a sliding window approach. Then NetSAP identifies states from a reordering of the time series of inferred networks according to a user-defined metric. The procedure for unsupervised identification of states was developed originally for the analysis of molecular dynamics simulations of proteins.

RESULTS

We tested NetSAP on neural network simulations of GABAergic inhibitory interneurons. Most simulation parameters are chosen to reproduce literature observations, and we keep noise terms as control parameters to regulate the coherence of the simulated signals. NetSAP is able to identify multiple states even in the case of high internal noise and low signal coherence. We provide evidence that NetSAP is robust for networks with up to about 50% of the neurons spiking randomly. NetSAP is scalable and its code is open source.

COMPARISON WITH EXISTING METHODS

NetSAP outperforms common analysis techniques, such as PCA and k-means clustering, on a simulated recording of voltage traces of 50 neurons.

CONCLUSIONS

NetSAP analysis is an efficient tool to identify voltage patterns from neuronal recordings.

Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience

Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox—called seqNMF—with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral data sets. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs.