Model-based decoupling of evoked and spontaneous neural activity in calcium imaging data

Whole-Brain Calcium Imaging in Drosophila during Sleep and Wake

Genetically encoded calcium indicators (GECIs) allow for the noninvasive evaluation of neuronal activity in vivo, and imaging GECIs in Drosophila has become commonplace for understanding neural functions and connectivity in this system. GECIs can also be used as read-outs for studying sleep in this model organism. Here, we describe a methodology for tracking the activity of neurons in the fly brain using a two-photon (2p) microscopy system. This method can be adapted to perform functional studies of neural activity in Drosophila under both spontaneous and evoked conditions, as well as during spontaneous or induced sleep. We first describe a tethering and surgical procedure that allows survival under the microscopy conditions required for long-term recordings. We then outline the steps and reagents required for optogenetic activation of sleep-promoting neurons while simultaneously recording neural activity from the fly brain. We also describe the procedure for recording from two different locations-namely, the top of the head (e.g., to record mushroom body calyx activity) or the back of the head (e.g., to record central complex activity). We also provide different strategies for recording from GECIs confined to the cell body versus the entire neuron. Finally, we describe the steps required for analyzing the multidimensional data that can be acquired. In all, this protocol shows how to perform calcium imaging experiments in tethered flies, with a focus on acquiring spontaneous and induced sleep data.

Disentangling signal and noise in neural responses through generative modeling

Measurements of neural responses to identically repeated experimental events often exhibit large amounts of variability. This noise is distinct from signal , operationally defined as the average expected response across repeated trials for each given event. Accurately distinguishing signal from noise is important, as each is a target that is worthy of study (many believe noise reflects important aspects of brain function) and it is important not to confuse one for the other. Here, we introduce a principled modeling approach in which response measurements are explicitly modeled as the sum of samples from multivariate signal and noise distributions. In our proposed method-termed Generative Modeling of Signal and Noise (GSN)-the signal distribution is estimated by subtracting the estimated noise distribution from the estimated data distribution. We validate GSN using ground-truth simulations and demonstrate the application of GSN to empirical fMRI data. In doing so, we illustrate a simple consequence of GSN: by disentangling signal and noise components in neural responses, GSN denoises principal components analysis and improves estimates of dimensionality. We end by discussing other situations that may benefit from GSN's characterization of signal and noise, such as estimation of noise ceilings for computational models of neural activity. A code toolbox for GSN is provided with both MATLAB and Python implementations.

Sensory cortical ensembles exhibit differential coupling to ripples in distinct hippocampal subregions

Cortical neurons activated during recent experiences often reactivate with dorsal hippocampal CA1 ripples during subsequent rest. Less is known about cortical interactions with intermediate hippocampal CA1, whose connectivity, functions, and ripple events differ from dorsal CA1. We identified three clusters of putative excitatory neurons in mouse visual cortex that are preferentially excited together with either dorsal or intermediate CA1 ripples or suppressed before both ripples. Neurons in each cluster were evenly distributed across primary and higher visual cortices and co-active even in the absence of ripples. These ensembles exhibited similar visual responses but different coupling to thalamus and pupil-indexed arousal. We observed a consistent activity sequence preceding and predicting ripples: (1) suppression of ripple-suppressed cortical neurons, (2) thalamic silence, and (3) activation of intermediate CA1-ripple-activated cortical neurons. We propose that coordinated dynamics of these ensembles relay visual experiences to distinct hippocampal subregions for incorporation into different cognitive maps.

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.

Sensory cortical ensembles exhibit differential coupling to ripples in distinct hippocampal subregions

Cortical neurons activated during recent experiences often reactivate with dorsal hippocampal CA1 sharp-wave ripples (SWRs) during subsequent rest. Less is known about cortical interactions with intermediate hippocampal CA1, whose connectivity, functions, and SWRs differ from those of dorsal CA1. We identified three clusters of visual cortical excitatory neurons that are excited together with either dorsal or intermediate CA1 SWRs, or suppressed before both SWRs. Neurons in each cluster were distributed across primary and higher visual cortices and co-active even in the absence of SWRs. These ensembles exhibited similar visual responses but different coupling to thalamus and pupil-indexed arousal. We observed a consistent activity sequence: (i) suppression of SWR-suppressed cortical neurons, (ii) thalamic silence, and (iii) activation of the cortical ensemble preceding and predicting intermediate CA1 SWRs. We propose that the coordinated dynamics of these ensembles relay visual experiences to distinct hippocampal subregions for incorporation into different cognitive maps.

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.

Dimensionality reduction of calcium-imaged neuronal population activity

Calcium imaging has been widely adopted for its ability to record from large neuronal populations. To summarize the time course of neural activity, dimensionality reduction methods, which have been applied extensively to population spiking activity, may be particularly useful. However, it is unclear if the dimensionality reduction methods applied to spiking activity are appropriate for calcium imaging. We thus carried out a systematic study of design choices based on standard dimensionality reduction methods. We also developed a method to perform deconvolution and dimensionality reduction simultaneously (Calcium Imaging Linear Dynamical System, CILDS). CILDS most accurately recovered the single-trial, low-dimensional time courses from simulated calcium imaging data. CILDS also outperformed the other methods on calcium imaging recordings from larval zebrafish and mice. More broadly, this study represents a foundation for summarizing calcium imaging recordings of large neuronal populations using dimensionality reduction in diverse experimental settings.

A deep learning framework for inference of single-trial neural population dynamics from calcium imaging with subframe temporal resolution

In many areas of the brain, neural populations act as a coordinated network whose state is tied to behavior on a millisecond timescale. Two-photon (2p) calcium imaging is a powerful tool to probe such network-scale phenomena. However, estimating the network state and dynamics from 2p measurements has proven challenging because of noise, inherent nonlinearities and limitations on temporal resolution. Here we describe Recurrent Autoencoder for Discovering Imaged Calcium Latents (RADICaL), a deep learning method to overcome these limitations at the population level. RADICaL extends methods that exploit dynamics in spiking activity for application to deconvolved calcium signals, whose statistics and temporal dynamics are quite distinct from electrophysiologically recorded spikes. It incorporates a new network training strategy that capitalizes on the timing of 2p sampling to recover network dynamics with high temporal precision. In synthetic tests, RADICaL infers the network state more accurately than previous methods, particularly for high-frequency components. In 2p recordings from sensorimotor areas in mice performing a forelimb reach task, RADICaL infers network state with close correspondence to single-trial variations in behavior and maintains high-quality inference even when neuronal populations are substantially reduced.

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.

Not so spontaneous: Multi-dimensional representations of behaviors and context in sensory areas

Sensory areas are spontaneously active in the absence of sensory stimuli. This spontaneous activity has long been studied; however, its functional role remains largely unknown. Recent advances in technology, allowing large-scale neural recordings in the awake and behaving animal, have transformed our understanding of spontaneous activity. Studies using these recordings have discovered high-dimensional spontaneous activity patterns, correlation between spontaneous activity and behavior, and dissimilarity between spontaneous and sensory-driven activity patterns. These findings are supported by evidence from developing animals, where a transition toward these characteristics is observed as the circuit matures, as well as by evidence from mature animals across species. These newly revealed characteristics call for the formulation of a new role for spontaneous activity in neural sensory computation.

Inference of Multiplicative Factors Underlying Neural Variability in Calcium Imaging Data

Understanding brain function requires disentangling the high-dimensional activity of populations of neurons. Calcium imaging is an increasingly popular technique for monitoring such neural activity, but computational tools for interpreting extracted calcium signals are lacking. While there has been a substantial development of factor-analysis-type methods for neural spike train analysis, similar methods targeted at calcium imaging data are only beginning to emerge. Here we develop a flexible modeling framework that identifies low-dimensional latent factors in calcium imaging data with distinct additive and multiplicative modulatory effects. Our model includes spike-and-slab sparse priors that regularize additive factor activity and gaussian process priors that constrain multiplicative effects to vary only gradually, allowing for the identification of smooth and interpretable changes in multiplicative gain. These factors are estimated from the data using a variational expectation-maximization algorithm that requires a differentiable reparameterization of both continuous and discrete latent variables. After demonstrating our method on simulated data, we apply it to experimental data from the zebrafish optic tectum, uncovering low-dimensional fluctuations in multiplicative excitability that govern trial-to-trial variation in evoked responses.