Fast non-negative deconvolution for spike train inference from population calcium imaging

Calcium imaging for observing spiking activity from large populations of neurons are quickly gaining popularity. While the raw data are fluorescence movies, the underlying spike trains are of interest. This work presents a fast non-negative deconvolution filter to infer the approximately most likely spike train for each neuron, given the fluorescence observations. This algorithm outperforms optimal linear deconvolution (Wiener filtering) on both simulated and biological data. The performance gains come from restricting the inferred spike trains to be positive (using an interior-point method), unlike the Wiener filter. The algorithm is fast enough that even when imaging over 100 neurons, inference can be performed on the set of all observed traces faster than real-time. Performing optimal spatial filtering on the images further refines the estimates. Importantly, all the parameters required to perform the inference can be estimated using only the fluorescence data, obviating the need to perform joint electrophysiological and imaging calibration experiments.Comment: 22 pages, 10 figure

A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data

Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a single neuron in the network and the coupling between the chains reflecting the network's connectivity matrix. We derive a Monte Carlo Expectation--Maximization algorithm for fitting the model parameters; to obtain the sufficient statistics in a computationally-efficient manner, we introduce a specialized blockwise-Gibbs algorithm for sampling from the joint activity of all observed neurons given the observed fluorescence data. We perform large-scale simulations of randomly connected neuronal networks with biophysically realistic parameters and find that the proposed methods can accurately infer the connectivity in these networks given reasonable experimental and computational constraints. In addition, the estimation accuracy may be improved significantly by incorporating prior knowledge about the sparseness of connectivity in the network, via standard L$_1$ penalization methods.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS303 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Benchmarking spike rate inference in population calcium imaging

A fundamental challenge in calcium imaging has been to infer spike rates of neurons from the measured noisy fluorescence traces. We systematically evaluate different spike inference algorithms on a large benchmark dataset (>100,000 spikes) recorded from varying neural tissue (V1 and retina) using different calcium indicators (OGB-1 and GCaMP6). In addition, we introduce a new algorithm based on supervised learning in flexible probabilistic models and find that it performs better than other published techniques. Importantly, it outperforms other algorithms even when applied to entirely new datasets for which no simultaneously recorded data is available. Future data acquired in new experimental conditions can be used to further improve the spike prediction accuracy and generalization performance of the model. Finally, we show that comparing algorithms on artificial data is not informative about performance on real data, suggesting that benchmarking different methods with real-world datasets may greatly facilitate future algorithmic developments in neuroscience

Improved spike inference accuracy by estimating the peak amplitude of unitary [Ca 2+ ] transients in weakly GCaMP6f expressing hippocampal pyramidal cells

Investigating neuronal activity using genetically encoded Ca2+ indicators in behaving animals is hampered by inaccuracies in spike inference from fluorescent tracers. Here we combine two‐photon [Ca2+] imaging with cell‐attached recordings, followed by post hoc determination of the expression level of GCaMP6f, to explore how it affects the amplitude, kinetics and temporal summation of somatic [Ca2+] transients in mouse hippocampal pyramidal cells (PCs). The amplitude of unitary [Ca2+] transients (evoked by a single action potential) negatively correlates with GCaMP6f expression, but displays large variability even among PCs with similarly low expression levels. The summation of fluorescence signals is frequency‐dependent, supralinear and also shows remarkable cell‐to‐cell variability. We performed experimental data‐based simulations and found that spike inference error rates using MLspike depend strongly on unitary peak amplitudes and GCaMP6f expression levels. We provide simple methods for estimating the unitary [Ca2+] transients in individual weakly GCaMP6f‐expressing PCs, with which we achieve spike inference error rates of ∼5%

Generative Model based Training of Deep Neural Networks for Event Detection in Microscopy Data

Several imaging techniques employed in the life sciences heavily rely on machine learning methods to make sense of the data that they produce. These include calcium imaging and multi-electrode recordings of neural activity, single molecule localization microscopy, spatially-resolved transcriptomics and particle tracking, among others. All of them only produce indirect readouts of the spatiotemporal events they aim to record. The objective when analysing data from these methods is the identification of patterns that indicate the location of the sought-after events, e.g. spikes in neural recordings or fluorescent particles in microscopy data. Existing approaches for this task invert a forward model, i.e. a mathematical description of the process that generates the observed patterns for a given set of underlying events, using established methods like MCMC or variational inference. Perhaps surprisingly, for a long time deep learning saw little use in this domain, even though it became the dominant approach in the field of pattern recognition over the previous decade. The principal reason is that in the absence of labeled data needed for supervised optimization it remains unclear how neural networks can be trained to solve these tasks. To unlock the potential of deep learning, this thesis proposes different methods for training neural networks using forward models and without relying on labeled data. The thesis rests on two publications: In the first publication we introduce an algorithm for spike extraction from calcium imaging time traces. Building on the variational autoencoder framework, we simultaneously train a neural network that performs spike inference and optimize the parameters of the forward model. This approach combines several advantages that were previously incongruous: it is fast at test-time, can be applied to different non-linear forward models and produces samples from the posterior distribution over spike trains. The second publication deals with the localization of fluorescent particles in single molecule localization microscopy. We show that an accurate forward model can be used to generate simulations that act as a surrogate for labeled training data. Careful design of the output representation and loss function result in a method with outstanding precision across experimental designs and imaging conditions. Overall this thesis highlights how neural networks can be applied for precise, fast and flexible model inversion on this class of problems and how this opens up new avenues to achieve performance beyond what was previously possible

Statistical Machine Learning & Deep Neural Networks Applied to Neural Data Analysis

Computational neuroscience seeks to discover the underlying mechanisms by which neural activity is generated. With the recent advancement in neural data acquisition methods, the bottleneck of this pursuit is the analysis of ever-growing volume of neural data acquired in numerous labs from various experiments. These analyses can be broadly divided into two categories. First, extraction of high quality neuronal signals from noisy large scale recordings. Second, inference for statistical models aimed at explaining the neuronal signals and underlying processes that give rise to them. Conventionally, majority of the methodologies employed for this effort are based on statistics and signal processing. However, in recent years recruiting Artificial Neural Networks (ANN) for neural data analysis is gaining traction. This is due to their immense success in computer vision and natural language processing, and the stellar track record of ANN architectures generalizing to a wide variety of problems. In this work we investigate and improve upon statistical and ANN machine learning methods applied to multi-electrode array recordings and inference for dynamical systems that play critical roles in computational neuroscience. In the first and second part of this thesis, we focus on spike sorting problem. The analysis of large-scale multi-neuronal spike train data is crucial for current and future of neuroscience research. However, this type of data is not available directly from recordings and require further processing to be converted into spike trains. Dense multi-electrode arrays (MEA) are standard methods for collecting such recordings. The processing needed to extract spike trains from these raw electrical signals is carried out by ``spike sorting'' algorithms. We introduce a robust and scalable MEA spike sorting pipeline YASS (Yet Another Spike Sorter) to address many challenges that are inherent to this task. We primarily pay attention to MEA data collected from the primate retina for important reasons such as the unique challenges and available side information that ultimately assist us in scoring different spike sorting pipelines. We also introduce a Neural Network architecture and an accompanying training scheme specifically devised to address the challenging task of deconvolution in MEA recordings. In the last part, we shift our attention to inference for non-linear dynamics. Dynamical systems are the governing force behind many real world phenomena and temporally correlated data. Recently, a number of neural network architectures have been proposed to address inference for nonlinear dynamical systems. We introduce two different methods based on normalizing flows for posterior inference in latent non-linear dynamical systems. We also present gradient-based amortized posterior inference approaches using the auto-encoding variational Bayes framework that can be applied to a wide range of generative models with nonlinear dynamics. We call our method (FNF). FNF performs favorably against state-of-the-art inference methods in terms of accuracy of predictions and quality of uncovered codes and dynamics on synthetic data

Fast Objective Coupled Planar Illumination Microscopy

Among optical imaging techniques light sheet fluorescence microscopy stands out as one of the most attractive for capturing high-speed biological dynamics unfolding in three dimensions. The technique is potentially millions of times faster than point-scanning techniques such as two-photon microscopy. This potential is especially poignant for neuroscience applications due to the fact that interactions between neurons transpire over mere milliseconds within tissue volumes spanning hundreds of cubic microns. However current-generation light sheet microscopes are limited by volume scanning rate and/or camera frame rate. We begin by reviewing the optical principles underlying light sheet fluorescence microscopy and the origin of these rate bottlenecks. We present an analysis leading us to the conclusion that Objective Coupled Planar Illumination (OCPI) microscopy is a particularly promising technique for recording the activity of large populations of neurons at high sampling rate. We then present speed-optimized OCPI microscopy, the first fast light sheet technique to avoid compromising image quality or photon efficiency. We enact two strategies to develop the fast OCPI microscope. First, we devise a set of optimizations that increase the rate of the volume scanning system to 40 Hz for volumes up to 700 microns thick. Second, we introduce Multi-Camera Image Sharing (MCIS), a technique to scale imaging rate by incorporating additional cameras. MCIS can be applied not only to OCPI but to any widefield imaging technique, circumventing the limitations imposed by the camera. Detailed design drawings are included to aid in dissemination to other research groups. We also demonstrate fast calcium imaging of the larval zebrafish brain and find a heartbeat-induced motion artifact. We recommend a new preprocessing step to remove the artifact through filtering. This step requires a minimal sampling rate of 15 Hz, and we expect it to become a standard procedure in zebrafish imaging pipelines. In the last chapter we describe essential computational considerations for controlling a fast OCPI microscope and processing the data that it generates. We introduce a new image processing pipeline developed to maximize computational efficiency when analyzing these multi-terabyte datasets, including a novel calcium imaging deconvolution algorithm. Finally we provide a demonstration of how combined innovations in microscope hardware and software enable inference of predictive relationships between neurons, a promising complement to more conventional correlation-based analyses

Modeling and Analysis of Neural Spike Trains

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