Identification of interacting neural populations: methods and statistical considerations.

As improved recording technologies have created new opportunities for neurophysiological investigation, emphasis has shifted from individual neurons to multiple populations that form circuits, and it has become important to provide evidence of cross-population coordinated activity. We review various methods for doing so, placing them in six major categories while avoiding technical descriptions and instead focusing on high-level motivations and concerns. Our aim is to indicate what the methods can achieve and the circumstances under which they are likely to succeed. Toward this end, we include a discussion of four cross-cutting issues: the definition of neural populations, trial-to-trial variability and Poisson-like noise, time-varying dynamics, and causality.

A biophysical and statistical modeling paradigm for connecting neural physiology and function.

To understand single neuron computation, it is necessary to know how specific physiological parameters affect neural spiking patterns that emerge in response to specific stimuli. Here we present a computational pipeline combining biophysical and statistical models that provides a link between variation in functional ion channel expression and changes in single neuron stimulus encoding. More specifically, we create a mapping from biophysical model parameters to stimulus encoding statistical model parameters. Biophysical models provide mechanistic insight, whereas statistical models can identify associations between spiking patterns and the stimuli they encode. We used public biophysical models of two morphologically and functionally distinct projection neuron cell types: mitral cells (MCs) of the main olfactory bulb, and layer V cortical pyramidal cells (PCs). We first simulated sequences of action potentials according to certain stimuli while scaling individual ion channel conductances. We then fitted point process generalized linear models (PP-GLMs), and we constructed a mapping between the parameters in the two types of models. This framework lets us detect effects on stimulus encoding of changing an ion channel conductance. The computational pipeline combines models across scales and can be applied as a screen of channels, in any cell type of interest, to identify ways that channel properties influence single neuron computation.

Oscillating neural circuits: Phase, amplitude, and the complex normal distribution.

Multiple oscillating time series are typically analyzed in the frequency domain, where coherence is usually said to represent the magnitude of the correlation between two signals at a particular frequency. The correlation being referenced is complex-valued and is similar to the real-valued Pearson correlation in some ways but not others. We discuss the dependence among oscillating series in the context of the multivariate complex normal distribution, which plays a role for vectors of complex random variables analogous to the usual multivariate normal distribution for vectors of real-valued random variables. We emphasize special cases that are valuable for the neural data we are interested in and provide new variations on existing results. We then introduce a complex latent variable model for narrowly band-pass-filtered signals at some frequency, and show that the resulting maximum likelihood estimate produces a latent coherence that is equivalent to the magnitude of the complex canonical correlation at the given frequency. We also derive an equivalence between partial coherence and the magnitude of complex partial correlation, at a given frequency. Our theoretical framework leads to interpretable results for an interesting multivariate dataset from the Allen Institute for Brain Science.

Les séries temporelles à oscillations multiples sont généralement étudiées dans le domaine fréquentiel, où la cohérence est souvent considérée comme l'amplitude de la corrélation entre deux signaux à une fréquence spécifique. Cette corrélation est à valeurs complexes et présente des similitudes avec la corrélation de Pearson pour les valeurs réelles, tout en présentant des différences distinctes. Dans cette étude, les auteurs explorent la dépendance entre les séries oscillantes en utilisant la distribution normale complexe multivariée. Cette distribution est l'équivalent de la distribution normale multivariée classique, mais adaptée aux vecteurs de variables aléatoires complexes plutôt qu'aux vecteurs de variables aléatoires réelles. Les auteurs mettent l'accent sur des cas spécifiques qui revêtent une importance particulière pour les données neuronales qui les intéressent, tout en proposant de nouvelles approches et des variations des résultats existants. Ils introduisent un modèle de variables latentes complexes pour les signaux filtrés en bande passante étroite à une fréquence donnée. Ils démontrent ensuite que l'estimation du maximum de vraisemblance dans ce modèle produit une cohérence latente équivalente à l'amplitude de la corrélation canonique complexe à la fréquence spécifiée. Ils établissent également une équivalence entre la cohérence partielle et l'amplitude de la corrélation partielle complexe, toujours à une fréquence donnée. Leur approche théorique conduit à des résultats interprétables pour un ensemble de données multivariées intéressant provenant de l'Allen Institute for Brain Science.

Population burst propagation across interacting areas of the brain.

For many perceptual and behavioral tasks, a prominent feature of neural spike trains involves high firing rates across relatively short intervals of time. We call these events "population bursts." Because during a population burst information is, presumably, transmitted from one part of the brain to another, burst timing should reveal activity related to the flow of information across neural circuits. We developed a statistical method (based on a point process model) of determining, accurately, the time of the maximum (peak) population firing rate on a trial-by-trial basis and used it to characterize burst propagation across areas. We then examined the tendency of peak firing rates in distinct brain areas to shift earlier or later in time, together, across repeated trials, and found this trial-to-trial coupling of peak times to be a sensitive indicator of interaction across populations. In the data we examined, from the Allen Brain Observatory, we found many very strong correlations (95% confidence intervals above 0.75) in cases where standard methods were unable to demonstrate cross-area correlation. The statistical model introduced cross-area covariation only through population-level trial-dependent time shifts and gain constants (values of which were learned from the data), yet it provided very good fits to data histograms, including histograms of spike count correlations within and across visual areas. Our results demonstrate the utility of carefully assessing timing and propagation, across brain regions, of transient bursts in neural population activity, based on multiple spike train recordings.NEW & NOTEWORTHY We developed a novel statistical method for identifying coordinated propagation of activity across populations of spiking neurons, with high temporal accuracy. Using simultaneous recordings from three visual areas we document precise timing relationships on a trial-by-trial basis, and we show how previously existing techniques can fail to discover coordinated activity in cases where the new approach finds very strong cross-area correlation.

Cross-population coupling of neural activity based on Gaussian process current source densities.

Because local field potentials (LFPs) arise from multiple sources in different spatial locations, they do not easily reveal coordinated activity across neural populations on a trial-to-trial basis. As we show here, however, once disparate source signals are decoupled, their trial-to-trial fluctuations become more accessible, and cross-population correlations become more apparent. To decouple sources we introduce a general framework for estimation of current source densities (CSDs). In this framework, the set of LFPs result from noise being added to the transform of the CSD by a biophysical forward model, while the CSD is considered to be the sum of a zero-mean, stationary, spatiotemporal Gaussian process, having fast and slow components, and a mean function, which is the sum of multiple time-varying functions distributed across space, each varying across trials. We derived biophysical forward models relevant to the data we analyzed. In simulation studies this approach improved identification of source signals compared to existing CSD estimation methods. Using data recorded from primate auditory cortex, we analyzed trial-to-trial fluctuations in both steady-state and task-evoked signals. We found cortical layer-specific phase coupling between two probes and showed that the same analysis applied directly to LFPs did not recover these patterns. We also found task-evoked CSDs to be correlated across probes, at specific cortical depths. Using data from Neuropixels probes in mouse visual areas, we again found evidence for depth-specific phase coupling of primary visual cortex and lateromedial area based on the CSDs.

Human iPSC-derived cardiomyocytes and pyridyl-phenyl mexiletine analogs.

In the United States, approximately one million individuals are hospitalized every year for arrhythmias, making arrhythmias one of the top causes of healthcare expenditures. Mexiletine is currently used as an antiarrhythmic drug but has limitations. The purpose of this work was to use normal and Long QT syndrome Type 3 (LQTS3) patient-derived human induced pluripotent stem cell (iPSC)-derived cardiomyocytes to identify an analog of mexiletine with superior drug-like properties. Compared to racemic mexiletine, medicinal chemistry optimization of substituted racemic pyridyl phenyl mexiletine analogs resulted in a more potent sodium channel inhibitor with greater selectivity for the sodium over the potassium channel and for late over peak sodium current.

Teaching Computation in Neuroscience: Notes on the 2019 Society for Neuroscience Professional Development Workshop on Teaching.

The 2019 Society for Neuroscience Professional Development Workshop on Teaching reviewed current tools, approaches, and examples for teaching computation in neuroscience. Robert Kass described the statistical foundations that students need to properly analyze data. Pascal Wallisch compared MATLAB and Python as programming languages for teaching students. Adrienne Fairhall discussed computational methods, training opportunities, and curricular considerations. Walt Babiec provided a view from the trenches on practical aspects of teaching computational neuroscience. Mathew Abrams concluded the session with an overview of resources for teaching and learning computational modeling in neuroscience.

KCNE1 and KCNE3 modulate KCNQ1 channels by affecting different gating transitions.

KCNE ß-subunits assemble with and modulate the properties of voltage-gated K+ channels. In the heart, KCNE1 associates with the α-subunit KCNQ1 to generate the slowly activating, voltage-dependent potassium current (IKs) in the heart that controls the repolarization phase of cardiac action potentials. By contrast, in epithelial cells from the colon, stomach, and kidney, KCNE3 coassembles with KCNQ1 to form K+ channels that are voltage-independent K+ channels in the physiological voltage range and important for controlling water and salt secretion and absorption. How KCNE1 and KCNE3 subunits modify KCNQ1 channel gating so differently is largely unknown. Here, we use voltage clamp fluorometry to determine how KCNE1 and KCNE3 affect the voltage sensor and the gate of KCNQ1. By separating S4 movement and gate opening by mutations or phosphatidylinositol 4,5-bisphosphate depletion, we show that KCNE1 affects both the S4 movement and the gate, whereas KCNE3 affects the S4 movement and only affects the gate in KCNQ1 if an intact S4-to-gate coupling is present. Further, we show that a triple mutation in the middle of the transmembrane (TM) segment of KCNE3 introduces KCNE1-like effects on the second S4 movement and the gate. In addition, we show that differences in two residues at the external end of the KCNE TM segments underlie differences in the effects of the different KCNEs on the first S4 movement and the voltage sensor-to-gate coupling.

Detection of Nav1.5 Conformational Change in Mammalian Cells Using the Noncanonical Amino Acid ANAP.

Nav1.5 inactivation is necessary for healthy conduction of the cardiac action potential. Genetic mutations of Nav1.5 perturb inactivation and cause potentially fatal arrhythmias associated with long QT syndrome type 3. The exact structural dynamics of the inactivation complex is unknown. To sense inactivation gate conformational change in live mammalian cells, we incorporated the solvatochromic fluorescent noncanonical amino acid 3-((6-acetylnaphthalen-2-yl)amino)-2-aminopropanoic acid (ANAP) into single sites in the Nav1.5 inactivation gate. ANAP was incorporated in full-length and C-terminally truncated Nav1.5 channels using mammalian cell synthetase-tRNA technology. ANAP-incorporated channels were expressed in mammalian cells, and they exhibited pathophysiological function. A spectral imaging potassium depolarization assay was designed to detect ANAP emission shifts associated with Nav1.5 conformational change. Site-specific intracellular ANAP incorporation affords live-cell imaging and detection of Nav1.5 inactivation gate conformational change in mammalian cells.

Exploring spatiotemporal neural dynamics of the human visual cortex.

The human visual cortex is organized in a hierarchical manner. Although previous evidence supporting this hypothesis has been accumulated, specific details regarding the spatiotemporal information flow remain open. Here we present detailed spatiotemporal correlation profiles of neural activity with low-level and high-level features derived from an eight-layer neural network pretrained for object recognition. These correlation profiles indicate an early-to-late shift from low-level features to high-level features and from low-level regions to higher-level regions along the visual hierarchy, consistent with feedforward information flow. Additionally, we computed three sets of features from the low- and high-level features provided by the neural network: object-category-relevant low-level features (the common components between low-level and high-level features), low-level features roughly orthogonal to high-level features (the residual Layer 1 features), and unique high-level features that were roughly orthogonal to low-level features (the residual Layer 7 features). Contrasting the correlation effects of the common components and the residual Layer 1 features, we observed that the early visual cortex (EVC) exhibited a similar amount of correlation with the two feature sets early in time, but in a later time window, the EVC exhibited a higher and longer correlation effect with the common components (i.e., the low-level object-category-relevant features) than with the low-level residual features-an effect unlikely to arise from purely feedforward information flow. Overall, our results indicate that non-feedforward processes, for example, top-down influences from mental representations of categories, may facilitate differentiation between these two types of low-level features within the EVC.

Stability of point process spiking neuron models.

Point process regression models, based on generalized linear model (GLM) technology, have been widely used for spike train analysis, but a recent paper by Gerhard et al. described a kind of instability, in which fitted models can generate simulated spike trains with explosive firing rates. We analyze the problem by extending the methods of Gerhard et al. First, we improve their instability diagnostic and extend it to a wider class of models. Next, we point out some common situations in which instability can be traced to model lack of fit. Finally, we investigate distinctions between models that use a single filter to represent the effects of all spikes prior to any particular time t, as in a 2008 paper by Pillow et al., and those that allow different filters for each spike prior to time t, as in a 2001 paper by Kass and Ventura. We re-analyze the data sets used by Gerhard et al., introduce an additional data set that exhibits bursting, and use a well-known model described by Izhikevich to simulate spike trains from various ground truth scenarios. We conclude that models with multiple filters tend to avoid instability, but there are unlikely to be universal rules. Instead, care in data fitting is required and models need to be assessed for each unique set of data.

Detecting multivariate cross-correlation between brain regions.

The problem of identifying functional connectivity from multiple time series data recorded in each of two or more brain areas arises in many neuroscientific investigations. For a single stationary time series in each of two brain areas statistical tools such as cross-correlation and Granger causality may be applied. On the other hand, to examine multivariate interactions at a single time point, canonical correlation, which finds the linear combinations of signals that maximize the correlation, may be used. We report here a new method that produces interpretations much like these standard techniques and, in addition, 1) extends the idea of canonical correlation to 3-way arrays (with dimensionality number of signals by number of time points by number of trials), 2) allows for nonstationarity, 3) also allows for nonlinearity, 4) scales well as the number of signals increases, and 5) captures predictive relationships, as is done with Granger causality. We demonstrate the effectiveness of the method through simulation studies and illustrate by analyzing local field potentials recorded from a behaving primate. NEW & NOTEWORTHY Multiple signals recorded from each of multiple brain regions may contain information about cross-region interactions. This article provides a method for visualizing the complicated interdependencies contained in these signals and assessing them statistically. The method combines signals optimally but allows the resulting measure of dependence to change, both within and between regions, as the responses evolve dynamically across time. We demonstrate the effectiveness of the method through numerical simulations and by uncovering a novel connectivity pattern between hippocampus and prefrontal cortex during a declarative memory task.

Adjusted regularization of cortical covariance.

It is now common to record dozens to hundreds or more neurons simultaneously, and to ask how the network activity changes across experimental conditions. A natural framework for addressing questions of functional connectivity is to apply Gaussian graphical modeling to neural data, where each edge in the graph corresponds to a non-zero partial correlation between neurons. Because the number of possible edges is large, one strategy for estimating the graph has been to apply methods that aim to identify large sparse effects using an [Formula: see text] penalty. However, the partial correlations found in neural spike count data are neither large nor sparse, so techniques that perform well in sparse settings will typically perform poorly in the context of neural spike count data. Fortunately, the correlated firing for any pair of cortical neurons depends strongly on both their distance apart and the features for which they are tuned. We introduce a method that takes advantage of these known, strong effects by allowing the penalty to depend on them: thus, for example, the connection between pairs of neurons that are close together will be penalized less than pairs that are far apart. We show through simulations that this physiologically-motivated procedure performs substantially better than off-the-shelf generic tools, and we illustrate by applying the methodology to populations of neurons recorded with multielectrode arrays implanted in macaque visual cortex areas V1 and V4.

Inferring oscillatory modulation in neural spike trains.

Oscillations are observed at various frequency bands in continuous-valued neural recordings like the electroencephalogram (EEG) and local field potential (LFP) in bulk brain matter, and analysis of spike-field coherence reveals that spiking of single neurons often occurs at certain phases of the global oscillation. Oscillatory modulation has been examined in relation to continuous-valued oscillatory signals, and independently from the spike train alone, but behavior or stimulus triggered firing-rate modulation, spiking sparseness, presence of slow modulation not locked to stimuli and irregular oscillations with large variability in oscillatory periods, present challenges to searching for temporal structures present in the spike train. In order to study oscillatory modulation in real data collected under a variety of experimental conditions, we describe a flexible point-process framework we call the Latent Oscillatory Spike Train (LOST) model to decompose the instantaneous firing rate in biologically and behaviorally relevant factors: spiking refractoriness, event-locked firing rate non-stationarity, and trial-to-trial variability accounted for by baseline offset and a stochastic oscillatory modulation. We also extend the LOST model to accommodate changes in the modulatory structure over the duration of the experiment, and thereby discover trial-to-trial variability in the spike-field coherence of a rat primary motor cortical neuron to the LFP theta rhythm. Because LOST incorporates a latent stochastic auto-regressive term, LOST is able to detect oscillations when the firing rate is low, the modulation is weak, and when the modulating oscillation has a broad spectral peak.

Inter-subject alignment of MEG datasets in a common representational space.

Pooling neural imaging data across subjects requires aligning recordings from different subjects. In magnetoencephalography (MEG) recordings, sensors across subjects are poorly correlated both because of differences in the exact location of the sensors, and structural and functional differences in the brains. It is possible to achieve alignment by assuming that the same regions of different brains correspond across subjects. However, this relies on both the assumption that brain anatomy and function are well correlated, and the strong assumptions that go into solving the under-determined inverse problem given the high-dimensional source space. In this article, we investigated an alternative method that bypasses source-localization. Instead, it analyzes the sensor recordings themselves and aligns their temporal signatures across subjects. We used a multivariate approach, multiset canonical correlation analysis (M-CCA), to transform individual subject data to a low-dimensional common representational space. We evaluated the robustness of this approach over a synthetic dataset, by examining the effect of different factors that add to the noise and individual differences in the data. On an MEG dataset, we demonstrated that M-CCA performs better than a method that assumes perfect sensor correspondence and a method that applies source localization. Last, we described how the standard M-CCA algorithm could be further improved with a regularization term that incorporates spatial sensor information. Hum Brain Mapp 38:4287-4301, 2017. © 2017 Wiley Periodicals, Inc.

Population Vectors Can Provide Near Optimal Integration of Information.

Much attention has been paid to the question of how Bayesian integration of information could be implemented by a simple neural mechanism. We show that population vectors based on point-process inputs combine evidence in a form that closely resembles Bayesian inference, with each input spike carrying information about the tuning of the input neuron. We also show that population vectors can combine information relatively accurately in the presence of noisy synaptic encoding of tuning curves.

Change-point detection of cognitive states across multiple trials in functional neuroimaging.

Many functional neuroimaging-based studies involve repetitions of a task that may require several phases, or states, of mental activity. An appealing idea is to use relevant brain regions to identify the states. We developed a novel change-point methodology that adapts to the repeated trial structure of such experiments by assuming the number of states stays fixed across similar trials while allowing the timing of change-points to change across trials. Model fitting is based on reversible-jump MCMC. Simulation studies verified its ability to identify change-points successfully. We applied this technique to data collected via functional magnetic resonance imaging (fMRI) while each of 20 subjects solved unfamiliar arithmetic problems. Our methodology supplies both a summary of state dimensionality and uncertainty assessments about number of states and the timing of state transitions. Copyright © 2016 John Wiley & Sons, Ltd.