Decoding neuronal spike trains: how important are correlations?

Calibrating Bayesian Decoders of Neural Spiking Activity

Accurately decoding external variables from observations of neural activity is a major challenge in systems neuroscience. Bayesian decoders, which provide probabilistic estimates, are some of the most widely used. Here we show how, in many common settings, the probabilistic predictions made by traditional Bayesian decoders are overconfident. That is, the estimates for the decoded stimulus or movement variables are more certain than they should be. We then show how Bayesian decoding with latent variables, taking account of low-dimensional shared variability in the observations, can improve calibration, although additional correction for overconfidence is still needed. Using data from males, we examine (1) decoding the direction of grating stimuli from spike recordings in the primary visual cortex in monkeys, (2) decoding movement direction from recordings in the primary motor cortex in monkeys, (3) decoding natural images from multiregion recordings in mice, and (4) decoding position from hippocampal recordings in rats. For each setting, we characterize the overconfidence, and we describe a possible method to correct miscalibration post hoc. Properly calibrated Bayesian decoders may alter theoretical results on probabilistic population coding and lead to brain-machine interfaces that more accurately reflect confidence levels when identifying external variables.

Information decomposition and the informational architecture of the brain

To explain how the brain orchestrates information-processing for cognition, we must understand information itself. Importantly, information is not a monolithic entity. Information decomposition techniques provide a way to split information into its constituent elements: unique, redundant, and synergistic information. We review how disentangling synergistic and redundant interactions is redefining our understanding of integrative brain function and its neural organisation. To explain how the brain navigates the trade-offs between redundancy and synergy, we review converging evidence integrating the structural, molecular, and functional underpinnings of synergy and redundancy; their roles in cognition and computation; and how they might arise over evolution and development. Overall, disentangling synergistic and redundant information provides a guiding principle for understanding the informational architecture of the brain and cognition.

Gradients of O-information highlight synergy and redundancy in physiological applications

The study of high order dependencies in complex systems has recently led to the introduction of statistical synergy, a novel quantity corresponding to a form of emergence in which patterns at large scales are not traceable from lower scales. As a consequence, several works in the last years dealt with the synergy and its counterpart, the redundancy. In particular, the O-information is a signed metric that measures the balance between redundant and synergistic statistical dependencies. In spite of its growing use, this metric does not provide insight about the role played by low-order scales in the formation of high order effects. To fill this gap, the framework for the computation of the O-information has been recently expanded introducing the so-called gradients of this metric, which measure the irreducible contribution of a variable (or a group of variables) to the high order informational circuits of a system. Here, we review the theory behind the O-information and its gradients and present the potential of these concepts in the field of network physiology, showing two new applications relevant to brain functional connectivity probed via functional resonance imaging and physiological interactions among the variability of heart rate, arterial pressure, respiration and cerebral blood flow.

NeuroDecodeR: a package for neural decoding in R

Neural decoding is a powerful method to analyze neural activity. However, the code needed to run a decoding analysis can be complex, which can present a barrier to using the method. In this paper we introduce a package that makes it easy to perform decoding analyses in the R programing language. We describe how the package is designed in a modular fashion which allows researchers to easily implement a range of different analyses. We also discuss how to format data to be able to use the package, and we give two examples of how to use the package to analyze real data. We believe that this package, combined with the rich data analysis ecosystem in R, will make it significantly easier for researchers to create reproducible decoding analyses, which should help increase the pace of neuroscience discoveries.

Introducing the STReaC (Spike Train Response Classification) toolbox

Background

This work presents a toolbox that implements methodology for automated classification of diverse neural responses to optogenetic stimulation or other changes in conditions, based on spike train recordings.

New Method

The toolbox implements what we call the Spike Train Response Classification algorithm (STReaC), which compares measurements of activity during a baseline period with analogous measurements during a subsequent period to identify various responses that might result from an event such as introduction of a sustained stimulus. The analyzed response types span a variety of patterns involving distinct time courses of increased firing, or excitation, decreased firing, or inhibition, or combinations of these. Excitation (inhibition) is identified from a comparative analysis of the spike density function (interspike interval function) for the baseline period relative to the corresponding function for the response period.

Results

The STReaC algorithm as implemented in this toolbox provides a user-friendly, tunable, objective methodology that can detect a variety of neuronal response types and associated subtleties. We demonstrate this with single-unit neural recordings of rodent substantia nigra pars reticulata (SNr) during optogenetic stimulation of the globus pallidus externa (GPe).

Comparison with existing methods

In several examples, we illustrate how the toolbox classifies responses in situations in which traditional methods (spike counting and visual inspection) either fail to detect a response or provide a false positive.

Conclusions

The STReaC toolbox provides a simple, efficient approach for classifying spike trains into a variety of response types defined relative to a period of baseline spiking.

Decreased Modulation of Population Correlations in Auditory Cortex Is Associated with Decreased Auditory Detection Performance in Old Mice

Age-related hearing loss (presbycusis) affects one-third of the world's population. One hallmark of presbycusis is difficulty hearing in noisy environments. Presbycusis can be separated into two components: the aging ear and the aging brain. To date, the role of the aging brain in presbycusis is not well understood. Activity in the primary auditory cortex (A1) during a behavioral task is because of a combination of responses representing the acoustic stimuli, attentional gain, and behavioral choice. Disruptions in any of these aspects can lead to decreased auditory processing. To investigate how these distinct components are disrupted in aging, we performed in vivo 2-photon Ca2+ imaging in both male and female mice (Thy1-GCaMP6s × CBA/CaJ mice) that retain peripheral hearing into old age. We imaged A1 neurons of young adult (2-6 months) and old mice (16-24 months) during a tone detection task in broadband noise. While young mice performed well, old mice performed worse at low signal-to-noise ratios. Calcium imaging showed that old animals have increased prestimulus activity, reduced attentional gain, and increased noise correlations. Increased correlations in old animals exist regardless of cell tuning and behavioral outcome, and these correlated networks exist over a much larger portion of cortical space. Neural decoding techniques suggest that this prestimulus activity is predictive of old animals making early responses. Together, our results suggest a model in which old animals have higher and more correlated prestimulus activity and cannot fully suppress this activity, leading to the decreased representation of targets among distracting stimuli.SIGNIFICANCE STATEMENT Aging inhibits the ability to hear clearly in noisy environments. We show that the aging auditory cortex is unable to fully suppress its responses to background noise. During an auditory behavior, fewer neurons were suppressed in the old relative to young animals, which leads to higher prestimulus activity and more false alarms. We show that this excess activity additionally leads to increased correlations between neurons, reducing the amount of relevant stimulus information in the auditory cortex. Future work identifying the lost circuits that are responsible for proper background suppression could provide new targets for therapeutic strategies to preserve auditory processing ability into old age.

A Flexible Artificial Sensory Nerve Enabled by Nanoparticle-Assembled Synaptic Devices for Neuromorphic Tactile Recognition

Tactile perception enabled by somatosensory system in human is essential for dexterous tool usage, communication, and interaction. Imparting tactile recognition functions to advanced robots and interactive systems can potentially improve their cognition and intelligence. Here, a flexible artificial sensory nerve that mimics the tactile sensing, neural coding, and synaptic processing functions in human sensory nerve is developed to achieve neuromorphic tactile recognition at device level without relying on algorithms or computing resources. An interfacial self-assembly technique, which produces uniform and defect-less thin film of semiconductor nanoparticles on arbitrary substrates, is employed to prepare the flexible synaptic device. The neural facilitation and sensory memory characteristics of the proton-gating synaptic device enable this system to identify material hardness during robotic grasping and recognize tapping patterns during tactile interaction in a continuous, real-time, high-accuracy manner, demonstrating neuromorphic intelligence and recognition capabilities. This artificial sensory nerve produced in wearable and portable form can be readily integrated with advanced robots and smart human-machine interfaces for implementing human-like tactile cognition in neuromorphic electronics toward robotic and wearable applications.

A general decoding strategy explains the relationship between behavior and correlated variability

Improvements in perception are frequently accompanied by decreases in correlated variability in sensory cortex. This relationship is puzzling because overall changes in correlated variability should minimally affect optimal information coding. We hypothesize that this relationship arises because instead of using optimal strategies for decoding the specific stimuli at hand, observers prioritize generality: a single set of neuronal weights to decode any stimuli. We tested this using a combination of multineuron recordings in the visual cortex of behaving rhesus monkeys and a cortical circuit model. We found that general decoders optimized for broad rather than narrow sets of visual stimuli better matched the animals’ decoding strategy, and that their performance was more related to the magnitude of correlated variability. In conclusion, the inverse relationship between perceptual performance and correlated variability can be explained by observers using a general decoding strategy, capable of decoding neuronal responses to the variety of stimuli encountered in natural vision.

Stochastic bursting in networks of excitable units with delayed coupling

We investigate the phenomenon of stochastic bursting in a noisy excitable unit with multiple weak delay feedbacks, by virtue of a directed tree lattice model. We find statistical properties of the appearing sequence of spikes and expressions for the power spectral density. This simple model is extended to a network of three units with delayed coupling of a star type. We find the power spectral density of each unit and the cross-spectral density between any two units. The basic assumptions behind the analytical approach are the separation of timescales, allowing for a description of the spike train as a point process, and weakness of coupling, allowing for a representation of the action of overlapped spikes via the sum of the one-spike excitation probabilities.

Context-dependent relationships between locus coeruleus firing patterns and coordinated neural activity in the anterior cingulate cortex

Ascending neuromodulatory projections from the locus coeruleus (LC) affect cortical neural networks via the release of norepinephrine (NE). However, the exact nature of these neuromodulatory effects on neural activity patterns in vivo is not well understood. Here, we show that in awake monkeys, LC activation is associated with changes in coordinated activity patterns in the anterior cingulate cortex (ACC). These relationships, which are largely independent of changes in firing rates of individual ACC neurons, depend on the type of LC activation: ACC pairwise correlations tend to be reduced when ongoing (baseline) LC activity increases but enhanced when external events evoke transient LC responses. Both relationships covary with pupil changes that reflect LC activation and arousal. These results suggest that modulations of information processing that reflect changes in coordinated activity patterns in cortical networks can result partly from ongoing, context-dependent, arousal-related changes in activation of the LC-NE system.

Decoding complex state space trajectories for neural computing

In biological neural circuits as well as in bio-inspired information processing systems, trajectories in high-dimensional state-space encode the solutions to computational tasks performed by complex dynamical systems. Due to the high state-space dimensionality and the number of possible encoding trajectories rapidly growing with input signal dimension, decoding these trajectories constitutes a major challenge on its own, in particular, as exponentially growing (space or time) requirements for decoding would render the original computational paradigm inefficient. Here, we suggest an approach to overcome this problem. We propose an efficient decoding scheme for trajectories emerging in spiking neural circuits that exhibit linear scaling with input signal dimensionality. We focus on the dynamics near a sequence of unstable saddle states that naturally emerge in a range of physical systems and provide a novel paradigm for analog computing, for instance, in the form of heteroclinic computing. Identifying simple measures of coordinated activity (synchrony) that are commonly applicable to all trajectories representing the same percept, we design robust readouts whose sizes and time requirements increase only linearly with the system size. These results move the conceptual boundary so far hindering the implementation of heteroclinic computing in hardware and may also catalyze efficient decoding strategies in spiking neural networks in general.

Altered Response Dynamics and Increased Population Correlation to Tonal Stimuli Embedded in Noise in Aging Auditory Cortex

Age-related hearing loss (presbycusis) is a chronic health condition that affects one-third of the world population. One hallmark of presbycusis is a difficulty hearing in noisy environments. Presbycusis can be separated into two components: alterations of peripheral mechanotransduction of sound in the cochlea and central alterations of auditory processing areas of the brain. Although the effects of the aging cochlea in hearing loss have been well studied, the role of the aging brain in hearing loss is less well understood. Therefore, to examine how age-related central processing changes affect hearing in noisy environments, we used a mouse model (Thy1-GCaMP6s X CBA) that has excellent peripheral hearing in old age. We used in vivo two-photon Ca2+ imaging to measure the responses of neuronal populations in auditory cortex (ACtx) of adult (2-6 months, nine male, six female, 4180 neurons) and aging mice (15-17 months, six male, three female, 1055 neurons) while listening to tones in noisy backgrounds. We found that ACtx neurons in aging mice showed larger responses to tones and have less suppressed responses consistent with reduced inhibition. Aging neurons also showed less sensitivity to temporal changes. Population analysis showed that neurons in aging mice showed higher pairwise activity correlations and showed a reduced diversity in responses to sound stimuli. Using neural decoding techniques, we show a loss of information in neuronal populations in the aging brain. Thus, aging not only affects the responses of single neurons but also affects how these neurons jointly represent stimuli.SIGNIFICANCE STATEMENT Aging results in hearing deficits particularly under challenging listening conditions. We show that auditory cortex contains distinct subpopulations of excitatory neurons that preferentially encode different stimulus features and that aging selectively reduces certain subpopulations. We also show that aging increases correlated activity between neurons and thereby reduces the response diversity in auditory cortex. The loss of population response diversity leads to a decrease of stimulus information and deficits in sound encoding, especially in noisy backgrounds. Future work determining the identities of circuits affected by aging could provide new targets for therapeutic strategies.

Neural tuning and representational geometry

A central goal of neuroscience is to understand the representations formed by brain activity patterns and their connection to behaviour. The classic approach is to investigate how individual neurons encode stimuli and how their tuning determines the fidelity of the neural representation. Tuning analyses often use the Fisher information to characterize the sensitivity of neural responses to small changes of the stimulus. In recent decades, measurements of large populations of neurons have motivated a complementary approach, which focuses on the information available to linear decoders. The decodable information is captured by the geometry of the representational patterns in the multivariate response space. Here we review neural tuning and representational geometry with the goal of clarifying the relationship between them. The tuning induces the geometry, but different sets of tuned neurons can induce the same geometry. The geometry determines the Fisher information, the mutual information and the behavioural performance of an ideal observer in a range of psychophysical tasks. We argue that future studies can benefit from considering both tuning and geometry to understand neural codes and reveal the connections between stimuli, brain activity and behaviour.

Uncovering structured responses of neural populations recorded from macaque monkeys with linear support vector machines

When a mammal, such as a macaque monkey, sees a complex natural image, many neurons in its visual cortex respond simultaneously. Here, we provide a protocol for studying the structure of population responses in laminar recordings with a machine learning model, the linear support vector machine. To unravel the role of single neurons in population responses and the structure of noise correlations, we use a multivariate decoding technique on time-averaged responses.

For complete details on the use and execution of this protocol, please refer to Koren et al. (2020a).

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Linear support vector machine (SVM) is an efficient model for decoding from neural data

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Permutation test is a rigorous method for testing the significance of results

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Neural responses along the cortical depth are heterogeneous

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Decoding weights and noise correlations share a similar structure

Sparse Coding in Temporal Association Cortex Improves Complex Sound Discriminability

The mouse auditory cortex is comprised of several auditory fields spanning the dorsoventral axis of the temporal lobe. The ventral most auditory field is the temporal association cortex (TeA), which remains largely unstudied. Using Neuropixels probes, we simultaneously recorded from primary auditory cortex (AUDp), secondary auditory cortex (AUDv), and TeA, characterizing neuronal responses to pure tones and frequency modulated (FM) sweeps in awake head-restrained female mice. As compared with AUDp and AUDv, single-unit (SU) responses to pure tones in TeA were sparser, delayed, and prolonged. Responses to FMs were also sparser. Population analysis showed that the sparser responses in TeA render it less sensitive to pure tones, yet more sensitive to FMs. When characterizing responses to pure tones under anesthesia, the distinct signature of TeA was changed considerably as compared with that in awake mice, implying that responses in TeA are strongly modulated by non-feedforward connections. Together, these findings provide a basic electrophysiological description of TeA as an integral part of sound processing along the cortical hierarchy.SIGNIFICANCE STATEMENT This is the first comprehensive characterization of the auditory responses in the awake mouse auditory temporal association cortex (TeA). The study provides the foundations for further investigation of TeA and its involvement in auditory learning, plasticity, auditory driven behaviors etc. The study was conducted using state of the art data collection tools, allowing for simultaneous recording from multiple cortical regions and numerous neurons.

Robust information routing by dorsal subiculum neurons

The dorsal hippocampus conveys various information associated with spatial navigation; however, how the information is distributed to multiple downstream areas remains unknown. We investigated this by identifying axonal projections using optogenetics during large-scale recordings from the rat subiculum, the major hippocampal output structure. Subicular neurons demonstrated a noise-resistant representation of place, speed, and trajectory, which was as accurate as or even more accurate than that of hippocampal CA1 neurons. Speed- and trajectory-dependent firings were most prominent in neurons projecting to the retrosplenial cortex and nucleus accumbens, respectively. Place-related firing was uniformly observed in neurons targeting the retrosplenial cortex, nucleus accumbens, anteroventral thalamus, and medial mammillary body. Theta oscillations and sharp-wave/ripples tightly controlled the firing of projection neurons in a target region-specific manner. In conclusion, the dorsal subiculum robustly routes diverse navigation-associated information to downstream areas.

Linear Response of General Observables in Spiking Neuronal Network Models

We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allow us to predict the influence of a weak amplitude time dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how the linear response is explicitly related to the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike train statistics. We illustrate our results with numerical simulations performed over a discrete time integrate and fire model.

Electric Stimulation Elicits Heterogeneous Responses in ON but Not OFF Retinal Ganglion Cells to Transmit Rich Neural Information

Retinal implants electrically stimulate surviving retinal neurons to restore vision in people blinded by outer retinal degeneration. Although the healthy retina is known to transmit a vast amount of visual information to the brain, it has not been studied whether prosthetic vision contains a similar amount of information. Here, we assessed the neural information transmitted by population responses arising in brisk transient (BT) and brisk sustained (BS) subtypes of ON and OFF retinal ganglion cells (RGCs) in the rabbit retina. To correlate the response heterogeneity and the information transmission, we first quantified the cell-to-cell heterogeneity by calculating the spike time tiling coefficient (STTC) across spiking patterns of RGCs in each type. Then, we computed the neural information encoded by the RGC population in a given type. In responses to light stimulation, spiking activities were more heterogeneous in OFF than ON RGCs (STTC_AVG = 0.36, 0.45, 0.77 and 0.55 for OFF BT, OFF BS, ON BT, and ON BS, respectively). Interestingly, however, in responses to electric stimulation, both BT and BS subtypes of OFF RGCs showed remarkably homogeneous spiking patterns across cells (STTC_AVG = 0.93 and 0.82 for BT and BS, respectively), whereas the two subtypes of ON RGCs showed slightly increased populational heterogeneity compared to light-evoked responses (STTC_AVG = 0.71 and 0.63 for BT and BS, respectively). Consequently, the neural information encoded by the electrically-evoked responses of a population of 15 RGCs was substantially lower in the OFF than the ON pathway: OFF BT and BS cells transmit only ~23% and ~53% of the neural information transmitted by their ON counterparts. Together with previously-reported natural spiking activities in ON RGCs, the higher neural information may make ON responses more recognizable, eliciting the biased percepts of bright phosphenes.

Physiological constraints of visual pathway lead to more efficient coding of information in retina

Nowadays, numerous studies have investigated the modeling of efficient neural encoding processes in the retina of the eye to encode the sensory data. Retina, as the innermost coat of the eye, is the first and the most important area of the visual neural system of mammalians, which is responsible for neural processes. Retina encodes the information of light intensity into a sequence of spikes, and sends them to retinal ganglion cells (RGCs) for further processing. An appropriate retinal encoding model should be adapted to the real retina as much as possible by considering the physiological constraints of the visual pathway to transfer most of the information of the input signal to the brain without too much redundancy of the channel. In this paper, inspired from the existing linear models of retinal encoding process, which have employed input noise and the spatial locality of the RGCs receptive fields (RFs) in the calculation of the encoding matrix, two extra physiological constraints, adapted from the real retina are taken into account so as to achieve a more realistic model for themammalian retina. These new constraints that are the correlation between RGCs and the spatial locality of the photoreceptors' projective fields (PFs), are modeled in a mathematical form and analyzed in detail. To quantify fidelity of the proposed encoding matrix and prove its superiority over existing models, various parameters of the models are calculated and presented in this paper: mean square error between the original and reconstructed image (MSE), the redundancy of the channel, the amount of information transferred through the channel, and the amount of wasted capacity for carrying input noise, to name a few. The results of these calculations show that the proposed model transfers input information with less redundancy of the channel. In other words, it reduces a portion of channel capacity which is wasted for carrying the input noise in comparison to the existing models. Also, due to considering extra physiological constraints in the proposed model, it is acceptable to have a slightly higher amount of MSE value in order to become similar to the real retina.

Noise-Correlation Is Modulated by Reward Expectation in the Primary Motor Cortex Bilaterally During Manual and Observational Tasks in Primates

Reward modulation is represented in the motor cortex (M1) and could be used to implement more accurate decoding models to improve brain-computer interfaces (BCIs; Zhao et al., 2018). Analyzing trial-to-trial noise-correlations between neural units in the presence of rewarding (R) and non-rewarding (NR) stimuli adds to our understanding of cortical network dynamics. We utilized Pearson's correlation coefficient to measure shared variability between simultaneously recorded units (32-112) and found significantly higher noise-correlation and positive correlation between the populations' signal- and noise-correlation during NR trials as compared to R trials. This pattern is evident in data from two non-human primates (NHPs) during single-target center out reaching tasks, both manual and action observation versions. We conducted a mean matched noise-correlation analysis to decouple known interactions between event-triggered firing rate changes and neural correlations. Isolated reward discriminatory units demonstrated stronger correlational changes than units unresponsive to reward firing rate modulation, however, the qualitative response was similar, indicating correlational changes within the network as a whole can serve as another information channel to be exploited by BCIs that track the underlying cortical state, such as reward expectation, or attentional modulation. Reward expectation and attention in return can be utilized with reinforcement learning (RL) towards autonomous BCI updating.

Binless Kernel Machine: Modeling Spike Train Transformation for Cognitive Neural Prostheses

Modeling spike train transformation among brain regions helps in designing a cognitive neural prosthesis that restores lost cognitive functions. Various methods analyze the nonlinear dynamic spike train transformation between two cortical areas with low computational eficiency. The application of a real-time neural prosthesis requires computational eficiency, performance stability, and better interpretation of the neural firing patterns that modulate target spike generation. We propose the binless kernel machine in the point-process framework to describe nonlinear dynamic spike train transformations. Our approach embeds the binless kernel to eficiently capture the feedforward dynamics of spike trains and maps the input spike timings into reproducing kernel Hilbert space (RKHS). An inhomogeneous Bernoulli process is designed to combine with a kernel logistic regression that operates on the binless kernel to generate an output spike train as a point process. Weights of the proposed model are estimated by maximizing the log likelihood of output spike trains in RKHS, which allows a global-optimal solution. To reduce computational complexity, we design a streaming-based clustering algorithm to extract typical and important spike train features. The cluster centers and their weights enable the visualization of the important input spike train patterns that motivate or inhibit output neuron firing. We test the proposed model on both synthetic data and real spike train data recorded from the dorsal premotor cortex and the primary motor cortex of a monkey performing a center-out task. Performances are evaluated by discrete-time rescaling Kolmogorov-Smirnov tests. Our model outperforms the existing methods with higher stability regardless of weight initialization and demonstrates higher eficiency in analyzing neural patterns from spike timing with less historical input (50%). Meanwhile, the typical spike train patterns selected according to weights are validated to encode output spike from the spike train of single-input neuron and the interaction of two input neurons.

Higher-Order Cumulants Drive Neuronal Activity Patterns, Inducing UP-DOWN States in Neural Populations

A major challenge in neuroscience is to understand the role of the higher-order correlations structure of neuronal populations. The dichotomized Gaussian model (DG) generates spike trains by means of thresholding a multivariate Gaussian random variable. The DG inputs are Gaussian distributed, and thus have no interactions beyond the second order in their inputs; however, they can induce higher-order correlations in the outputs. We propose a combination of analytical and numerical techniques to estimate higher-order, above the second, cumulants of the firing probability distributions. Our findings show that a large amount of pairwise interactions in the inputs can induce the system into two possible regimes, one with low activity (“DOWN state”) and another one with high activity (“UP state”), and the appearance of these states is due to a combination between the third- and fourth-order cumulant. This could be part of a mechanism that would help the neural code to upgrade specific information about the stimuli, motivating us to examine the behavior of the critical fluctuations through the Binder cumulant close to the critical point. We show, using the Binder cumulant, that higher-order correlations in the outputs generate a critical neural system that portrays a second-order phase transition.

Auditory cortex shapes sound responses in the inferior colliculus

The extensive feedback from the auditory cortex (AC) to the inferior colliculus (IC) supports critical aspects of auditory behavior but has not been extensively characterized. Previous studies demonstrated that activity in IC is altered by focal electrical stimulation and pharmacological inactivation of AC, but these methods lack the ability to selectively manipulate projection neurons. We measured the effects of selective optogenetic modulation of cortico-collicular feedback projections on IC sound responses in mice. Activation of feedback increased spontaneous activity and decreased stimulus selectivity in IC, whereas suppression had no effect. To further understand how microcircuits in AC may control collicular activity, we optogenetically modulated the activity of different cortical neuronal subtypes, specifically parvalbumin-positive (PV) and somatostatin-positive (SST) inhibitory interneurons. We found that modulating the activity of either type of interneuron did not affect IC sound-evoked activity. Combined, our results identify that activation of excitatory projections, but not inhibition-driven changes in cortical activity, affects collicular sound responses.

Selective Changes in Noise Correlations Contribute to an Enhanced Representation of Saccadic Targets in Prefrontal Neuronal Ensembles

An ensemble of neurons can provide a dynamic representation of external stimuli, ongoing processes, or upcoming actions. This dynamic representation could be achieved by changes in the activity of individual neurons and/or their interactions. To investigate these possibilities, we simultaneously recorded from ensembles of prefrontal neurons in non-human primates during a memory-guided saccade task. Using both decoding and encoding methods, we examined changes in the information content of individual neurons and that of ensembles between visual encoding and saccadic target selection. We found that individual neurons maintained their limited spatial sensitivity between these cognitive states, whereas the ensemble selectively improved its encoding of spatial locations far from the neurons’ preferred locations. This population-level “encoding expansion” was not due to the ceiling effect at the preferred locations and was accompanied by selective changes in noise correlations for non-preferred locations. Moreover, the encoding expansion was observed for ensembles of different types of neurons and could not be explained by shifts in the preferred location of individual neurons. Our results demonstrate that the representation of space by neuronal ensembles is dynamically enhanced prior to saccades, and this enhancement occurs alongside changes in noise correlations more than changes in the activity of individual neurons.

Quantifying encoding redundancy induced by rate correlations in Poisson neurons

Temporal correlations in neuronal spike trains are known to introduce redundancy to stimulus encoding. However, exact methods to describe how these correlations impact neural information transmission quantitatively are lacking. Here, we provide a general measure for the information carried by correlated rate modulations only, neglecting other spike correlations, and use it to investigate the effect of rate correlations on encoding redundancy. We derive it analytically by calculating the mutual information between a time-correlated, rate modulating signal and the resulting spikes of Poisson neurons. Whereas this information is determined by spike autocorrelations only, the redundancy in information encoding due to rate correlations depends on both the distribution and the autocorrelation of the rate histogram. We further demonstrate that at very small signal strengths the information carried by rate correlated spikes becomes identical to that of independent spikes, in effect measuring the signal modulation depth. In contrast, a vanishing signal correlation time maximizes information but does not generally yield the information of independent spikes. Overall, our study sheds light on the role of signal-induced temporal correlations for neural coding, by providing insight into how signal features shape redundancy and by establishing mathematical links between existing methods.

Attentional Modulation of Visual Spatial Integration: Psychophysical Evidence Supported by Population Coding Modeling

Two prominent strategies that the human visual system uses to reduce incoming information are spatial integration and selective attention. Whereas spatial integration summarizes and combines information over the visual field, selective attention can single it out for scrutiny. The way in which these well-known mechanisms-with rather opposing effects-interact remains largely unknown. To address this, we had observers perform a gaze-contingent search task that nudged them to deploy either spatial or feature-based attention to maximize performance. We found that, depending on the type of attention employed, visual spatial integration strength changed either in a strong and localized or a more modest and global manner compared with a baseline condition. Population code modeling revealed that a single mechanism can account for both observations: Attention acts beyond the neuronal encoding stage to tune the spatial integration weights of neural populations. Our study shows how attention and integration interact to optimize the information flow through the brain.

Population Coding and Correlated Variability in Electrosensory Pathways

The fact that perception and behavior depend on the simultaneous and coordinated activity of neural populations is well established. Understanding encoding through neuronal population activity is however complicated by the statistical dependencies between the activities of neurons, which can be present in terms of both their mean (signal correlations) and their response variability (noise correlations). Here, we review the state of knowledge regarding population coding and the influence of correlated variability in the electrosensory pathways of the weakly electric fish Apteronotus leptorhynchus. We summarize known population coding strategies at the peripheral level, which are largely unaffected by noise correlations. We then move on to the hindbrain, where existing data from the electrosensory lateral line lobe (ELL) shows the presence of noise correlations. We summarize the current knowledge regarding the mechanistic origins of noise correlations and known mechanisms of stimulus dependent correlation shaping in ELL. We finish by considering future directions for understanding population coding in the electrosensory pathways of weakly electric fish, highlighting the benefits of this model system for understanding the origins and impact of noise correlations on population coding.

Assessing the Relevance of Specific Response Features in the Neural Code

The study of the neural code aims at deciphering how the nervous system maps external stimuli into neural activity—the encoding phase—and subsequently transforms such activity into adequate responses to the original stimuli—the decoding phase. Several information-theoretical methods have been proposed to assess the relevance of individual response features, as for example, the spike count of a given neuron, or the amount of correlation in the activity of two cells. These methods work under the premise that the relevance of a feature is reflected in the information loss that is induced by eliminating the feature from the response. The alternative methods differ in the procedure by which the tested feature is removed, and the algorithm with which the lost information is calculated. Here we compare these methods, and show that more often than not, each method assigns a different relevance to the tested feature. We demonstrate that the differences are both quantitative and qualitative, and connect them with the method employed to remove the tested feature, as well as the procedure to calculate the lost information. By studying a collection of carefully designed examples, and working on analytic derivations, we identify the conditions under which the relevance of features diagnosed by different methods can be ranked, or sometimes even equated. The condition for equality involves both the amount and the type of information contributed by the tested feature. We conclude that the quest for relevant response features is more delicate than previously thought, and may yield to multiple answers depending on methodological subtleties.

Nonlinear Modeling of Neural Interaction for Spike Prediction Using the Staged Point-Process Model

Neurons communicate nonlinearly through spike activities. Generalized linear models (GLMs) describe spike activities with a cascade of a linear combination across inputs, a static nonlinear function, and an inhomogeneous Bernoulli or Poisson process, or Cox process if a self-history term is considered. This structure considers the output nonlinearity in spike generation but excludes the nonlinear interaction among input neurons. Recent studies extend GLMs by modeling the interaction among input neurons with a quadratic function, which considers the interaction between every pair of input spikes. However, quadratic effects may not fully capture the nonlinear nature of input interaction. We therefore propose a staged point-process model to describe the nonlinear interaction among inputs using a few hidden units, which follows the idea of artificial neural networks. The output firing probability conditioned on inputs is formed as a cascade of two linear-nonlinear (a linear combination plus a static nonlinear function) stages and an inhomogeneous Bernoulli process. Parameters of this model are estimated by maximizing the log likelihood on output spike trains. Unlike the iterative reweighted least squares algorithm used in GLMs, where the performance is guaranteed by the concave condition, we propose a modified Levenberg-Marquardt (L-M) algorithm, which directly calculates the Hessian matrix of the log likelihood, for the nonlinear optimization in our model. The proposed model is tested on both synthetic data and real spike train data recorded from the dorsal premotor cortex and primary motor cortex of a monkey performing a center-out task. Performances are evaluated by discrete-time rescaled Kolmogorov-Smirnov tests, where our model statistically outperforms a GLM and its quadratic extension, with a higher goodness-of-fit in the prediction results. In addition, the staged point-process model describes nonlinear interaction among input neurons with fewer parameters than quadratic models, and the modified L-M algorithm also demonstrates fast convergence.

Information-Theoretical Analysis of the Neural Code in the Rodent Temporal Lobe

In the study of the neural code, information-theoretical methods have the advantage of making no assumptions about the probabilistic mapping between stimuli and responses. In the sensory domain, several methods have been developed to quantify the amount of information encoded in neural activity, without necessarily identifying the specific stimulus or response features that instantiate the code. As a proof of concept, here we extend those methods to the encoding of kinematic information in a navigating rodent. We estimate the information encoded in two well-characterized codes, mediated by the firing rate of neurons, and by the phase-of-firing with respect to the theta-filtered local field potential. In addition, we also consider a novel code, mediated by the delta-filtered local field potential. We find that all three codes transmit significant amounts of kinematic information, and informative neurons tend to employ a combination of codes. Cells tend to encode conjunctions of kinematic features, so that most of the informative neurons fall outside the traditional cell types employed to classify spatially-selective units. We conclude that a broad perspective on the candidate stimulus and response features expands the repertoire of strategies with which kinematic information is encoded.

A Moment-Based Maximum Entropy Model for Fitting Higher-Order Interactions in Neural Data

Correlations in neural activity have been demonstrated to have profound consequences for sensory encoding. To understand how neural populations represent stimulus information, it is therefore necessary to model how pairwise and higher-order spiking correlations between neurons contribute to the collective structure of population-wide spiking patterns. Maximum entropy models are an increasingly popular method for capturing collective neural activity by including successively higher-order interaction terms. However, incorporating higher-order interactions in these models is difficult in practice due to two factors. First, the number of parameters exponentially increases as higher orders are added. Second, because triplet (and higher) spiking events occur infrequently, estimates of higher-order statistics may be contaminated by sampling noise. To address this, we extend previous work on the Reliable Interaction class of models to develop a normalized variant that adaptively identifies the specific pairwise and higher-order moments that can be estimated from a given dataset for a specified confidence level. The resulting “Reliable Moment” model is able to capture cortical-like distributions of population spiking patterns. Finally, we show that, compared with the Reliable Interaction model, the Reliable Moment model infers fewer strong spurious higher-order interactions and is better able to predict the frequencies of previously unobserved spiking patterns.

Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

The spiking activity of neuronal networks follows laws that are not time-reversal symmetric; the notion of pre-synaptic and post-synaptic neurons, stimulus correlations and noise correlations have a clear time order. Therefore, a biologically realistic statistical model for the spiking activity should be able to capture some degree of time irreversibility. We use the thermodynamic formalism to build a framework in the context maximum entropy models to quantify the degree of time irreversibility, providing an explicit formula for the information entropy production of the inferred maximum entropy Markov chain. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.

Noise correlations in the human brain and their impact on pattern classification

Multivariate decoding methods, such as multivoxel pattern analysis (MVPA), are highly effective at extracting information from brain imaging data. Yet, the precise nature of the information that MVPA draws upon remains controversial. Most current theories emphasize the enhanced sensitivity imparted by aggregating across voxels that have mixed and weak selectivity. However, beyond the selectivity of individual voxels, neural variability is correlated across voxels, and such noise correlations may contribute importantly to accurate decoding. Indeed, a recent computational theory proposed that noise correlations enhance multivariate decoding from heterogeneous neural populations. Here we extend this theory from the scale of neurons to functional magnetic resonance imaging (fMRI) and show that noise correlations between heterogeneous populations of voxels (i.e., voxels selective for different stimulus variables) contribute to the success of MVPA. Specifically, decoding performance is enhanced when voxels with high vs. low noise correlations (measured during rest or in the background of the task) are selected during classifier training. Conversely, voxels that are strongly selective for one class in a GLM or that receive high classification weights in MVPA tend to exhibit high noise correlations with voxels selective for the other class being discriminated against. Furthermore, we use simulations to show that this is a general property of fMRI data and that selectivity and noise correlations can have distinguishable influences on decoding. Taken together, our findings demonstrate that if there is signal in the data, the resulting above-chance classification accuracy is modulated by the magnitude of noise correlations.

A central challenge in cognitive neuroscience is decoding mental representations from patterns of brain activity. With functional magnetic resonance imaging (fMRI), multivariate decoding methods like multivoxel pattern analysis (MVPA) have produced numerous discoveries about the brain. However, what information these methods draw upon remains the subject of debate. Typically, each voxel is thought to contribute information through its selectivity (i.e., how differently it responds to the classes being decoded), with improved sensitivity reflecting the aggregation of selectivity across voxels. We show that this interpretation downplays an important factor: MVPA is also highly attuned to noise correlations between voxels with opposite selectivity. Across several analyses of an fMRI dataset, we demonstrate a positive relationship between the magnitude of noise correlations and multivariate decoding performance. Indeed, voxels more selective for one class, or heavily weighted in MVPA, tend to be more strongly correlated with voxels selective for the opposite class. Furthermore, using a model to simulate different levels of selectivity and noise correlations, we find that the benefit of noise correlations for decoding is a general property of fMRI data. These findings help elucidate the computational underpinnings of multivariate decoding in cognitive neuroscience and provide insight into the nature of neural representations.

Optimizing for generalization in the decoding of internally generated activity in the hippocampus

The decoding of a sensory or motor variable from neural activity benefits from a known ground truth against which decoding performance can be compared. In contrast, the decoding of covert, cognitive neural activity, such as occurs in memory recall or planning, typically cannot be compared to a known ground truth. As a result, it is unclear how decoders of such internally generated activity should be configured in practice. We suggest that if the true code for covert activity is unknown, decoders should be optimized for generalization performance using cross-validation. Using ensemble recording data from hippocampal place cells, we show that this cross-validation approach results in different decoding error, different optimal decoding parameters, and different distributions of error across the decoded variable space. In addition, we show that a minor modification to the commonly used Bayesian decoding procedure, which enables the use of spike density functions, results in substantially lower decoding errors. These results have implications for the interpretation of covert neural activity, and suggest easy-to-implement changes to commonly used procedures across domains, with applications to hippocampal place cells in particular. © 2017 Wiley Periodicals, Inc.

Effect of interacting second- and third-order stimulus-dependent correlations on population-coding asymmetries

Spike correlations among neurons are widely encountered in the brain. Although models accounting for pairwise interactions have proved able to capture some of the most important features of population activity at the level of the retina, the evidence shows that pairwise neuronal correlation analysis does not resolve cooperative population dynamics by itself. By means of a series expansion for short time scales of the mutual information conveyed by a population of neurons, the information transmission can be broken down into firing rate and correlational components. In a proposed extension of this framework, we investigate the information components considering both second- and higher-order correlations. We show that the existence of a mixed stimulus-dependent correlation term defines a new scenario for the interplay between pairwise and higher-than-pairwise interactions in noise and signal correlations that would lead either to redundancy or synergy in the information-theoretic sense.

Spike Pattern Structure Influences Synaptic Efficacy Variability under STDP and Synaptic Homeostasis. II: Spike Shuffling Methods on LIF Networks

Synapses may undergo variable changes during plasticity because of the variability of spike patterns such as temporal stochasticity and spatial randomness. Here, we call the variability of synaptic weight changes during plasticity to be efficacy variability. In this paper, we investigate how four aspects of spike pattern statistics (i.e., synchronous firing, burstiness/regularity, heterogeneity of rates and heterogeneity of cross-correlations) influence the efficacy variability under pair-wise additive spike-timing dependent plasticity (STDP) and synaptic homeostasis (the mean strength of plastic synapses into a neuron is bounded), by implementing spike shuffling methods onto spike patterns self-organized by a network of excitatory and inhibitory leaky integrate-and-fire (LIF) neurons. With the increase of the decay time scale of the inhibitory synaptic currents, the LIF network undergoes a transition from asynchronous state to weak synchronous state and then to synchronous bursting state. We first shuffle these spike patterns using a variety of methods, each designed to evidently change a specific pattern statistics; and then investigate the change of efficacy variability of the synapses under STDP and synaptic homeostasis, when the neurons in the network fire according to the spike patterns before and after being treated by a shuffling method. In this way, we can understand how the change of pattern statistics may cause the change of efficacy variability. Our results are consistent with those of our previous study which implements spike-generating models on converging motifs. We also find that burstiness/regularity is important to determine the efficacy variability under asynchronous states, while heterogeneity of cross-correlations is the main factor to cause efficacy variability when the network moves into synchronous bursting states (the states observed in epilepsy).

Thalamic neuron models encode stimulus information by burst-size modulation

Thalamic neurons have been long assumed to fire in tonic mode during perceptive states, and in burst mode during sleep and unconsciousness. However, recent evidence suggests that bursts may also be relevant in the encoding of sensory information. Here, we explore the neural code of such thalamic bursts. In order to assess whether the burst code is generic or whether it depends on the detailed properties of each bursting neuron, we analyzed two neuron models incorporating different levels of biological detail. One of the models contained no information of the biophysical processes entailed in spike generation, and described neuron activity at a phenomenological level. The second model represented the evolution of the individual ionic conductances involved in spiking and bursting, and required a large number of parameters. We analyzed the models' input selectivity using reverse correlation methods and information theory. We found that n-spike bursts from both models transmit information by modulating their spike count in response to changes to instantaneous input features, such as slope, phase, amplitude, etc. The stimulus feature that is most efficiently encoded by bursts, however, need not coincide with one of such classical features. We therefore searched for the optimal feature among all those that could be expressed as a linear transformation of the time-dependent input current. We found that bursting neurons transmitted 6 times more information about such more general features. The relevant events in the stimulus were located in a time window spanning ~100 ms before and ~20 ms after burst onset. Most importantly, the neural code employed by the simple and the biologically realistic models was largely the same, implying that the simple thalamic neuron model contains the essential ingredients that account for the computational properties of the thalamic burst code. Thus, our results suggest the n-spike burst code is a general property of thalamic neurons.

Stabilizing synchrony by inhomogeneity

We show that for two weakly coupled identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony can only be seen in the absence of noise and an arbitrarily weak noise can destroy entrainment and generate intermittent phase slips. Small inhomogeneity–mismatch in the intrinsic firing rate of the neurons–can stabilize the phase locking and lead to more precise relative spike timing of the two neurons. The results can explain how for a class of neuronal models, including leaky integrate-fire model, inhomogeneity can increase correlation of spike trains when the neurons are synaptically connected.

Spatial precision of population activity in primate area MT

The middle temporal (MT) area is a cortical area integral to the "where" pathway of primate visual processing, signaling the movement and position of objects in the visual world. The receptive field of a single MT neuron is sensitive to the direction of object motion but is too large to signal precise spatial position. Here, we asked if the activity of MT neurons could be combined to support the high spatial precision required in the where pathway. With the use of multielectrode arrays, we recorded simultaneously neural activity at 24-65 sites in area MT of anesthetized marmoset monkeys. We found that although individual receptive fields span more than 5° of the visual field, the combined population response can support fine spatial discriminations (<0.2°). This is because receptive fields at neighboring sites overlapped substantially, and changes in spatial position are therefore projected onto neural activity in a large ensemble of neurons. This fine spatial discrimination is supported primarily by neurons with receptive fields flanking the target locations. Population performance is degraded (by 13-22%) when correlations in neural activity are ignored, further reflecting the contribution of population neural interactions. Our results show that population signals can provide high spatial precision despite large receptive fields, allowing area MT to represent both the motion and the position of objects in the visual world.

Task engagement selectively modulates neural correlations in primary auditory cortex

Noise correlations (r(noise)) between neurons can affect a neural population's discrimination capacity, even without changes in mean firing rates of neurons. r(noise), the degree to which the response variability of a pair of neurons is correlated, has been shown to change with attention with most reports showing a reduction in r(noise). However, the effect of reducing r(noise) on sensory discrimination depends on many factors, including the tuning similarity, or tuning correlation (r(tuning)), between the pair. Theoretically, reducing r(noise) should enhance sensory discrimination when the pair exhibits similar tuning, but should impair discrimination when tuning is dissimilar. We recorded from pairs of neurons in primary auditory cortex (A1) under two conditions: while rhesus macaque monkeys (Macaca mulatta) actively performed a threshold amplitude modulation (AM) detection task and while they sat passively awake. We report that, for pairs with similar AM tuning, average r(noise) in A1 decreases when the animal performs the AM detection task compared with when sitting passively. For pairs with dissimilar tuning, the average r(noise) did not significantly change between conditions. This suggests that attention-related modulation can target selective subcircuits to decorrelate noise. These results demonstrate that engagement in an auditory task enhances population coding in primary auditory cortex by selectively reducing deleterious r(noise) and leaving beneficial r(noise) intact.

Mutual information against correlations in binary communication channels

Background

Explaining how the brain processing is so fast remains an open problem (van Hemmen JL, Sejnowski T., 2004). Thus, the analysis of neural transmission (Shannon CE, Weaver W., 1963) processes basically focuses on searching for effective encoding and decoding schemes. According to the Shannon fundamental theorem, mutual information plays a crucial role in characterizing the efficiency of communication channels. It is well known that this efficiency is determined by the channel capacity that is already the maximal mutual information between input and output signals. On the other hand, intuitively speaking, when input and output signals are more correlated, the transmission should be more efficient. A natural question arises about the relation between mutual information and correlation. We analyze the relation between these quantities using the binary representation of signals, which is the most common approach taken in studying neuronal processes of the brain.

Results

We present binary communication channels for which mutual information and correlation coefficients behave differently both quantitatively and qualitatively. Despite this difference in behavior, we show that the noncorrelation of binary signals implies their independence, in contrast to the case for general types of signals.

Conclusions

Our research shows that the mutual information cannot be replaced by sheer correlations. Our results indicate that neuronal encoding has more complicated nature which cannot be captured by straightforward correlations between input and output signals once the mutual information takes into account the structure and patterns of the signals.

Exploration of synergistic and redundant information sharing in static and dynamical Gaussian systems

To fully characterize the information that two source variables carry about a third target variable, one must decompose the total information into redundant, unique, and synergistic components, i.e., obtain a partial information decomposition (PID). However, Shannon's theory of information does not provide formulas to fully determine these quantities. Several recent studies have begun addressing this. Some possible definitions for PID quantities have been proposed and some analyses have been carried out on systems composed of discrete variables. Here we present an in-depth analysis of PIDs on Gaussian systems, both static and dynamical. We show that, for a broad class of Gaussian systems, previously proposed PID formulas imply that (i) redundancy reduces to the minimum information provided by either source variable and hence is independent of correlation between sources, and (ii) synergy is the extra information contributed by the weaker source when the stronger source is known and can either increase or decrease with correlation between sources. We find that Gaussian systems frequently exhibit net synergy, i.e., the information carried jointly by both sources is greater than the sum of information carried by each source individually. Drawing from several explicit examples, we discuss the implications of these findings for measures of information transfer and information-based measures of complexity, both generally and within a neuroscience setting. Importantly, by providing independent formulas for synergy and redundancy applicable to continuous time-series data, we provide an approach to characterizing and quantifying information sharing amongst complex system variables.

Energy coding in neural network with inhibitory neurons

This paper aimed at assessing and comparing the effects of the inhibitory neurons in the neural network on the neural energy distribution, and the network activities in the absence of the inhibitory neurons to understand the nature of neural energy distribution and neural energy coding. Stimulus, synchronous oscillation has significant difference between neural networks with and without inhibitory neurons, and this difference can be quantitatively evaluated by the characteristic energy distribution. In addition, the synchronous oscillation difference of the neural activity can be quantitatively described by change of the energy distribution if the network parameters are gradually adjusted. Compared with traditional method of correlation coefficient analysis, the quantitative indicators based on nervous energy distribution characteristics are more effective in reflecting the dynamic features of the neural network activities. Meanwhile, this neural coding method from a global perspective of neural activity effectively avoids the current defects of neural encoding and decoding theory and enormous difficulties encountered. Our studies have shown that neural energy coding is a new coding theory with high efficiency and great potential.

Decoding thalamic afferent input using microcircuit spiking activity

A behavioral response appropriate to a sensory stimulus depends on the collective activity of thousands of interconnected neurons. The majority of cortical connections arise from neighboring neurons, and thus understanding the cortical code requires characterizing information representation at the scale of the cortical microcircuit. Using two-photon calcium imaging, we densely sampled the thalamically evoked response of hundreds of neurons spanning multiple layers and columns in thalamocortical slices of mouse somatosensory cortex. We then used a biologically plausible decoder to characterize the representation of two distinct thalamic inputs, at the level of the microcircuit, to reveal those aspects of the activity pattern that are likely relevant to downstream neurons. Our data suggest a sparse code, distributed across lamina, in which a small population of cells carries stimulus-relevant information. Furthermore, we find that, within this subset of neurons, decoder performance improves when noise correlations are taken into account.

Improved estimation and interpretation of correlations in neural circuits

Ambitious projects aim to record the activity of ever larger and denser neuronal populations in vivo. Correlations in neural activity measured in such recordings can reveal important aspects of neural circuit organization. However, estimating and interpreting large correlation matrices is statistically challenging. Estimation can be improved by regularization, i.e. by imposing a structure on the estimate. The amount of improvement depends on how closely the assumed structure represents dependencies in the data. Therefore, the selection of the most efficient correlation matrix estimator for a given neural circuit must be determined empirically. Importantly, the identity and structure of the most efficient estimator informs about the types of dominant dependencies governing the system. We sought statistically efficient estimators of neural correlation matrices in recordings from large, dense groups of cortical neurons. Using fast 3D random-access laser scanning microscopy of calcium signals, we recorded the activity of nearly every neuron in volumes 200 μm wide and 100 μm deep (150-350 cells) in mouse visual cortex. We hypothesized that in these densely sampled recordings, the correlation matrix should be best modeled as the combination of a sparse graph of pairwise partial correlations representing local interactions and a low-rank component representing common fluctuations and external inputs. Indeed, in cross-validation tests, the covariance matrix estimator with this structure consistently outperformed other regularized estimators. The sparse component of the estimate defined a graph of interactions. These interactions reflected the physical distances and orientation tuning properties of cells: The density of positive 'excitatory' interactions decreased rapidly with geometric distances and with differences in orientation preference whereas negative 'inhibitory' interactions were less selective. Because of its superior performance, this 'sparse+latent' estimator likely provides a more physiologically relevant representation of the functional connectivity in densely sampled recordings than the sample correlation matrix.

Independent theta phase coding accounts for CA1 population sequences and enables flexible remapping

Hippocampal place cells encode an animal's past, current, and future location through sequences of action potentials generated within each cycle of the network theta rhythm. These sequential representations have been suggested to result from temporally coordinated synaptic interactions within and between cell assemblies. Instead, we find through simulations and analysis of experimental data that rate and phase coding in independent neurons is sufficient to explain the organization of CA1 population activity during theta states. We show that CA1 population activity can be described as an evolving traveling wave that exhibits phase coding, rate coding, spike sequences and that generates an emergent population theta rhythm. We identify measures of global remapping and intracellular theta dynamics as critical for distinguishing mechanisms for pacemaking and coordination of sequential population activity. Our analysis suggests that, unlike synaptically coupled assemblies, independent neurons flexibly generate sequential population activity within the duration of a single theta cycle.

DOI:http://dx.doi.org/10.7554/eLife.03542.001

When we explore a new place, we naturally create a mental map of the location as we go. This mental map is stored in a region of the brain called the hippocampus, which contains cells called place cells. These cells can carry information about our past, present, and future location in the form of electrical signals. They connect to each other to form networks and it has been proposed that these connections can store the information needed for the mental maps.

Real-time maps are represented in the information carried by the electrical signals themselves. A physical location is specified by the individual place cell that is activated, and by the timing of the electrical signal it produces relative to a ‘brain wave’ called the theta rhythm. Brain waves are patterns of electrical signals activated in sets of brain cells and the theta rhythm is produced in the hippocampus of an animal as it explores its surroundings.

Previous experiments suggested that when a rat explores an area, several sets of brain cells in the hippocampus are activated in sequence within each cycle of the theta rhythm. As the rat moves forward, the sequence shifts to different sets of cells to reflect the upcoming locations ahead of the rat. It has been thought that these sequences are triggered by the individual connections between the place cells.

Here, Chadwick et al. developed mathematical models of the electrical activity in the brains of rats as they explored. They used these models to analyze data from previous experiments and found that the sequences of electrical activity arise from the timing of each cell's activity relative to the theta rhythm, rather than from the connections between the cells.

Chadwick et al.'s findings suggest that the mental map may be highly flexible, allowing vast numbers of distinct memories to be stored within the same network of place cells without interference. Future studies will involve investigating the role of brain waves in the forming new mental maps and creating new memories.

DOI:http://dx.doi.org/10.7554/eLife.03542.002

Activation of parallel fiber feedback by spatially diffuse stimuli reduces signal and noise correlations via independent mechanisms in a cerebellum-like structure

Correlations between the activities of neighboring neurons are observed ubiquitously across systems and species and are dynamically regulated by several factors such as the stimulus' spatiotemporal extent as well as by the brain's internal state. Using the electrosensory system of gymnotiform weakly electric fish, we recorded the activities of pyramidal cell pairs within the electrosensory lateral line lobe (ELL) under spatially localized and diffuse stimulation. We found that both signal and noise correlations were markedly reduced (>40%) under the latter stimulation. Through a network model incorporating key anatomical features of the ELL, we reveal how activation of diffuse parallel fiber feedback from granule cells by spatially diffuse stimulation can explain both the reduction in signal as well as the reduction in noise correlations seen experimentally through independent mechanisms. First, we show that burst-timing dependent plasticity, which leads to a negative image of the stimulus and thereby reduces single neuron responses, decreases signal but not noise correlations. Second, we show trial-to-trial variability in the responses of single granule cells to sensory input reduces noise but not signal correlations. Thus, our model predicts that the same feedback pathway can simultaneously reduce both signal and noise correlations through independent mechanisms. To test this prediction experimentally, we pharmacologically inactivated parallel fiber feedback onto ELL pyramidal cells. In agreement with modeling predictions, we found that inactivation increased both signal and noise correlations but that there was no significant relationship between magnitude of the increase in signal correlations and the magnitude of the increase in noise correlations. The mechanisms reported in this study are expected to be generally applicable to the cerebellum as well as other cerebellum-like structures. We further discuss the implications of such decorrelation on the neural coding strategies used by the electrosensory and by other systems to process natural stimuli.

Correlated activity is observed ubiquitously in the CNS but how activation of specific neural circuits affects correlated activity under behaviorally relevant contexts is poorly understood. Here, through a combination of electrophysiology, pharmacology, and mathematical modeling, we show that activation of the same parallel fiber feedback pathway leads to simultaneous reductions in both signal and noise correlations via independent mechanisms. Specifically, we show that feedback in the form of a negative image of the stimulus is necessary in order to attenuate signal but not noise correlations. Moreover, we show that trial-to-trial variability in the spiking responses of neurons providing this feedback is necessary to attenuate noise but not signal correlations. Our model thus predicts that activation of the same feedback pathway can simultaneously reduce both signal and noise correlations through independent mechanisms. In agreement with modeling prediction, pharmacological inactivation led to a strong increase in both signal and noise correlations but the magnitude of the change in signal correlation was not related to the magnitude of the change in noise correlations. Our proposed mechanism for simultaneous control of both signal and noise correlations is generic and is thus likely to be applicable to the cerebellum and to other cerebellar-like structures.

Neuronal spike train entropy estimation by history clustering

Neurons send signals to each other by means of sequences of action potentials (spikes). Ignoring variations in spike amplitude and shape that are probably not meaningful to a receiving cell, the information content, or entropy of the signal depends on only the timing of action potentials, and because there is no external clock, only the interspike intervals, and not the absolute spike times, are significant. Estimating spike train entropy is a difficult task, particularly with small data sets, and many methods of entropy estimation have been proposed. Here we present two related model-based methods for estimating the entropy of neural signals and compare them to existing methods. One of the methods is fast and reasonably accurate, and it converges well with short spike time records; the other is impractically time-consuming but apparently very accurate, relying on generating artificial data that are a statistical match to the experimental data. Using the slow, accurate method to generate a best-estimate entropy value, we find that the faster estimator converges to this value more closely and with smaller data sets than many existing entropy estimators.

Modified multidimensional scaling approach to analyze financial markets

Detrended cross-correlation coefficient (σDCCA) and dynamic time warping (DTW) are introduced as the dissimilarity measures, respectively, while multidimensional scaling (MDS) is employed to translate the dissimilarities between daily price returns of 24 stock markets. We first propose MDS based on σDCCA dissimilarity and MDS based on DTW dissimilarity creatively, while MDS based on Euclidean dissimilarity is also employed to provide a reference for comparisons. We apply these methods in order to further visualize the clustering between stock markets. Moreover, we decide to confront MDS with an alternative visualization method, "Unweighed Average" clustering method, for comparison. The MDS analysis and "Unweighed Average" clustering method are employed based on the same dissimilarity. Through the results, we find that MDS gives us a more intuitive mapping for observing stable or emerging clusters of stock markets with similar behavior, while the MDS analysis based on σDCCA dissimilarity can provide more clear, detailed, and accurate information on the classification of the stock markets than the MDS analysis based on Euclidean dissimilarity. The MDS analysis based on DTW dissimilarity indicates more knowledge about the correlations between stock markets particularly and interestingly. Meanwhile, it reflects more abundant results on the clustering of stock markets and is much more intensive than the MDS analysis based on Euclidean dissimilarity. In addition, the graphs, originated from applying MDS methods based on σDCCA dissimilarity and DTW dissimilarity, may also guide the construction of multivariate econometric models.