The spatial structure of stimuli shapes the timescale of correlations in population spiking activity

Nonresponsive Neurons Improve Population Coding of Object Location

Understanding how heterogeneous neural populations represent sensory input to give rise to behavior remains a central problem in systems neuroscience. Here we investigated how midbrain neurons within the electrosensory system of Apteronotus leptorhynchus code for object location in space. In vivo simultaneous recordings were achieved via Neuropixels probes, high-density electrode arrays, with the stimulus positioned at different locations relative to the animal. Midbrain neurons exhibited heterogeneous response profiles, with a significant proportion (65%) seemingly nonresponsive to moving stimuli. Remarkably, we found that nonresponsive neurons increased population coding of object location through synergistic interactions with responsive neurons by effectively reducing noise. Mathematical modeling demonstrated that increased response heterogeneity together with the experimentally observed correlations was sufficient to give rise to independent encoding by responsive neurons. Furthermore, the addition of nonresponsive neurons in the model gave rise to synergistic population coding. Taken together, our findings reveal that nonresponsive neurons, which are frequently excluded from analysis, can significantly improve population coding of object location through synergistic interactions with responsive neurons. Combinations of responsive and nonresponsive neurons have been observed in sensory systems across taxa; it is likely that similar synergistic interactions improve population coding across modalities and behavioral tasks.

What is the dynamical regime of cerebral cortex?

Many studies have shown that the excitation and inhibition received by cortical neurons remain roughly balanced across many conditions. A key question for understanding the dynamical regime of cortex is the nature of this balancing. Theorists have shown that network dynamics can yield systematic cancellation of most of a neuron's excitatory input by inhibition. We review a wide range of evidence pointing to this cancellation occurring in a regime in which the balance is loose, meaning that the net input remaining after cancellation of excitation and inhibition is comparable in size with the factors that cancel, rather than tight, meaning that the net input is very small relative to the canceling factors. This choice of regime has important implications for cortical functional responses, as we describe: loose balance, but not tight balance, can yield many nonlinear population behaviors seen in sensory cortical neurons, allow the presence of correlated variability, and yield decrease of that variability with increasing external stimulus drive as observed across multiple cortical areas.

Self-consistent formulations for stochastic nonlinear neuronal dynamics

Neural dynamics is often investigated with tools from bifurcation theory. However, many neuron models are stochastic, mimicking fluctuations in the input from unknown parts of the brain or the spiking nature of signals. Noise changes the dynamics with respect to the deterministic model; in particular classical bifurcation theory cannot be applied. We formulate the stochastic neuron dynamics in the Martin-Siggia-Rose de Dominicis-Janssen (MSRDJ) formalism and present the fluctuation expansion of the effective action and the functional renormalization group (fRG) as two systematic ways to incorporate corrections to the mean dynamics and time-dependent statistics due to fluctuations in the presence of nonlinear neuronal gain. To formulate self-consistency equations, we derive a fundamental link between the effective action in the Onsager-Machlup (OM) formalism, which allows the study of phase transitions, and the MSRDJ effective action, which is computationally advantageous. These results in particular allow the derivation of an OM effective action for systems with non-Gaussian noise. This approach naturally leads to effective deterministic equations for the first moment of the stochastic system; they explain how nonlinearities and noise cooperate to produce memory effects. Moreover, the MSRDJ formulation yields an effective linear system that has identical power spectra and linear response. Starting from the better known loopwise approximation, we then discuss the use of the fRG as a method to obtain self-consistency beyond the mean. We present a new efficient truncation scheme for the hierarchy of flow equations for the vertex functions by adapting the Blaizot, Méndez, and Wschebor approximation from the derivative expansion to the vertex expansion. The methods are presented by means of the simplest possible example of a stochastic differential equation that has generic features of neuronal dynamics.

Inferring and validating mechanistic models of neural microcircuits based on spike-train data

The interpretation of neuronal spike train recordings often relies on abstract statistical models that allow for principled parameter estimation and model selection but provide only limited insights into underlying microcircuits. In contrast, mechanistic models are useful to interpret microcircuit dynamics, but are rarely quantitatively matched to experimental data due to methodological challenges. Here we present analytical methods to efficiently fit spiking circuit models to single-trial spike trains. Using derived likelihood functions, we statistically infer the mean and variance of hidden inputs, neuronal adaptation properties and connectivity for coupled integrate-and-fire neurons. Comprehensive evaluations on synthetic data, validations using ground truth in-vitro and in-vivo recordings, and comparisons with existing techniques demonstrate that parameter estimation is very accurate and efficient, even for highly subsampled networks. Our methods bridge statistical, data-driven and theoretical, model-based neurosciences at the level of spiking circuits, for the purpose of a quantitative, mechanistic interpretation of recorded neuronal population activity.

It is difficult to fit mechanistic, biophysically constrained circuit models to spike train data from in vivo extracellular recordings. Here the authors present analytical methods that enable efficient parameter estimation for integrate-and-fire circuit models and inference of the underlying connectivity structure in subsampled networks.

Novel Functions of Feedback in Electrosensory Processing

Environmental signals act as input and are processed across successive stages in the brain to generate a meaningful behavioral output. However, a ubiquitous observation is that descending feedback projections from more central to more peripheral brain areas vastly outnumber ascending feedforward projections. Such projections generally act to modify how sensory neurons respond to afferent signals. Recent studies in the electrosensory system of weakly electric fish have revealed novel functions for feedback pathways in that their transformation of the afferent input generates neural firing rate responses to sensory signals mediating perception and behavior. In this review, we focus on summarizing these novel and recently uncovered functions and put them into context by describing the more "classical" functions of feedback in the electrosensory system. We further highlight the parallels between the electrosensory system and other systems as well as outline interesting future directions.

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.

Feedback optimizes neural coding and perception of natural stimuli

Growing evidence suggests that sensory neurons achieve optimal encoding by matching their tuning properties to the natural stimulus statistics. However, the underlying mechanisms remain unclear. Here we demonstrate that feedback pathways from higher brain areas mediate optimized encoding of naturalistic stimuli via temporal whitening in the weakly electric fish Apteronotus leptorhynchus. While one source of direct feedback uniformly enhances neural responses, a separate source of indirect feedback selectively attenuates responses to low frequencies, thus creating a high-pass neural tuning curve that opposes the decaying spectral power of natural stimuli. Additionally, we recorded from two populations of higher brain neurons responsible for the direct and indirect descending inputs. While one population displayed broadband tuning, the other displayed high-pass tuning and thus performed temporal whitening. Hence, our results demonstrate a novel function for descending input in optimizing neural responses to sensory input through temporal whitening that is likely to be conserved across systems and species.

A theoretical framework for analyzing coupled neuronal networks: Application to the olfactory system

Determining how synaptic coupling within and between regions is modulated during sensory processing is an important topic in neuroscience. Electrophysiological recordings provide detailed information about neural spiking but have traditionally been confined to a particular region or layer of cortex. Here we develop new theoretical methods to study interactions between and within two brain regions, based on experimental measurements of spiking activity simultaneously recorded from the two regions. By systematically comparing experimentally-obtained spiking statistics to (efficiently computed) model spike rate statistics, we identify regions in model parameter space that are consistent with the experimental data. We apply our new technique to dual micro-electrode array in vivo recordings from two distinct regions: olfactory bulb (OB) and anterior piriform cortex (PC). Our analysis predicts that: i) inhibition within the afferent region (OB) has to be weaker than the inhibition within PC, ii) excitation from PC to OB is generally stronger than excitation from OB to PC, iii) excitation from PC to OB and inhibition within PC have to both be relatively strong compared to presynaptic inputs from OB. These predictions are validated in a spiking neural network model of the OB–PC pathway that satisfies the many constraints from our experimental data. We find when the derived relationships are violated, the spiking statistics no longer satisfy the constraints from the data. In principle this modeling framework can be adapted to other systems and be used to investigate relationships between other neural attributes besides network connection strengths. Thus, this work can serve as a guide to further investigations into the relationships of various neural attributes within and across different regions during sensory processing.

Sensory processing is known to span multiple regions of the nervous system. However, electrophysiological recordings during sensory processing have traditionally been limited to a single region or brain layer. With recent advances in experimental techniques, recorded spiking activity from multiple regions simultaneously is feasible. However, other important quantities— such as inter-region connection strengths—cannot yet be measured. Here, we develop new theoretical tools to leverage data obtained by recording from two different brain regions simultaneously. We address the following questions: what are the crucial neural network attributes that enable sensory processing across different regions, and how are these attributes related to one another? With a novel theoretical framework to efficiently calculate spiking statistics, we can characterize a high dimensional parameter space that satisfies data constraints. We apply our results to the olfactory system to make specific predictions about effective network connectivity. Our framework relies on incorporating relatively easy-to-measure quantities to predict hard-to-measure interactions across multiple brain regions. Because this work is adaptable to other systems, we anticipate it will be a valuable tool for analysis of other larger scale brain recordings.

Differential receptive field organizations give rise to nearly identical neural correlations across three parallel sensory maps in weakly electric fish

Understanding how neural populations encode sensory information thereby leading to perception and behavior (i.e., the neural code) remains an important problem in neuroscience. When investigating the neural code, one must take into account the fact that neural activities are not independent but are actually correlated with one another. Such correlations are seen ubiquitously and have a strong impact on neural coding. Here we investigated how differences in the antagonistic center-surround receptive field (RF) organization across three parallel sensory maps influence correlations between the activities of electrosensory pyramidal neurons. Using a model based on known anatomical differences in receptive field center size and overlap, we initially predicted large differences in correlated activity across the maps. However, in vivo electrophysiological recordings showed that, contrary to modeling predictions, electrosensory pyramidal neurons across all three segments displayed nearly identical correlations. To explain this surprising result, we incorporated the effects of RF surround in our model. By systematically varying both the RF surround gain and size relative to that of the RF center, we found that multiple RF structures gave rise to similar levels of correlation. In particular, incorporating known physiological differences in RF structure between the three maps in our model gave rise to similar levels of correlation. Our results show that RF center overlap alone does not determine correlations which has important implications for understanding how RF structure influences correlated neural activity.

Growing evidence across nervous systems and species shows that the activities of neighboring neurons are not independent but are correlated with one another, which has important implications for neural coding. Such correlations are generally thought to be due to shared input. However, how this shared input is integrated by neurons in order to give rise to correlated activity is not well understood in general. Here we investigated how receptive field structure determines correlations between the activities of electrosensory pyramidal neurons in weakly electric fish. To do so, we used a combination of mathematical modeling of the known antagonistic center-surround RF structure as well as in vivo electrophysiological recordings. Our results show that the amount of receptive field center overlap alone is not sufficient to explain experimentally observed neural correlations in general. This is because our experimental data shows that pyramidal neurons with very different amounts of receptive field center overlap display almost identical correlations between their activities. Further, our modeling shows that both receptive field center and surround play important roles in determining correlated activity, such that very different combinations of relative RF surround strength and size can generate nearly identical correlations between neural activities. We discuss the implications of our results for sensory processing.

Locking of correlated neural activity to ongoing oscillations

Population-wide oscillations are ubiquitously observed in mesoscopic signals of cortical activity. In these network states a global oscillatory cycle modulates the propensity of neurons to fire. Synchronous activation of neurons has been hypothesized to be a separate channel of signal processing information in the brain. A salient question is therefore if and how oscillations interact with spike synchrony and in how far these channels can be considered separate. Experiments indeed showed that correlated spiking co-modulates with the static firing rate and is also tightly locked to the phase of beta-oscillations. While the dependence of correlations on the mean rate is well understood in feed-forward networks, it remains unclear why and by which mechanisms correlations tightly lock to an oscillatory cycle. We here demonstrate that such correlated activation of pairs of neurons is qualitatively explained by periodically-driven random networks. We identify the mechanisms by which covariances depend on a driving periodic stimulus. Mean-field theory combined with linear response theory yields closed-form expressions for the cyclostationary mean activities and pairwise zero-time-lag covariances of binary recurrent random networks. Two distinct mechanisms cause time-dependent covariances: the modulation of the susceptibility of single neurons (via the external input and network feedback) and the time-varying variances of single unit activities. For some parameters, the effectively inhibitory recurrent feedback leads to resonant covariances even if mean activities show non-resonant behavior. Our analytical results open the question of time-modulated synchronous activity to a quantitative analysis.

Stimulus background influences phase invariant coding by correlated neural activity

Previously we reported that correlations between the activities of peripheral afferents mediate a phase invariant representation of natural communication stimuli that is refined across successive processing stages thereby leading to perception and behavior in the weakly electric fish Apteronotus leptorhynchus (Metzen et al., 2016). Here, we explore how phase invariant coding and perception of natural communication stimuli are affected by changes in the sinusoidal background over which they occur. We found that increasing background frequency led to phase locking, which decreased both detectability and phase invariant coding. Correlated afferent activity was a much better predictor of behavior as assessed from both invariance and detectability than single neuron activity. Thus, our results provide not only further evidence that correlated activity likely determines perception of natural communication signals, but also a novel explanation as to why these preferentially occur on top of low frequency as well as low-intensity sinusoidal backgrounds.

Burst Firing in the Electrosensory System of Gymnotiform Weakly Electric Fish: Mechanisms and Functional Roles

Neurons across sensory systems and organisms often display complex patterns of action potentials in response to sensory input. One example of such a pattern is the tendency of neurons to fire packets of action potentials (i.e., a burst) followed by quiescence. While it is well known that multiple mechanisms can generate bursts of action potentials at both the single-neuron and the network level, the functional role of burst firing in sensory processing is not so well understood to date. Here we provide a comprehensive review of the known mechanisms and functions of burst firing in processing of electrosensory stimuli in gymnotiform weakly electric fish. We also present new evidence from existing data showing that bursts and isolated spikes provide distinct information about stimulus variance. It is likely that these functional roles will be generally applicable to other systems and species.

The mechanics of state-dependent neural correlations

Simultaneous recordings from large neural populations are becoming increasingly common. An important feature of population activity is the trial-to-trial correlated fluctuation of spike train outputs from recorded neuron pairs. Similar to the firing rate of single neurons, correlated activity can be modulated by a number of factors, from changes in arousal and attentional state to learning and task engagement. However, the physiological mechanisms that underlie these changes are not fully understood. We review recent theoretical results that identify three separate mechanisms that modulate spike train correlations: changes in input correlations, internal fluctuations and the transfer function of single neurons. We first examine these mechanisms in feedforward pathways and then show how the same approach can explain the modulation of correlations in recurrent networks. Such mechanistic constraints on the modulation of population activity will be important in statistical analyses of high-dimensional neural data.

Adaptation to second order stimulus features by electrosensory neurons causes ambiguity

Understanding the coding strategies used to process sensory input remains a central problem in neuroscience. Growing evidence suggests that sensory systems process natural stimuli efficiently by ensuring a close match between neural tuning and stimulus statistics through adaptation. However, adaptation causes ambiguity as the same response can be elicited by different stimuli. The mechanisms by which the brain resolves ambiguity remain poorly understood. Here we investigated adaptation in electrosensory pyramidal neurons within different parallel maps in the weakly electric fish Apteronotus leptorhynchus. In response to step increases in stimulus variance, we found that pyramidal neurons within the lateral segment (LS) displayed strong scale invariant adaptation whereas those within the centromedial segment (CMS) instead displayed weaker degrees of scale invariant adaptation. Signal detection analysis revealed that strong adaptation in LS neurons significantly reduced stimulus discriminability. In contrast, weaker adaptation displayed by CMS neurons led to significantly lesser impairment of discriminability. Thus, while LS neurons display adaptation that is matched to natural scene statistics, thereby optimizing information transmission, CMS neurons instead display weaker adaptation and would instead provide information about the context in which these statistics occur. We propose that such a scheme is necessary for decoding by higher brain structures.

Neural correlations enable invariant coding and perception of natural stimuli in weakly electric fish

Neural representations of behaviorally relevant stimulus features displaying invariance with respect to different contexts are essential for perception. However, the mechanisms mediating their emergence and subsequent refinement remain poorly understood in general. Here, we demonstrate that correlated neural activity allows for the emergence of an invariant representation of natural communication stimuli that is further refined across successive stages of processing in the weakly electric fish Apteronotus leptorhynchus. Importantly, different patterns of input resulting from the same natural communication stimulus occurring in different contexts all gave rise to similar behavioral responses. Our results thus reveal how a generic neural circuit performs an elegant computation that mediates the emergence and refinement of an invariant neural representation of natural stimuli that most likely constitutes a neural correlate of perception.

DOI:http://dx.doi.org/10.7554/eLife.12993.001

We can effortlessly recognize an object – a car, for example – in many different contexts such as when seen from behind, under different lighting levels or even from different viewpoints. This phenomenon is known as perceptual invariance: objects are correctly recognized, despite variations in exactly what is seen (or otherwise sensed). However, it is still not clear how the brain processes perceptual information to recognize the same object under a wide variety of contexts.

Some fish, such as the brown ghost knifefish, produce a weak electric signal that they can alter to communicate with other members of their species. A communication call may be produced in a variety of contexts that alter which aspects of the signal nearby fish detect. Despite this, fish tend to respond to a given communication call in the same way regardless of its context; this suggests that these fish also have perceptual invariance.

The communication calls of weakly electric fish can be easily mimicked in a laboratory and produce reliable behavioral responses, which makes these fish a good model for understanding how perceptual invariance might be coded in the brain. Therefore, Metzen et al. recorded the activity of the receptor neurons that first respond to communication calls in weakly electric fish. The results revealed that a given communication signal made the firing patterns of all receptor neurons in the fish’s brain more similar to each other, regardless of the signal’s context. This occurs despite the changes in context causing single receptor neurons to respond in different ways. At each stage of the process by which information is transmitted from the receptor neurons to neurons deeper in the brain, the similarity in the neurons’ firing patterns is refined, thereby giving rise to perceptual invariance.

While perceptual invariance to a given object in different contexts is desirable, it is also important to be able to distinguish between different objects. This implies that neurons should respond similarly to stimuli associated with the same object and differently to stimuli associated with different objects. Further studies are now needed to confirm whether this is the case.

DOI:http://dx.doi.org/10.7554/eLife.12993.002

Balanced ionotropic receptor dynamics support signal estimation via voltage-dependent membrane noise

Encoding behaviorally relevant stimuli in a noisy background is critical for animals to survive in their natural environment. We identify core biophysical and synaptic mechanisms that permit the encoding of low-frequency signals in pyramidal neurons of the weakly electric fish Apteronotus leptorhynchus, an animal that can accurately encode even miniscule amplitude modulations of its self-generated electric field. We demonstrate that slow NMDA receptor (NMDA-R)-mediated excitatory postsynaptic potentials (EPSPs) are able to summate over many interspike intervals (ISIs) of the primary electrosensory afferents (EAs), effectively eliminating the baseline EA ISI correlations from the pyramidal cell input. Together with a dynamic balance of NMDA-R and GABA-A-R currents, this permits stimulus-evoked changes in EA spiking to be transmitted efficiently to target electrosensory lobe (ELL) pyramidal cells, for encoding low-frequency signals. Interestingly, AMPA-R activity is depressed and appears to play a negligible role in the generation of action potentials. Instead, we hypothesize that cell-intrinsic voltage-dependent membrane noise supports the encoding of perithreshold sensory input; this noise drives a significant proportion of pyramidal cell spikes. Together, these mechanisms may be sufficient for the ELL to encode signals near the threshold of behavioral detection.

Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

Oscillatorylike behavior in feedforward neuronal networks

We demonstrate how rhythmic activity can arise in neural networks from feedforward rather than recurrent circuitry and, in so doing, we provide a mechanism capable of explaining the temporal decorrelation of γ-band oscillations. We compare the spiking activity of a delayed recurrent network of inhibitory neurons with that of a feedforward network with the same neural properties and axonal delays. Paradoxically, these very different connectivities can yield very similar spike-train statistics in response to correlated input. This happens when neurons are noisy and axonal delays are short. A Taylor expansion of the feedback network's susceptibility-or frequency-dependent gain function-can then be stopped at first order to a good approximation, thus matching the feedforward net's susceptibility. The feedback network is known to display oscillations; these oscillations imply that the spiking activity of the population is felt by all neurons within the network, leading to direct spike correlations in a given neuron. On the other hand, in the output layer of the feedforward net, the interaction between the external drive and the delayed feedforward projection of this drive by the input layer causes indirect spike correlations: spikes fired by a given output layer neuron are correlated only through the activity of the input layer neurons. High noise and short delays partially bridge the gap between these two types of correlation, yielding similar spike-train statistics for both networks. This similarity is even stronger when the delay is distributed, as confirmed by linear response theory.

Coding stimulus amplitude by correlated neural activity

While correlated activity is observed ubiquitously in the brain, its role in neural coding has remained controversial. Recent experimental results have demonstrated that correlated but not single-neuron activity can encode the detailed time course of the instantaneous amplitude (i.e., envelope) of a stimulus. These have furthermore demonstrated that such coding required and was optimal for a nonzero level of neural variability. However, a theoretical understanding of these results is still lacking. Here we provide a comprehensive theoretical framework explaining these experimental findings. Specifically, we use linear response theory to derive an expression relating the correlation coefficient to the instantaneous stimulus amplitude, which takes into account key single-neuron properties such as firing rate and variability as quantified by the coefficient of variation. The theoretical prediction was in excellent agreement with numerical simulations of various integrate-and-fire type neuron models for various parameter values. Further, we demonstrate a form of stochastic resonance as optimal coding of stimulus variance by correlated activity occurs for a nonzero value of noise intensity. Thus, our results provide a theoretical explanation of the phenomenon by which correlated but not single-neuron activity can code for stimulus amplitude and how key single-neuron properties such as firing rate and variability influence such coding. Correlation coding by correlated but not single-neuron activity is thus predicted to be a ubiquitous feature of sensory processing for neurons responding to weak input.

Coding of envelopes by correlated but not single-neuron activity requires neural variability

Understanding how the brain processes sensory information is often complicated by the fact that neurons exhibit trial-to-trial variability in their responses to stimuli. Indeed, the role of variability in sensory coding is still highly debated. Here, we examined how variability influences neural responses to naturalistic stimuli consisting of a fast time-varying waveform (i.e., carrier or first order) whose amplitude (i.e., envelope or second order) varies more slowly. Recordings were made from fish electrosensory and monkey vestibular sensory neurons. In both systems, we show that correlated but not single-neuron activity can provide detailed information about second-order stimulus features. Using a simple mathematical model, we made the strong prediction that such correlation-based coding of envelopes requires neural variability. Strikingly, the performance of correlated activity at predicting the envelope was similarly optimally tuned to a nonzero level of variability in both systems, thereby confirming this prediction. Finally, we show that second-order sensory information can only be decoded if one takes into account joint statistics when combining neural activities. Our results thus show that correlated but not single-neural activity can transmit information about the envelope, that such transmission requires neural variability, and that this information can be decoded. We suggest that envelope coding by correlated activity is a general feature of sensory processing that will be found across species and systems.

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.

Subtractive, divisive and non-monotonic gain control in feedforward nets linearized by noise and delays

The control of input-to-output mappings, or gain control, is one of the main strategies used by neural networks for the processing and gating of information. Using a spiking neural network model, we studied the gain control induced by a form of inhibitory feedforward circuitry-also known as "open-loop feedback"-, which has been experimentally observed in a cerebellum-like structure in weakly electric fish. We found, both analytically and numerically, that this network displays three different regimes of gain control: subtractive, divisive, and non-monotonic. Subtractive gain control was obtained when noise is very low in the network. Also, it was possible to change from divisive to non-monotonic gain control by simply modulating the strength of the feedforward inhibition, which may be achieved via long-term synaptic plasticity. The particular case of divisive gain control has been previously observed in vivo in weakly electric fish. These gain control regimes were robust to the presence of temporal delays in the inhibitory feedforward pathway, which were found to linearize the input-to-output mappings (or f-I curves) via a novel variability-increasing mechanism. Our findings highlight the feedforward-induced gain control analyzed here as a highly versatile mechanism of information gating in the brain.

The correlation structure of local neuronal networks intrinsically results from recurrent dynamics

Correlated neuronal activity is a natural consequence of network connectivity and shared inputs to pairs of neurons, but the task-dependent modulation of correlations in relation to behavior also hints at a functional role. Correlations influence the gain of postsynaptic neurons, the amount of information encoded in the population activity and decoded by readout neurons, and synaptic plasticity. Further, it affects the power and spatial reach of extracellular signals like the local-field potential. A theory of correlated neuronal activity accounting for recurrent connectivity as well as fluctuating external sources is currently lacking. In particular, it is unclear how the recently found mechanism of active decorrelation by negative feedback on the population level affects the network response to externally applied correlated stimuli. Here, we present such an extension of the theory of correlations in stochastic binary networks. We show that (1) for homogeneous external input, the structure of correlations is mainly determined by the local recurrent connectivity, (2) homogeneous external inputs provide an additive, unspecific contribution to the correlations, (3) inhibitory feedback effectively decorrelates neuronal activity, even if neurons receive identical external inputs, and (4) identical synaptic input statistics to excitatory and to inhibitory cells increases intrinsically generated fluctuations and pairwise correlations. We further demonstrate how the accuracy of mean-field predictions can be improved by self-consistently including correlations. As a byproduct, we show that the cancellation of correlations between the summed inputs to pairs of neurons does not originate from the fast tracking of external input, but from the suppression of fluctuations on the population level by the local network. This suppression is a necessary constraint, but not sufficient to determine the structure of correlations; specifically, the structure observed at finite network size differs from the prediction based on perfect tracking, even though perfect tracking implies suppression of population fluctuations.

The co-occurrence of action potentials of pairs of neurons within short time intervals has been known for a long time. Such synchronous events can appear time-locked to the behavior of an animal, and also theoretical considerations argue for a functional role of synchrony. Early theoretical work tried to explain correlated activity by neurons transmitting common fluctuations due to shared inputs. This, however, overestimates correlations. Recently, the recurrent connectivity of cortical networks was shown responsible for the observed low baseline correlations. Two different explanations were given: One argues that excitatory and inhibitory population activities closely follow the external inputs to the network, so that their effects on a pair of cells mutually cancel. Another explanation relies on negative recurrent feedback to suppress fluctuations in the population activity, equivalent to small correlations. In a biological neuronal network one expects both, external inputs and recurrence, to affect correlated activity. The present work extends the theoretical framework of correlations to include both contributions and explains their qualitative differences. Moreover, the study shows that the arguments of fast tracking and recurrent feedback are not equivalent, only the latter correctly predicts the cell-type specific correlations.

Neuromodulation of early electrosensory processing in gymnotiform weakly electric fish

Sensory neurons continually adapt their processing properties in response to changes in the sensory environment or the brain's internal state. Neuromodulators are thought to mediate such adaptation through a variety of receptors and their action has been implicated in processes such as attention, learning and memory, aggression, reproductive behaviour and state-dependent mechanisms. Here, we review recent work on neuromodulation of electrosensory processing by acetylcholine and serotonin in the weakly electric fish Apteronotus leptorhynchus. Specifically, our review focuses on how experimental application of these neuromodulators alters excitability and responses to sensory input of pyramidal cells within the hindbrain electrosensory lateral line lobe. We then discuss current hypotheses on the functional roles of these two neuromodulatory pathways in regulating electrosensory processing at the organismal level and the need for identifying the natural behavioural conditions that activate these pathways.

Short-term synaptic depression and stochastic vesicle dynamics reduce and shape neuronal correlations

Correlated neuronal activity is an important feature in many neural codes, a neural correlate of a variety of cognitive states, as well as a signature of several disease states in the nervous system. The cellular and circuit mechanics of neural correlations is a vibrant area of research. Synapses throughout the cortex exhibit a form of short-term depression where increased presynaptic firing rates deplete neurotransmitter vesicles, which transiently reduces synaptic efficacy. The release and recovery of these vesicles are inherently stochastic, and this stochasticity introduces variability into the conductance elicited by depressing synapses. The impact of spiking and subthreshold membrane dynamics on the transfer of neuronal correlations has been studied intensively, but an investigation of the impact of short-term synaptic depression and stochastic vesicle dynamics on correlation transfer is lacking. We find that short-term synaptic depression and stochastic vesicle dynamics can substantially reduce correlations, shape the timescale over which these correlations occur, and alter the dependence of spiking correlations on firing rate. Our results show that short-term depression and stochastic vesicle dynamics need to be taken into account when modeling correlations in neuronal populations.