Neural heterogeneities and stimulus properties affect burst coding in vivo

Fractional order memcapacitive neuromorphic elements reproduce and predict neuronal function

There is an increasing need to implement neuromorphic systems that are both energetically and computationally efficient. There is also great interest in using electric elements with memory, memelements, that can implement complex neuronal functions intrinsically. A feature not widely incorporated in neuromorphic systems is history-dependent action potential time adaptation which is widely seen in real cells. Previous theoretical work shows that power-law history dependent spike time adaptation, seen in several brain areas and species, can be modeled with fractional order differential equations. Here, we show that fractional order spiking neurons can be implemented using super-capacitors. The super-capacitors have fractional order derivative and memcapacitive properties. We implemented two circuits, a leaky integrate and fire and a Hodgkin-Huxley. Both circuits show power-law spiking time adaptation and optimal coding properties. The spiking dynamics reproduced previously published computer simulations. However, the fractional order Hodgkin-Huxley circuit showed novel dynamics consistent with criticality. We compared the responses of this circuit to recordings from neurons in the weakly-electric fish that have previously been shown to perform fractional order differentiation of their sensory input. The criticality seen in the circuit was confirmed in spontaneous recordings in the live fish. Furthermore, the circuit also predicted long-lasting stimulation that was also corroborated experimentally. Our work shows that fractional order memcapacitors provide intrinsic memory dependence that could allow implementation of computationally efficient neuromorphic devices. Memcapacitors are static elements that consume less energy than the most widely studied memristors, thus allowing the realization of energetically efficient neuromorphic devices.

Descending pathways increase sensory neural response heterogeneity to facilitate decoding and behavior

The functional role of heterogeneous spiking responses of otherwise similarly tuned neurons to stimulation, which has been observed ubiquitously, remains unclear to date. Here, we demonstrate that such response heterogeneity serves a beneficial function that is used by downstream brain areas to generate behavioral responses that follows the detailed timecourse of the stimulus. Multi-unit recordings from sensory pyramidal cells within the electrosensory system of Apteronotus leptorhynchus were performed and revealed highly heterogeneous responses that were similar for all cell types. By comparing the coding properties of a given neural population before and after inactivation of descending pathways, we found that heterogeneities were beneficial as decoding was then more robust to the addition of noise. Taken together, our results not only reveal that descending pathways actively promote response heterogeneity within a given cell type, but also uncover a beneficial function for such heterogeneity that is used by the brain to generate behavior.

Serotonin increases population coding of behaviorally relevant stimuli by enhancing responses of ON but not OFF-type sensory neurons

How neural populations encode sensory input to generate behavioral responses remains a central problem in systems neuroscience. Here we investigated how neuromodulation influences population coding of behaviorally relevant stimuli to give rise to behavior in the electrosensory system of the weakly electric fish Apteronotus leptorhynchus. We performed multi-unit recordings from ON and OFF sensory pyramidal cells in response to stimuli whose amplitude (i.e., envelope) varied in time, before and after electrical stimulation of the raphe nuclei. Overall, raphe stimulation increased population coding by ON- but not by OFF-type cells, despite both cell types showing similar sensitivities to the stimulus at the single neuron level. Surprisingly, only changes in population coding by ON-type cells were correlated with changes in behavioral responses. Taken together, our results show that neuromodulation differentially affects ON vs. OFF-type cells in order to enhance perception of behaviorally relevant sensory input.

Burst activity plays no role in the field-to-field variability and rate remapping of grid cells

Grid cells in rodent medial entorhinal cortex are thought to play a key role for spatial navigation. When the animal is freely moving in an open arena the firing fields of each grid cell tend to form a highly regular, hexagonal lattice spanning the environment. However, firing rates vary from field to field and change under contextual modifications, whereas the field locations shift at most by a small amount under such "rate remapping." The observed differences in firing rate could reflect overall activity changes or changes in the detailed spike-train statistics. As these two alternatives imply distinct neural coding schemes, we investigated whether temporal firing patterns vary from field to field and whether they change under rate remapping. Focusing on short time scales, we found that the proportion of bursts compared to all discharge events is similar in all firing fields of a given grid cell and does not change under rate remapping. For each cell, mean firing rates with bursts are proportional to mean firing rates without bursts. However, this ratio varies across cells. Additionally, we looked at how rate remapping relates to entorhinal theta-frequency oscillations. Theta-phase coding was preserved despite firing-rate changes from rate remapping but we did not observe differences between the first and second half of the theta cycle, as had been reported for CA1. Our results indicate that both, the heterogeneity between firing fields and rate remapping, are not due to altered firing patterns on short time scales but reflect location-specific changes at the firing-rate level.

On the Validity of Neural Mass Models

Modeling the dynamics of neural masses is a common approach in the study of neural populations. Various models have been proven useful to describe a plenitude of empirical observations including self-sustained local oscillations and patterns of distant synchronization. We discuss the extent to which mass models really resemble the mean dynamics of a neural population. In particular, we question the validity of neural mass models if the population under study comprises a mixture of excitatory and inhibitory neurons that are densely (inter-)connected. Starting from a network of noisy leaky integrate-and-fire neurons, we formulated two different population dynamics that both fall into the category of seminal Freeman neural mass models. The derivations contained several mean-field assumptions and time scale separation(s) between membrane and synapse dynamics. Our comparison of these neural mass models with the averaged dynamics of the population reveals bounds in the fraction of excitatory/inhibitory neuron as well as overall network degree for a mass model to provide adequate estimates. For substantial parameter ranges, our models fail to mimic the neural network's dynamics proper, be that in de-synchronized or in (high-frequency) synchronized states. Only around the onset of low-frequency synchronization our models provide proper estimates of the mean potential dynamics. While this shows their potential for, e.g., studying resting state dynamics obtained by encephalography with focus on the transition region, we must accept that predicting the more general dynamic outcome of a neural network via its mass dynamics requires great care.

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.

Neural Processing of Communication Signals: The Extent of Sender-Receiver Matching Varies across Species of Apteronotus

As communication signal properties change, through genetic drift or selective pressure, the sensory systems that receive these signals must also adapt to maintain sensitivity and adaptability in an array of contexts. Shedding light on this process helps us to understand how sensory codes are tailored to specific tasks. In a species of weakly electric fish, Apteronotus albifrons, we examined the unique neurophysiological properties that support the encoding of electrosensory communication signals that the animal encounters in social exchanges. We compare our findings to the known coding properties of the closely related species Apteronotus leptorhynchus to establish how these animals differ in their ability to encode their distinctive communication signals. While there are many similarities between these two species, we found notable differences leading to relatively poor coding of the details of chirp structure occurring on high-frequency background beats. As a result, small differences in chirp properties are poorly resolved by the nervous system. We performed behavioral tests to relate A. albifrons chirp coding strategies to its use of chirps during social encounters. Our results suggest that A. albifrons does not exchange frequent chirps in a nonbreeding condition, particularly when the beat frequency is high. These findings parallel the mediocre chirp coding accuracy in that they both point to a reduced reliance on frequent and rich exchange of information through chirps during these social interactions. Therefore, our study suggests that neural coding strategies in the CNS vary across species in a way that parallels the behavioral use of the sensory signals.

Temporal coding and rate remapping: Representation of nonspatial information in the hippocampus

Hippocampal place cells represent nonspatial information through a process called rate remapping, which involves a change in the firing rate of a place cell without changes in its spatial specificity. However, many hippocampal phenomena occur on very short time scales over which long-term average firing rates are not an appropriate description of activity. To understand how rate remapping relates to fine-scale temporal firing phenomena, we asked how rate remapping affected burst firing and trial-to-trial spike count variability. In addition, we looked at how rate remapping relates to the theta-frequency oscillations of the hippocampus, which are thought to temporally organize firing on time scales faster than 100 ms. We found that theta phase coding was preserved through changes in firing rate due to rate remapping. Interestingly, rate remapping in CA1 in response to task demands preferentially occurred during the first half of the theta cycle. The other half of the theta cycle contained preferential expression of phase precession, a phenomenon associated with place cell sequences, in agreement with previous results. This difference of place cell coding during different halves of the theta cycle supports recent theoretical suggestions that different processes occur during the two halves of the theta cycle. The differentiation between the halves of the theta cycle was not clear in recordings from CA3 during rate remapping induced by task-irrelevant sensory changes. These findings provide new insight into the way that temporal coding is utilized in the hippocampus and how rate remapping is expressed through that temporal code.

Serotonin Selectively Increases Detectability of Motion Stimuli in the Electrosensory System

Serotonergic innervation of sensory areas is found ubiquitously across the central nervous system of vertebrates. Here, we used a system's level approach to investigate the role of serotonin on processing motion stimuli in the electrosensory system of the weakly electric fish Apteronotus albifrons. We found that exogenous serotonin application increased the firing activity of pyramidal neural responses to both looming and receding motion. Separating spikes belonging to bursts from those that were isolated revealed that this effect was primarily due to increased burst firing. Moreover, when investigating whether firing activity during stimulation could be discriminated from baseline (i.e., in the absence of stimulation), we found that serotonin increased stimulus discriminability only for some stimuli. This is because increased burst firing was most prominent for these. Further, the effects of serotonin were highly heterogeneous, with some neurons displaying large while others instead displaying minimal changes in responsiveness following serotonin application. Further analysis revealed that serotonin application had the greatest effect on neurons with low baseline firing rates and little to no effect on neurons with high baseline firing rates. Finally, the effects of serotonin on sensory neuron responses were largely independent of object velocity. Our results therefore reveal a novel function for the serotonergic system in selectively enhancing discriminability for motion stimuli.

Optimized Parallel Coding of Second-Order Stimulus Features by Heterogeneous Neural Populations

Efficient processing of sensory input is essential to ensure an organism's survival in its natural environment. Growing evidence suggests that sensory neurons can optimally encode natural stimuli by ensuring that their tuning opposes stimulus statistics, such that the resulting neuronal response contains equal power at all frequencies (i.e., is "white"). Such temporal decorrelation or whitening has been observed across modalities, but the effects of neural heterogeneities on determining tuning and thus responses to natural stimuli have not been investigated. Here, we investigate how heterogeneities in sensory pyramidal neurons organized in three parallel maps representing the body surface determine responses to second-order electrosensory stimulus features in the weakly electric fish Apteronotus leptorhynchus While some sources of heterogeneities such as ON- and OFF-type responses to first-order did not affect responses to second-order electrosensory stimulus features, other sources of heterogeneity within and across the maps strongly determined responses. We found that these cells effectively performed a fractional differentiation operation on their input with exponents ranging from zero (no differentiation) to 0.4 (strong differentiation). Varying adaptation in a simple model explained these heterogeneities and predicted a strong correlation between fractional differentiation and adaptation. Using natural stimuli, we found that only a small fraction of neurons implemented temporal whitening. Rather, a large fraction of neurons did not perform any significant whitening and thus preserved natural input statistics in their responses. We propose that this information is needed to properly decode optimized information sent in parallel through temporally whitened responses based on context.

SIGNIFICANCE STATEMENT

We demonstrate that heterogeneities in the same sensory neuron type can either have no or significant influence on their responses to second-order stimulus features. While an ON- or OFF-type response to first-order stimulus attributes has no significant influence on responses to second-order stimulus features, we found that only a small fraction of sensory neurons optimally encoded natural stimuli through high-pass filtering, thereby implementing temporal whitening. Surprisingly, a large fraction of sensory neurons performed little if no filtering of stimuli, thereby preserving natural stimulus statistics. We hypothesize that this pathway is necessary to properly decode optimized information contained in temporally whitened responses based on context.

Electrosensory neural responses to natural electro-communication stimuli are distributed along a continuum

Neural heterogeneities are seen ubiquitously within the brain and greatly complicate classification efforts. Here we tested whether the responses of an anatomically well-characterized sensory neuron population to natural stimuli could be used for functional classification. To do so, we recorded from pyramidal cells within the electrosensory lateral line lobe (ELL) of the weakly electric fish Apteronotus leptorhynchus in response to natural electro-communication stimuli as these cells can be anatomically classified into six different types. We then used two independent methodologies to functionally classify responses: one relies of reducing the dimensionality of a feature space while the other directly compares the responses themselves. Both methodologies gave rise to qualitatively similar results: while ON and OFF-type cells could easily be distinguished from one another, ELL pyramidal neuron responses are actually distributed along a continuum rather than forming distinct clusters due to heterogeneities. We discuss the implications of our results for neural coding and highlight some potential advantages.

SK channel subtypes enable parallel optimized coding of behaviorally relevant stimulus attributes: A review

Ion channels play essential roles toward determining how neurons respond to sensory input to mediate perception and behavior. Small conductance calcium-activated potassium (SK) channels are found ubiquitously throughout the brain and have been extensively characterized both molecularly and physiologically in terms of structure and function. It is clear that SK channels are key determinants of neural excitability as they mediate important neuronal response properties such as spike frequency adaptation. However, the functional roles of the different known SK channel subtypes are not well understood. Here we review recent evidence from the electrosensory system of weakly electric fish suggesting that the function of different SK channel subtypes is to optimize the processing of independent but behaviorally relevant stimulus attributes. Indeed, natural sensory stimuli frequently consist of a fast time-varying waveform (i.e., the carrier) whose amplitude (i.e., the envelope) varies slowly and independently. We first review evidence showing how somatic SK2 channels mediate tuning and responses to carrier waveforms. We then review evidence showing how dendritic SK1 channels instead determine tuning and optimize responses to envelope waveforms based on their statistics as found in the organism's natural environment in an independent fashion. The high degree of functional homology between SK channels in electric fish and their mammalian orthologs, as well as the many important parallels between the electrosensory system and the mammalian visual, auditory, and vestibular systems, suggest that these functional roles are conserved across systems and species.

Subsecond Sensory Modulation of Serotonin Levels in a Primary Sensory Area and Its Relation to Ongoing Communication Behavior in a Weakly Electric Fish

Serotonergic neurons of the raphe nuclei of vertebrates project to most regions of the brain and are known to significantly affect sensory processing. The subsecond dynamics of sensory modulation of serotonin levels and its relation to behavior, however, remain unknown. We used fast-scan cyclic voltammetry to measure serotonin release in the electrosensory system of weakly electric fish, Apteronotus leptorhynchus. These fish use an electric organ to generate a quasi-sinusoidal electric field for communicating with conspecifics. In response to conspecific signals, they frequently produce signal modulations called chirps. We measured changes in serotonin concentration in the hindbrain electrosensory lobe (ELL) with a resolution of 0.1 s concurrently with chirping behavior evoked by mimics of conspecific electric signals. We show that serotonin release can occur phase locked to stimulus onset as well as spontaneously in the ELL region responsible for processing these signals. Intense auditory stimuli, on the other hand, do not modulate serotonin levels in this region, suggesting modality specificity. We found no significant correlation between serotonin release and chirp production on a trial-by-trial basis. However, on average, in the trials where the fish chirped, there was a reduction in serotonin release in response to stimuli mimicking similar-sized same-sex conspecifics. We hypothesize that the serotonergic system is part of an intricate sensory–motor loop: serotonin release in a sensory area is triggered by sensory input, giving rise to motor output, which can in turn affect serotonin release at the timescale of the ongoing sensory experience and in a context-dependent manner.

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.

Neural heterogeneities determine response characteristics to second-, but not first-order stimulus features

Neural heterogeneities are seen ubiquitously, but how they determine neural response properties remains unclear. Here we show that heterogeneities can either strongly, or not at all, influence neural responses to a given stimulus feature. Specifically, we recorded from peripheral electroreceptor neurons, which display strong heterogeneities in their resting discharge activity, in response to naturalistic stimuli consisting of a fast time-varying waveform (i.e., first-order) whose amplitude (i.e., second-order or envelope) varied slowly in the weakly electric fish Apteronotus leptorhynchus. Although electroreceptors displayed relatively homogeneous responses to first-order stimulus features, further analysis revealed two subpopulations with similar sensitivities that were excited or inhibited by increases in the envelope, respectively, for stimuli whose frequency content spanned the natural range. We further found that a linear-nonlinear cascade model incorporating the known linear response characteristics to first-order features and a static nonlinearity accurately reproduced experimentally observed responses to both first- and second-order features for all stimuli tested. Importantly, this model correctly predicted that the response magnitude is independent of either the stimulus waveform's or the envelope's frequency content. Further analysis of our model led to the surprising prediction that the mean discharge activity can be used to determine whether a given neuron is excited or inhibited by increases in the envelope. This prediction was validated by our experimental data. Thus, our results provide key insight as to how neural heterogeneities can determine response characteristics to some, but not other, behaviorally relevant stimulus features.

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.

Differential effects of excitatory and inhibitory heterogeneity on the gain and asynchronous state of sparse cortical networks

Recent experimental and theoretical studies have highlighted the importance of cell-to-cell differences in the dynamics and functions of neural networks, such as in different types of neural coding or synchronization. It is still not known, however, how neural heterogeneity can affect cortical computations, or impact the dynamics of typical cortical circuits constituted of sparse excitatory and inhibitory networks. In this work, we analytically and numerically study the dynamics of a typical cortical circuit with a certain level of neural heterogeneity. Our circuit includes realistic features found in real cortical populations, such as network sparseness, excitatory, and inhibitory subpopulations of neurons, and different cell-to-cell heterogeneities for each type of population in the system. We find highly differentiated roles for heterogeneity, depending on the subpopulation in which it is found. In particular, while heterogeneity among excitatory neurons non-linearly increases the mean firing rate and linearizes the f-I curves, heterogeneity among inhibitory neurons may decrease the network activity level and induces divisive gain effects in the f-I curves of the excitatory cells, providing an effective gain control mechanism to influence information flow. In addition, we compute the conditions for stability of the network activity, finding that the synchronization onset is robust to inhibitory heterogeneity, but it shifts to lower input levels for higher excitatory heterogeneity. Finally, we provide an extension of recently reported heterogeneity-induced mechanisms for signal detection under rate coding, and we explore the validity of our findings when multiple sources of heterogeneity are present. These results allow for a detailed characterization of the role of neural heterogeneity in asynchronous cortical networks.

Motion processing across multiple topographic maps in the electrosensory system

Animals can efficiently process sensory stimuli whose attributes vary over orders of magnitude by devoting specific neural pathways to process specific features in parallel. Weakly electric fish offer an attractive model system as electrosensory pyramidal neurons responding to amplitude modulations of their self‐generated electric field are organized into three parallel maps of the body surface. While previous studies have shown that these fish use parallel pathways to process stationary stimuli, whether a similar strategy is used to process motion stimuli remains unknown to this day. We recorded from electrosensory pyramidal neurons in the weakly electric fish Apteronotus leptorhynchus across parallel maps of the body surface (centromedial, centrolateral, and lateral) in response to objects moving at velocities spanning the natural range. Contrary to previous observations made with stationary stimuli, we found that all cells responded in a similar fashion to moving objects. Indeed, all cells showed a stronger directionally nonselective response when the object moved at a larger velocity. In order to explain these results, we built a mathematical model incorporating the known antagonistic center–surround receptive field organization of these neurons. We found that this simple model could quantitatively account for our experimentally observed differences seen across E and I‐type cells across all three maps. Our results thus provide strong evidence against the hypothesis that weakly electric fish use parallel neural pathways to process motion stimuli and we discuss their implications for sensory processing in general.

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.

Neural maps in the electrosensory system of weakly electric fish

The active electrosense of weakly electric fish is evolutionarily and developmentally related to passive electrosensation and the lateral line system. It shows the most highly differentiated topographic maps of the receptor array of all these senses. It is organized into three maps in the hindbrain that are, in turn, composed of columns, each consisting of six pyramidal cell classes. The cells in each column have different spatiotemporal processing properties yielding a total of 18 topographic representations of the body surface. The differential filtering by the hindbrain maps is used by superimposed maps in the multi-layered midbrain electrosensory region to extract specific stimulus features related to communication and foraging. At levels beyond the midbrain, topographic mapping of the body surface appears to be lost.

Bursts and isolated spikes code for opposite movement directions in midbrain electrosensory neurons

Directional selectivity, in which neurons respond strongly to an object moving in a given direction but weakly or not at all to the same object moving in the opposite direction, is a crucial computation that is thought to provide a neural correlate of motion perception. However, directional selectivity has been traditionally quantified by using the full spike train, which does not take into account particular action potential patterns. We investigated how different action potential patterns, namely bursts (i.e. packets of action potentials followed by quiescence) and isolated spikes, contribute to movement direction coding in a mathematical model of midbrain electrosensory neurons. We found that bursts and isolated spikes could be selectively elicited when the same object moved in opposite directions. In particular, it was possible to find parameter values for which our model neuron did not display directional selectivity when the full spike train was considered but displayed strong directional selectivity when bursts or isolated spikes were instead considered. Further analysis of our model revealed that an intrinsic burst mechanism based on subthreshold T-type calcium channels was not required to observe parameter regimes for which bursts and isolated spikes code for opposite movement directions. However, this burst mechanism enhanced the range of parameter values for which such regimes were observed. Experimental recordings from midbrain neurons confirmed our modeling prediction that bursts and isolated spikes can indeed code for opposite movement directions. Finally, we quantified the performance of a plausible neural circuit and found that it could respond more or less selectively to isolated spikes for a wide range of parameter values when compared with an interspike interval threshold. Our results thus show for the first time that different action potential patterns can differentially encode movement and that traditional measures of directional selectivity need to be revised in such cases.

Parallel coding of first- and second-order stimulus attributes by midbrain electrosensory neurons

Natural stimuli often have time-varying first-order (i.e., mean) and second-order (i.e., variance) attributes that each carry critical information for perception and can vary independently over orders of magnitude. Experiments have shown that sensory systems continuously adapt their responses based on changes in each of these attributes. This adaptation creates ambiguity in the neural code as multiple stimuli may elicit the same neural response. While parallel processing of first- and second-order attributes by separate neural pathways is sufficient to remove this ambiguity, the existence of such pathways and the neural circuits that mediate their emergence have not been uncovered to date. We recorded the responses of midbrain electrosensory neurons in the weakly electric fish Apteronotus leptorhynchus to stimuli with first- and second-order attributes that varied independently in time. We found three distinct groups of midbrain neurons: the first group responded to both first- and second-order attributes, the second group responded selectively to first-order attributes, and the last group responded selectively to second-order attributes. In contrast, all afferent hindbrain neurons responded to both first- and second-order attributes. Using computational analyses, we show how inputs from a heterogeneous population of ON- and OFF-type afferent neurons are combined to give rise to response selectivity to either first- or second-order stimulus attributes in midbrain neurons. Our study thus uncovers, for the first time, generic and widely applicable mechanisms by which parallel processing of first- and second-order stimulus attributes emerges in the brain.

Cellular and circuit properties supporting different sensory coding strategies in electric fish and other systems

Neural codes often seem tailored to the type of information they must carry. Here we contrast the encoding strategies for two different communication signals in electric fish and describe the underlying cellular and network properties that implement them. We compare an aggressive signal that needs to be quickly detected, to a courtship signal whose quality needs to be evaluated. The aggressive signal is encoded by synchronized bursts and a predictive feedback input is crucial in separating background noise from the communication signal. The courtship signal is accurately encoded through a heterogenous population response allowing the discrimination of signal differences. Most importantly we show that the same strategies are used in other systems arguing that they evolved similar solutions because they faced similar tasks.

Coding movement direction by burst firing in electrosensory neurons

Directional selectivity, in which neurons respond strongly to an object moving in a given direction ("preferred") but respond weakly or not at all to an object moving in the opposite direction ("null"), is a critical computation achieved in brain circuits. Previous measures of direction selectivity have compared the numbers of action potentials elicited by each direction of movement, but most sensory neurons display patterning, such as bursting, in their spike trains. To examine the contribution of patterned responses to direction selectivity, we recorded from midbrain neurons in weakly electric fish and found that most neurons responded with a combination of both bursts and isolated spikes to moving object stimuli. In these neurons, we separated bursts and isolated spikes using an interspike interval (ISI) threshold. The directional bias of bursts was significantly higher than that of either the full spike train or the isolated spike train. To examine the encoding and decoding of bursts, we built biologically plausible models that examine 1) the upstream mechanisms that generate these spiking patterns and 2) downstream decoders of bursts. Our model of upstream mechanisms uses an interaction between afferent input and subthreshold calcium channels to give rise to burst firing that occurs preferentially for one direction of movement. We tested this model in vivo by application of calcium antagonists, which reduced burst firing and eliminated the differences in direction selectivity between bursts, isolated spikes, and the full spike train. Our model of downstream decoders used strong synaptic facilitation to achieve qualitatively similar results to those obtained using the ISI threshold criterion. This model shows that direction selective information carried by bursts can be decoded by downstream neurons using biophysically plausible mechanisms.

Efficient computation via sparse coding in electrosensory neural networks

The electric sense combines spatial aspects of vision and touch with temporal features of audition. Its accessible neural architecture shares similarities with mammalian sensory systems and allows for recordings from successive brain areas to test hypotheses about neural coding. Further, electrosensory stimuli encountered during prey capture, navigation, and communication, can be readily synthesized in the laboratory. These features enable analyses of the neural circuitry that reveal general principles of encoding and decoding, such as segregation of information into separate streams and neural response sparsification. A systems level understanding arises via linkage between cellular differentiation and network architecture, revealed by in vitro and in vivo analyses, while computational modeling reveals how single cell dynamics and connectivity shape the sparsification process.

Nonrenewal spike train statistics: causes and functional consequences on neural coding

Many neurons display significant patterning in their spike trains (e.g. oscillations, bursting), and there is accumulating evidence that information is contained in these patterns. In many cases, this patterning is caused by intrinsic mechanisms rather than external signals. In this review, we focus on spiking activity that displays nonrenewal statistics (i.e. memory that persists from one firing to the next). Such statistics are seen in both peripheral and central neurons and appear to be ubiquitous in the CNS. We review the principal mechanisms that can give rise to nonrenewal spike train statistics. These are separated into intrinsic mechanisms such as relative refractoriness and network mechanisms such as coupling with delayed inhibitory feedback. Next, we focus on the functional roles for nonrenewal spike train statistics. These can either increase or decrease information transmission. We also focus on how such statistics can give rise to an optimal integration timescale at which spike train variability is minimal and how this might be exploited by sensory systems to maximize the detection of weak signals. We finish by pointing out some interesting future directions for research in this area. In particular, we explore the interesting possibility that synaptic dynamics might be matched with the nonrenewal spiking statistics of presynaptic spike trains in order to further improve information transmission.

Inhibition of SK and M channel-mediated currents by 5-HT enables parallel processing by bursts and isolated spikes

Although serotonergic innervation of sensory brain areas is ubiquitous, its effects on sensory information processing remain poorly understood. We investigated these effects in pyramidal neurons within the electrosensory lateral line lobe (ELL) of weakly electric fish. Surprisingly, we found that 5-HT is present at different levels across the different ELL maps; the presence of 5-HT fibers was highest in the map that processes intraspecies communication signals. Electrophysiological recordings revealed that 5-HT increased excitability and burst firing through a decreased medium afterhyperpolarization resulting from reduced small-conductance calcium-activated (SK) currents as well as currents mediated by an M-type potassium channel. We next investigated how 5-HT alters responses to sensory input. 5-HT application decreased the rheobase current, increased the gain, and decreased first spike latency. Moreover, it reduced discriminability between different stimuli, as quantified by the mutual information rate. We hypothesized that 5-HT shifts pyramidal neurons into a burst-firing mode where bursts, when considered as events, can detect the presence of particular stimulus features. We verified this hypothesis using signal detection theory. Our results indeed show that serotonin-induced bursts of action potentials, when considered as events, could detect specific stimulus features that were distinct from those detected by isolated spikes. Moreover, we show the novel result that isolated spikes transmit more information after 5-HT application. Our results suggest a novel function for 5-HT in that it enables differential processing by action potential patterns in response to current injection.

In vivo conditions influence the coding of stimulus features by bursts of action potentials

The functional role of burst firing (i.e. the firing of packets of action potentials followed by quiescence) in sensory processing is still under debate. Should bursts be considered as unitary events that signal the presence of a particular feature in the sensory environment or is information about stimulus attributes contained within their temporal structure? We compared the coding of stimulus attributes by bursts in vivo and in vitro of electrosensory pyramidal neurons in weakly electric fish by computing correlations between burst and stimulus attributes. Our results show that, while these correlations were strong in magnitude and significant in vitro, they were actually much weaker in magnitude if at all significant in vivo. We used a mathematical model of pyramidal neuron activity in vivo and showed that such a model could reproduce the correlations seen in vitro, thereby suggesting that differences in burst coding were not due to differences in bursting seen in vivo and in vitro. We next tested whether variability in the baseline (i.e. without stimulation) activity of ELL pyramidal neurons could account for these differences. To do so, we injected noise into our model whose intensity was calibrated to mimic baseline activity variability as quantified by the coefficient of variation. We found that this noise caused significant decreases in the magnitude of correlations between burst and stimulus attributes and could account for differences between in vitro and in vivo conditions. We then tested this prediction experimentally by directly injecting noise in vitro through the recording electrode. Our results show that this caused a lowering in magnitude of the correlations between burst and stimulus attributes in vitro and gave rise to values that were quantitatively similar to those seen under in vivo conditions. While it is expected that noise in the form of baseline activity variability will lower correlations between burst and stimulus attributes, our results show that such variability can account for differences seen in vivo. Thus, the high variability seen under in vivo conditions has profound consequences on the coding of information by bursts in ELL pyramidal neurons. In particular, our results support the viewpoint that bursts serve as a detector of particular stimulus features but do not carry detailed information about such features in their structure.

Neural heterogeneities influence envelope and temporal coding at the sensory periphery

Peripheral sensory neurons respond to stimuli containing a wide range of spatio-temporal frequencies. We investigated electroreceptor neuron coding in the gymnotiform wave-type weakly electric fish Apteronotus leptorhynchus. Previous studies used low to mid temporal frequencies (<256 Hz) and showed that electroreceptor neuron responses to sensory stimuli could be almost exclusively accounted for by linear models, thereby implying a rate code. We instead used temporal frequencies up to 425 Hz, which is in the upper behaviorally relevant range for this species. We show that electroreceptors can: (A) respond up to the highest frequencies tested and (B) display strong nonlinearities in their responses to such stimuli. These nonlinearities were manifested by the fact that the responses to repeated presentations of the same stimulus were coherent at temporal frequencies outside of those contained in the stimulus waveform. Specifically, these consisted of low frequencies corresponding to the time varying contrast or envelope of the stimulus as well as higher harmonics of the frequencies contained in the stimulus. Heterogeneities in the afferent population influenced nonlinear coding as afferents with the lowest baseline firing rates tended to display the strongest nonlinear responses. To understand the link between afferent heterogeneity and nonlinear responsiveness, we used a phenomenological mathematical model of electrosensory afferents. Varying a single parameter in the model was sufficient to account for the variability seen in our experimental data and yielded a prediction: nonlinear responses to the envelope and at higher harmonics are both due to afferents with lower baseline firing rates displaying greater degrees of rectification in their responses. This prediction was verified experimentally as we found that the coherence between the half-wave rectified stimulus and the response resembled the coherence between the responses to repeated presentations of the stimulus in our dataset. This result shows that rectification cannot only give rise to responses to low frequency envelopes but also at frequencies that are higher than those contained in the stimulus. The latter result implies that information is contained in the fine temporal structure of electroreceptor afferent spike trains. Our results show that heterogeneities in peripheral neuronal populations can have dramatic consequences on the nature of the neural code.