Nonlinear information processing in a model sensory system

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.

Stimulator compensation and generation of Gaussian noise stimuli with defined amplitude spectra for studying input–output relations of sensory systems

Gaussian noise is an important stimulus for the study of biological systems, especially sensory and neural systems. Since these systems are inherently nonlinear, the properties of the noise strongly influence the outcome of the analysis. Therefore, it is crucial to use a well-defined and controlled noise stimulus. In this paper, we first use the example of an insect filiform sensillum, a simple mechanoreceptor with a single sensory cell, to show that changes in the amplitude and spectral properties of the noise stimulus indeed affect the linear transfer function of the sensillum. We then explain step-by-step how to use the inverse fast Fourier transform to generate a Gaussian noise that has an arbitrary user-defined amplitude spectrum, including a band-limited white noise with a perfectly sharp cutoff edge. Finally, we demonstrate how such a perfect band-limited Gaussian white noise stimulus can also be generated with a non-perfect stimulator using a simple procedure that compensates for the filtering properties of the stimulator. With this approach, one can generate well-defined Gaussian noise stimuli that can be adapted to any application. For example, one can generate visual, sound, or vibrational stimuli for experimental research in visual physiology, auditory physiology, and biotremology, as well as inputs for testing various models in theoretical research.

Information transmission in recurrent networks: Consequences of network noise for synchronous and asynchronous signal encoding

Information about natural time-dependent stimuli encoded by the sensory periphery or communication between cortical networks may span a large frequency range or be localized to a smaller frequency band. Biological systems have been shown to multiplex such disparate broadband and narrow-band signals and then discriminate them in later populations by employing either an integration (low-pass) or coincidence detection (bandpass) encoding strategy. Analytical expressions have been developed for both encoding methods in feedforward populations of uncoupled neurons and confirm that the integration of a population's output low-pass filters the information, whereas synchronous output encodes less information overall and retains signal information in a selected frequency band. The present study extends the theory to recurrent networks and shows that recurrence may sharpen the synchronous bandpass filter. The frequency of the pass band is significantly influenced by the synaptic strengths, especially for inhibition-dominated networks. Synchronous information transfer is also increased when network models take into account heterogeneity that arises from the stochastic distribution of the synaptic weights.

Neurostimulation stabilizes spiking neural networks by disrupting seizure-like oscillatory transitions

An improved understanding of the mechanisms underlying neuromodulatory approaches to mitigate seizure onset is needed to identify clinical targets for the treatment of epilepsy. Using a Wilson–Cowan-motivated network of inhibitory and excitatory populations, we examined the role played by intrinsic and extrinsic stimuli on the network’s predisposition to sudden transitions into oscillatory dynamics, similar to the transition to the seizure state. Our joint computational and mathematical analyses revealed that such stimuli, be they noisy or periodic in nature, exert a stabilizing influence on network responses, disrupting the development of such oscillations. Based on a combination of numerical simulations and mean-field analyses, our results suggest that high variance and/or high frequency stimulation waveforms can prevent multi-stability, a mathematical harbinger of sudden changes in network dynamics. By tuning the neurons’ responses to input, stimuli stabilize network dynamics away from these transitions. Furthermore, our research shows that such stabilization of neural activity occurs through a selective recruitment of inhibitory cells, providing a theoretical undergird for the known key role these cells play in both the healthy and diseased brain. Taken together, these findings provide new vistas on neuromodulatory approaches to stabilize neural microcircuit activity.

Information filtering by coincidence detection of synchronous population output: analytical approaches to the coherence function of a two-stage neural system

Information about time-dependent sensory stimuli is encoded in the activity of neural populations; distinct aspects of the stimulus are read out by different types of neurons: while overall information is perceived by integrator cells, so-called coincidence detector cells are driven mainly by the synchronous activity in the population that encodes predominantly high-frequency content of the input signal (high-pass information filtering). Previously, an analytically accessible statistic called the partial synchronous output was introduced as a proxy for the coincidence detector cell's output in order to approximate its information transmission. In the first part of the current paper, we compare the information filtering properties (specifically, the coherence function) of this proxy to those of a simple coincidence detector neuron. We show that the latter's coherence function can indeed be well-approximated by the partial synchronous output with a time scale and threshold criterion that are related approximately linearly to the membrane time constant and firing threshold of the coincidence detector cell. In the second part of the paper, we propose an alternative theory for the spectral measures (including the coherence) of the coincidence detector cell that combines linear-response theory for shot-noise driven integrate-and-fire neurons with a novel perturbation ansatz for the spectra of spike-trains driven by colored noise. We demonstrate how the variability of the synaptic weights for connections from the population to the coincidence detector can shape the information transmission of the entire two-stage system.

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.

Coding strategies in the otolith system differ for translational head motion vs. static orientation relative to gravity

The detection of gravito-inertial forces by the otolith system is essential for our sense of balance and accurate perception. To date, however, how this system encodes the self-motion stimuli that are experienced during everyday activities remains unknown. Here, we addressed this fundamental question directly by recording from single otolith afferents in monkeys during naturalistic translational self-motion and changes in static head orientation. Otolith afferents with higher intrinsic variability transmitted more information overall about translational self-motion than their regular counterparts, owing to stronger nonlinearities that enabled precise spike timing including phase locking. By contrast, more regular afferents better discriminated between different static head orientations relative to gravity. Using computational methods, we further demonstrated that coupled increases in intrinsic variability and sensitivity accounted for the observed functional differences between afferent classes. Together, our results indicate that irregular and regular otolith afferents use different strategies to encode naturalistic self-motion and static head orientation relative to gravity.

Information transmission of mean and variance coding in integrate-and-fire neurons

Neurons process information by translating continuous signals into patterns of discrete spike times. An open question is how much information these spike times contain about signals which modulate either the mean or the variance of the somatic currents in neurons, as is observed experimentally. Here we calculate the exact information contained in discrete spike times about a continuous signal in both encoding strategies. We show that the information content about mean modulating signals is generally substantially larger than about variance modulating signals for biological parameters. Our analysis further reveals that higher information transmission is associated with a larger proportion of nonlinear signal encoding. Our study measures the complete information content of mean and variance coding and provides a method to determine what fraction of the total information is linearly decodable.

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.

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.

Descending pathways generate perception of and neural responses to weak sensory input

Natural sensory stimuli frequently consist of a fast time-varying waveform whose amplitude or contrast varies more slowly. While changes in contrast carry behaviorally relevant information necessary for sensory perception, their processing by the brain remains poorly understood to this day. Here, we investigated the mechanisms that enable neural responses to and perception of low-contrast stimuli in the electrosensory system of the weakly electric fish Apteronotus leptorhynchus. We found that fish reliably detected such stimuli via robust behavioral responses. Recordings from peripheral electrosensory neurons revealed stimulus-induced changes in firing activity (i.e., phase locking) but not in their overall firing rate. However, central electrosensory neurons receiving input from the periphery responded robustly via both phase locking and increases in firing rate. Pharmacological inactivation of feedback input onto central electrosensory neurons eliminated increases in firing rate but did not affect phase locking for central electrosensory neurons in response to low-contrast stimuli. As feedback inactivation eliminated behavioral responses to these stimuli as well, our results show that it is changes in central electrosensory neuron firing rate that are relevant for behavior, rather than phase locking. Finally, recordings from neurons projecting directly via feedback to central electrosensory neurons revealed that they provide the necessary input to cause increases in firing rate. Our results thus provide the first experimental evidence that feedback generates both neural and behavioral responses to low-contrast stimuli that are commonly found in the natural environment.

Feedback input from more central to more peripheral brain areas is found ubiquitously in the central nervous system of vertebrates. In this study, we used a combination of electrophysiological, behavioral, and pharmacological approaches to reveal a novel function for feedback pathways in generating neural and behavioral responses to weak sensory input in the weakly electric fish. We first determined that weak sensory input gives rise to responses that are phase locked in both peripheral sensory neurons and in the central neurons that are their downstream targets. However, central neurons also responded to weak sensory inputs that were not relayed via a feedforward input from the periphery, because complete inactivation of the feedback pathway abolished increases in firing rate but not the phase locking in response to weak sensory input. Because such inactivation also abolished the behavioral responses, our results show that the increases in firing rate in central neurons, and not the phase locking, are decoded downstream to give rise to perception. Finally, we discovered that the neurons providing feedback input were also activated by weak sensory input, thereby offering further evidence that feedback is necessary to elicit increases in firing rate that are needed for perception.

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.

Statistics of Natural Communication Signals Observed in the Wild Identify Important Yet Neglected Stimulus Regimes in Weakly Electric Fish

Sensory systems evolve in the ecological niches that each species is occupying. Accordingly, encoding of natural stimuli by sensory neurons is expected to be adapted to the statistics of these stimuli. For a direct quantification of sensory scenes, we tracked natural communication behavior of male and female weakly electric fish, Apteronotus rostratus, in their Neotropical rainforest habitat with high spatiotemporal resolution over several days. In the context of courtship, we observed large quantities of electrocommunication signals. Echo responses, acknowledgment signals, and their synchronizing role in spawning demonstrated the behavioral relevance of these signals. In both courtship and aggressive contexts, we observed robust behavioral responses in stimulus regimes that have so far been neglected in electrophysiological studies of this well characterized sensory system and that are well beyond the range of known best frequency and amplitude tuning of the electroreceptor afferents' firing rate modulation. Our results emphasize the importance of quantifying sensory scenes derived from freely behaving animals in their natural habitats for understanding the function and evolution of neural systems.SIGNIFICANCE STATEMENT The processing mechanisms of sensory systems have evolved in the context of the natural lives of organisms. To understand the functioning of sensory systems therefore requires probing them in the stimulus regimes in which they evolved. We took advantage of the continuously generated electric fields of weakly electric fish to explore electrosensory stimulus statistics in their natural Neotropical habitat. Unexpectedly, many of the electrocommunication signals recorded during courtship, spawning, and aggression had much smaller amplitudes or higher frequencies than stimuli used so far in neurophysiological characterizations of the electrosensory system. Our results demonstrate that quantifying sensory scenes derived from freely behaving animals in their natural habitats is essential to avoid biases in the choice of stimuli used to probe brain function.

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.

Feedback Synthesizes Neural Codes for Motion

In senses as diverse as vision, hearing, touch, and the electrosense, sensory neurons receive bottom-up input from the environment, as well as top-down input from feedback loops involving higher brain regions [1-4]. Through connectivity with local inhibitory interneurons, these feedback loops can exert both positive and negative control over fundamental aspects of neural coding, including bursting [5, 6] and synchronous population activity [7, 8]. Here we show that a prominent midbrain feedback loop synthesizes a neural code for motion reversal in the hindbrain electrosensory ON- and OFF-type pyramidal cells. This top-down mechanism generates an accurate bidirectional encoding of object position, despite the inability of the electrosensory afferents to generate a consistent bottom-up representation [9, 10]. The net positive activity of this midbrain feedback is additionally regulated through a hindbrain feedback loop, which reduces stimulus-induced bursting and also dampens the ON and OFF cell responses to interfering sensory input [11]. We demonstrate that synthesis of motion representations and cancellation of distracting signals are mediated simultaneously by feedback, satisfying an accepted definition of spatial attention [12]. The balance of excitatory and inhibitory feedback establishes a "focal" distance for optimized neural coding, whose connection to a classic motion-tracking behavior provides new insight into the computational roles of feedback and active dendrites in spatial localization [13, 14].

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.

Synchronous spikes are necessary but not sufficient for a synchrony code in populations of spiking neurons

Synchronous activity in populations of neurons potentially encodes special stimulus features. Selective readout of either synchronous or asynchronous activity allows formation of two streams of information processing. Theoretical work predicts that such a synchrony code is a fundamental feature of populations of spiking neurons if they operate in specific noise and stimulus regimes. Here we experimentally test the theoretical predictions by quantifying and comparing neuronal response properties in tuberous and ampullary electroreceptor afferents of the weakly electric fish Apteronotus leptorhynchus These related systems show similar levels of synchronous activity, but only in the more irregularly firing tuberous afferents a synchrony code is established, whereas in the more regularly firing ampullary afferents it is not. The mere existence of synchronous activity is thus not sufficient for a synchrony code. Single-cell features such as the irregularity of spiking and the frequency dependence of the neuron's transfer function determine whether synchronous spikes possess a distinct meaning for the encoding of time-dependent signals.

Electrosensory processing in Apteronotus albifrons: implications for general and specific neural coding strategies across wave-type weakly electric fish species

Understanding how the brain processes sensory input to generate behavior remains an important problem in neuroscience. Towards this end, it is useful to compare results obtained across multiple species to gain understanding as to the general principles of neural coding. Here we investigated hindbrain pyramidal cell activity in the weakly electric fish Apteronotus albifrons We found strong heterogeneities when looking at baseline activity. Additionally, ON- and OFF-type cells responded to increases and decreases of sinusoidal and noise stimuli, respectively. While both cell types displayed band-pass tuning, OFF-type cells were more broadly tuned than their ON-type counterparts. The observed heterogeneities in baseline activity as well as the greater broadband tuning of OFF-type cells were both similar to those previously reported in other weakly electric fish species, suggesting that they constitute general features of sensory processing. However, we found that peak tuning occurred at frequencies ∼15 Hz in A. albifrons, which is much lower than values reported in the closely related species Apteronotus leptorhynchus and the more distantly related species Eigenmannia virescens In response to stimuli with time-varying amplitude (i.e., envelope), ON- and OFF-type cells displayed similar high-pass tuning curves characteristic of fractional differentiation and possibly indicate optimized coding. These tuning curves were qualitatively similar to those of pyramidal cells in the closely related species A. leptorhynchus In conclusion, comparison between our and previous results reveals general and species-specific neural coding strategies. We hypothesize that differences in coding strategies, when observed, result from different stimulus distributions in the natural/social environment.

Self-motion evokes precise spike timing in the primate vestibular system

The accurate representation of self-motion requires the efficient processing of sensory input by the vestibular system. Conventional wisdom is that vestibular information is exclusively transmitted through changes in firing rate, yet under this assumption vestibular neurons display relatively poor detection and information transmission. Here, we carry out an analysis of the system's coding capabilities by recording neuronal responses to repeated presentations of naturalistic stimuli. We find that afferents with greater intrinsic variability reliably discriminate between different stimulus waveforms through differential patterns of precise (∼6 ms) spike timing, while those with minimal intrinsic variability do not. A simple mathematical model provides an explanation for this result. Postsynaptic central neurons also demonstrate precise spike timing, suggesting that higher brain areas also represent self-motion using temporally precise firing. These findings demonstrate that two distinct sensory channels represent vestibular information: one using rate coding and the other that takes advantage of precise spike timing.

Early vestibular pathways are thought to code sensory inputs regarding self-motion via changes in firing rate. Here, the authors record from both regular and irregular afferents in macaques, and find both irregular afferents and central neurons also represent self-motion via temporally precise spike timing.

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.

Contrast coding in the electrosensory system: parallels with visual computation

To identify and interact with moving objects, including other members of the same species, an animal's nervous system must correctly interpret patterns of contrast in the physical signals (such as light or sound) that it receives from the environment. In weakly electric fish, the motion of objects in the environment and social interactions with other fish create complex patterns of contrast in the electric fields that they produce and detect. These contrast patterns can extend widely over space and time and represent a multitude of relevant features, as is also true for other sensory systems. Mounting evidence suggests that the computational principles underlying contrast coding in electrosensory neural networks are conserved elements of spatiotemporal processing that show strong parallels with the vertebrate visual system.

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.

Bilinearity in spatiotemporal integration of synaptic inputs

Neurons process information via integration of synaptic inputs from dendrites. Many experimental results demonstrate dendritic integration could be highly nonlinear, yet few theoretical analyses have been performed to obtain a precise quantitative characterization analytically. Based on asymptotic analysis of a two-compartment passive cable model, given a pair of time-dependent synaptic conductance inputs, we derive a bilinear spatiotemporal dendritic integration rule. The summed somatic potential can be well approximated by the linear summation of the two postsynaptic potentials elicited separately, plus a third additional bilinear term proportional to their product with a proportionality coefficient [Formula: see text]. The rule is valid for a pair of synaptic inputs of all types, including excitation-inhibition, excitation-excitation, and inhibition-inhibition. In addition, the rule is valid during the whole dendritic integration process for a pair of synaptic inputs with arbitrary input time differences and input locations. The coefficient [Formula: see text] is demonstrated to be nearly independent of the input strengths but is dependent on input times and input locations. This rule is then verified through simulation of a realistic pyramidal neuron model and in electrophysiological experiments of rat hippocampal CA1 neurons. The rule is further generalized to describe the spatiotemporal dendritic integration of multiple excitatory and inhibitory synaptic inputs. The integration of multiple inputs can be decomposed into the sum of all possible pairwise integration, where each paired integration obeys the bilinear rule. This decomposition leads to a graph representation of dendritic integration, which can be viewed as functionally sparse.

Vesicles derived via AP-3-dependent recycling contribute to asynchronous release and influence information transfer

Action potentials trigger synchronous and asynchronous neurotransmitter release. Temporal properties of both types of release could be altered in an activity-dependent manner. While the effects of activity-dependent changes in synchronous release on postsynaptic signal integration have been studied, the contribution of asynchronous release to information transfer during natural stimulus patterns is unknown. Here we find that during trains of stimulations, asynchronous release contributes to the precision of action potential firing. Our data show that this form of release is selectively diminished in AP-3b2 KO animals, which lack functional neuronal AP-3, an adaptor protein regulating vesicle formation from endosomes generated during bulk endocytosis. We find that in the absence of neuronal AP-3, asynchronous release is attenuated and the activity-dependent increase in the precision of action potential timing is compromised. Lack of asynchronous release decreases the capacity of synaptic information transfer and renders synaptic communication less reliable in response to natural stimulus patterns.

A neural code for looming and receding motion is distributed over a population of electrosensory ON and OFF contrast cells

Object saliency is based on the relative local-to-background contrast in the physical signals that underlie perceptual experience. As such, contrast-detecting neurons (ON/OFF cells) are found in many sensory systems, responding respectively to increased or decreased intensity within their receptive field centers. This differential sensitivity suggests that ON and OFF cells initiate segregated streams of information for positive and negative sensory contrast. However, while recording in vivo from the ON and OFF cells of Apteronotus leptorhynchus, we report that the reversal of stimulus motion triggers paradoxical responses to electrosensory contrast. By considering the instantaneous firing rates of both ON and OFF cell populations, a bidirectionally symmetric representation of motion is achieved for both positive and negative contrast stimuli. Whereas the firing rates of the individual contrast detecting neurons convey scalar information, such as object distance, it is their sequential activation over longer timescales that track changes in the direction of movement.

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.

Interacting linear and nonlinear characteristics produce population coding asymmetries between ON and OFF cells in the retina

The early visual system is a model for understanding the roles of cell populations in parallel processing. Cells in this system can be classified according to their responsiveness to different stimuli; a prominent example is the division between cells that respond to stimuli of opposite contrasts (ON vs OFF cells). These two cell classes display many asymmetries in their physiological characteristics (including temporal characteristics, spatial characteristics, and nonlinear characteristics) that, individually, are known to have important roles in population coding. Here we describe a novel distinction between the information that ON and OFF ganglion cell populations carry in mouse--that OFF cells are able to signal motion information about both light and dark objects, while ON cells have a selective deficit at signaling the motion of dark objects. We found that none of the previously reported asymmetries in physiological characteristics could account for this distinction. We therefore analyzed its basis via a recently developed linear-nonlinear-Poisson model that faithfully captures input/output relationships for a broad range of stimuli (Bomash et al., 2013). While the coding differences between ON and OFF cell populations could not be ascribed to the linear or nonlinear components of the model individually, they had a simple explanation in the way that these components interact. Sensory transformations in other systems can likewise be described by these models, and thus our findings suggest that similar interactions between component properties may help account for the roles of cell classes in population coding more generally.

Statistics of the electrosensory input in the freely swimming weakly electric fish Apteronotus leptorhynchus

The neural computations underlying sensory-guided behaviors can best be understood in view of the sensory stimuli to be processed under natural conditions. This input is often actively shaped by the movements of the animal and its sensory receptors. Little is known about natural sensory scene statistics taking into account the concomitant movement of sensory receptors in freely moving animals. South American weakly electric fish use a self-generated quasi-sinusoidal electric field for electrolocation and electrocommunication. Thousands of cutaneous electroreceptors detect changes in the transdermal potential (TDP) as the fish interact with conspecifics and the environment. Despite substantial knowledge about the circuitry and physiology of the electrosensory system, the statistical properties of the electrosensory input evoked by natural swimming movements have never been measured directly. Using underwater wireless telemetry, we recorded the TDP of Apteronotus leptorhynchus as they swam freely by themselves and during interaction with a conspecific. Swimming movements caused low-frequency TDP amplitude modulations (AMs). Interacting with a conspecific caused additional AMs around the difference frequency of their electric fields, with the amplitude of the AMs (envelope) varying at low frequencies due to mutual movements. Both AMs and envelopes showed a power-law relationship with frequency, indicating spectral scale invariance. Combining a computational model of the electric field with video tracking of movements, we show that specific swimming patterns cause characteristic spatiotemporal sensory input correlations that contain information that may be used by the brain to guide behavior.

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.

Speed-invariant encoding of looming object distance requires power law spike rate adaptation

Neural representations of a moving object's distance and approach speed are essential for determining appropriate orienting responses, such as those observed in the localization behaviors of the weakly electric fish, Apteronotus leptorhynchus. We demonstrate that a power law form of spike rate adaptation transforms an electroreceptor afferent's response to "looming" object motion, effectively parsing information about distance and approach speed into distinct measures of the firing rate. Neurons with dynamics characterized by fixed time scales are shown to confound estimates of object distance and speed. Conversely, power law adaptation modifies an electroreceptor afferent's response according to the time scales present in the stimulus, generating a rate code for looming object distance that is invariant to speed and acceleration. Consequently, estimates of both object distance and approach speed can be uniquely determined from an electroreceptor afferent's firing rate, a multiplexed neural code operating over the extended time scales associated with behaviorally relevant stimuli.

Phenomenological incorporation of nonlinear dendritic integration using integrate-and-fire neuronal frameworks

It has been discovered recently in experiments that the dendritic integration of excitatory glutamatergic inputs and inhibitory GABAergic inputs in hippocampus CA1 pyramidal neurons obeys a simple arithmetic rule as V(S)(Exp) ≈ V(E)(Exp) + V(I)(Exp) + kV(E)(Exp) V(I)(Exp), where V(S)(Exp), V(E)(Exp) and V(I)(Exp) are the respective voltage values of the summed somatic potential, the excitatory postsynaptic potential (EPSP) and the inhibitory postsynaptic potential measured at the time when the EPSP reaches its peak value. Moreover, the shunting coefficient k in this rule only depends on the spatial location but not the amplitude of the excitatory or inhibitory input on the dendrite. In this work, we address the theoretical issue of how much the above dendritic integration rule can be accounted for using subthreshold membrane potential dynamics in the soma as characterized by the conductance-based integrate-and-fire (I&F) model. Then, we propose a simple I&F neuron model that incorporates the spatial dependence of the shunting coefficient k by a phenomenological parametrization. Our analytical and numerical results show that this dendritic-integration-rule-based I&F (DIF) model is able to capture many experimental observations and it also yields predictions that can be used to verify the validity of the DIF model experimentally. In addition, the DIF model incorporates the dendritic integration effects dynamically and is applicable to more general situations than those in experiments in which excitatory and inhibitory inputs occur simultaneously in time. Finally, we generalize the DIF neuronal model to incorporate multiple inputs and obtain a similar dendritic integration rule that is consistent with the results obtained by using a realistic neuronal model with multiple compartments. This generalized DIF model can potentially be used to study network dynamics that may involve effects arising from dendritic integrations.

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

Throughout the central nervous system, the timescale over which pairs of neural spike trains are correlated is shaped by stimulus structure and behavioral context. Such shaping is thought to underlie important changes in the neural code, but the neural circuitry responsible is largely unknown. In this study, we investigate a stimulus-induced shaping of pairwise spike train correlations in the electrosensory system of weakly electric fish. Simultaneous single unit recordings of principal electrosensory cells show that an increase in the spatial extent of stimuli increases correlations at short () timescales while simultaneously reducing correlations at long () timescales. A spiking network model of the first two stages of electrosensory processing replicates this correlation shaping, under the assumptions that spatially broad stimuli both saturate feedforward afferent input and recruit an open-loop inhibitory feedback pathway. Our model predictions are experimentally verified using both the natural heterogeneity of the electrosensory system and pharmacological blockade of descending feedback projections. For weak stimuli, linear response analysis of the spiking network shows that the reduction of long timescale correlation for spatially broad stimuli is similar to correlation cancellation mechanisms previously suggested to be operative in mammalian cortex. The mechanism for correlation shaping supports population-level filtering of irrelevant distractor stimuli, thereby enhancing the population response to relevant prey and conspecific communication inputs.

The size of a stimulus that is sensed by the nervous system can control the activity of neurons in sensory areas. How neural wiring supports this dependence remains an open question. We explore this general phenomenon using weakly electric fish, which possess a sensory system that detects electric field modulations produced by the surrounding environment. In particular, these animals' nervous systems are tuned to detect the difference between spatially compact prey inputs and spatially broad communication calls from other fish. In experiment, we discover that these two classes of stimuli differentially control the synchrony between pairs of electrosensory neurons. Using a computational model, we predict that this modulation is related to feedforward and feedback neural pathways in the electrosensory system, and we verify this prediction with experiments. This architecture prevents low frequency distractor stimuli, such as the animal's own tail motion, from driving neural population responses. With our model, we demonstrate how a common neural architecture enables a population-level code for behaviorally relevant stimuli.

Information filtering by synchronous spikes in a neural population

Information about time-dependent sensory stimuli is encoded by the spike trains of neurons. Here we consider a population of uncoupled but noisy neurons (each subject to some intrinsic noise) that are driven by a common broadband signal. We ask specifically how much information is encoded in the synchronous activity of the population and how this information transfer is distributed with respect to frequency bands. In order to obtain some insight into the mechanism of information filtering effects found previously in the literature, we develop a mathematical framework to calculate the coherence of the synchronous output with the common stimulus for populations of simple neuron models. Within this frame, the synchronous activity is treated as the product of filtered versions of the spike trains of a subset of neurons. We compare our results for the simple cases of (1) a Poisson neuron with a rate modulation and (2) an LIF neuron with intrinsic white current noise and a current stimulus. For the Poisson neuron, formulas are particularly simple but show only a low-pass behavior of the coherence of synchronous activity. For the LIF model, in contrast, the coherence function of the synchronous activity shows a clear peak at high frequencies, comparable to recent experimental findings. We uncover the mechanism for this shift in the maximum of the coherence and discuss some biological implications of our findings.

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.

Temporal precision and reliability in the velocity regime of a hair-cell sensory system: the mechanosensory lateral line of goldfish, Carassius auratus

Fish and aquatic frogs detect minute water motion by means of a specialized mechanosensory system, the lateral line. Ubiquitous in fish, the lateral-line system is characterized by hair-cell based sensory structures across the fish's surface called neuromasts. These neuromasts occur free-standing on the skin as superficial neuromasts (SN) or are recessed into canals as canal neuromasts. SNs respond to rapid changes of water velocity in a small layer of fluid around the fish, including the so-called boundary layer. Although omnipresent, the boundary layer's impact on the SN response is still a matter of debate. For the first time using an information-theoretic approach to this sensory system, we have investigated the SN afferents encoding capabilities. Combining covariance analysis, phase analysis, and modeling of recorded neuronal responses of primary lateral line afferents, we show that encoding by the SNs is adequately described as a linear, velocity-responsive mechanism. Afferent responses display a bimodal distribution of opposite Wiener kernels that likely reflected the two hair-cell populations within a given neuromast. Using frozen noise stimuli, we further demonstrate that SN afferents respond in an extremely precise manner and with high reproducibility across a broad frequency band (10-150 Hz), revealing that an optimal decoder would need to rely extensively on a temporal code. This was further substantiated by means of signal reconstruction of spike trains that were time shifted with respect to their original. On average, a time shift of 3.5 ms was enough to diminish the encoding capabilities of primary afferents by 70%. Our results further demonstrate that the SNs' encoding capability is linearly related to the stimulus outside the boundary layer, and that the boundary layer can, therefore, be neglected while interpreting lateral line response of SN afferents to hydrodynamic stimuli.

Sensory coding in oscillatory electroreceptors of paddlefish

Coherence and information theoretic analyses were applied to quantitate the response properties and the encoding of time-varying stimuli in paddlefish electroreceptors (ERs), studied in vivo. External electrical stimuli were Gaussian noise waveforms of varied frequency band and strength, including naturalistic waveforms derived from zooplankton prey. Our coherence analyses elucidated the role of internal oscillations and transduction processes in shaping the 0.5-20 Hz best frequency tuning of these electroreceptors, to match the electrical signals emitted by zooplankton prey. Stimulus-response coherence fell off above approximately 20 Hz, apparently due to intrinsic limits of transduction, but was detectable up to 40-50 Hz. Aligned with this upper fall off was a narrow band of intense internal noise at ∼25 Hz, due to prominent membrane potential oscillations in cells of sensory epithelia, which caused a narrow deadband of external insensitivity. Using coherence analysis, we showed that more than 76% of naturalistic stimuli of weak strength, ∼1 μV∕cm, was linearly encoded into an afferent spike train, which transmitted information at a rate of ∼30 bits∕s. Stimulus transfer to afferent spike timing became essentially nonlinear as the stimulus strength was increased to induce bursting firing. Strong stimuli, as from nearby zooplankton prey, acted to synchronize the bursting responses of afferents, including across populations of electroreceptors, providing a plausible mechanism for reliable information transfer to higher-order neurons through noisy synapses.

Identifying temporal codes in spontaneously active sensory neurons

The manner in which information is encoded in neural signals is a major issue in Neuroscience. A common distinction is between rate codes, where information in neural responses is encoded as the number of spikes within a specified time frame (encoding window), and temporal codes, where the position of spikes within the encoding window carries some or all of the information about the stimulus. One test for the existence of a temporal code in neural responses is to add artificial time jitter to each spike in the response, and then assess whether or not information in the response has been degraded. If so, temporal encoding might be inferred, on the assumption that the jitter is small enough to alter the position, but not the number, of spikes within the encoding window. Here, the effects of artificial jitter on various spike train and information metrics were derived analytically, and this theory was validated using data from afferent neurons of the turtle vestibular and paddlefish electrosensory systems, and from model neurons. We demonstrate that the jitter procedure will degrade information content even when coding is known to be entirely by rate. For this and additional reasons, we conclude that the jitter procedure by itself is not sufficient to establish the presence of a temporal code.

Information analysis of posterior canal afferents in the turtle, Trachemys scripta elegans

We have used sinusoidal and band-limited Gaussian noise stimuli along with information measures to characterize the linear and non-linear responses of morpho-physiologically identified posterior canal (PC) afferents and to examine the relationship between mutual information rate and other physiological parameters. Our major findings are: 1) spike generation in most PC afferents is effectively a stochastic renewal process, and spontaneous discharges are fully characterized by their first order statistics; 2) a regular discharge, as measured by normalized coefficient of variation (cv*), reduces intrinsic noise in afferent discharges at frequencies below the mean firing rate; 3) coherence and mutual information rates, calculated from responses to band-limited Gaussian noise, are jointly determined by gain and intrinsic noise (discharge regularity), the two major determinants of signal to noise ratio in the afferent response; 4) measures of optimal non-linear encoding were only moderately greater than optimal linear encoding, indicating that linear stimulus encoding is limited primarily by internal noise rather than by non-linearities; and 5) a leaky integrate and fire model reproduces these results and supports the suggestion that the combination of high discharge regularity and high discharge rates serves to extend the linear encoding range of afferents to higher frequencies. These results provide a framework for future assessments of afferent encoding of signals generated during natural head movements and for comparison with coding strategies used by other sensory systems. This article is part of a Special Issue entitled: Neural Coding.

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.

Brain-generated estradiol drives long-term optimization of auditory coding to enhance the discrimination of communication signals

Auditory processing and hearing-related pathologies are heavily influenced by steroid hormones in a variety of vertebrate species, including humans. The hormone estradiol has been recently shown to directly modulate the gain of central auditory neurons, in real time, by controlling the strength of inhibitory transmission via a nongenomic mechanism. The functional relevance of this modulation, however, remains unknown. Here we show that estradiol generated in the songbird homolog of the mammalian auditory association cortex, rapidly enhances the effectiveness of the neural coding of complex, learned acoustic signals in awake zebra finches. Specifically, estradiol increases mutual information rates, coding efficiency, and the neural discrimination of songs. These effects are mediated by estradiol's modulation of both the rate and temporal coding of auditory signals. Interference with the local action or production of estradiol in the auditory forebrain of freely behaving animals disrupts behavioral responses to songs, but not to other behaviorally relevant communication signals. Our findings directly show that estradiol is a key regulator of auditory function in the adult vertebrate brain.

Temporal encoding in a nervous system

We examined the extent to which temporal encoding may be implemented by single neurons in the cercal sensory system of the house cricket Acheta domesticus. We found that these neurons exhibit a greater-than-expected coding capacity, due in part to an increased precision in brief patterns of action potentials. We developed linear and non-linear models for decoding the activity of these neurons. We found that the stimuli associated with short-interval patterns of spikes (ISIs of 8 ms or less) could be predicted better by second-order models as compared to linear models. Finally, we characterized the difference between these linear and second-order models in a low-dimensional subspace, and showed that modification of the linear models along only a few dimensions improved their predictive power to parity with the second order models. Together these results show that single neurons are capable of using temporal patterns of spikes as fundamental symbols in their neural code, and that they communicate specific stimulus distributions to subsequent neural structures.

The information coding schemes used within nervous systems have been the focus of an entire field within neuroscience. An unresolved issue within the general coding problem is the determination of the neural “symbols” with which information is encoded in neural spike trains, analogous to the determination of the nucleotide sequences used to represent proteins in molecular biology. The goal of our study was to determine if pairs of consecutive action potentials contain more or different information about the stimuli that elicit them than would be predicted from an analysis of individual action potentials. We developed linear and non-linear coding models and used likelihood analysis to address this question for sensory interneurons in the cricket cercal sensory system. Our results show that these neurons' spike trains can be decomposed into sequences of two neural symbols: isolated single spikes and short-interval spike doublets. Given the ubiquitous nature of similar neural activity reported in other systems, we suspect that the implementation of such temporal encoding schemes may be widespread across animal phyla. Knowledge of the basic coding units used by single cells will help in building the large-scale neural network models necessary for understanding how nervous systems function.

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.

Estimating Neuronal Information: Logarithmic Binning of Neuronal Inter-Spike Intervals

Neurons communicate via the relative timing of all-or-none biophysical signals called spikes. For statistical analysis, the time between spikes can be accumulated into inter-spike interval histograms. Information theoretic measures have been estimated from these histograms to assess how information varies across organisms, neural systems, and disease conditions. Because neurons are computational units that, to the extent they process time, work not by discrete clock ticks but by the exponential decays of numerous intrinsic variables, we propose that neuronal information measures scale more naturally with the logarithm of time. For the types of inter-spike interval distributions that best describe neuronal activity, the logarithm of time enables fewer bins to capture the salient features of the distributions. Thus, discretizing the logarithm of inter-spike intervals, as compared to the inter-spike intervals themselves, yields histograms that enable more accurate entropy and information estimates for fewer bins and less data. Additionally, as distribution parameters vary, the entropy and information calculated from the logarithm of the inter-spike intervals are substantially better behaved, e.g., entropy is independent of mean rate, and information is equally affected by rate gains and divisions. Thus, when compiling neuronal data for subsequent information analysis, the logarithm of the inter-spike intervals is preferred, over the untransformed inter-spike intervals, because it yields better information estimates and is likely more similar to the construction used by nature herself.