Neural dynamics of envelope coding

Beat encoding at mistuned octaves within single electrosensory neurons

Beats are slow periodic amplitude modulations resulting from the superposition of two spectrally close periodic signals. The difference frequency between the signals sets the frequency of the beat. A field study in the electric fish Apteronotus rostratus showed the behavioral relevance of very high difference frequencies. Contrary to expectations from previous studies, our electrophysiological data show strong responses of p-type electroreceptor afferents whenever the difference frequency approaches integer multiples (mistuned octaves) of the fish's own electric field frequency (carrier). Mathematical reasoning and simulations show that common approaches to extract amplitude modulations, such as Hilbert transform or half-wave rectification, are not sufficient to explain the responses at carrier octaves. Instead, half-wave rectification needs to be smoothed out, for example by a cubic function. Because electroreceptive afferents share many properties with auditory nerve fibers, these mechanisms may underly the human perception of beats at mistuned octaves as described by Ohm and Helmholtz.

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.

Electrosensory Contrast Signals for Interacting Weakly Electric Fish

Active sensory systems have evolved to properly encode natural stimuli including those created by conspecifics, yet little is known about the properties of such stimuli. We consider the electrosensory signal at the skin of a fixed weakly electric fish in the presence of a swimming conspecific. The dipole recordings are obtained in parallel with video tracking of the position of the animals. This enables the quantification of the relationships between the recording dipole and the positions of the head, midbody and tail of the freely swimming fish. The contrast of the signal at the skin is shown to be well-fitted by a decreasing exponential function of distance. It is thus anti-correlated with distance; it is also correlated with the second envelope (i.e., the envelope of the envelope) of the raw recorded signal. The variance of the contrast signal is highest at short range. However, the coefficient of variation (CV) of this signal increases with distance. We find a range of position and associated contrast patterns under quasi-2D swimming conditions. This is quantified using global measures of the visit times of the free fish within measurable range, with each visit causing a bump in contrast. The durations of these bumps as well as the times between these bumps are well reproduced by a doubly stochastic process formed by a dichotomous (two-state) noise with Poisson statistics multiplying a colored noise [Ornstein-Uhlenbeck (OU) process]. Certain rapid body movements such as bending or turning are seen to produce contrast drops that may be part of cloaking strategies.

Binaural unmasking of the accuracy of envelope-signal representation in rat auditory cortex but not auditory midbrain

Accurate neural representations of acoustic signals under noisy conditions are critical for animals' survival. Detecting signal against background noise can be improved by binaural hearing particularly when an interaural-time-difference (ITD) disparity is introduced between the signal and the noise, a phenomenon known as binaural unmasking. Previous studies have mainly focused on the binaural unmasking effect on response magnitudes, and it is not clear whether binaural unmasking affects the accuracy of central representations of target acoustic signals and the relative contributions of different central auditory structures to this accuracy. Frequency following responses (FFRs), which are sustained phase-locked neural activities, can be used for measuring the accuracy of the representation of signals. Using intracranial recordings of local field potentials, this study aimed to assess whether the binaural unmasking effects include an improvement of the accuracy of neural representations of sound-envelope signals in the rat IC and/or auditory cortex (AC). The results showed that (1) when a narrow-band noise was presented binaurally, the stimulus-response (S-R) coherence of the FFRs to the envelope (FFR_envelope) of the narrow-band noise recorded in the IC was higher than that recorded in the AC. (2) Presenting a broad-band masking noise caused a larger reduction of the S-R coherence for FFR_envelope in the IC than that in the AC. (3) Introducing an ITD disparity between the narrow-band signal noise and the broad-band masking noise did not affect the IC S-R coherence, but enhanced both the AC S-R coherence and the coherence between the IC FFR_envelope and AC FFR_envelope. Thus, although the accuracy of representing envelope signals in the AC is lower than that in the IC, it can be binaurally unmasked, indicating a binaural-unmasking mechanism that is formed during the signal transmission from the IC to the AC.

Neural representation of interaural correlation in human auditory brainstem: Comparisons between temporal-fine structure and envelope

Central processing of interaural correlation (IAC), which depends on the precise representation of acoustic signals from the two ears, is essential for both localization and recognition of auditory objects. A complex soundwave is initially filtered by the peripheral auditory system into multiple narrowband waves, which are further decomposed into two functionally distinctive components: the quickly-varying temporal-fine structure (TFS) and the slowly-varying envelope. In rats, a narrowband noise can evoke auditory-midbrain frequency-following responses (FFRs) that contain both the TFS component (FFR_TFS) and the envelope component (FFR_Env), which represent the TFS and envelope of the narrowband noise, respectively. These two components are different in sensitivity to the interaural time disparity. In human listeners, the present study investigated whether the FFR_TFS and FFR_Env components of brainstem FFRs to a narrowband noise are different in sensitivity to IAC and whether there are potential brainstem mechanisms underlying the integration of the two components. The results showed that although both the amplitude of FFR_TFS and that of FFR_Env were significantly affected by shifts of IAC between 1 and 0, the stimulus-to-response correlation for FFR_TFS, but not that for FFR_Env, was sensitive to the IAC shifts. Moreover, in addition to the correlation between the binaurally evoked FFR_TFS and FFR_Env, the correlation between the IAC-shift-induced change of FFR_TFS and that of FFR_Env was significant. Thus, the TFS information is more precisely represented in the human auditory brainstem than the envelope information, and the correlation between FFR_TFS and FFR_Env for the same narrowband noise suggest a brainstem binding mechanism underlying the perceptual integration of the TFS and envelope signals.

Targeting alpha-band oscillations in a cortical model with amplitude-modulated high-frequency transcranial electric stimulation

Non-invasive brain stimulation to target specific network activity patterns, e.g. transcranial alternating current stimulation (tACS), has become an essential tool to understand the causal role of neuronal oscillations in cognition and behavior. However, conventional sinusoidal tACS limits the ability to record neuronal activity during stimulation and lacks spatial focality. One particularly promising new tACS stimulation paradigm uses amplitude-modulated (AM) high-frequency waveforms (AM-tACS) with a slow signal envelope that may overcome the limitations. Moreover. AM-tACS using high-frequency carrier signals is more tolerable than conventional tACS, e.g. in terms of skin irritation and occurrence of phosphenes, when applied at the same current intensities (e.g. 1-2 mA). Yet, the fundamental mechanism of neuronal target-engagement by AM-tACS waveforms has remained unknown. We used a computational model of cortex to investigate how AM-tACS modulates endogenous oscillations and compared the target engagement mechanism to the case of conventional (unmodulated) low-frequency tACS. Analysis of stimulation amplitude and frequency indicated that cortical oscillations were phase-locked to the envelope of the AM stimulation signal, which thus exhibits the same target engagement mechanism as conventional (unmodulated) low frequency tACS. However, in the computational model substantially higher current intensities were needed for AM-tACS than for low-frequency (unmodulated) tACS waveforms to achieve pronounced phase synchronization. Our analysis of the carrier frequency suggests that there might be a trade-off between the use of high-frequency carriers and the stimulation amplitude required for successful entrainment. Together, our computational simulations support the use of slow-envelope high frequency carrier AM waveforms as a tool for noninvasive modulation of brain oscillations. More empirical data will be needed to identify the optimal stimulation parameters and to evaluate tolerability and safety of both, AM- and conventional tACS.

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.

Auditory midbrain representation of a break in interaural correlation

The auditory peripheral system filters broadband sounds into narrowband waves and decomposes narrowband waves into quickly varying temporal fine structures (TFSs) and slowly varying envelopes. When a noise is presented binaurally (with the interaural correlation being 1), human listeners can detect a transient break in interaural correlation (BIC), which does not alter monaural inputs substantially. The central correlates of BIC are unknown. This study examined whether phase locking-based frequency-following responses (FFRs) of neuron populations in the rat auditory midbrain [inferior colliculus (IC)] to interaurally correlated steady-state narrowband noises are modulated by introduction of a BIC. The results showed that the noise-induced FFR exhibited both a TFS component (FFRTFS) and an envelope component (FFREnv), signaling the center frequency and bandwidth, respectively. Introduction of either a BIC or an interaurally correlated amplitude gap (which had the summated amplitude matched to the BIC) significantly reduced both FFRTFS and FFREnv. However, the BIC-induced FFRTFS reduction and FFREnv reduction were not correlated with the amplitude gap-induced FFRTFS reduction and FFREnv reduction, respectively. Thus, although introduction of a BIC does not affect monaural inputs, it causes a temporary reduction in sustained responses of IC neuron populations to the noise. This BIC-induced FFR reduction is not based on a simple linear summation of noise signals.

Enhanced multiple vibrational resonances by Na+ and K+ dynamics in a neuron model

Some neuronal receptors perceive external input in the form of hybrid periodic signals. The signal detection may be based on the mechanism of vibrational resonance, in which a system's response to the low frequency signal can become optimal by an appropriate choice of the vibration amplitude of HFS. The vibrational resonance effect is investigated in a neuron model in which the intra- and extra-cellular potassium and sodium concentrations are allowed to evolve temporally, depending on ion currents, Na⁺-K⁺ pumps, glial buffering, and ion diffusion. Our results reveal that, compared to the vibrational resonances in the model with constant ion concentrations, the significantly enhanced vibrational multi-resonances can be observed for the single neuron system where the potassium and sodium ion concentrations vary temporally. Thus, in contradiction to a popular view that ion concentrations dynamics play little role in signal detection, we indicate that the neuron's response to an external subthreshold signal can be largely improved by sodium and potassium dynamics.

Perception and coding of envelopes in weakly electric fishes

Natural sensory stimuli have a rich spatiotemporal structure and can often be characterized as a high frequency signal that is independently modulated at lower frequencies. This lower frequency modulation is known as the envelope. Envelopes are commonly found in a variety of sensory signals, such as contrast modulations of visual stimuli and amplitude modulations of auditory stimuli. While psychophysical studies have shown that envelopes can carry information that is essential for perception, how envelope information is processed in the brain is poorly understood. Here we review the behavioral salience and neural mechanisms for the processing of envelopes in the electrosensory system of wave-type gymnotiform weakly electric fishes. These fish can generate envelope signals through movement, interactions of their electric fields in social groups or communication signals. The envelopes that result from the first two behavioral contexts differ in their frequency content, with movement envelopes typically being of lower frequency. Recent behavioral evidence has shown that weakly electric fish respond in robust and stereotypical ways to social envelopes to increase the envelope frequency. Finally, neurophysiological results show how envelopes are processed by peripheral and central electrosensory neurons. Peripheral electrosensory neurons respond to both stimulus and envelope signals. Neurons in the primary hindbrain recipient of these afferents, the electrosensory lateral line lobe (ELL), exhibit heterogeneities in their responses to stimulus and envelope signals. Complete segregation of stimulus and envelope information is achieved in neurons in the target of ELL efferents, the midbrain torus semicircularis (Ts).

Beyond the Jamming Avoidance Response: weakly electric fish respond to the envelope of social electrosensory signals

Recent studies have shown that central nervous system neurons in weakly electric fish respond to artificially constructed electrosensory envelopes, but the behavioral relevance of such stimuli is unclear. Here we investigate the possibility that social context creates envelopes that drive behavior. When Eigenmannia virescens are in groups of three or more, the interactions between their pseudo-sinusoidal electric fields can generate 'social envelopes'. We developed a simple mathematical prediction for how fish might respond to such social envelopes. To test this prediction, we measured the responses of E. virescens to stimuli consisting of two sinusoids, each outside the range of the Jamming Avoidance Response (JAR), that when added to the fish's own electric field produced low-frequency (below 10 Hz) social envelopes. Fish changed their electric organ discharge (EOD) frequency in response to these envelopes, which we have termed the Social Envelope Response (SER). In 99% of trials, the direction of the SER was consistent with the mathematical prediction. The SER was strongest in response to the lowest initial envelope frequency tested (2 Hz) and depended on stimulus amplitude. The SER generally resulted in an increase of the envelope frequency during the course of a trial, suggesting that this behavior may be a mechanism for avoiding low-frequency social envelopes. Importantly, the direction of the SER was not predicted by the superposition of two JAR responses: the SER was insensitive to the amplitude ratio between the sinusoids used to generate the envelope, but was instead predicted by the sign of the difference of difference frequencies.

Closed-loop stabilization of the jamming avoidance response reveals its locally unstable and globally nonlinear dynamics

The jamming avoidance response, or JAR, in the weakly electric fish has been analyzed at all levels of organization, from whole-organism behavior down to specific ion channels. Nevertheless, a parsimonious description of the JAR behavior in terms of a dynamical system model has not been achieved at least in part due to the fact that 'avoidance' behaviors are both intrinsically unstable and nonlinear. We overcame the instability of the JAR in Eigenmannia virescens by closing a feedback loop around the behavioral response of the animal. Specifically, the instantaneous frequency of a jamming stimulus was tied to the fish's own electrogenic frequency by a feedback law. Without feedback, the fish's own frequency diverges from the stimulus frequency, but appropriate feedback stabilizes the behavior. After stabilizing the system, we measured the responses in the fish's instantaneous frequency to various stimuli. A delayed first-order linear system model fit the behavior near the equilibrium. Coherence to white noise stimuli together with quantitative agreement across stimulus types supported this local linear model. Next, we examined the intrinsic nonlinearity of the behavior using clamped-frequency-difference experiments to extend the model beyond the neighborhood of the equilibrium. The resulting nonlinear model is composed of competing motor return and sensory escape terms. The model reproduces responses to step and ramp changes in the difference frequency (dF)and predicts a 'snap-through' bifurcation as a function of dF that we confirmed experimentally.

Coding conspecific identity and motion in the electric sense

Interactions among animals can result in complex sensory signals containing a variety of socially relevant information, including the number, identity, and relative motion of conspecifics. How the spatiotemporal properties of such evolving naturalistic signals are encoded is a key question in sensory neuroscience. Here, we present results from experiments and modeling that address this issue in the context of the electric sense, which combines the spatial aspects of vision and touch, with the temporal aspects of audition. Wave-type electric fish, such as the brown ghost knifefish, Apteronotus leptorhynchus, used in this study, are uniquely identified by the frequency of their electric organ discharge (EOD). Multiple beat frequencies arise from the superposition of the EODs of each fish. We record the natural electrical signals near the skin of a “receiving” fish that are produced by stationary and freely swimming conspecifics. Using spectral analysis, we find that the primary beats, and the secondary beats between them (“beats of beats”), can be greatly influenced by fish swimming; the resulting motion produces low-frequency envelopes that broaden all the beat peaks and reshape the “noise floor”. We assess the consequences of this motion on sensory coding using a model electroreceptor. We show that the primary and secondary beats are encoded in the afferent spike train, but that motion acts to degrade this encoding. We also simulate the response of a realistic population of receptors, and find that it can encode the motion envelope well, primarily due to the receptors with lower firing rates. We discuss the implications of our results for the identification of conspecifics through specific beat frequencies and its possible hindrance by active swimming.

Effectively processing information from a sensory scene is essential for animal survival. Motion in a sensory scene complicates this task by dynamically modifying signal properties. To address this general issue, we focus on weakly electric fish. Each fish produces a weak electrical carrier signal with a characteristic frequency. Electroreceptors on its skin encode the modulations of this carrier caused by nearby objects and other animals, enabling this fish to thrive in its nocturnal environment. Little is known about how swimming movements influence natural electrosensory scenes, specifically in the context of detection and identification of, and communication with conspecifics. Using recordings involving free-swimming fish, we characterize the amplitude modulations of the carrier signal arising from small groups of fish. The differences between individual frequencies (beats) are prominent features of these signals, with the number of beats reflecting the number of neighbours. We also find that the distance and motion of a free-swimming fish are represented in a slow modulation of the beat at the receiving fish. Modeling shows that these stimulus features can be effectively encoded in the activity of the electroreceptors, but that encoding quality of some features can be degraded by motion, suggesting that active swimming could hinder conspecific identification.

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.

Spike train statistics for consonant and dissonant musical accords in a simple auditory sensory model

The phenomena of dissonance and consonance in a simple auditory sensory model composed of three neurons are considered. Two of them, here so-called sensory neurons, are driven by noise and subthreshold periodic signals with different ratio of frequencies, and its outputs plus noise are applied synaptically to a third neuron, so-called interneuron. We present a theoretical analysis with a probabilistic approach to investigate the interspike intervals statistics of the spike train generated by the interneuron. We find that tones with frequency ratios that are considered consonant by musicians produce at the third neuron inter-firing intervals statistics densities that are very distinctive from densities obtained using tones with ratios that are known to be dissonant. In other words, at the output of the interneuron, inharmonious signals give rise to blurry spike trains, while the harmonious signals produce more regular, less noisy, spike trains. Theoretical results are compared with numerical simulations.

Coupling of mesoscopic brain oscillations: recent advances in analytical and theoretical perspectives

Oscillatory brain activities have been traditionally studied in the context of how oscillations at a single frequency recorded from a single area could reveal functional insights. Recent advances in methodology used in signal analysis have revealed that cross-frequency coupling, within or between functional related areas, is more informative in determining the possible roles played by brain oscillations. In this review, we begin by describing the cellular basis of oscillatory field potentials and its theorized as well as demonstrated role in brain function. The recent development of mathematical tools that allow the investigation of cross-frequency and cross-area oscillation coupling will be presented and discussed in the context of recent advances in oscillation research based on animal data. Particularly, some pitfalls and caveats of methods currently available are discussed. Data generated from the application of examined techniques are integrated back into the theoretical framework regarding the functional role of brain oscillations. We suggest that the coupling of oscillatory activities at different frequencies between brain regions is crucial for understanding the brain from a functional ensemble perspective. Effort should be directed to elucidate how cross-frequency and area coupling are modulated and controlled. To achieve this, only the correct application of analytical tools may shed light on the intricacies of information representation, generation, binding, encoding, storage and retrieval in the brain.