Nonlinear information processing in a model sensory system

Information transmission and detection thresholds in the vestibular nuclei: single neurons vs. population encoding

Understanding how sensory neurons transmit information about relevant stimuli remains a major goal in neuroscience. Of particular relevance are the roles of neural variability and spike timing in neural coding. Peripheral vestibular afferents display differential variability that is correlated with the importance of spike timing; regular afferents display little variability and use a timing code to transmit information about sensory input. Irregular afferents, conversely, display greater variability and instead use a rate code. We studied how central neurons within the vestibular nuclei integrate information from both afferent classes by recording from a group of neurons termed vestibular only (VO) that are known to make contributions to vestibulospinal reflexes and project to higher-order centers. We found that, although individual central neurons had sensitivities that were greater than or equal to those of individual afferents, they transmitted less information. In addition, their velocity detection thresholds were significantly greater than those of individual afferents. This is because VO neurons display greater variability, which is detrimental to information transmission and signal detection. Combining activities from multiple VO neurons increased information transmission. However, the information rates were still much lower than those of equivalent afferent populations. Furthermore, combining responses from multiple VO neurons led to lower velocity detection threshold values approaching those measured from behavior (∼ 2.5 vs. 0.5-1°/s). Our results suggest that the detailed time course of vestibular stimuli encoded by afferents is not transmitted by VO neurons. Instead, they suggest that higher vestibular pathways must integrate information from central vestibular neuron populations to give rise to behaviorally observed detection thresholds.

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

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

Model-Based Decoding, Information Estimation, and Change-Point Detection Techniques for Multineuron Spike Trains

One of the central problems in systems neuroscience is to understand how neural spike trains convey sensory information. Decoding methods, which provide an explicit means for reading out the information contained in neural spike responses, offer a powerful set of tools for studying the neural coding problem. Here we develop several decoding methods based on point-process neural encoding models, or forward models that predict spike responses to stimuli. These models have concave log-likelihood functions, which allow efficient maximum-likelihood model fitting and stimulus decoding. We present several applications of the encoding model framework to the problem of decoding stimulus information from population spike responses: (1) a tractable algorithm for computing the maximum a posteriori (MAP) estimate of the stimulus, the most probable stimulus to have generated an observed single- or multiple-neuron spike train response, given some prior distribution over the stimulus; (2) a gaussian approximation to the posterior stimulus distribution that can be used to quantify the fidelity with which various stimulus features are encoded; (3) an efficient method for estimating the mutual information between the stimulus and the spike trains emitted by a neural population; and (4) a framework for the detection of change-point times (the time at which the stimulus undergoes a change in mean or variance) by marginalizing over the posterior stimulus distribution. We provide several examples illustrating the performance of these estimators with simulated and real neural data.

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.

Coding of Stimuli by Ampullary Afferents in Gnathonemus petersii

Weakly electric fish use electroreception for both active and passive electrolocation and for electrocommunication. While both active and passive electrolocation systems are prominent in weakly electric Mormyriform fishes, knowledge of their passive electrolocation ability is still scarce. To better estimate the contribution of passive electric sensing to the orientation toward electric stimuli in weakly electric fishes, we investigated frequency tuning applying classical input-output characterization and stimulus reconstruction methods to reveal the encoding capabilities of ampullary receptor afferents. Ampullary receptor afferents were most sensitive (threshold: 40 μV/cm) at low frequencies (<10 Hz) and appear to be tuned to a mix of amplitude and slope of the input signals. The low-frequency tuning was corroborated by behavioral experiments, but behavioral thresholds were one order of magnitude higher. The integration of simultaneously recorded afferents of similar frequency-tuning resulted in strongly enhanced signal-to-noise ratios and increased mutual information rates but did not increase the range of frequencies detectable by the system. Theoretically the neuronal integration of input from receptors experiencing opposite polarities of a stimulus (left and right side of the fish) was shown to enhance encoding of such stimuli, including an increase of bandwidth. Covariance and coherence analysis showed that spiking of ampullary afferents is sufficiently explained by the spike-triggered average, i.e., receptors respond to a single linear feature of the stimulus. Our data support the notion of a division of labor of the active and passive electrosensory systems in weakly electric fishes based on frequency tuning. Future experiments will address the role of central convergence of ampullary input that we expect to lead to higher sensitivity and encoding power of the system.

Spontaneous dynamics and response properties of a Hodgkin-Huxley-type neuron model driven by harmonic synaptic noise

We study statistical properties, response dynamics, and information transmission in a Hodgkin-Huxley-type neuron system, modeling peripheral electroreceptors in paddlefish. In addition to sodium and potassium currents, the neuron model includes fast calcium and slow afterhyperpolarization (AHP) potassium currents. The synaptic transmission from sensory epithelium is modeled by a Poission process with a rate modulated by narrow-band noise, mimicking stochastic epithelial oscillations observed experimentally. We study how the interplay of parameters of AHP current and synaptic noise affects the statistics of spontaneous dynamics and response properties of the system. In particular, we confirm predictions made earlier with perfect integrate and fire and phase neuron models that epithelial oscillations enhance stimulus-response coherence and thus information transmission in electroreceptor system. In addition, we consider a strong stimulus regime and show that coherent epithelial oscillations may reduce variability of electroreceptor responses to time-varying stimuli.

Subthreshold membrane conductances enhance directional selectivity in vertebrate sensory neurons

Directional selectivity, in which neurons respond preferentially to one "preferred" direction of movement over the opposite "null" direction, is a critical computation that is found in the central nervous systems of many animals. Such responses are generated using two mechanisms: spatiotemporal convergence via pathways that differ in the timing of information from different locations on the receptor array and the nonlinear integration of this information. Previous studies have showed that various mechanisms may act as nonlinear integrators by suppressing the response in the null direction. Here we show, through a combination of mathematical modeling and in vivo intracellular recordings, that subthreshold membrane conductances can act as a nonlinear integrator by increasing the response in the preferred direction of motion only, thereby enhancing the directional bias. Such subthreshold conductances are ubiquitous in the CNS and therefore may be used in a wide array of computations that involve the enhancement of an existing bias arising from differential spatiotemporal filtering.

Neural heterogeneities and stimulus properties affect burst coding in vivo

Many neurons tend to fire clusters of action potentials called bursts followed by quiescence in response to sensory input. While the mechanisms that underlie burst firing are generally well understood in vitro, the functional role of these bursts in generating behavioral responses to sensory input in vivo are less clear. Pyramidal cells within the electrosensory lateral line lobe (ELL) of weakly electric fish offer an attractive model system for studying the coding properties of burst firing, because the anatomy and physiology of the electrosensory circuitry are well understood, and the burst mechanism of ELL pyramidal cells has been thoroughly characterized in vitro. We investigated the coding properties of bursts generated by these cells in vivo in response to mimics of behaviorally relevant sensory input. We found that heterogeneities within the pyramidal cell population had quantitative but not qualitative effects on burst coding for the low frequency components of broadband time varying input. Moreover, spatially localized stimuli mimicking, for example, prey tended to elicit more bursts than spatially global stimuli mimicking conspecific-related stimuli. We also found small but significant correlations between burst attributes such as the number of spikes per burst or the interspike interval during the burst and stimulus attributes such as stimulus amplitude or slope. These correlations were much weaker in magnitude than those observed in vitro. More surprisingly, our results show that correlations between burst and stimulus attributes actually decreased in magnitude when we used low frequency stimuli that are expected to promote burst firing. We propose that this discrepancy is attributable to differences between ELL pyramidal cell burst firing under in vivo and in vitro conditions.

Effects of restraint and immobilization on electrosensory behaviors of weakly electric fish

Weakly electric fishes have been an important model system in behavioral neuroscience for more than 40 years. These fishes use a specialized electric organ to produce an electric field that is typically below 1 volt/cm and serves in many behaviors including social communication and prey detection. Electrical behaviors are easy to study because inexpensive and widely available tools enable continuous monitoring of the electric field of individual or groups of interacting fish. Weakly electric fish have been routinely used in tightly controlled neurophysiological experiments in which the animal is immobilized using neuromuscular blockers (e.g., curare). Although experiments that involve immobilization are generally discouraged because it eliminates movement-based behavioral signs of pain and distress, many observable electrosensory behaviors in fish persist when the animal is immobilized. Weakly electric fish thus offer a unique opportunity to assess the effects of immobilization on behaviors including those that may reflect pain and distress. We investigated the effects of both immobilization and restraint on a variety of electrosensory behaviors in four species of weakly electric fishes and observed minor effects that were not consistent between the species tested or between particular behaviors. In general, we observed small increases and decreases in response magnitude to particular electrosensory stimuli. Stressful events such as asphyxiation and handling, however, resulted in significant changes in the fishes electrosensory behaviors. Signs of pain and distress include marked reductions in responses to electrosensory stimuli, inconsistent responses, and reductions in or complete cessation of the autogenous electric field.

Noise Shaping in Neural Populations with Global Delayed Feedback

The interplay between intrinsic and network dynamics has been the focus of many investigations. Here we use a combination of theoretical and numerical approaches to study the effects of delayed global feedback on the information transmission properties of neural networks. Specifically, we compare networks of neurons that display intrinsic interspike interval correlations (nonrenewal) to networks that do not (renewal). We find that excitatory and inhibitory delays can tune information transmission by single neurons but not by the entire network. Most surprisingly, addition of a delay can change the dependence of the information on the coupling strength for renewal neurons and not for nonrenewal neurons. Our results show that intrinsic ISI correlations can have nontrivial interactions with network-induced phenomena.

Differences in the time course of short-term depression across receptive fields are correlated with directional selectivity in electrosensory neurons

Directional selectivity, in which neurons respond preferentially to one direction of movement ("preferred") over the opposite direction ("null"), is a critical computation that is found in the nervous systems of many animals. Here we show the first experimental evidence for a correlation between differences in short-term depression and direction-selective responses to moving objects. As predicted by quantitative models, the observed differences in the time courses of short-term depression at different locations within receptive fields were correlated with measures of direction selectivity in awake, behaving weakly electric fish (Apteronotus leptorhynchus). Because short-term depression is ubiquitous in the central nervous systems of vertebrate animals, it may be a common mechanism used for the generation of directional selectivity and other spatiotemporal computations.

SK channels gate information processing in vivo by regulating an intrinsic bursting mechanism seen in vitro

Understanding the mechanistic substrates of neural computations that lead to behavior remains a fundamental problem in neuroscience. In particular, the contributions of intrinsic neural properties such as burst firing and dendritic morphology to the processing of behaviorally relevant sensory input have received much interest recently. Pyramidal cells within the electrosensory lateral line lobe of weakly electric fish display an intrinsic bursting mechanism that relies on somato-dendritic interactions when recorded in vitro: backpropagating somatic action potentials trigger dendritic action potentials that lead to a depolarizing afterpotential (DAP) at the soma. We recorded intracellularly from these neurons in vivo and found firing patterns that were quite different from those seen in vitro: we found no evidence for DAPs as each somatic action potential was followed by a pronounced afterhyperpolarization (AHP). Calcium chelators injected in vivo reduced the AHP, thereby unmasking the DAP and inducing in vitro-like bursting in pyramidal cells. These bursting dynamics significantly reduced the cell's ability to encode the detailed time course of sensory input. We performed additional in vivo pharmacological manipulations and mathematical modeling to show that calcium influx through N-methyl-d-aspartate (NMDA) receptors activate dendritic small conductance (SK) calcium-activated potassium channels, which causes an AHP that counteracts the DAP and leads to early termination of the burst. Our results show that ion channels located in dendrites can have a profound influence on the processing of sensory input by neurons in vivo through the modulation of an intrinsic bursting mechanism.

Noise shaping in neural populations

Many neurons display intrinsic interspike interval correlations in their spike trains. However, the effects of such correlations on information transmission in neural populations are not well understood. We quantified signal processing using linear response theory supported by numerical simulations in networks composed of two different models: One model generates a renewal process where interspike intervals are not correlated while the other generates a nonrenewal process where subsequent interspike intervals are negatively correlated. Our results show that the fractional rate of increase in information rate as a function of network size and stimulus intensity is lower for the nonrenewal model than for the renewal one. We show that this is mostly due to the lower amount of effective noise in the nonrenewal model. We also show the surprising result that coupling has opposite effects in renewal and nonrenewal networks: Excitatory (inhibitory coupling) will decrease (increase) the information rate in renewal networks while inhibitory (excitatory coupling) will decrease (increase) the information rate in nonrenewal networks. We discuss these results and their applicability to other classes of excitable systems.

Postsynaptic receptive field size and spike threshold determine encoding of high-frequency information via sensitivity to synchronous presynaptic activity

Parallel sensory streams carrying distinct information about various stimulus properties have been observed in several sensory systems, including the visual system. What remains unclear is why some of these streams differ in the size of their receptive fields (RFs). In the electrosensory system, neurons with large RFs have short-latency responses and are tuned to high-frequency inputs. Conversely, neurons with small RFs are low-frequency tuned and exhibit longer-latency responses. What principle underlies this organization? We show experimentally that synchronous electroreceptor afferent (P-unit) spike trains selectively encode high-frequency stimulus information from broadband signals. This finding relies on a comparison of stimulus-spike output coherence using output trains obtained by either summing pairs of recorded afferent spike trains or selecting synchronous spike trains based on coincidence within a small time window. We propose a physiologically realistic decoding mechanism, based on postsynaptic RF size and postsynaptic output rate normalization that tunes target pyramidal cells in different electrosensory maps to low- or high-frequency signal components. By driving realistic neuron models with experimentally obtained P-unit spike trains, we show that a small RF is matched with a postsynaptic integration regime leading to responses over a broad range of frequencies, and a large RF with a fluctuation-driven regime that requires synchronous presynaptic input and therefore selectively encodes higher frequencies, confirming recent experimental data. Thus our work reveals that the frequency content of a broadband stimulus extracted by pyramidal cells, from P-unit afferents, depends on the amount of feedforward convergence they receive.

Temporal processing across multiple topographic maps in the electrosensory system

Multiple topographic representations of sensory space are common in the nervous system and presumably allow organisms to separately process particular features of incoming sensory stimuli that vary widely in their attributes. We compared the response properties of sensory neurons within three maps of the body surface that are arranged strictly in parallel to two classes of stimuli that mimic prey and conspecifics, respectively. We used information-theoretic approaches and measures of phase locking to quantify neuronal responses. Our results show that frequency tuning in one of the three maps does not depend on stimulus class. This map acts as a low-pass filter under both conditions. A previously described stimulus-class-dependent switch in frequency tuning is shown to occur in the other two maps. Only a fraction of the information encoded by all neurons could be recovered through a linear decoder. Particularly striking were low-pass neurons the information of which in the high-frequency range could not be decoded linearly. We then explored whether intrinsic cellular mechanisms could partially account for the differences in frequency tuning across maps. Injection of a Ca2+ chelator had no effect in the map with low-pass characteristics. However, injection of the same Ca2+ chelator in the other two maps switched the tuning of neurons from band-pass/high-pass to low-pass. These results show that Ca2+-dependent processes play an important part in determining the functional roles of different sensory maps and thus shed light on the evolution of this important feature of the vertebrate brain.

From stimulus estimation to combination sensitivity: encoding and processing of amplitude and timing information in parallel, convergent sensory pathways

Information theoretical approaches to sensory processing in electric fish have focused on the encoding of amplitude modulations in a single sensory pathway in the South American gymnotiforms. To assess the generality of these studies, we investigated the encoding of amplitude and phase modulations in the distantly related African fish Gymnarchus. In both the amplitude- and time-coding pathways, primary afferents accurately estimated the time course of random modulations whereas hindbrain neurons extracted information about specific stimulus features. Despite exhibiting a clear preference for encoding amplitude or phase, afferents and hindbrain neurons could encode significant amounts of modulation of their nonpreferred attribute. Although no increase in feature extraction performance occurred where the two pathways converge in the midbrain, neurons there were increasingly sensitive to simultaneous modulation of both attributes. A shift from accurate stimulus estimation in the periphery to increasingly sparse representations of specific features appears to be a general strategy in electrosensory processing.

Ionic and neuromodulatory regulation of burst discharge controls frequency tuning

Sensory neurons encode natural stimuli by changes in firing rate or by generating specific firing patterns, such as bursts. Many neural computations rely on the fact that neurons can be tuned to specific stimulus frequencies. It is thus important to understand the mechanisms underlying frequency tuning. In the electrosensory system of the weakly electric fish, Apteronotus leptorhynchus, the primary processing of behaviourally relevant sensory signals occurs in pyramidal neurons of the electrosensory lateral line lobe (ELL). These cells encode low frequency prey stimuli with bursts of spikes and high frequency communication signals with single spikes. We describe here how bursting in pyramidal neurons can be regulated by intrinsic conductances in a cell subtype specific fashion across the sensory maps found within the ELL, thereby regulating their frequency tuning. Further, the neuromodulatory regulation of such conductances within individual cells and the consequences to frequency tuning are highlighted. Such alterations in the tuning of the pyramidal neurons may allow weakly electric fish to preferentially select for certain stimuli under various behaviourally relevant circumstances.

Population coding by electrosensory neurons

Sensory stimuli typically activate many receptors at once and therefore should lead to increases in correlated activity among central neurons. Such correlated activity could be a critical feature in the encoding and decoding of information in central circuits. Here we characterize correlated activity in response to two biologically relevant classes of sensory stimuli in the primary electrosensory nuclei, the electrosensory lateral line lobe, of the weakly electric fish Apteronotus leptorhynchus. Our results show that these neurons can display significant correlations in their baseline activities that depend on the amount of receptive field overlap. A detailed analysis of spike trains revealed that correlated activity resulted predominantly from a tendency to fire synchronous or anti-synchronous bursts of spikes. We also explored how different stimulation protocols affected correlated activity: while prey-like stimuli increased correlated activity, conspecific-like stimuli decreased correlated activity. We also computed the correlations between the variabilities of each neuron to repeated presentations of the same stimulus (noise correlations) and found lower amounts of noise correlation for communication stimuli. Therefore the decrease in correlated activity seen with communication stimuli is caused at least in part by reduced noise correlations. This differential modulation in correlated activity occurred because of changes in burst firing at the individual neuron level. Our results show that different categories of behaviorally relevant input will differentially affect correlated activity. In particular, we show that the number of correlated bursts within a given time window could be used by postsynaptic neurons to distinguish between both stimulus categories.

Threshold fatigue and information transfer

Neurons in vivo must process sensory information in the presence of significant noise. It is thus plausible to assume that neural systems have developed mechanisms to reduce this noise. Theoretical studies have shown that threshold fatigue (i.e. cumulative increases in the threshold during repetitive firing) could lead to noise reduction at certain frequencies bands and thus improved signal transmission as well as noise increases and decreased signal transmission at other frequencies: a phenomenon called noise shaping. There is, however, no experimental evidence that threshold fatigue actually occurs and, if so, that it will actually lead to noise shaping. We analyzed action potential threshold variability in intracellular recordings in vivo from pyramidal neurons in weakly electric fish and found experimental evidence for threshold fatigue: an increase in instantaneous firing rate was on average accompanied by an increase in action potential threshold. We show that, with a minor modification, the standard Hodgkin-Huxley model can reproduce this phenomenon. We next compared the performance of models with and without threshold fatigue. Our results show that threshold fatigue will lead to a more regular spike train as well as robustness to intrinsic noise via noise shaping. We finally show that the increased/reduced noise levels due to threshold fatigue correspond to decreased/increased information transmission at different frequencies.

Information Rate and Spike-Timing Precision of Proprioceptive Afferents

Proprioception in the first two joints of crustacean limbs is mediated by chordotonal organs that utilize spike-mediated information coding and transmission and by nonspiking proprioceptive afferents that use graded transmission at information rates in excess of 2,500 bits/s. Chordotonal organs operate in parallel with the graded receptors, but the information rates of the spiking chordotonal afferents have not been previously determined. Lower-bound estimates of chordotonal afferent information rates were calculated using stimulus reconstruction, which assumes linear encoding of the stimulus. The information rate was also directly estimated from the spike train entropy, which makes no a priori assumptions with respect to the coding scheme used by the system. Lower-bound information rate estimates ranged from 43 to 69 bits/s, whereas the direct estimates ranged from 24 to 278 bits/s. Comparison of both estimates derived from the same data set indicates that a linear decoder could recover an average of 59% of the information from the spike train. Afferent spike timing was found to be extremely precise, with spikes evoked with an average timing jitter of 0.55 ms. Information rate was correlated with the mean jitter and the noise entropy of the spike train could be predicted from the mean firing rate and mean jitter. Direct stimulation of single afferents by current injection into the soma revealed that the average timing jitter was <0.1 ms, indicating that intrinsic membrane properties, spike generation, and mechanotransduction mechanisms are the major sources of timing jitter in this system.

Muscarinic receptors control frequency tuning through the downregulation of an A-type potassium current

The functional role of cholinergic input in the modulation of sensory responses was studied using a combination of in vivo and in vitro electrophysiology supplemented by mathematical modeling. The electrosensory system of weakly electric fish recognizes different environmental stimuli by their unique alteration of a self-generated electric field. Variations in the patterns of stimuli are primarily distinguished based on their frequency. Pyramidal neurons in the electrosensory lateral line lobe (ELL) are often tuned to respond to specific input frequencies. Alterations in the tuning of the pyramidal neurons may allow weakly electric fish to preferentially select for certain stimuli. Here we show that muscarinic receptor activation in vivo enhances the excitability, burst firing, and subsequently the response of pyramidal cells to naturalistic sensory input. Through a combination of in vitro electrophysiology and mathematical modeling, we reveal that this enhanced excitability and bursting likely results from the down-regulation of an A-type potassium current. Further, we provide an explanation of the mechanism by which these currents can mediate frequency tuning.

Limits of linear rate coding of dynamic stimuli by electroreceptor afferents

We estimated the frequency-intensity (f-I) curves of P-unit electroreceptors using 4-Hz random amplitude modulations (RAMs) and using the covariance method (50-Hz RAMs). Both methods showed that P units are linear encoders of stimulus amplitude with additive noise; the gain of the f-I curve was, on average, 0.32 and 2.38 spikesxs(-1)xmicroV(-1) for the low- and high-frequency cutoffs, respectively. There were two sources of apparent noise in the encoding process: the first was the variability of baseline P-unit discharge and the second was the variation of receptor discharge due to variability of the stimulus slope independent of its intensity. The covariance method showed that a linear combination of eigenvectors representing the time-weighted stimulus intensity (E1) and its derivative (E2) could account for, on average, 92% of the total response variability; E1 by itself accounted for 76% of the variability. The low gain of the low-frequency f-I curve implies that detection of small (1 microV) signals would require integration over many receptors ( approximately 1,200) and time (200 ms); even then, signals that elicit behavioral responses could not be detected using rate coding with the estimated gain and noise levels. Weak signals at the limit of behavioral thresholds could be detected if the animal were able to extract E1 from the population of responding P units; we propose a tentative mechanism for this operation although there is no evidence as to whether it is actually implemented in the nervous system of these fish.

Neural variability, detection thresholds, and information transmission in the vestibular system

A fundamental issue in neural coding is the role of spike timing variation in information transmission of sensory stimuli. Vestibular afferents are particularly well suited to study this issue because they are classified as either regular or irregular based on resting discharge variability as well as morphology. Here, we compared the responses of each afferent class to sinusoidal and random head rotations using both information theoretic and gain measures. Information theoretic measures demonstrated that regular afferents transmitted, on average, two times more information than irregular afferents, despite having significantly lower gains. Moreover, consistent with information theoretic measures, regular afferents had angular velocity detection thresholds that were 50% lower than those of irregular afferents (approximately 4 vs 8 degrees/s). Finally, to quantify the information carried by spike times, we added spike-timing jitter to the spike trains of both regular and irregular afferents. Our results showed that this significantly reduced information transmitted by regular afferents whereas it had little effect on irregular afferents. Thus, information is carried in the spike times of regular but not irregular afferents. Using a simple leaky integrate and fire model with a dynamic threshold, we show that differential levels of intrinsic noise can explain differences in the resting discharge, the responses to sensory stimuli, as well as the information carried by action potential timings of each afferent class. Our experimental and modeling results provide new insights as to how neural variability influences the strategy used by two different classes of sensory neurons to encode behaviorally relevant stimuli.