Frequency-tuned cerebellar channels and burst-induced LTD lead to the cancellation of redundant sensory inputs

Sensorimotor adaptation to destabilizing dynamics in weakly electric fish

Humans and other animals can readily learn to compensate for changes in the dynamics of movement. Such changes can result from an injury or changes in the weight of carried objects. These changes in dynamics can lead not only to reduced performance but also to dramatic instabilities. We evaluated the impacts of compensatory changes in control policies in relation to stability and robustness in Eigenmannia virescens, a species of weakly electric fish. We discovered that these fish retune their sensorimotor control system in response to experimentally generated destabilizing dynamics. Specifically, we used an augmented reality system to manipulate sensory feedback during an image stabilization task in which a fish maintained its position within a refuge. The augmented reality system measured the fish's movements in real time. These movements were passed through a high-pass filter and multiplied by a gain factor before being fed back to the refuge motion. We adjusted the gain factor to gradually destabilize the fish's sensorimotor loop. The fish retuned their sensorimotor control system to compensate for the experimentally induced destabilizing dynamics. This retuning was partially maintained when the augmented reality feedback was abruptly removed. The compensatory changes in sensorimotor control improved tracking performance as well as control-theoretic measures of robustness, including reduced sensitivity to disturbances and improved phase margins.

Silences, spikes and bursts: Three-part knot of the neural code

When a neuron breaks silence, it can emit action potentials in a number of patterns. Some responses are so sudden and intense that electrophysiologists felt the need to single them out, labelling action potentials emitted at a particularly high frequency with a metonym - bursts. Is there more to bursts than a figure of speech? After all, sudden bouts of high-frequency firing are expected to occur whenever inputs surge. The burst coding hypothesis advances that the neural code has three syllables: silences, spikes and bursts. We review evidence supporting this ternary code in terms of devoted mechanisms for burst generation, synaptic transmission and synaptic plasticity. We also review the learning and attention theories for which such a triad is beneficial.

A mechanism for differential control of axonal and dendritic spiking underlying learning in a cerebellum-like circuit

In addition to the action potentials used for axonal signaling, many neurons generate dendritic "spikes" associated with synaptic plasticity. However, in order to control both plasticity and signaling, synaptic inputs must be able to differentially modulate the firing of these two spike types. Here, we investigate this issue in the electrosensory lobe (ELL) of weakly electric mormyrid fish, where separate control over axonal and dendritic spikes is essential for the transmission of learned predictive signals from inhibitory interneurons to the output stage of the circuit. Through a combination of experimental and modeling studies, we uncover a novel mechanism by which sensory input selectively modulates the rate of dendritic spiking by adjusting the amplitude of backpropagating axonal action potentials. Interestingly, this mechanism does not require spatially segregated synaptic inputs or dendritic compartmentalization but relies instead on an electrotonically distant spike initiation site in the axon-a common biophysical feature of neurons.

The voltage and spiking responses of subthreshold resonant neurons to structured and fluctuating inputs: persistence and loss of resonance and variability

We systematically investigate the response of neurons to oscillatory currents and synaptic-like inputs and we extend our investigation to non-structured synaptic-like spiking inputs with more realistic distributions of presynaptic spike times. We use two types of chirp-like inputs consisting of (i) a sequence of cycles with discretely increasing frequencies over time, and (ii) a sequence having the same cycles arranged in an arbitrary order. We develop and use a number of frequency-dependent voltage response metrics to capture the different aspects of the voltage response, including the standard impedance (Z) and the peak-to-trough amplitude envelope ([Formula: see text]) profiles. We show that Z-resonant cells (cells that exhibit subthreshold resonance in response to sinusoidal inputs) also show [Formula: see text]-resonance in response to sinusoidal inputs, but generally do not (or do it very mildly) in response to square-wave and synaptic-like inputs. In the latter cases the resonant response using Z is not predictive of the preferred frequencies at which the neurons spike when the input amplitude is increased above subthreshold levels. We also show that responses to conductance-based synaptic-like inputs are attenuated as compared to the response to current-based synaptic-like inputs, thus providing an explanation to previous experimental results. These response patterns were strongly dependent on the intrinsic properties of the participating neurons, in particular whether the unperturbed Z-resonant cells had a stable node or a focus. In addition, we show that variability emerges in response to chirp-like inputs with arbitrarily ordered patterns where all signals (trials) in a given protocol have the same frequency content and the only source of uncertainty is the subset of all possible permutations of cycles chosen for a given protocol. This variability is the result of the multiple different ways in which the autonomous transient dynamics is activated across cycles in each signal (different cycle orderings) and across trials. We extend our results to include high-rate Poisson distributed current- and conductance-based synaptic inputs and compare them with similar results using additive Gaussian white noise. We show that the responses to both Poisson-distributed synaptic inputs are attenuated with respect to the responses to Gaussian white noise. For cells that exhibit oscillatory responses to Gaussian white noise (band-pass filters), the response to conductance-based synaptic inputs are low-pass filters, while the response to current-based synaptic inputs may remain band-pass filters, consistent with experimental findings. Our results shed light on the mechanisms of communication of oscillatory activity among neurons in a network via subthreshold oscillations and resonance and the generation of network resonance.

Complexity Collapse, Fluctuating Synchrony, and Transient Chaos in Neural Networks With Delay Clusters

Neural circuits operate with delays over a range of time scales, from a few milliseconds in recurrent local circuitry to tens of milliseconds or more for communication between populations. Modeling usually incorporates single fixed delays, meant to represent the mean conduction delay between neurons making up the circuit. We explore conditions under which the inclusion of more delays in a high-dimensional chaotic neural network leads to a reduction in dynamical complexity, a phenomenon recently described as multi-delay complexity collapse (CC) in delay-differential equations with one to three variables. We consider a recurrent local network of 80% excitatory and 20% inhibitory rate model neurons with 10% connection probability. An increase in the width of the distribution of local delays, even to unrealistically large values, does not cause CC, nor does adding more local delays. Interestingly, multiple small local delays can cause CC provided there is a moderate global delayed inhibitory feedback and random initial conditions. CC then occurs through the settling of transient chaos onto a limit cycle. In this regime, there is a form of noise-induced order in which the mean activity variance decreases as the noise increases and disrupts the synchrony. Another novel form of CC is seen where global delayed feedback causes “dropouts,” i.e., epochs of low firing rate network synchrony. Their alternation with epochs of higher firing rate asynchrony closely follows Poisson statistics. Such dropouts are promoted by larger global feedback strength and delay. Finally, periodic driving of the chaotic regime with global feedback can cause CC; the extinction of chaos can outlast the forcing, sometimes permanently. Our results suggest a wealth of phenomena that remain to be discovered in networks with clusters of delays.

Vibrational resonance in a neuron-astrocyte coupled model

Recent findings have revealed that not only neurons but also astrocytes, a special type of glial cells, are major players of neuronal information processing. It is now widely accepted that they contribute to the regulation of their microenvironment by cross-talking with neurons via gliotransmitters. In this context, we here study the phenomenon of vibrational resonance in neurons by considering their interaction with astrocytes. Our analysis of a neuron-astrocyte pair reveals that intracellular dynamics of astrocytes can induce a double vibrational resonance effect in the weak signal detection performance of a neuron, exhibiting two distinct wells centred at different high-frequency driving amplitudes. We also identify the underlying mechanism of this behaviour, showing that the interaction of widely separated time scales of neurons, astrocytes and driving signals is the key factor for the emergence and control of double vibrational resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Burst-dependent synaptic plasticity can coordinate learning in hierarchical circuits

Synaptic plasticity is believed to be a key physiological mechanism for learning. It is well established that it depends on pre- and postsynaptic activity. However, models that rely solely on pre- and postsynaptic activity for synaptic changes have, so far, not been able to account for learning complex tasks that demand credit assignment in hierarchical networks. Here we show that if synaptic plasticity is regulated by high-frequency bursts of spikes, then pyramidal neurons higher in a hierarchical circuit can coordinate the plasticity of lower-level connections. Using simulations and mathematical analyses, we demonstrate that, when paired with short-term synaptic dynamics, regenerative activity in the apical dendrites and synaptic plasticity in feedback pathways, a burst-dependent learning rule can solve challenging tasks that require deep network architectures. Our results demonstrate that well-known properties of dendrites, synapses and synaptic plasticity are sufficient to enable sophisticated learning in hierarchical circuits.

Statistical Analysis of Decoding Performances of Diverse Populations of Neurons

A central theme in computational neuroscience is determining the neural correlates of efficient and accurate coding of sensory signals. Diversity, or heterogeneity, of intrinsic neural attributes is known to exist in many brain areas and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. Here we consider this question with data from in vivo recordings of neurons in the electrosensory system of weakly electric fish subject to the same realization of noisy stimuli; we use a generalized linear model (GLM) to assess the accuracy of (Bayesian) decoding of stimulus given a population spiking response. The long recordings enable us to consider many uncoupled networks and a relatively wide range of heterogeneity, as well as many instances of the stimuli, thus enabling us to address this question with statistical power. The GLM decoding is performed on a single long time series of data to mimic realistic conditions rather than using trial-averaged data for better model fits. For a variety of fixed network sizes, we generally find that the optimal levels of heterogeneity are at intermediate values, and this holds in all core components of GLM. These results are robust to several measures of decoding performance, including the absolute value of the error, error weighted by the uncertainty of the estimated stimulus, and the correlation between the actual and estimated stimulus. Although a quadratic fit to decoding performance as a function of heterogeneity is statistically significant, the result is highly variable with low R2 values. Taken together, intermediate levels of neural heterogeneity are indeed a prominent attribute for efficient coding even within a single time series, but the performance is highly variable.

Neural Networks: How a Multi-Layer Network Learns to Disentangle Exogenous from Self-Generated Signals

Artificial multi-layer networks can learn difficult tasks, such as recognizing faces, but their architecture and learning rules appear to be very different from those of biological neural networks. Experimental and computational studies of a two-layered biological neural network have revealed how the learning rules used in artificial neural networks can be efficiently implemented by neurons with complex dynamics and precisely organized connectivity.

Descending pathways mediate adaptive optimized coding of natural stimuli in weakly electric fish

Biological systems must be flexible to environmental changes to survive. This is exemplified by the fact that sensory systems continuously adapt to changes in the environment to optimize coding and behavioral responses. However, the nature of the underlying mechanisms remains poorly understood in general. Here, we investigated the mechanisms mediating adaptive optimized coding of naturalistic stimuli with varying statistics depending on the animal's velocity during movement. We found that central neurons adapted their responses to stimuli with different power spectral densities such as to optimally encode them, thereby ensuring that behavioral responses are, in turn, better matched to the new stimulus statistics. Sensory adaptation further required descending inputs from the forebrain as well as the raphe nuclei. Our findings thus reveal a previously unknown functional role for descending pathways in mediating adaptive optimized coding of natural stimuli that is likely generally applicable across sensory systems and species.

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.

Internally Generated Predictions Enhance Neural and Behavioral Detection of Sensory Stimuli in an Electric Fish

Studies of cerebellum-like circuits in fish have demonstrated that synaptic plasticity shapes the motor corollary discharge responses of granule cells into highly-specific predictions of self-generated sensory input. However, the functional significance of such predictions, known as negative images, has not been directly tested. Here we provide evidence for improvements in neural coding and behavioral detection of prey-like stimuli due to negative images. In addition, we find that manipulating synaptic plasticity leads to specific changes in circuit output that disrupt neural coding and detection of prey-like stimuli. These results link synaptic plasticity, neural coding, and behavior and also provide a circuit-level account of how combining external sensory input with internally generated predictions enhances sensory processing.

Data-driven inference for stationary jump-diffusion processes with application to membrane voltage fluctuations in pyramidal neurons

The emergent activity of biological systems can often be represented as low-dimensional, Langevin-type stochastic differential equations. In certain systems, however, large and abrupt events occur and violate the assumptions of this approach. We address this situation here by providing a novel method that reconstructs a jump-diffusion stochastic process based solely on the statistics of the original data. Our method assumes that these data are stationary, that diffusive noise is additive, and that jumps are Poisson. We use threshold-crossing of the increments to detect jumps in the time series. This is followed by an iterative scheme that compensates for the presence of diffusive fluctuations that are falsely detected as jumps. Our approach is based on probabilistic calculations associated with these fluctuations and on the use of the Fokker-Planck and the differential Chapman-Kolmogorov equations. After some validation cases, we apply this method to recordings of membrane noise in pyramidal neurons of the electrosensory lateral line lobe of weakly electric fish. These recordings display large, jump-like depolarization events that occur at random times, the biophysics of which is unknown. We find that some pyramidal cells increase their jump rate and noise intensity as the membrane potential approaches spike threshold, while their drift function and jump amplitude distribution remain unchanged. As our method is fully data-driven, it provides a valuable means to further investigate the functional role of these jump-like events without relying on unconstrained biophysical models.

Generalization of learned responses in the mormyrid electrosensory lobe

Appropriate generalization of learned responses to new situations is vital for adaptive behavior. We provide a circuit-level account of generalization in the electrosensory lobe (ELL) of weakly electric mormyrid fish. Much is already known in this system about a form of learning in which motor corollary discharge signals cancel responses to the uninformative input evoked by the fish's own electric pulses. However, for this cancellation to be useful under natural circumstances, it must generalize accurately across behavioral regimes, specifically different electric pulse rates. We show that such generalization indeed occurs in ELL neurons, and develop a circuit-level model explaining how this may be achieved. The mechanism involves regularized synaptic plasticity and an approximate matching of the temporal dynamics of motor corollary discharge and electrosensory inputs. Recordings of motor corollary discharge signals in mossy fibers and granule cells provide direct evidence for such matching.

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.

Selective and Context-Dependent Social and Behavioral Effects of Δ9-Tetrahydrocannabinol in Weakly Electric Fish

Cannabinoid (CB) receptors are widespread in the nervous system and influence a variety of behaviors. Weakly electric fish have been a useful model system in the study of the neural basis of behavior, but we know nothing of the role played by the CB system. Here, we determine the overall behavioral effect of a nonselective CB receptor agonist, namely Δ9-tetrahydrocannabinol (THC), in the weakly electric fish Apte-ronotus leptorhynchus. Using various behavioral paradigms involving social stimuli, we show that THC decreases locomotor behavior, as in many species, and influences communication and social behavior. Across the different experiments, we found that the propensity to emit communication signals (chirps) and seek social interactions was affected in a context-dependent manner. We explicitly tested this hypothesis by comparing the behavioral effects of THC injection in fish placed in a novel versus a familiar social and physical environment. THC-injected fish were less likely to chirp than control fish in familiar situations but not in novel ones. The tendency to be in close proximity to other fish was affected only in novel environments, with control fish clustering more than THC-injected ones. By identifying behaviors affected by CB agonists, our study can guide further comparative and neurophysiological studies of the role of the CB system using a weakly electric fish as a model.

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.

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.

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

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

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

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

Short-term synaptic plasticity across topographic maps in the electrosensory system

The early pathways underlying the active electric sense of the weakly electric fish Apteronotus leptorhynchus involve three parallel processing streams. An array of tuberous electroreceptors distributed over the skin provides inputs to the electrosensory lateral line lobe (ELL), forming the basis for three topographic maps: LS (lateral segment), CLS (centrolateral segment), and CMS (centromedial segment). In addition, each map receives topographically preserved inputs from a direct feedback pathway. How this feedback contributes to the distinct spatiotemporal filtering properties of ELL pyramidal neurons across maps is not clear. We used an in vitro approach to characterize short-term plasticity (STP) in the direct feedback synapses onto pyramidal neurons in each map. Our findings indicated that the dynamics of STP varied across maps in a manner that was consistent with the temporal filtering properties of pyramidal neurons in vivo. Using a modeling approach, we found that the STP of direct feedback synapses in CMS was best described by a simple facilitation-depression model. On the other hand, STP in LS was best described by synaptic facilitation with a use-dependent recovery rate. These results suggest that differential regulation of overlapping STP processes in feedback pathways can contribute to the functional specialization of topographic sensory maps.

Weak signal amplification and detection by higher-order sensory neurons

Sensory systems must extract behaviorally relevant information and therefore often exhibit a very high sensitivity. How the nervous system reaches such high sensitivity levels is an outstanding question in neuroscience. Weakly electric fish (Apteronotus leptorhynchus/albifrons) are an excellent model system to address this question because detailed background knowledge is available regarding their behavioral performance and its underlying neuronal substrate. Apteronotus use their electrosense to detect prey objects. Therefore, they must be able to detect electrical signals as low as 1 μV while using a sensory integration time of <200 ms. How these very weak signals are extracted and amplified by the nervous system is not yet understood. We studied the responses of cells in the early sensory processing areas, namely, the electroreceptor afferents (EAs) and pyramidal cells (PCs) of the electrosensory lobe (ELL), the first-order electrosensory processing area. In agreement with previous work we found that EAs cannot encode very weak signals with a spike count code. However, PCs can encode prey mimic signals by their firing rate, revealing a huge signal amplification between EAs and PCs and also suggesting differences in their stimulus encoding properties. Using a simple leaky integrate-and-fire (LIF) model we predict that the target neurons of PCs in the midbrain torus semicircularis (TS) are able to detect very weak signals. In particular, TS neurons could do so by assuming biologically plausible convergence rates as well as very simple decoding strategies such as temporal integration, threshold crossing, and combining the inputs of PCs.

A role for mixed corollary discharge and proprioceptive signals in predicting the sensory consequences of movements

Animals must distinguish behaviorally relevant patterns of sensory stimulation from those that are attributable to their own movements. In principle, this distinction could be made based on internal signals related to motor commands, known as corollary discharge (CD), sensory feedback, or some combination of both. Here we use an advantageous model system--the electrosensory lobe (ELL) of weakly electric mormyrid fish--to directly examine how CD and proprioceptive feedback signals are transformed into negative images of the predictable electrosensory consequences of the fish's motor commands and/or movements. In vivo recordings from ELL neurons and theoretical modeling suggest that negative images are formed via anti-Hebbian plasticity acting on random, nonlinear mixtures of CD and proprioception. In support of this, we find that CD and proprioception are randomly mixed in spinal mossy fibers and that properties of granule cells are consistent with a nonlinear recoding of these signals. The mechanistic account provided here may be relevant to understanding how internal models of movement consequences are implemented in other systems in which similar components (e.g., mixed sensory and motor signals and synaptic plasticity) are found.

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.

Plastic corollary discharge predicts sensory consequences of movements in a cerebellum-like circuit

The capacity to predict the sensory consequences of movements is critical for sensory, motor, and cognitive function. Though it is hypothesized that internal signals related to motor commands, known as corollary discharge, serve to generate such predictions, this process remains poorly understood at the neural circuit level. Here we demonstrate that neurons in the electrosensory lobe (ELL) of weakly electric mormyrid fish generate negative images of the sensory consequences of the fish's own movements based on ascending spinal corollary discharge signals. These results generalize previous findings describing mechanisms for generating negative images of the effects of the fish's specialized electric organ discharge (EOD) and suggest that a cerebellum-like circuit endowed with associative synaptic plasticity acting on corollary discharge can solve the complex and ubiquitous problem of predicting sensory consequences of movements.

Sensory processing and corollary discharge effects in posterior caudal lobe Purkinje cells in a weakly electric mormyrid fish

Although it has been suggested that the cerebellum functions to predict the sensory consequences of motor commands, how such predictions are implemented in cerebellar circuitry remains largely unknown. A detailed and relatively complete account of predictive mechanisms has emerged from studies of cerebellum-like sensory structures in fish, suggesting that comparisons of the cerebellum and cerebellum-like structures may be useful. Here we characterize electrophysiological response properties of Purkinje cells in a region of the cerebellum proper of weakly electric mormyrid fish, the posterior caudal lobe (LCp), which receives the same mossy fiber inputs and projects to the same target structures as the electrosensory lobe (ELL), a well-studied cerebellum-like structure. We describe patterns of simple spike and climbing fiber activation in LCp Purkinje cells in response to motor corollary discharge, electrosensory, and proprioceptive inputs and provide evidence for two functionally distinct Purkinje cell subtypes within LCp. Protocols that induce rapid associative plasticity in ELL fail to induce plasticity in LCp, suggesting differences in the adaptive functions of the two structures. Similarities and differences between LCp and ELL are discussed in light of these results.

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.

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

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

Dendritic SK channels convert NMDA-R-dependent LTD to burst timing-dependent plasticity

Feedback and descending projections from higher to lower brain centers play a prominent role in all vertebrate sensory systems. Feedback might be optimized for the specific sensory processing tasks in their target brain centers, but it has been difficult to connect the properties of feedback synapses to sensory tasks. Here, we use the electrosensory system of a gymnotiform fish ( Apteronotus leptorhynchus) to address this problem. Cerebellar feedback to pyramidal cells in the first central electrosensory processing region, the electrosensory lateral line lobe (ELL), is critical for canceling spatially and temporally redundant electrosensory input. The ELL contains four electrosensory maps, and we have previously analyzed the synaptic and network bases of the redundancy reduction mechanism in a map (centrolateral segment; CLS) believed to guide electrolocation behavior. In the CLS, only long-term depression was induced by pairing feedback presynaptic and pyramidal cell postsynaptic bursts. In this paper, we turn to an ELL map (lateral segment; LS) known to encode electrocommunication signals. We find remarkable differences in synaptic plasticity of the morphologically identical cerebellar feedback input to the LS. In the LS, pyramidal cell SK channels permit long-term potentiation (LTP) of feedback synapses when pre- and postsynaptic bursts occur at the same time. We hypothesize that LTP in this map is required for enhancing the encoding of weak electrocommunication signals. We conclude that feedback inputs that appear morphologically identical in sensory maps dedicated to different tasks, nevertheless display different synaptic plasticity rules contributing to differential sensory processing in these maps.

Normalization of input patterns in an associative network

Numerous brain structures have a cerebellum-like architecture in which inputs diverge onto a large number of granule cells that converge onto principal cells. Plasticity at granule cell-to-principal cell synapses is thought to allow these structures to associate spatially distributed patterns of granule cell activity with appropriate principal cell responses. Storing large sets of associations requires the patterns involved to be normalized, i.e., to have similar total amounts of granule cell activity. Using a general model of associative learning, we describe two ways in which granule cells can be configured to promote normalization. First, we show how heterogeneity in firing thresholds across granule cells can restrict pattern-to-pattern variation in total activity while also limiting spatial overlap between patterns. These effects combine to allow fast and flexible learning. Second, we show that the perceptron learning rule selectively silences those synapses that contribute most to pattern-to-pattern variation in the total input to a principal cell. This provides a simple functional interpretation for the experimental observation that many granule cell-to-Purkinje cell synapses in the cerebellum are silent. Since our model is quite general, these principles may apply to a wide range of associative circuits.

Serotonin selectively enhances perception and sensory neural responses to stimuli generated by same-sex conspecifics

Centrifugal serotonergic fibers innervating sensory brain areas are seen ubiquitously across systems and species but their function remains unclear. Here we examined the functional role of serotonergic innervation onto electrosensory neurons in weakly electric fish by eliciting endogenous release through electrical stimulation as well as exogenous focal application of serotonin in the vicinity of the cell being recorded from. Both approaches showed that the function of serotonergic input onto electrosensory pyramidal neurons is to render them more excitable by reducing the spike afterhyperpolarization amplitude and thereby promoting burst firing. Further, serotonergic input selectively improved neuronal responses to stimuli that occur during interactions between same-sex conspecifics but not to stimuli associated with either prey or that occur during interactions between opposite-sex conspecifics. Finally, we tested whether serotonin-mediated enhanced pyramidal neuron responses to stimuli associated with same-sex conspecifics actually increase perception by the animal. Our behavioral experiments show that exogenous injection and endogenous release of serotonin both increase the magnitude of behavioral responses to stimuli associated with same-sex conspecifics as well as simultaneously decrease aggressive behaviors. Thus, our data indicate that the serotonergic system inhibits aggressive behavior toward same-sex conspecifics, while at the same time increasing perception of stimuli associated with these individuals. This function is likely to be conserved across systems and species.

Learning contrast-invariant cancellation of redundant signals in neural systems

Cancellation of redundant information is a highly desirable feature of sensory systems, since it would potentially lead to a more efficient detection of novel information. However, biologically plausible mechanisms responsible for such selective cancellation, and especially those robust to realistic variations in the intensity of the redundant signals, are mostly unknown. In this work, we study, via in vivo experimental recordings and computational models, the behavior of a cerebellar-like circuit in the weakly electric fish which is known to perform cancellation of redundant stimuli. We experimentally observe contrast invariance in the cancellation of spatially and temporally redundant stimuli in such a system. Our model, which incorporates heterogeneously-delayed feedback, bursting dynamics and burst-induced STDP, is in agreement with our in vivo observations. In addition, the model gives insight on the activity of granule cells and parallel fibers involved in the feedback pathway, and provides a strong prediction on the parallel fiber potentiation time scale. Finally, our model predicts the existence of an optimal learning contrast around 15% contrast levels, which are commonly experienced by interacting fish.

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.

Expression of the cannabinoid CB1 receptor in the gymnotiform fish brain and its implications for the organization of the teleost pallium

Cannabinoid CB1 receptors (CB1R) are widely distributed in the brains of many vertebrates, but whether their functions are conserved is unknown. The weakly electric fish, Apteronotus leptorhynchus (Apt), has been well studied for its brain structure, behavior, sensory processing, and learning and memory. It therefore offers an attractive model for comparative studies of CB1R functions. We sequenced partial AptCB1R mRNAs and performed in situ hybridization to localize its expression. Partial AptCB1R protein sequence was highly conserved to zebrafish (90.7%) and mouse (81.9%) orthologs. AptCB1R mRNA was highly expressed in the telencephalon. Subpallial neurons (dorsal, central, intermediate regions and part of the ventral region, Vd/Vc/Vi, and Vv) expressed high levels of AptCB1R transcript. The central region of dorsocentral telencephalon (DC(core) ) strongly expressed CB1R mRNA; cells in DC(core) project to midbrain regions involved in electrosensory/visual function. The lateral and rostral regions of DC surrounding DC(core) (DC(shell) ) lack AptCB1R mRNA. The rostral division of the dorsomedial telencephalon (DM1) highly expresses AptCB1R mRNA. In dorsolateral division (DL) AptCB1R mRNA was expressed in a gradient that declined in a rostrocaudal manner. In diencephalon, AptCB1R RNA probe weakly stained the central-posterior (CP) and prepacemaker (PPn) nuclei. In mesencephalon, AptCB1R mRNA is expressed in deep layers of the dorsal (electrosensory) torus semicircularis (TSd). In hindbrain, AptCB1R RNA probe weakly labeled inhibitory interneurons in the electrosensory lateral line lobe (ELL). Unlike mammals, only few cerebellar granule cells expressed AptCB1R transcripts and these were located in the center of eminentia granularis pars posterior (EGp), a cerebellar region involved in feedback to ELL.

Modeling cancelation of periodic inputs with burst-STDP and feedback

Prediction and cancelation of redundant information is an important feature that many neural systems must display in order to efficiently code external signals. We develop an analytic framework for such cancelation in sensory neurons produced by a cerebellar-like structure in wave-type electric fish. Our biologically plausible mechanism is motivated by experimental evidence of cancelation of periodic input arising from the proximity of conspecifics as well as tail motion. This mechanism involves elements present in a wide range of systems: (1) stimulus-driven feedback to the neurons acting as detectors, (2) a large variety of temporal delays in the pathways transmitting such feedback, responsible for producing frequency channels, and (3) burst-induced long-term plasticity. The bursting arises from back-propagating action potentials. Bursting events drive the input frequency-dependent learning rule, which in turn affects the feedback input and thus the burst rate. We show how the mean firing rate and the rate of production of 2- and 4-spike bursts (the main learning events) can be estimated analytically for a leaky integrate-and-fire model driven by (slow) sinusoidal, back-propagating and feedback inputs as well as rectified filtered noise. The effect of bursts on the average synaptic strength is also derived. Our results shed light on why bursts rather than single spikes can drive learning in such networks "online", i.e. in the absence of a correlative discharge. Phase locked spiking in frequency specific channels together with a frequency-dependent STDP window size regulate burst probability and duration self-consistently to implement cancelation.

The neuroethology of electrocommunication: how signal background influences sensory encoding and behaviour in Apteronotus leptorhynchus

Weakly-electric fish are a well-established model system for neuroethological studies on communication and aggression. Sensory encoding of their electric communication signals, as well as behavioural responses to these signals, have been investigated in great detail under laboratory conditions. In the wave-type brown ghost knifefish, Apteronotus leptorhynchus, transient increases in the frequency of the generated electric field, called chirps, are particularly well-studied, since they can be readily evoked by stimulating a fish with artificial signals mimicking conspecifics. When two fish interact, both their quasi-sinusoidal electric fields (called electric organ discharge, EOD) superimpose, resulting in a beat, an amplitude modulation at the frequency difference between the two EODs. Although chirps themselves are highly stereotyped signals, the shape of the amplitude modulation resulting from a chirp superimposed on a beat background depends on a number of parameters, such as the beat frequency, modulation depth, and beat phase at which the chirp is emitted. Here we review the influence of these beat parameters on chirp encoding in the three primary stages of the electrosensory pathway: electroreceptor afferents, the hindbrain electrosensory lateral line lobe, and midbrain torus semicircularis. We then examine the role of these parameters, which represent specific features of various social contexts, on the behavioural responses of A. leptorhynchus. Some aspects of the behaviour may be explained by the coding properties of early sensory neurons to chirp stimuli. However, the complexity and diversity of behavioural responses to chirps in the context of different background parameters cannot be explained solely on the basis of the sensory responses and thus suggest that critical roles are played by higher processing stages.

Bursting neurons and ultrasound avoidance in crickets

Decision making in invertebrates often relies on simple neural circuits composed of only a few identified neurons. The relative simplicity of these circuits makes it possible to identify the key computation and neural properties underlying decisions. In this review, we summarize recent research on the neural basis of ultrasound avoidance in crickets, a response that allows escape from echolocating bats. The key neural property shaping behavioral output is high-frequency bursting of an identified interneuron, AN2, which carries information about ultrasound stimuli from receptor neurons to the brain. AN2's spike train consists of clusters of spikes - bursts - that may be interspersed with isolated, non-burst spikes. AN2 firing is necessary and sufficient to trigger avoidance steering but only high-rate firing, such as occurs in bursts, evokes this response. AN2 bursts are therefore at the core of the computation involved in deciding whether or not to steer away from ultrasound. Bursts in AN2 are triggered by synaptic input from nearly synchronous bursts in ultrasound receptors. Thus the population response at the very first stage of sensory processing - the auditory receptor - already differentiates the features of the stimulus that will trigger a behavioral response from those that will not. Adaptation, both intrinsic to AN2 and within ultrasound receptors, scales the burst-generating features according to the stimulus statistics, thus filtering out background noise and ensuring that bursts occur selectively in response to salient peaks in ultrasound intensity. Furthermore AN2's sensitivity to ultrasound varies adaptively with predation pressure, through both developmental and evolutionary mechanisms. We discuss how this key relationship between bursting and the triggering of avoidance behavior is also observed in other invertebrate systems such as the avoidance of looming visual stimuli in locusts or heat avoidance in beetles.

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

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

Preparing for the unpredictable: adaptive feedback enhances the response to unexpected communication signals

To interact with the environment efficiently, the nervous system must generate expectations about redundant sensory signals and detect unexpected ones. Neural circuits can, for example, compare a prediction of the sensory signal that was generated by the nervous system with the incoming sensory input, to generate a response selective to novel stimuli. In the first-order electrosensory neurons of a gymnotiform electric fish, a negative image of low-frequency redundant communication signals is subtracted from the neural response via feedback, allowing unpredictable signals to be extracted. Here we show that the cancelling feedback not only suppresses the predictable signal but also actively enhances the response to the unpredictable communication signal. A transient mismatch between the predictive feedback and incoming sensory input causes both to be positive: the soma is suddenly depolarized by the unpredictable input, whereas the neuron's apical dendrites remain depolarized by the lagging cancelling feedback. The apical dendrites allow the backpropagation of somatic spikes. We show that backpropagation is enhanced when the dendrites are depolarized, causing the unpredictable excitatory input to evoke spike bursts. As a consequence, the feedback driven by a predictable low-frequency signal not only suppresses the response to a redundant stimulus but also induces a bursting response triggered by unpredictable communication signals.

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.