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Spatially nonlinear stimulus integration by retinal ganglion cells lies at the heart of various computations performed by the retina. It arises from the nonlinear transmission of signals that ganglion cells receive from bipolar cells, which thereby constitute functional subunits within a ganglion cell's receptive field. Inferring these subunits from recorded ganglion cell activity promises a new avenue for studying the functional architecture of the retina. This calls for efficient methods, which leave sufficient experimental time to leverage the acquired knowledge for further investigating identified subunits. Here, we combine concepts from super-resolution microscopy and computed tomography and introduce super-resolved tomographic reconstruction (STR) as a technique to efficiently stimulate and locate receptive field subunits. Simulations demonstrate that this approach can reliably identify subunits across a wide range of model variations, and application in recordings of primate parasol ganglion cells validates the experimental feasibility. STR can potentially reveal comprehensive subunit layouts within only a few tens of minutes of recording time, making it ideal for online analysis and closed-loop investigations of receptive field substructure in retina recordings., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Krüppel et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Saccades are a fundamental part of natural vision. They interrupt fixations of the visual gaze and rapidly shift the image that falls onto the retina. These stimulus dynamics can cause activation or suppression of different retinal ganglion cells, but how they affect the encoding of visual information in different types of ganglion cells is largely unknown. Here, we recorded spiking responses to saccade-like shifts of luminance gratings from ganglion cells in isolated marmoset retinas and investigated how the activity depended on the combination of presaccadic and postsaccadic images. All identified cell types, On and Off parasol and midget cells, as well as a type of Large Off cells, displayed distinct response patterns, including particular sensitivity to either the presaccadic or the postsaccadic image or combinations thereof. In addition, Off parasol and Large Off cells, but not On cells, showed pronounced sensitivity to whether the image changed across the transition. Stimulus sensitivity of On cells could be explained based on their responses to step changes in light intensity, whereas Off cells, in particular, parasol and the Large Off cells, seem to be affected by additional interactions that are not triggered during simple light-intensity flashes. Together, our data show that ganglion cells in the primate retina are sensitive to different combinations of presaccadic and postsaccadic visual stimuli. This contributes to the functional diversity of the output signals of the retina and to asymmetries between On and Off pathways and provides evidence of signal processing beyond what is triggered by isolated steps in light intensity. SIGNIFICANCE STATEMENT Sudden eye movements (saccades) shift our direction of gaze, bringing new images in focus on our retinas. To study how retinal neurons deal with these rapid image transitions, we recorded spiking activity from ganglion cells, the output neurons of the retina, in isolated retinas of marmoset monkeys while shifting a projected image in a saccade-like fashion across the retina. We found that the cells do not just respond to the newly fixated image, but that different types of ganglion cells display different sensitivities to the presaccadic and postsaccadic stimulus patterns. Certain Off cells, for example, are sensitive to changes in the image across transitions, which contributes to differences between On and Off information channels and extends the range of encoded stimulus features., (Copyright © 2023 the authors.)

Extracellular vesicles (EVs) are important mediators in intercellular communication. However, understanding the biological origin and functional effects of EVs subtypes has been challenging due to the moderate differences in their physical properties and absence of reliable markers. Here, we characterize the proteomes of ectosomes and exosomes using an improved differential ultracentrifugation protocol and quantitative proteomics. Our analyses revealed singular proteomic profiles for ectosomes and exosomes that enabled us to establish specific protein markers that can be used for their biochemical distinction. Cytoskeleton and glycolytic proteins are distinctively present in ectosomes, while endosomal sorting complexes proteins and tetraspanins are enriched in exosomes. Furthermore, annexin-A2 was identified as a specific marker for ectosomes derived from cell media and human cerebrospinal fluid. Expression of EGFP as a cytosolic reporter leads to its incorporation in EVs and enables their imaging with higher resolution. Assessment of neuronal network activity using multi-electrode array recordings demonstrated that spontaneous neuronal activity can be modulated by EVs. Ectosomes and exosomes internalization in neuronal cells disrupted their regular synchronized bursting activity, resulting in overall lower and more disorganized spiking activity. Our findings suggest that EVs cargoes reflect core intracellular processes, and their functional properties might regulate basic biological and pathological processes. SIGNIFICANCE: This article presents novel approaches for studying the origin, composition, and biological effects in neuronal activity of ectosomes and exosomes. Our findings suggest that EVs cargoes reflect core intracellular processes, and their functional properties might regulate basic biological and pathological processes. Ultimately, our study also forms the foundation for future biomarker studies and for the understanding of the molecular basis of different diseases., Competing Interests: Declaration of Competing Interest The authors report no conflict of interest., (Copyright © 2022 Elsevier B.V. All rights reserved.)

An ultimate goal in retina science is to understand how the neural circuit of the retina processes natural visual scenes. Yet most studies in laboratories have long been performed with simple, artificial visual stimuli such as full-field illumination, spots of light, or gratings. The underlying assumption is that the features of the retina thus identified carry over to the more complex scenario of natural scenes. As the application of corresponding natural settings is becoming more commonplace in experimental investigations, this assumption is being put to the test and opportunities arise to discover processing features that are triggered by specific aspects of natural scenes. Here, we review how natural stimuli have been used to probe, refine, and complement knowledge accumulated under simplified stimuli, and we discuss challenges and opportunities along the way toward a comprehensive understanding of the encoding of natural scenes.

The center-surround receptive field of retinal ganglion cells represents a fundamental concept for how the retina processes and encodes visual information. Yet, traditional approaches of using the receptive field as a linear filter to integrate light intensity over space often do not capture the responses of a ganglion cell to complex visual stimuli. Thus, models with local nonlinearities in subunits of the receptive field or with local temporal dynamics are emerging to better reflect relevant aspects of retinal circuitry and capture stimulus encoding. Here, we review recent efforts to identify such receptive-field substructure and evaluate its role in visual stimulus encoding. The concomitant development of new computational tools may pave the way toward a model-based, functional approach to retinal circuit analysis., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2022 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

A central goal in sensory neuroscience is to understand the neuronal signal processing involved in the encoding of natural stimuli. A critical step towards this goal is the development of successful computational encoding models. For ganglion cells in the vertebrate retina, the development of satisfactory models for responses to natural visual scenes is an ongoing challenge. Standard models typically apply linear integration of visual stimuli over space, yet many ganglion cells are known to show nonlinear spatial integration, in particular when stimulated with contrast-reversing gratings. We here study the influence of spatial nonlinearities in the encoding of natural images by ganglion cells, using multielectrode-array recordings from isolated salamander and mouse retinas. We assess how responses to natural images depend on first- and second-order statistics of spatial patterns inside the receptive field. This leads us to a simple extension of current standard ganglion cell models. We show that taking not only the weighted average of light intensity inside the receptive field into account but also its variance over space can partly account for nonlinear integration and substantially improve response predictions of responses to novel images. For salamander ganglion cells, we find that response predictions for cell classes with large receptive fields profit most from including spatial contrast information. Finally, we demonstrate how this model framework can be used to assess the spatial scale of nonlinear integration. Our results underscore that nonlinear spatial stimulus integration translates to stimulation with natural images. Furthermore, the introduced model framework provides a simple, yet powerful extension of standard models and may serve as a benchmark for the development of more detailed models of the nonlinear structure of receptive fields., Competing Interests: The authors have declared that no competing interests exist.

Background: Various cellular pathways have been implicated in the transfer of disease-related proteins between cells, contributing to disease progression and neurodegeneration. However, the overall effects of protein transfer are still unclear., Objective: Here, we performed a systematic comparison of basic molecular mechanisms involved in the release of alpha-synuclein, Tau, and huntingtin, and evaluated functional effects upon internalization by receiving cells., Methods: Evaluation of protein release to the extracellular space in a free form and in extracellular vesicles using an optimized ultracentrifugation protocol. The extracellular effects of the proteins and extracellular vesicles in primary neuronal cultures were assessed using multi-channel electrophysiological recordings combined with a customized spike sorting framework., Results: We demonstrate cells differentially release free-forms of each protein to the extracellular space. Importantly, neuronal activity is distinctly modulated upon protein internalization in primary cortical cultures. In addition, these disease-related proteins also occur in extracellular vesicles, and are enriched in ectosomes. Internalization of ectosomes and exosomes by primary microglial or astrocytic cells elicits the production of pro-inflammatory cytokines, and modifies spontaneous electrical activity in neurons., Objective: Overall, our study demonstrates that released proteins can have detrimental effects for surrounding cells, and suggests protein release pathways may be exploited as therapeutic targets in different neurodegenerative diseases.

The retina dissects the visual scene into parallel information channels, which extract specific visual features through nonlinear processing. The first nonlinear stage is typically considered to occur at the output of bipolar cells, resulting from nonlinear transmitter release from synaptic terminals. In contrast, we show here that bipolar cells themselves can act as nonlinear processing elements at the level of their somatic membrane potential. Intracellular recordings from bipolar cells in the salamander retina revealed frequent nonlinear integration of visual signals within bipolar cell receptive field centers, affecting the encoding of artificial and natural stimuli. These nonlinearities provide sensitivity to spatial structure below the scale of bipolar cell receptive fields in both bipolar and downstream ganglion cells and appear to arise at the excitatory input into bipolar cells. Thus, our data suggest that nonlinear signal pooling starts earlier than previously thought: that is, at the input stage of bipolar cells., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2021 The Author(s). Published by Elsevier Inc. All rights reserved.)

How neurons encode natural stimuli is a fundamental question for sensory neuroscience. In the early visual system, standard encoding models assume that neurons linearly filter incoming stimuli through their receptive fields, but artificial stimuli, such as contrast-reversing gratings, often reveal nonlinear spatial processing. We investigated to what extent such nonlinear processing is relevant for the encoding of natural images in retinal ganglion cells in mice of either sex. We found that standard linear receptive field models yielded good predictions of responses to flashed natural images for a subset of cells but failed to capture the spiking activity for many others. Cells with poor model performance displayed pronounced sensitivity to fine spatial contrast and local signal rectification as the dominant nonlinearity. By contrast, sensitivity to high-frequency contrast-reversing gratings, a classical test for nonlinear spatial integration, was not a good predictor of model performance and thus did not capture the variability of nonlinear spatial integration under natural images. In addition, we also observed a class of nonlinear ganglion cells with inverse tuning for spatial contrast, responding more strongly to spatially homogeneous than to spatially structured stimuli. These findings highlight the diversity of receptive field nonlinearities as a crucial component for understanding early sensory encoding in the context of natural stimuli. SIGNIFICANCE STATEMENT Experiments with artificial visual stimuli have revealed that many types of retinal ganglion cells pool spatial input signals nonlinearly. However, it is still unclear how relevant this nonlinear spatial integration is when the input signals are natural images. Here we analyze retinal responses to natural scenes in large populations of mouse ganglion cells. We show that nonlinear spatial integration strongly influences responses to natural images for some ganglion cells, but not for others. Cells with nonlinear spatial integration were sensitive to spatial structure inside their receptive fields, and a small group of cells displayed a surprising sensitivity to spatially homogeneous stimuli. Traditional analyses with contrast-reversing gratings did not predict this variability of nonlinear spatial integration under natural images., (Copyright © 2021 Karamanlis and Gollisch.)

The computations performed by a neural circuit depend on how it integrates its input signals into an output of its own. In the retina, ganglion cells integrate visual information over time, space, and chromatic channels. Unlike the former two, chromatic integration is largely unexplored. Analogous to classical studies of spatial integration, we here study chromatic integration in mouse retina by identifying chromatic stimuli for which activation from the green or UV color channel is maximally balanced by deactivation through the other color channel. This reveals nonlinear chromatic integration in subsets of On, Off, and On-Off ganglion cells. Unlike the latter two, nonlinear On cells display response suppression rather than activation under balanced chromatic stimulation. Furthermore, nonlinear chromatic integration occurs independently of nonlinear spatial integration, depends on contributions from the rod pathway and on surround inhibition, and may provide information about chromatic boundaries, such as the skyline in natural scenes.

Salamanders have been habitual residents of research laboratories for more than a century, and their history in science is tightly interwoven with vision research. Nevertheless, many vision scientists - even those working with salamanders - may be unaware of how much our knowledge about vision, and particularly the retina, has been shaped by studying salamanders. In this review, we take a tour through the salamander history in vision science, highlighting the main contributions of salamanders to our understanding of the vertebrate retina. We further point out specificities of the salamander visual system and discuss the perspectives of this animal system for future vision research., (Copyright © 2020 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Neurons in sensory systems are often tuned to particular stimulus features. During complex naturalistic stimulation, however, multiple features may simultaneously affect neuronal responses, which complicates the readout of individual features. To investigate feature representation under complex stimulation, we studied how direction-selective ganglion cells in salamander retina respond to texture motion where direction, velocity, and spatial pattern inside the receptive field continuously change. We found that the cells preserve their direction preference under this stimulation, yet their direction encoding becomes ambiguous due to simultaneous activation by luminance changes. The ambiguities can be resolved by considering populations of direction-selective cells with different preferred directions. This gives rise to synergistic motion decoding, yielding more information from the population than the summed information from single-cell responses. Strong positive response correlations between cells with different preferred directions amplify this synergy. Our results show how correlated population activity can enhance feature extraction in complex visual scenes., (Copyright © 2019 The Authors. Published by Elsevier Inc. All rights reserved.)

The processing capabilities of biological vision systems are still vastly superior to artificial vision, even though this has been an active area of research for over half a century. Current artificial vision techniques integrate many insights from biology yet they remain far-off the capabilities of animals and humans in terms of speed, power, and performance. A key aspect to modeling the human visual system is the ability to accurately model the behavior and computation within the retina. In particular, we focus on modeling the retinal ganglion cells (RGCs) as they convey the accumulated data of real world images as action potentials onto the visual cortex via the optic nerve. Computational models that approximate the processing that occurs within RGCs can be derived by quantitatively fitting the sets of physiological data using an input-output analysis where the input is a known stimulus and the output is neuronal recordings. Currently, these input-output responses are modeled using computational combinations of linear and nonlinear models that are generally complex and lack any relevance to the underlying biophysics. In this paper, we illustrate how system identification techniques, which take inspiration from biological systems, can accurately model retinal ganglion cell behavior, and are a viable alternative to traditional linear-nonlinear approaches.

Relay neurons in the dorsal lateral geniculate nucleus (dLGN) receive excitatory inputs from retinal ganglion cells (RGCs). Retinogeniculate synapses are characterized by a prominent short-term depression of AMPA receptor (AMPAR)-mediated currents, but the underlying mechanisms and its function for visual integration are not known. Here we identify CKAMP44 as a crucial auxiliary subunit of AMPARs in dLGN relay neurons, where it increases AMPAR-mediated current amplitudes and modulates gating of AMPARs. Importantly, CKAMP44 is responsible for the distinctive short-term depression in retinogeniculate synapses by reducing the rate of recovery from desensitization of AMPARs. Genetic deletion of CKAMP44 strongly reduces synaptic short-term depression, which leads to increased spike probability of relay neurons when activated with high-frequency inputs from retinogeniculate synapses. Finally, in vivo recordings reveal augmented ON- and OFF-responses of dLGN neurons in CKAMP44 knockout (CKAMP44 -/- ) mice, demonstrating the importance of CKAMP44 for modulating synaptic short-term depression and visual input integration.

Retinal ganglion cells adapt to changes in visual contrast by adjusting their response kinetics and sensitivity. While much work has focused on the time scales of these adaptation processes, less is known about the spatial scale of contrast adaptation. For example, do small, localized contrast changes affect a cell's signal processing across its entire receptive field? Previous investigations have provided conflicting evidence, suggesting that contrast adaptation occurs either locally within subregions of a ganglion cell's receptive field or globally over the receptive field in its entirety. Here, we investigated the spatial extent of contrast adaptation in ganglion cells of the isolated mouse retina through multielectrode-array recordings. We applied visual stimuli so that ganglion cell receptive fields contained regions where the average contrast level changed periodically as well as regions with constant average contrast level. This allowed us to analyze temporal stimulus integration and sensitivity separately for stimulus regions with and without contrast changes. We found that the spatial scope of contrast adaptation depends strongly on cell identity, with some ganglion cells displaying clear local adaptation, whereas others, in particular large transient ganglion cells, adapted globally to contrast changes. Thus, the spatial scope of contrast adaptation in mouse retinal ganglion cells appears to be cell-type specific. This could reflect differences in mechanisms of contrast adaptation and may contribute to the functional diversity of different ganglion cell types. NEW & NOTEWORTHY Understanding whether adaptation of a neuron in a sensory system can occur locally inside the receptive field or whether it always globally affects the entire receptive field is important for understanding how the neuron processes complex sensory stimuli. For mouse retinal ganglion cells, we here show that both local and global contrast adaptation exist and that this diversity in spatial scope can contribute to the functional diversity of retinal ganglion cell types., (Copyright © 2017 the American Physiological Society.)

Purpose: Phosphene perception is a characteristic side effect of heart rate-reducing medication that acts on hyperpolarization-activated cyclic nucleotide-gated (HCN) ion channels. It is hypothesized that these phosphenes are caused by blocking HCN channels in photoreceptors and neurons of the retina, yet the underlying changes in visual signal processing in the retina caused by the HCN channel block are still unknown., Methods: We examined the effects of pharmacologic HCN channel block on the encoding of visual signals in retinal ganglion cells by recording ganglion cell spiking activity from isolated mouse retinas mounted on multielectrode arrays. Spontaneous activity and responses to various visual stimuli were measured before, during, and after administration of 3 μM ivabradine., Results: Retinal ganglion cells generally showed slower response kinetics and reduced sensitivity to high temporal frequencies under ivabradine. Moreover, ivabradine differentially affected the sensitivity of On and Off ganglion cells. On cells showed reduced response gain, whereas Off cells experienced an increase in response threshold. In line with these differential effects, Off cells, in contrast to On cells, also showed reduced baseline activity during visual stimulation and reduced spontaneous activity. Furthermore, Off cells, but not On cells, showed increased burst-like spiking activity in the presence of ivabradine., Conclusions: Our data suggest that pharmacologic HCN channel block in the retina leads to a shift in the relative activity of the On and Off pathways of the retina. We hypothesize that this imbalance may underlie the medication-induced perception of phosphenes.

Neurons in sensory systems often pool inputs over arrays of presynaptic cells, giving rise to functional subunits inside a neuron's receptive field. The organization of these subunits provides a signature of the neuron's presynaptic functional connectivity and determines how the neuron integrates sensory stimuli. Here we introduce the method of spike-triggered non-negative matrix factorization for detecting the layout of subunits within a neuron's receptive field. The method only requires the neuron's spiking responses under finely structured sensory stimulation and is therefore applicable to large populations of simultaneously recorded neurons. Applied to recordings from ganglion cells in the salamander retina, the method retrieves the receptive fields of presynaptic bipolar cells, as verified by simultaneous bipolar and ganglion cell recordings. The identified subunit layouts allow improved predictions of ganglion cell responses to natural stimuli and reveal shared bipolar cell input into distinct types of ganglion cells.How a neuron integrates sensory information requires knowledge about its functional presynaptic connections. Here the authors report a new method using non-negative matrix factorization to identify the layout of presynaptic bipolar cell inputs onto retinal ganglion cells and predict their responses to natural stimuli.

The postsynaptic adhesion proteins Neuroligins (NLs) are essential for proper synapse function, and their alterations are associated with a variety of neurodevelopmental disorders. It is increasingly clear that each NL isoform occupies specific subsets of synapses and is able to regulate the function of discrete networks. Studies of NL2 and NL4 in the retina in particular have contributed towards uncovering their role in inhibitory synapse function. In this study we show that NL3 is also predominantly expressed at inhibitory postsynapses in the retinal inner plexiform layer (IPL), where it colocalizes with both GABAA- and glycinergic receptor clusters in a 3:2 ratio. In the NL3 deletion-mutant (knockout or KO) mouse, we uncovered a dramatic reduction of the number of GABAAα2-subunit containing GABAA receptor clusters at the IPL. Retinal activity was thereafter assessed in KO and wild-type (WT) littermates by multi-electrode-array recordings of the output cells of retina, the retinal ganglion cells (RGCs). RGCs in the NL3 KO showed reduced spontaneous activity and an altered response to white noise stimulation. Moreover, upon application of light flashes, the proportion of cells firing at light offset (OFF RGCs) was significantly lower in the NL3 KO compared to WT littermates, whereas the relative number of cells firing at light onset (ON RGCs) increased. Interestingly, although GABAAα2-bearing receptors have been related to direction-selective circuits of the retina, features of direction selective-retinal ganglion cells recorded remained unperturbed in the NL3 KO. Together our data underscore the importance of NL3 for the integrity of specific GABAAergic retinal circuits and identifies NL3 as an important regulator of retinal activity.

Standard models of stimulus encoding in the retina postulate that image presentations activate neurons according to the increase of preferred contrast inside the receptive field. During natural vision, however, images do not arrive in isolation, but follow each other rapidly, separated by sudden gaze shifts. We here report that, contrary to standard models, specific ganglion cells in mouse retina are suppressed after a rapid image transition by changes in visual patterns across the transition, but respond with a distinct spike burst when the same pattern reappears. This sensitivity to image recurrence depends on opposing effects of glycinergic and GABAergic inhibition and can be explained by a circuit of local serial inhibition. Rapid image transitions thus trigger a mode of operation that differs from the processing of simpler stimuli and allows the retina to tag particular image parts or to detect transition types that lead to recurring stimulus patterns.

Advances in technology are opening new windows on the structural connectivity and functional dynamics of brain circuits. Quantitative frameworks are needed that integrate these data from anatomy and physiology. Here, we present a modeling approach that creates such a link. The goal is to infer the structure of a neural circuit from sparse neural recordings, using partial knowledge of its anatomy as a regularizing constraint. We recorded visual responses from the output neurons of the retina, the ganglion cells. We then generated a systematic sequence of circuit models that represents retinal neurons and connections and fitted them to the experimental data. The optimal models faithfully recapitulated the ganglion cell outputs. More importantly, they made predictions about dynamics and connectivity among unobserved neurons internal to the circuit, and these were subsequently confirmed by experiment. This circuit inference framework promises to facilitate the integration and understanding of big data in neuroscience., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

The processing of motion in visual scenes is important for detecting and tracking moving objects as well as for monitoring self-motion through the induced optic flow. Specialized neural circuits have been identified in the vertebrate retina for detecting motion direction or for distinguishing between object motion and self-motion, although little is known about how information about these distinct features of visual motion is combined. The salamander retina, which is a widely used model system for analyzing retinal function, contains object-motion-sensitive (OMS) ganglion cells, which strongly respond to local motion signals but are suppressed by global image motion. Yet, direction-selective (DS) ganglion cells have been conspicuously absent from characterizations of the salamander retina, despite their ubiquity in other model systems. We here show that the retina of axolotl salamanders contains at least two distinct classes of DS ganglion cells. For one of these classes, the cells display a strong preference for local over global motion in addition to their direction selectivity (OMS-DS cells) and thereby combine sensitivity to two distinct motion features. The OMS-DS cells are further distinct from standard (non-OMS) DS cells by their smaller receptive fields and different organization of preferred motion directions. Our results suggest that the two classes of DS cells specialize to encode motion direction of local and global motion stimuli, respectively, even for complex composite motion scenes. Furthermore, although the salamander DS cells are OFF-type, there is a strong analogy to the systems of ON and ON-OFF DS cells in the mammalian retina., Significance Statement: The retina contains specialized cells for motion processing. Among the retinal ganglion cells, which form the output neurons of the retina, some are known to report the direction of a moving stimulus (direction-selective cells), and others distinguish the motion of an object from a moving background. But little is known about how information about local object motion and information about motion direction interact. Here, we report that direction-selective ganglion cells can be identified in the salamander retina, where their existence had been unclear. Furthermore, there are two independent systems of direction-selective cells, and one of these combines direction selectivity with sensitivity to local motion. The output of these cells could assist in tracking moving objects and estimating their future position., (Copyright © 2016 the authors 0270-6474/16/3612203-14$15.00/0.)

Advances in neuronal recording techniques are leading to ever larger numbers of simultaneously monitored neurons. This poses the important analytical challenge of how to capture compactly all sensory information that neural population codes carry in their spatial dimension (differences in stimulus tuning across neurons at different locations), in their temporal dimension (temporal neural response variations), or in their combination (temporally coordinated neural population firing). Here we investigate the utility of tensor factorizations of population spike trains along space and time. These factorizations decompose a dataset of single-trial population spike trains into spatial firing patterns (combinations of neurons firing together), temporal firing patterns (temporal activation of these groups of neurons) and trial-dependent activation coefficients (strength of recruitment of such neural patterns on each trial). We validated various factorization methods on simulated data and on populations of ganglion cells simultaneously recorded in the salamander retina. We found that single-trial tensor space-by-time decompositions provided low-dimensional data-robust representations of spike trains that capture efficiently both their spatial and temporal information about sensory stimuli. Tensor decompositions with orthogonality constraints were the most efficient in extracting sensory information, whereas non-negative tensor decompositions worked well even on non-independent and overlapping spike patterns, and retrieved informative firing patterns expressed by the same population in response to novel stimuli. Our method showed that populations of retinal ganglion cells carried information in their spike timing on the ten-milliseconds-scale about spatial details of natural images. This information could not be recovered from the spike counts of these cells. First-spike latencies carried the majority of information provided by the whole spike train about fine-scale image features, and supplied almost as much information about coarse natural image features as firing rates. Together, these results highlight the importance of spike timing, and particularly of first-spike latencies, in retinal coding., Competing Interests: The authors have declared that no competing interests exist.

Fixational eye movements can rapidly shift the retinal image, but typically remain unnoticed. We identify and simulate a model mechanism for the suppression of erroneous motion signals under fixational eye movements. This mechanism exploits the non-linearities common to many classes of large retinal ganglion cells in the mammalian retina, and negates the need for extra-retinal signals or explicit gaze information. When tested using natural images undergoing simulated fixational eye movements, our model successfully distinguishes "real world" motion from retinal motion induced by eye movements. In addition, this model suggests a possible explanation for several fixational eye movement related visual illusions such as the Ouchi-Spillmann and "Out-of-focus" illusions., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

When visual contrast changes, retinal ganglion cells adapt by adjusting their sensitivity as well as their temporal filtering characteristics. The latter has classically been described by contrast-induced gain changes that depend on temporal frequency. Here, we explored a new perspective on contrast-induced changes in temporal filtering by using spike-triggered covariance analysis to extract multiple parallel temporal filters for individual ganglion cells. Based on multielectrode-array recordings from ganglion cells in the isolated salamander retina, we found that contrast adaptation of temporal filtering can largely be captured by contrast-invariant sets of filters with contrast-dependent weights. Moreover, differences among the ganglion cells in the filter sets and their contrast-dependent contributions allowed us to phenomenologically distinguish three types of filter changes. The first type is characterized by newly emerging features at higher contrast, which can be reproduced by computational models that contain response-triggered gain-control mechanisms. The second type follows from stronger adaptation in the Off pathway as compared to the On pathway in On-Off-type ganglion cells. Finally, we found that, in a subset of neurons, contrast-induced filter changes are governed by particularly strong spike-timing dynamics, in particular by pronounced stimulus-dependent latency shifts that can be observed in these cells. Together, our results show that the contrast dependence of temporal filtering in retinal ganglion cells has a multifaceted phenomenology and that a multi-filter analysis can provide a useful basis for capturing the underlying signal-processing dynamics.

Throughout different sensory systems, individual neurons integrate incoming signals over their receptive fields. The characteristics of this signal integration are crucial determinants for the neurons' functions. For ganglion cells in the vertebrate retina, receptive fields are characterized by the well-known center-surround structure and, although several studies have addressed spatial integration in the receptive field center, little is known about how visual signals are integrated in the surround. Therefore, we set out here to characterize signal integration and to identify relevant nonlinearities in the receptive field surround of ganglion cells in the isolated salamander retina by recording spiking activity with extracellular electrodes under visual stimulation of the center and surround. To quantify nonlinearities of spatial integration independently of subsequent nonlinearities of spike generation, we applied the technique of iso-response measurements as follows: using closed-loop experiments, we searched for different stimulus patterns in the surround that all reduced the center-evoked spiking activity by the same amount. The identified iso-response stimuli revealed strongly nonlinear spatial integration in the receptive field surrounds of all recorded cells. Furthermore, cell types that had been shown previously to have different nonlinearities in receptive field centers showed similar surround nonlinearities but differed systematically in the adaptive characteristics of the surround. Finally, we found that there is an optimal spatial scale of surround suppression; suppression was most effective when surround stimulation was organized into subregions of several hundred micrometers in diameter, indicating that the surround is composed of subunits that have strong center-surround organization themselves., (Copyright © 2014 the authors 0270-6474/14/347548-14$15.00/0.)

Ganglion cells in the vertebrate retina integrate visual information over their receptive fields. They do so by pooling presynaptic excitatory inputs from typically many bipolar cells, which themselves collect inputs from several photoreceptors. In addition, inhibitory interactions mediated by horizontal cells and amacrine cells modulate the structure of the receptive field. In many models, this spatial integration is assumed to occur in a linear fashion. Yet, it has long been known that spatial integration by retinal ganglion cells also incurs nonlinear phenomena. Moreover, several recent examples have shown that nonlinear spatial integration is tightly connected to specific visual functions performed by different types of retinal ganglion cells. This work discusses these advances in understanding the role of nonlinear spatial integration and reviews recent efforts to quantitatively study the nature and mechanisms underlying spatial nonlinearities. These new insights point towards a critical role of nonlinearities within ganglion cell receptive fields for capturing responses of the cells to natural and behaviorally relevant visual stimuli. In the long run, nonlinear phenomena of spatial integration may also prove important for implementing the actual neural code of retinal neurons when designing visual prostheses for the eye., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Retinal ganglion cells react to changes in visual contrast by adjusting their sensitivity and temporal filtering characteristics. This contrast adaptation has primarily been studied under spatially homogeneous stimulation. Yet, ganglion cell receptive fields are often characterized by spatial subfields, providing a substrate for nonlinear spatial processing. This raises the question whether contrast adaptation follows a similar subfield structure or whether it occurs globally over the receptive field even for local stimulation. We therefore recorded ganglion cell activity in isolated salamander retinas while locally changing visual contrast. Ganglion cells showed primarily global adaptation characteristics, with notable exceptions in certain aspects of temporal filtering. Surprisingly, some changes in filtering were most pronounced for locations where contrast did not change. This seemingly paradoxical effect can be explained by a simple computational model, which emphasizes the importance of local nonlinearities in the retina and suggests a reevaluation of previously reported local contrast adaptation., (Copyright © 2013 Elsevier Inc. All rights reserved.)

The space of sensory stimuli is complex and high-dimensional. Yet, single neurons in sensory systems are typically affected by only a small subset of the vast space of all possible stimuli. A proper understanding of the input-output transformation represented by a given cell therefore requires the identification of the subset of stimuli that are relevant in shaping the neuronal response. As an extension to the commonly-used spike-triggered average, the analysis of the spike-triggered covariance matrix provides a systematic methodology to detect relevant stimuli. As originally designed, the consistency of this method is guaranteed only if stimuli are drawn from a Gaussian distribution. Here we present a geometric proof of consistency, which provides insight into the foundations of the method, in particular, into the crucial role played by the geometry of stimulus space and symmetries in the stimulus-response relation. This approach leads to a natural extension of the applicability of the spike-triggered covariance technique to arbitrary spherical or elliptic stimulus distributions. The extension only requires a subtle modification of the original prescription. Furthermore, we present a new resampling method for assessing statistical significance of identified relevant stimuli, applicable to spherical and elliptic stimulus distributions. Finally, we exemplify the modified method and compare it to other prescriptions given in the literature.

Neurons in sensory systems can represent information not only by their firing rate, but also by the precise timing of individual spikes. For example, certain retinal ganglion cells, first identified in the salamander, encode the spatial structure of a new image by their first-spike latencies. Here we explore how this temporal code can be used by downstream neural circuits for computing complex features of the image that are not available from the signals of individual ganglion cells. To this end, we feed the experimentally observed spike trains from a population of retinal ganglion cells to an integrate-and-fire model of post-synaptic integration. The synaptic weights of this integration are tuned according to the recently introduced tempotron learning rule. We find that this model neuron can perform complex visual detection tasks in a single synaptic stage that would require multiple stages for neurons operating instead on neural spike counts. Furthermore, the model computes rapidly, using only a single spike per afferent, and can signal its decision in turn by just a single spike. Extending these analyses to large ensembles of simulated retinal signals, we show that the model can detect the orientation of a visual pattern independent of its phase, an operation thought to be one of the primitives in early visual processing. We analyze how these computations work and compare the performance of this model to other schemes for reading out spike-timing information. These results demonstrate that the retina formats spatial information into temporal spike sequences in a way that favors computation in the time domain. Moreover, complex image analysis can be achieved already by a simple integrate-and-fire model neuron, emphasizing the power and plausibility of rapid neural computing with spike times.

Throughout the nervous system, neurons integrate high-dimensional input streams and transform them into an output of their own. This integration of incoming signals involves filtering processes and complex non-linear operations. The shapes of these filters and non-linearities determine the computational features of single neurons and their functional roles within larger networks. A detailed characterization of signal integration is thus a central ingredient to understanding information processing in neural circuits. Conventional methods for measuring single-neuron response properties, such as reverse correlation, however, are often limited by the implicit assumption that stimulus integration occurs in a linear fashion. Here, we review a conceptual and experimental alternative that is based on exploring the space of those sensory stimuli that result in the same neural output. As demonstrated by recent results in the auditory and visual system, such iso-response stimuli can be used to identify the non-linearities relevant for stimulus integration, disentangle consecutive neural processing steps, and determine their characteristics with unprecedented precision. Automated closed-loop experiments are crucial for this advance, allowing rapid search strategies for identifying iso-response stimuli during experiments. Prime targets for the method are feed-forward neural signaling chains in sensory systems, but the method has also been successfully applied to feedback systems. Depending on the specific question, "iso-response" may refer to a predefined firing rate, single-spike probability, first-spike latency, or other output measures. Examples from different studies show that substantial progress in understanding neural dynamics and coding can be achieved once rapid online data analysis and stimulus generation, adaptive sampling, and computational modeling are tightly integrated into experiments.

How size and shape of presynaptic active zones are regulated at the molecular level has remained elusive. Here we provide insight from studying rod photoreceptor ribbon-type active zones after disruption of CAST/ERC2, one of the cytomatrix of the active zone (CAZ) proteins. Rod photoreceptors were present in normal numbers, and the a-wave of the electroretinogram (ERG)--reflecting their physiological population response--was unchanged in CAST knock-out (CAST(-/-)) mice. Using immunofluorescence and electron microscopy, we found that the size of the rod presynaptic active zones, their Ca(2+) channel complement, and the extension of the outer plexiform layer were diminished. Moreover, we observed sprouting of horizontal and bipolar cells toward the outer nuclear layer indicating impaired rod transmitter release. However, rod synapses of CAST(-/-) mice, unlike in mouse mutants for the CAZ protein Bassoon, displayed anchored ribbons, normal vesicle densities, clustered Ca(2+) channels, and essentially normal molecular organization. The reduction of the rod active zone size went along with diminished amplitudes of the b-wave in scotopic ERGs. Assuming, based on the otherwise intact synaptic structure, an unaltered function of the remaining release apparatus, we take our finding to suggest a scaling of release rate with the size of the active zone. Multielectrode-array recordings of retinal ganglion cells showed decreased contrast sensitivity. This was also observed by optometry, which, moreover, revealed reduced visual acuity. We conclude that CAST supports large active zone size and high rates of transmission at rod ribbon synapses, which are required for normal vision.

Neurons often integrate information from multiple parallel signaling streams. How a neuron combines these inputs largely determines its computational role in signal processing. Experimental assessment of neuronal signal integration, however, is often confounded by cell-intrinsic nonlinear processes that arise after signal integration has taken place. To overcome this problem and determine how ganglion cells in the salamander retina integrate visual contrast over space, we used automated online analysis of recorded spike trains and closed-loop control of the visual stimuli to identify different stimulus patterns that give the same neuronal response. These iso-response stimuli revealed a threshold-quadratic transformation as a fundamental nonlinearity within the receptive field center. Moreover, for a subset of ganglion cells, the method revealed an additional dynamic nonlinearity that renders these cells particularly sensitive to spatially homogeneous stimuli. This function is shown to arise from a local inhibition-mediated dynamic gain control mechanism., (Copyright © 2012 Elsevier Inc. All rights reserved.)

Congenital absence of cone photoreceptor function is associated with strongly impaired daylight vision and loss of color discrimination in human achromatopsia. Here, we introduce viral gene replacement therapy as a potential treatment for this disease in the CNGA3(-/-) mouse model. We show that such therapy can restore cone-specific visual processing in the central nervous system even if cone photoreceptors had been nonfunctional from birth. The restoration of cone vision was assessed at different stages along the visual pathway. Treated CNGA3(-/-) mice were able to generate cone photoreceptor responses and to transfer these signals to bipolar cells. In support, we found morphologically that treated cones expressed regular cyclic nucleotide-gated (CNG) channel complexes and opsins in outer segments, which previously they did not. Moreover, expression of CNGA3 normalized cyclic guanosine monophosphate (cGMP) levels in cones, delayed cone cell death and reduced the inflammatory response of Müller glia cells that is typical of retinal degenerations. Furthermore, ganglion cells from treated, but not from untreated, CNGA3(-/-) mice displayed cone-driven, light-evoked, spiking activity, indicating that signals generated in the outer retina are transmitted to the brain. Finally, we demonstrate that this newly acquired sensory information was translated into cone-mediated, vision-guided behavior.

We rely on our visual system to cope with the vast barrage of incoming light patterns and to extract features from the scene that are relevant to our well-being. The necessary reduction of visual information already begins in the eye. In this review, we summarize recent progress in understanding the computations performed in the vertebrate retina and how they are implemented by the neural circuitry. A new picture emerges from these findings that helps resolve a vexing paradox between the retina's structure and function. Whereas the conventional wisdom treats the eye as a simple prefilter for visual images, it now appears that the retina solves a diverse set of specific tasks and provides the results explicitly to downstream brain areas., (Copyright 2010 Elsevier Inc. All rights reserved.)

Our visual system can operate at fascinating speeds. Psychophysical experiments teach us that the processing of complex natural images and visual object recognition require a mere split second. Even in everyday life, our gaze seldom rests for long on any particular spot of the visual scene before a sudden movement of the eyes or the head shifts it to a new location. These observations challenge our understanding of how neurons in the visual system of the brain represent, process, and transmit the relevant visual information quickly enough. This article argues that the speed of visual processing provides an adjuvant framework for studying the neural code in the visual system. In the retina, which constitutes the first stage of visual processing, recent experiments have highlighted response features that allow for particularly rapid information transmission. This sets the stage for discussing some of the fundamental questions in the research of neural coding. How do downstream brain regions read out signals from the retina and combine them with intrinsic signals that accompany eye movements? And, how do the neural response features ultimately affect perception and behavior?

For understanding the computation and function of single neurons in sensory systems, one needs to investigate how sensory stimuli are related to a neuron's response and which biological mechanisms underlie this relationship. Mathematical models of the stimulus-response relationship have proved very useful in approaching these issues in a systematic, quantitative way. A starting point for many such analyses has been provided by phenomenological "linear-nonlinear" (LN) models, which comprise a linear filter followed by a static nonlinear transformation. The linear filter is often associated with the neuron's receptive field. However, the structure of the receptive field is generally a result of inputs from many presynaptic neurons, which may form parallel signal processing pathways. In the retina, for example, certain ganglion cells receive excitatory inputs from ON-type as well as OFF-type bipolar cells. Recent experiments have shown that the convergence of these pathways leads to intriguing response characteristics that cannot be captured by a single linear filter. One approach to adjust the LN model to the biological circuit structure is to use multiple parallel filters that capture ON and OFF bipolar inputs. Here, we review these new developments in modeling neuronal responses in the early visual system and provide details about one particular technique for obtaining the required sets of parallel filters from experimental data.

Natural vision is a highly dynamic process. Frequent body, head, and eye movements constantly bring new images onto the retina for brief periods, challenging our understanding of the neural code for vision. We report that certain retinal ganglion cells encode the spatial structure of a briefly presented image in the relative timing of their first spikes. This code is found to be largely invariant to stimulus contrast and robust to noisy fluctuations in response latencies. Mechanistically, the observed response characteristics result from different kinetics in two retinal pathways ("ON" and "OFF") that converge onto ganglion cells. This mechanism allows the retina to rapidly and reliably transmit new spatial information with the very first spikes emitted by a neural population.

Sensory systems extract behaviorally relevant information from a continuous stream of complex high-dimensional input signals. Understanding the detailed dynamics and precise neural code, even of a single neuron, is therefore a non-trivial task. Automated closed-loop approaches that integrate data analysis in the experimental design ease the investigation of sensory systems in three directions: First, adaptive sampling speeds up the data acquisition and thus increases the yield of an experiment. Second, model-driven stimulus exploration improves the quality of experimental data needed to discriminate between alternative hypotheses. Third, information-theoretic data analyses open up novel ways to search for those stimuli that are most efficient in driving a given neuron in terms of its firing rate or coding quality. Examples from different sensory systems show that, in all three directions, substantial progress can be achieved once rapid online data analysis, adaptive sampling, and computational modeling are tightly integrated into experiments.

The fundamental building block of every nervous system is the single neuron. Understanding how these exquisitely structured elements operate is an integral part of the quest to solve the mysteries of the brain. Quantitative mathematical models have proved to be an indispensable tool in pursuing this goal. We review recent advances and examine how single-cell models on five levels of complexity, from black-box approaches to detailed compartmental simulations, address key questions about neural dynamics and signal processing.

Neurons in sensory systems are commonly characterized by their receptive fields. These are experimentally often obtained by reverse-correlation analyses, for example, by calculating the spike-triggered average. The reverse-correlation approach, however, generally assumes a fixed temporal relation between spike-generating stimulus features and measured spikes. Temporal jitter of spikes will therefore distort the estimated receptive fields. Here, a novel extension of widely used reverse-correlation techniques (spike-triggered average as well as spike-triggered covariance) is presented that allows accurate measurements of receptive fields even in the presence of considerable spike-time jitter. It is shown that the method correctly recovers the receptive fields from simulated spike trains. When applied to recordings from auditory receptor cells of locusts, a considerable sharpening of receptive fields as compared to standard spike-triggered averages is observed. In addition, the multiple filters that are obtained from a conventional spike-triggered covariance analysis of these data can be collapsed into a single component if spike jitter is accounted for. Finally, it is shown how further effects on spike timing, such as systematic shifts in spike latency, can be included in the approach.

Sensory systems must translate incoming signals quickly and reliably so that an animal can act successfully in its environment. Even at the level of receptor neurons, however, functional aspects of the sensory encoding process are not yet fully understood. Specifically, this concerns the question how stimulus features and neural response characteristics lead to an efficient transmission of sensory information. To address this issue, we have recorded and analyzed spike trains from grasshopper auditory receptors, while systematically varying the stimulus statistics. The stimulus variations profoundly influenced the efficiency of neural encoding. This influence was largely attributable to the presence of specific stimulus features that triggered remarkably precise spikes whose trial-to-trial timing variability was as low as 0.15 ms--one order of magnitude shorter than typical stimulus time scales. Precise spikes decreased the noise entropy of the spike trains, thereby increasing the rate of information transmission. In contrast, the total spike train entropy, which quantifies the variety of different spike train patterns, hardly changed when stimulus conditions were altered, as long as the neural firing rate remained the same. This finding shows that stimulus distributions that were transmitted with high information rates did not invoke additional response patterns, but instead displayed exceptional temporal precision in their neural representation. The acoustic stimuli that led to the highest information rates and smallest spike-time jitter feature pronounced sound-pressure deflections lasting for 2-3 ms. These upstrokes are reminiscent of salient structures found in natural grasshopper communication signals, suggesting that precise spikes selectively encode particularly important aspects of the natural stimulus environment.

According to Barlow's seminal "efficient coding hypothesis," the coding strategy of sensory neurons should be matched to the statistics of stimuli that occur in an animal's natural habitat. Using an automatic search technique, we here test this hypothesis and identify stimulus ensembles that sensory neurons are optimized for. Focusing on grasshopper auditory receptor neurons, we find that their optimal stimulus ensembles differ from the natural environment, but largely overlap with a behaviorally important sub-ensemble of the natural sounds. This indicates that the receptors are optimized for peak rather than average performance. More generally, our results suggest that the coding strategies of sensory neurons are heavily influenced by differences in behavioral relevance among natural stimuli.

Reliable accounts of the variability observed in neural spike trains are a prerequisite for the proper interpretation of neural dynamics and coding principles. Models that accurately describe neural variability over a wide range of stimulation and response patterns are therefore highly desirable, especially if they can explain this variability in terms of basic neural observables and parameters such as firing rate and refractory period. In this work, we analyze the response variability recorded in vivo from locust auditory receptor neurons under acoustic stimulation. In agreement with results from other systems, our data suggest that neural refractoriness has a strong influence on spike-train variability. We therefore explore a stochastic model of spike generation that includes refractoriness through a recovery function. Because our experimental data are consistent with a renewal process, the recovery function can be derived from a single interspike-interval histogram obtained under constant stimulation. The resulting description yields quantitatively accurate predictions of the response variability over the whole range of firing rates for constant-intensity as well as amplitude-modulated sound stimuli. Model parameters obtained from constant stimulation can be used to predict the variability in response to dynamic stimuli. These results demonstrate that key ingredients of the stochastic response dynamics of a sensory neuron are faithfully captured by a simple stochastic model framework.

Every sensation begins with the conversion of a sensory stimulus into the response of a receptor neuron. Typically, this involves a sequence of multiple biophysical processes that cannot all be monitored directly. In this work, we present an approach that is based on analyzing different stimuli that cause the same final output, here defined as the probability of the receptor neuron to fire a single action potential. Comparing such iso-response stimuli within the framework of nonlinear cascade models allows us to extract the characteristics of individual signal-processing steps with a temporal resolution much finer than the trial-to-trial variability of the measured output spike times. Applied to insect auditory receptor cells, the technique reveals the sub-millisecond dynamics of the eardrum vibration and of the electrical potential and yields a quantitative four-step cascade model. The model accounts for the tuning properties of this class of neurons and explains their high temporal resolution under natural stimulation. Owing to its simplicity and generality, the presented method is readily applicable to other nonlinear cascades and a large variety of signal-processing systems.

Spike-frequency adaptation affects the response characteristics of many sensory neurons, and different biophysical processes contribute to this phenomenon. Many cellular mechanisms underlying adaptation are triggered by the spike output of the neuron in a feedback manner (e.g., specific potassium currents that are primarily activated by the spiking activity). In contrast, other components of adaptation may be caused by, in a feedforward way, the sensory or synaptic input, which the neuron receives. Examples include viscoelasticity of mechanoreceptors, transducer adaptation in hair cells, and short-term synaptic depression. For a functional characterization of spike-frequency adaptation, it is essential to understand the dependence of adaptation on the input and output of the neuron. Here, we demonstrate how an input-driven component of adaptation can be uncovered in vivo from recordings of spike trains in an insect auditory receptor neuron, even if the total adaptation is dominated by output-driven components. Our method is based on the identification of different inputs that yield the same output and sudden switches between these inputs. In particular, we determined for different sound frequencies those intensities that are required to yield a predefined steady-state firing rate of the neuron. We then found that switching between these sound frequencies causes transient deviations of the firing rate. These firing-rate deflections are evidence of input-driven adaptation and can be used to quantify how this adaptation component affects the neural activity. Based on previous knowledge of the processes in auditory transduction, we conclude that for the investigated auditory receptor neurons, this adaptation phenomenon is of mechanical origin.

We investigate the transduction of sound stimuli into neural responses and focus on locust auditory receptor cells. As in other mechanosensory model systems, these neurons integrate acoustic inputs over a fairly broad frequency range. To test three alternative hypotheses about the nature of this spectral integration (amplitude, energy, pressure), we perform intracellular recordings while stimulating with superpositions of pure tones. On the basis of online data analysis and automatic feedback to the stimulus generator, we systematically explore regions in stimulus space that lead to the same level of neural activity. Focusing on such iso-firing-rate regions allows for a rigorous quantitative comparison of the electrophysiological data with predictions from the three hypotheses that is independent of nonlinearities induced by the spike dynamics. We find that the dependence of the firing rates of the receptors on the composition of the frequency spectrum can be well described by an energy-integrator model. This result holds at stimulus onset as well as for the steady-state response, including the case in which adaptation effects depend on the stimulus spectrum. Predictions of the model for the responses to bandpass-filtered noise stimuli are verified accurately. Together, our data suggest that the sound-intensity coding of the receptors can be understood as a three-step process, composed of a linear filter, a summation of the energy contributions in the frequency domain, and a firing-rate encoding of the resulting effective sound intensity. These findings set quantitative constraints for future biophysical models.