Functional organization of ganglion cells in the salamander retina

Neural Activity in Quarks Language: Lattice Field Theory for a Network of Real Neurons

Brain-computer interfaces have seen extraordinary surges in developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This discrepancy becomes particularly pronounced when examining the collective neural activity at the micro and meso scale, where a coherent formalization that adequately describes neural interactions is still lacking. Here, we introduce a mathematical framework to analyze systems of natural neurons and interpret the related empirical observations in terms of lattice field theory, an established paradigm from theoretical particle physics and statistical mechanics. Our methods are tailored to interpret data from chronic neural interfaces, especially spike rasters from measurements of single neuron activity, and generalize the maximum entropy model for neural networks so that the time evolution of the system is also taken into account. This is obtained by bridging particle physics and neuroscience, paving the way for particle physics-inspired models of the neocortex.

Classification and analysis of retinal interneurons by computational structure under natural scenes

Inhibitory neurons are diverse across the brain, but for the visual system we lack the ability to functionally classify these neurons under complex natural stimuli. Here we take the approach of classifying retinal amacrine cell responses to natural scenes using optical recording and an interpretable neural network model. We fit mouse amacrine cell responses to a two-layer convolutional neural network model of a class shown previously to accurately capture salamander ganglion cell responses to natural scenes. Using an approach from interpretable machine learning, we determined for each stimulus the model interneurons that generated each amacrine response, analogous to the set of bipolar cells that target the amacrine population. From this analysis we clustered amacrine cells not by their natural scene responses, but by the model presynaptic neurons that constructed those responses, conservatively finding approximately seven groups by this approach. By analyzing the set of model presynaptic input neurons for each amacrine cluster, we find that distributed rather than dedicated inputs generate natural scene responses for different amacrine cell types. Additional analyses revealed distinct transient and sustained modes exhibited by the network during the response to simple flashes. These results give insight into the computational structure of how the diverse amacrine cell population responds to natural scenes, and generate multiple quantitative hypotheses for how synaptic inputs generate those responses.

Differences in nonlinearities determine retinal cell types

Classifying neurons in different types is still an open challenge. In the retina, recent works have taken advantage of the ability to record from a large number of cells to classify ganglion cells into different types based on functional information. Although the first attempts in this direction used the receptive field properties of each cell to classify them, more recent approaches have proposed to cluster ganglion cells directly based on their response to stimuli. These two approaches have not been compared directly. Here, we recorded the responses of a large number of ganglion cells and compared two methods for classifying them into functional groups, one based on the receptive field properties, and the other one using directly their responses to stimuli with various temporal frequencies. We show that the response-based approach allows separation of more types than the receptive field-based method, leading to a better classification. This better granularity is due to the fact that the response-based method takes into account not only the linear part of ganglion cell function but also some of the nonlinearities. A careful characterization of nonlinear processing is thus key to allowing functional classification of sensory neurons.NEW & NOTEWORTHY In the retina, ganglion cells can be classified based on their response to visual stimuli. Although some methods are based on the modeling of receptive fields, others rely on responses to characteristic stimuli. We compared these two classes of methods and show that the latter provides a higher discrimination performance. We also show that this gain arises from the ability to account for the nonlinear behavior of neurons.

Disynaptic inhibition shapes tuning of OFF-motion detectors in Drosophila

The circuitry underlying the detection of visual motion in Drosophila melanogaster is one of the best studied networks in neuroscience. Lately, electron microscopy reconstructions, algorithmic models, and functional studies have proposed a common motif for the cellular circuitry of an elementary motion detector based on both supralinear enhancement for preferred direction and sublinear suppression for null-direction motion. In T5 cells, however, all columnar input neurons (Tm1, Tm2, Tm4, and Tm9) are excitatory. So, how is null-direction suppression realized there? Using two-photon calcium imaging in combination with thermogenetics, optogenetics, apoptotics, and pharmacology, we discovered that it is via CT1, the GABAergic large-field amacrine cell, where the different processes have previously been shown to act in an electrically isolated way. Within each column, CT1 receives excitatory input from Tm9 and Tm1 and provides the sign-inverted, now inhibitory input signal onto T5. Ablating CT1 or knocking down GABA-receptor subunit Rdl significantly broadened the directional tuning of T5 cells. It thus appears that the signal of Tm1 and Tm9 is used both as an excitatory input for preferred direction enhancement and, through a sign inversion within the Tm1/Tm9-CT1 microcircuit, as an inhibitory input for null-direction suppression.

Simple model for encoding natural images by retinal ganglion cells with nonlinear spatial integration

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.

For understanding how sensory systems operate in the natural environment, an important goal is to develop models that capture neuronal responses to natural stimuli. For retinal ganglion cells, which connect the eye to the brain, current standard models often fail to capture responses to natural visual scenes. This shortcoming is at least partly rooted in the fact that ganglion cells may combine visual signals over space in a nonlinear fashion. We here show that a simple model, which not only considers the average light intensity inside a cell’s receptive field but also the variance of light intensity over space, can partly account for these nonlinearities and thereby improve current standard models. This provides an easy-to-obtain benchmark for modeling ganglion cell responses to natural images.

Efficient population coding depends on stimulus convergence and source of noise

Sensory organs transmit information to downstream brain circuits using a neural code comprised of spikes from multiple neurons. According to the prominent efficient coding framework, the properties of sensory populations have evolved to encode maximum information about stimuli given biophysical constraints. How information coding depends on the way sensory signals from multiple channels converge downstream is still unknown, especially in the presence of noise which corrupts the signal at different points along the pathway. Here, we calculated the optimal information transfer of a population of nonlinear neurons under two scenarios. First, a lumped-coding channel where the information from different inputs converges to a single channel, thus reducing the number of neurons. Second, an independent-coding channel when different inputs contribute independent information without convergence. In each case, we investigated information loss when the sensory signal was corrupted by two sources of noise. We determined critical noise levels at which the optimal number of distinct thresholds of individual neurons in the population changes. Comparing our system to classical physical systems, these changes correspond to first- or second-order phase transitions for the lumped- or the independent-coding channel, respectively. We relate our theoretical predictions to coding in a population of auditory nerve fibers recorded experimentally, and find signatures of efficient coding. Our results yield important insights into the diverse coding strategies used by neural populations to optimally integrate sensory stimuli in the presence of distinct sources of noise.

Nonlinear spatial integration in retinal bipolar cells shapes the encoding of artificial and natural stimuli

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.

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Some retinal bipolar cells represent visual contrast in a nonlinear fashion

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These bipolar cells also nonlinearly integrate visual signals over space

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The spatial nonlinearity affects the encoding of natural stimuli by bipolar cells

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The nonlinearity results from feedforward input, not from feedback inhibition

On the potential role of lateral connectivity in retinal anticipation

We analyse the potential effects of lateral connectivity (amacrine cells and gap junctions) on motion anticipation in the retina. Our main result is that lateral connectivity can-under conditions analysed in the paper-trigger a wave of activity enhancing the anticipation mechanism provided by local gain control (Berry et al. in Nature 398(6725):334-338, 1999; Chen et al. in J. Neurosci. 33(1):120-132, 2013). We illustrate these predictions by two examples studied in the experimental literature: differential motion sensitive cells (Baccus and Meister in Neuron 36(5):909-919, 2002) and direction sensitive cells where direction sensitivity is inherited from asymmetry in gap junctions connectivity (Trenholm et al. in Nat. Neurosci. 16:154-156, 2013). We finally present reconstructions of retinal responses to 2D visual inputs to assess the ability of our model to anticipate motion in the case of three different 2D stimuli.

Cellular and Synaptic Mechanisms That Differentiate Mitral Cells and Superficial Tufted Cells Into Parallel Output Channels in the Olfactory Bulb

A common feature of the primary processing structures of sensory systems is the presence of parallel output “channels” that convey different information about a stimulus. In the mammalian olfactory bulb, this is reflected in the mitral cells (MCs) and tufted cells (TCs) that have differing sensitivities to odors, with TCs being more sensitive than MCs. In this study, we examined potential mechanisms underlying the different responses of MCs vs. TCs. For TCs, we focused on superficial TCs (sTCs), which are a population of output TCs that reside in the superficial-most portion of the external plexiform layer, along with external tufted cells (eTCs), which are glutamatergic interneurons in the glomerular layer. Using whole-cell patch-clamp recordings in mouse bulb slices, we first measured excitatory currents in MCs, sTCs, and eTCs following olfactory sensory neuron (OSN) stimulation, separating the responses into a fast, monosynaptic component reflecting direct inputs from OSNs and a prolonged component partially reflecting eTC-mediated feedforward excitation. Responses were measured to a wide range of OSN stimulation intensities, simulating the different levels of OSN activity that would be expected to be produced by varying odor concentrations in vivo. Over a range of stimulation intensities, we found that the monosynaptic current varied significantly between the cell types, in the order of eTC > sTC > MC. The prolonged component was smaller in sTCs vs. both MCs and eTCs. sTCs also had much higher whole-cell input resistances than MCs, reflecting their smaller size and greater membrane resistivity. To evaluate how these different electrophysiological aspects contributed to spiking of the output MCs and sTCs, we used computational modeling. By exchanging the different cell properties in our modeled MCs and sTCs, we could evaluate each property's contribution to spiking differences between these cell types. This analysis suggested that the higher sensitivity of spiking in sTCs vs. MCs reflected both their larger monosynaptic OSN signal as well as their higher input resistance, while their smaller prolonged currents had a modest opposing effect. Taken together, our results indicate that both synaptic and intrinsic cellular features contribute to the production of parallel output channels in the olfactory bulb.

What the salamander eye has been telling the vision scientist's brain

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.

Clustering of Neural Activity: A Design Principle for Population Codes

We propose that correlations among neurons are generically strong enough to organize neural activity patterns into a discrete set of clusters, which can each be viewed as a population codeword. Our reasoning starts with the analysis of retinal ganglion cell data using maximum entropy models, showing that the population is robustly in a frustrated, marginally sub-critical, or glassy, state. This leads to an argument that neural populations in many other brain areas might share this structure. Next, we use latent variable models to show that this glassy state possesses well-defined clusters of neural activity. Clusters have three appealing properties: (i) clusters exhibit error correction, i.e., they are reproducibly elicited by the same stimulus despite variability at the level of constituent neurons; (ii) clusters encode qualitatively different visual features than their constituent neurons; and (iii) clusters can be learned by downstream neural circuits in an unsupervised fashion. We hypothesize that these properties give rise to a "learnable" neural code which the cortical hierarchy uses to extract increasingly complex features without supervision or reinforcement.

Functional characterization of retinal ganglion cells using tailored nonlinear modeling

The mammalian retina encodes the visual world in action potentials generated by 20-50 functionally and anatomically-distinct types of retinal ganglion cell (RGC). Individual RGC types receive synaptic input from distinct presynaptic circuits; therefore, their responsiveness to specific features in the visual scene arises from the information encoded in synaptic input and shaped by postsynaptic signal integration and spike generation. Unfortunately, there is a dearth of tools for characterizing the computations reflected in RGC spike output. Therefore, we developed a statistical model, the separable Nonlinear Input Model, to characterize the excitatory and suppressive components of RGC receptive fields. We recorded RGC responses to a correlated noise ("cloud") stimulus in an in vitro preparation of mouse retina and found that our model accurately predicted RGC responses at high spatiotemporal resolution. It identified multiple receptive fields reflecting the main excitatory and suppressive components of the response of each neuron. Significantly, our model accurately identified ON-OFF cells and distinguished their distinct ON and OFF receptive fields, and it demonstrated a diversity of suppressive receptive fields in the RGC population. In total, our method offers a rich description of RGC computation and sets a foundation for relating it to retinal circuitry.

Functional Diversity in the Retina Improves the Population Code

Within a given brain region, individual neurons exhibit a wide variety of different feature selectivities. Here, we investigated the impact of this extensive functional diversity on the population neural code. Our approach was to build optimal decoders to discriminate among stimuli using the spiking output of a real, measured neural population and compare its performance against a matched, homogeneous neural population with the same number of cells and spikes. Analyzing large populations of retinal ganglion cells, we found that the real, heterogeneous population can yield a discrimination error lower than the homogeneous population by several orders of magnitude and consequently can encode much more visual information. This effect increases with population size and with graded degrees of heterogeneity. We complemented these results with an analysis of coding based on the Chernoff distance, as well as derivations of inequalities on coding in certain limits, from which we can conclude that the beneficial effect of heterogeneity occurs over a broad set of conditions. Together, our results indicate that the presence of functional diversity in neural populations can enhance their coding fidelity appreciably. A noteworthy outcome of our study is that this effect can be extremely strong and should be taken into account when investigating design principles for neural circuits.

Non-parametric Physiological Classification of Retinal Ganglion Cells in the Mouse Retina

Retinal ganglion cells, the sole output neurons of the retina, exhibit surprising diversity. A recent study reported over 30 distinct types in the mouse retina, indicating that the processing of visual information is highly parallelised in the brain. The advent of high density multi-electrode arrays now enables recording from many hundreds to thousands of neurons from a single retina. Here we describe a method for the automatic classification of large-scale retinal recordings using a simple stimulus paradigm and a spike train distance measure as a clustering metric. We evaluate our approach using synthetic spike trains, and demonstrate that major known cell types are identified in high-density recording sessions from the mouse retina with around 1,000 retinal ganglion cells. A comparison across different retinas reveals substantial variability between preparations, suggesting pooling data across retinas should be approached with caution. As a parameter-free method, our approach is broadly applicable for cellular physiological classification in all sensory modalities.

Characterization of Retinal Functionality at Different Eccentricities in a Diurnal Rodent

Although the properties of the neurons of the visual system that process central and peripheral regions of the visual field have been widely researched in the visual cortex and the LGN, they have scarcely been documented for the retina. The retina is the first step in integrating optical signals, and despite considerable efforts to functionally characterize the different types of retinal ganglion cells (RGCs), a clear account of the particular functionality of cells with central vs. peripheral fields is still wanting. Here, we use electrophysiological recordings, gathered from retinas of the diurnal rodent Octodon degus, to show that RGCs with peripheral receptive fields (RF) are larger, faster, and have shorter transient responses. This translates into higher sensitivity at high temporal frequencies and a full frequency bandwidth when compared to RGCs with more central RF. We also observed that imbalances between ON and OFF cell populations are preserved with eccentricity. Finally, the high diversity of functional types of RGCs highlights the complexity of the computational strategies implemented in the early stages of visual processing, which could inspire the development of bio-inspired artificial systems.

A single retinal circuit model for multiple computations

Vision is dependent on extracting intricate features of the visual information from the outside world, and complex visual computations begin to take place as soon as at the retinal level. In multiple studies on salamander retinas, the responses of a subtype of retinal ganglion cells, i.e., fast/biphasic-OFF ganglion cells, have been shown to be able to realize multiple functions, such as the segregation of a moving object from its background, motion anticipation, and rapid encoding of the spatial features of a new visual scene. For each of these visual functions, modeling approaches using extended linear-nonlinear cascade models suggest specific preceding retinal circuitries merging onto fast/biphasic-OFF ganglion cells. However, whether multiple visual functions can be accommodated together in a certain retinal circuitry and how specific mechanisms for each visual function interact with each other have not been investigated. Here, we propose a physiologically consistent, detailed computational model of the retinal circuit based on the spatiotemporal dynamics and connections of each class of retinal neurons to implement object motion sensitivity, motion anticipation, and rapid coding in the same circuit. Simulations suggest that multiple computations can be accommodated together, thereby implying that the fast/biphasic-OFF ganglion cell has potential to output a train of spikes carrying multiple pieces of information on distinct features of the visual stimuli.

Bioinspired Approach to Modeling Retinal Ganglion Cells Using System Identification Techniques

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.

Learning to make external sensory stimulus predictions using internal correlations in populations of neurons

To compensate for sensory processing delays, the visual system must make predictions to ensure timely and appropriate behaviors. Recent work has found predictive information about the stimulus in neural populations early in vision processing, starting in the retina. However, to utilize this information, cells downstream must be able to read out the predictive information from the spiking activity of retinal ganglion cells. Here we investigate whether a downstream cell could learn efficient encoding of predictive information in its inputs from the correlations in the inputs themselves, in the absence of other instructive signals. We simulate learning driven by spiking activity recorded in salamander retina. We model a downstream cell as a binary neuron receiving a small group of weighted inputs and quantify the predictive information between activity in the binary neuron and future input. Input weights change according to spike timing-dependent learning rules during a training period. We characterize the readouts learned under spike timing-dependent synaptic update rules, finding that although the fixed points of learning dynamics are not associated with absolute optimal readouts they convey nearly all of the information conveyed by the optimal readout. Moreover, we find that learned perceptrons transmit position and velocity information of a moving-bar stimulus nearly as efficiently as optimal perceptrons. We conclude that predictive information is, in principle, readable from the perspective of downstream neurons in the absence of other inputs. This suggests an important role for feedforward prediction in sensory encoding.

The structured 'low temperature' phase of the retinal population code

Recent advances in experimental techniques have allowed the simultaneous recordings of populations of hundreds of neurons, fostering a debate about the nature of the collective structure of population neural activity. Much of this debate has focused on the empirical findings of a phase transition in the parameter space of maximum entropy models describing the measured neural probability distributions, interpreting this phase transition to indicate a critical tuning of the neural code. Here, we instead focus on the possibility that this is a first-order phase transition which provides evidence that the real neural population is in a 'structured', collective state. We show that this collective state is robust to changes in stimulus ensemble and adaptive state. We find that the pattern of pairwise correlations between neurons has a strength that is well within the strongly correlated regime and does not require fine tuning, suggesting that this state is generic for populations of 100+ neurons. We find a clear correspondence between the emergence of a phase transition, and the emergence of attractor-like structure in the inferred energy landscape. A collective state in the neural population, in which neural activity patterns naturally form clusters, provides a consistent interpretation for our results.

Different functional susceptibilities of mouse retinal ganglion cell subtypes to optic nerve crush injury

In optic neuropathies, the progressive deterioration of retinal ganglion cell (RGC) function leads to irreversible vision loss. Increasing experimental evidence suggests differing susceptibility for RGC functional subtypes. Here with multi-electrode array recordings, RGC functional loss was characterized at multiple time points in a mouse model of optic nerve crush. Firing rate, latency of response and receptive field size were analyzed for ON, OFF and ON-OFF RGCs separately. It was observed that responses and receptive fields of OFF cells were impaired earlier than ON cells after the injury. For the ON-OFF cells, the OFF component of response was also more susceptible to optic nerve injury than the ON component. Moreover, more ON transient cells survived than ON sustained cells post the crush, implying a diversified vulnerability for ON cells. Together, these data support the contention that RGCs' functional degeneration in optic nerve injury is subtype dependent, a fact that needs to be considered when developing treatments of glaucomatous retinal ganglion cell degeneration and other optic neuropathies.

Joint Encoding of Object Motion and Motion Direction in the Salamander Retina

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.

Inference of neuronal functional circuitry with spike-triggered non-negative matrix factorization

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.

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.

Neural Circuit Inference from Function to Structure

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.

Error-Robust Modes of the Retinal Population Code

Across the nervous system, certain population spiking patterns are observed far more frequently than others. A hypothesis about this structure is that these collective activity patterns function as population codewords–collective modes–carrying information distinct from that of any single cell. We investigate this phenomenon in recordings of ∼150 retinal ganglion cells, the retina’s output. We develop a novel statistical model that decomposes the population response into modes; it predicts the distribution of spiking activity in the ganglion cell population with high accuracy. We found that the modes represent localized features of the visual stimulus that are distinct from the features represented by single neurons. Modes form clusters of activity states that are readily discriminated from one another. When we repeated the same visual stimulus, we found that the same mode was robustly elicited. These results suggest that retinal ganglion cells’ collective signaling is endowed with a form of error-correcting code–a principle that may hold in brain areas beyond retina.

Neurons in most parts of the nervous system represent and process information in a collective fashion, yet the nature of this collective code is poorly understood. An important constraint placed on any such collective processing comes from the fact that individual neurons’ signaling is prone to corruption by noise. The information theory and engineering literatures have studied error-correcting codes that allow individual noise-prone coding units to “check” each other, forming an overall representation that is robust to errors. In this paper, we have analyzed the population code of one of the best-studied neural systems, the retina, and found that it is structured in a manner analogous to error-correcting schemes. Indeed, we found that the complex activity patterns over ~150 retinal ganglion cells, the output neurons of the retina, could be mapped onto collective code words, and that these code words represented precise visual information while suppressing noise. In order to analyze this coding scheme, we introduced a novel quantitative model of the retinal output that predicted neural activity patterns more accurately than existing state-of-the-art approaches.

Coding Properties of Mouse Retinal Ganglion Cells with Dual-Peak Patterns with Respect to Stimulus Intervals

How visual information is encoded in spikes of retinal ganglion cells (RGCs) is essential in visual neuroscience. In the present study, we investigated the coding properties of mouse RGCs with dual-peak patterns with respect to visual stimulus intervals. We first analyzed the response properties, and observed that the latencies and spike counts of the two response peaks in the dual-peak pattern exhibited systematic changes with the preceding light-OFF interval. We then applied linear discriminant analysis (LDA) to assess the relative contributions of response characteristics of both peaks in information coding regarding the preceding stimulus interval. It was found that for each peak, the discrimination results were far better than chance level based on either latency or spike count, and were further improved by using the combination of the two parameters. Furthermore, the best discrimination results were obtained when latencies and spike counts of both peaks were considered in combination. In addition, the correct rate for stimulation discrimination was higher when RGC population activity was considered as compare to single neuron's activity, and the correct rate was increased with the group size. These results suggest that rate coding, temporal coding, and population coding are all involved in encoding the different stimulus-interval patterns, and the two response peaks in the dual-peak pattern carry complementary information about stimulus interval.

Analysis of Neuronal Spike Trains, Deconstructed

As information flows through the brain, neuronal firing progresses from encoding the world as sensed by the animal to driving the motor output of subsequent behavior. One of the more tractable goals of quantitative neuroscience is to develop predictive models that relate the sensory or motor streams with neuronal firing. Here we review and contrast analytical tools used to accomplish this task. We focus on classes of models in which the external variable is compared with one or more feature vectors to extract a low-dimensional representation, the history of spiking and other variables are potentially incorporated, and these factors are nonlinearly transformed to predict the occurrences of spikes. We illustrate these techniques in application to datasets of different degrees of complexity. In particular, we address the fitting of models in the presence of strong correlations in the external variable, as occurs in natural sensory stimuli and in movement. Spectral correlation between predicted and measured spike trains is introduced to contrast the relative success of different methods.

Physiological and morphological characterization of ganglion cells in the salamander retina

Retinal ganglion cells (RGCs) integrate visual information from the retina and transmit collective signals to the brain. A systematic investigation of functional and morphological characteristics of various types of RGCs is important to comprehensively understand how the visual system encodes and transmits information via various RGC pathways. This study evaluated both physiological and morphological properties of 67 RGCs in dark-adapted flat-mounted salamander retina by examining light-evoked cation and chloride current responses via voltage-clamp recordings and visualizing morphology by Lucifer yellow fluorescence with a confocal microscope. Six groups of RGCs were described: asymmetrical ON-OFF RGCs, symmetrical ON RGCs, OFF RGCs, and narrow-, medium- and wide-field ON-OFF RGCs. Dendritic field diameters of RGCs ranged 102-490 μm: narrow field (<200 μm, 31% of RGCs), medium field (200-300 μm, 45%) and wide field (>300 μm, 24%). Dendritic ramification patterns of RGCs agree with the sublamina A/B rule. 34% of RGCs were monostratified, 24% bistratified and 42% diffusely stratified. 70% of ON RGCs and OFF RGCs were monostratified. Wide-field RGCs were diffusely stratified. 82% of RGCs generated light-evoked ON-OFF responses, while 11% generated ON responses and 7% OFF responses. Response sensitivity analysis suggested that some RGCs obtained separated rod/cone bipolar cell inputs whereas others obtained mixed bipolar cell inputs. 25% of neurons in the RGC layer were displaced amacrine cells. Although more types may be defined by more refined classification criteria, this report is to incorporate more physiological properties into RGC classification.

A method for electrophysiological characterization of hamster retinal ganglion cells using a high-density CMOS microelectrode array

Knowledge of neuronal cell types in the mammalian retina is important for the understanding of human retinal disease and the advancement of sight-restoring technology, such as retinal prosthetic devices. A somewhat less utilized animal model for retinal research is the hamster, which has a visual system that is characterized by an area centralis and a wide visual field with a broad binocular component. The hamster retina is optimally suited for recording on the microelectrode array (MEA), because it intrinsically lies flat on the MEA surface and yields robust, large-amplitude signals. However, information in the literature about hamster retinal ganglion cell functional types is scarce. The goal of our work is to develop a method featuring a high-density (HD) complementary metal-oxide-semiconductor (CMOS) MEA technology along with a sequence of standardized visual stimuli in order to categorize ganglion cells in isolated Syrian Hamster (Mesocricetus auratus) retina. Since the HD-MEA is capable of recording at a higher spatial resolution than most MEA systems (17.5 μm electrode pitch), we were able to record from a large proportion of RGCs within a selected region. Secondly, we chose our stimuli so that they could be run during the experiment without intervention or computation steps. The visual stimulus set was designed to activate the receptive fields of most ganglion cells in parallel and to incorporate various visual features to which different cell types respond uniquely. Based on the ganglion cell responses, basic cell properties were determined: direction selectivity, speed tuning, width tuning, transience, and latency. These properties were clustered to identify ganglion cell types in the hamster retina. Ultimately, we recorded up to a cell density of 2780 cells/mm² at 2 mm (42°) from the optic nerve head. Using five parameters extracted from the responses to visual stimuli, we obtained seven ganglion cell types.

Pharmacological study of direction selectivity in the archer fish retina

Direction selective cells have been found in the retina, the first level of the visual system, in mammals and recently also in the archer fish. These cells are involved in a variety of fast neural computation processes, from the control of eye movements to the detection of prey by the archer fish. The standard model for this mechanism in mammalian retina is well understood and is based on the asymmetry of inhibitory and excitatory inputs to the retinal ganglion cells. However, it remains unclear whether the mechanism that underlies direction selectivity is similar across animal classes. This study reports a pharmacological investigation designed to elucidate the mechanism that underlies motion detection in the archer fish retina. Direction selectivity in the retina was characterized under the influence of specific channel blockers that are known to be present in the different types of neurons of the retina. The results show that the direction-selective mechanism in the archer fish retina is modified only when the inhibitory channels of GABA and Glycine are manipulated. This suggests that the mechanism of direction selectivity in the archer fish retina is fundamentally different from the mechanism of direction selectivity in the mammalian retina.

Spike-Triggered Covariance Analysis Reveals Phenomenological Diversity of Contrast Adaptation in the Retina

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.

Our sensory systems have to process stimuli under a wide range of environmental conditions. To cope with this challenge, the involved neurons adapt by adjusting their signal processing to the recently encountered intensity range. In the visual system, one finds, for example, that higher visual contrast leads to changes in how visual signals are temporally filtered, making signal processing faster and more band-pass-like at higher contrast. By analyzing signals from neurons in the retina of salamanders, we here found that these adaptation effects can be described by a fixed set of filters, independent of contrast, whose relative contributions change with contrast. Also, we found that different phenomena contribute to this adaptation. In particular, some cells change their relative sensitivity to light increments and light decrements, whereas other cells are influenced by a strong contrast-dependence of the exact timing of their responses. Our results show that contrast adaptation in the retina is not an entirely homogeneous phenomenon, and that models with multiple filters can help in characterizing sensory adaptation.

High Accuracy Decoding of Dynamical Motion from a Large Retinal Population

Motion tracking is a challenge the visual system has to solve by reading out the retinal population. It is still unclear how the information from different neurons can be combined together to estimate the position of an object. Here we recorded a large population of ganglion cells in a dense patch of salamander and guinea pig retinas while displaying a bar moving diffusively. We show that the bar's position can be reconstructed from retinal activity with a precision in the hyperacuity regime using a linear decoder acting on 100+ cells. We then took advantage of this unprecedented precision to explore the spatial structure of the retina's population code. The classical view would have suggested that the firing rates of the cells form a moving hill of activity tracking the bar's position. Instead, we found that most ganglion cells in the salamander fired sparsely and idiosyncratically, so that their neural image did not track the bar. Furthermore, ganglion cell activity spanned an area much larger than predicted by their receptive fields, with cells coding for motion far in their surround. As a result, population redundancy was high, and we could find multiple, disjoint subsets of neurons that encoded the trajectory with high precision. This organization allows for diverse collections of ganglion cells to represent high-accuracy motion information in a form easily read out by downstream neural circuits.

Critical and maximally informative encoding between neural populations in the retina

Computation in the brain involves multiple types of neurons, yet the organizing principles for how these neurons work together remain unclear. Information theory has offered explanations for how different types of neurons can maximize the transmitted information by encoding different stimulus features. However, recent experiments indicate that separate neuronal types exist that encode the same filtered version of the stimulus, but then the different cell types signal the presence of that stimulus feature with different thresholds. Here we show that the emergence of these neuronal types can be quantitatively described by the theory of transitions between different phases of matter. The two key parameters that control the separation of neurons into subclasses are the mean and standard deviation (SD) of noise affecting neural responses. The average noise across the neural population plays the role of temperature in the classic theory of phase transitions, whereas the SD is equivalent to pressure or magnetic field, in the case of liquid-gas and magnetic transitions, respectively. Our results account for properties of two recently discovered types of salamander Off retinal ganglion cells, as well as the absence of multiple types of On cells. We further show that, across visual stimulus contrasts, retinal circuits continued to operate near the critical point whose quantitative characteristics matched those expected near a liquid-gas critical point and described by the nearest-neighbor Ising model in three dimensions. By operating near a critical point, neural circuits can maximize information transmission in a given environment while retaining the ability to quickly adapt to a new environment.

ViSAPy: a Python tool for biophysics-based generation of virtual spiking activity for evaluation of spike-sorting algorithms

BACKGROUND

New, silicon-based multielectrodes comprising hundreds or more electrode contacts offer the possibility to record spike trains from thousands of neurons simultaneously. This potential cannot be realized unless accurate, reliable automated methods for spike sorting are developed, in turn requiring benchmarking data sets with known ground-truth spike times.

NEW METHOD

We here present a general simulation tool for computing benchmarking data for evaluation of spike-sorting algorithms entitled ViSAPy (Virtual Spiking Activity in Python). The tool is based on a well-established biophysical forward-modeling scheme and is implemented as a Python package built on top of the neuronal simulator NEURON and the Python tool LFPy.

RESULTS

ViSAPy allows for arbitrary combinations of multicompartmental neuron models and geometries of recording multielectrodes. Three example benchmarking data sets are generated, i.e., tetrode and polytrode data mimicking in vivo cortical recordings and microelectrode array (MEA) recordings of in vitro activity in salamander retinas. The synthesized example benchmarking data mimics salient features of typical experimental recordings, for example, spike waveforms depending on interspike interval.

COMPARISON WITH EXISTING METHODS

ViSAPy goes beyond existing methods as it includes biologically realistic model noise, synaptic activation by recurrent spiking networks, finite-sized electrode contacts, and allows for inhomogeneous electrical conductivities. ViSAPy is optimized to allow for generation of long time series of benchmarking data, spanning minutes of biological time, by parallel execution on multi-core computers.

CONCLUSION

ViSAPy is an open-ended tool as it can be generalized to produce benchmarking data or arbitrary recording-electrode geometries and with various levels of complexity.

Toward functional classification of neuronal types

How many types of neurons are there in the brain? This basic neuroscience question remains unsettled despite many decades of research. Classification schemes have been proposed based on anatomical, electrophysiological, or molecular properties. However, different schemes do not always agree with each other. This raises the question of whether one can classify neurons based on their function directly. For example, among sensory neurons, can a classification scheme be devised that is based on their role in encoding sensory stimuli? Here, theoretical arguments are outlined for how this can be achieved using information theory by looking at optimal numbers of cell types and paying attention to two key properties: correlations between inputs and noise in neural responses. This theoretical framework could help to map the hierarchical tree relating different neuronal classes within and across species.

Effects of spike-triggered negative feedback on receptive-field properties

Sensory neurons are often described in terms of a receptive field, that is, a linear kernel through which stimuli are filtered before they are further processed. If information transmission is assumed to proceed in a feedforward cascade, the receptive field may be interpreted as the external stimulus' profile maximizing neuronal output. The nervous system, however, contains many feedback loops, and sensory neurons filter more currents than the ones representing the transduced external stimulus. Some of the additional currents are generated by the output activity of the neuron itself, and therefore constitute feedback signals. By means of a time-frequency analysis of the input/output transformation, here we show how feedback modifies the receptive field. The model is applicable to various types of feedback processes, from spike-triggered intrinsic conductances to inhibitory synaptic inputs from nearby neurons. We distinguish between the intrinsic receptive field (filtering all input currents) and the effective receptive field (filtering only external stimuli). Whereas the intrinsic receptive field summarizes the biophysical properties of the neuron associated to subthreshold integration and spike generation, only the effective receptive field can be interpreted as the external stimulus' profile maximizing neuronal output. We demonstrate that spike-triggered feedback shifts low-pass filtering towards band-pass processing, transforming integrator neurons into resonators. For strong feedback, a sharp resonance in the spectral neuronal selectivity may appear. Our results provide a unified framework to interpret a collection of previous experimental studies where specific feedback mechanisms were shown to modify the filtering properties of neurons.

The neural circuit mechanisms underlying the retinal response to motion reversal

To make up for delays in visual processing, retinal circuitry effectively predicts that a moving object will continue moving in a straight line, allowing retinal ganglion cells to anticipate the object's position. However, a sudden reversal of motion triggers a synchronous burst of firing from a large group of ganglion cells, possibly signaling a violation of the retina's motion prediction. To investigate the neural circuitry underlying this response, we used a combination of multielectrode array and whole-cell patch recordings to measure the responses of individual retinal ganglion cells in the tiger salamander to reversing stimuli. We found that different populations of ganglion cells were responsible for responding to the reversal of different kinds of objects, such as bright versus dark objects. Using pharmacology and designed stimuli, we concluded that ON and OFF bipolar cells both contributed to the reversal response, but that amacrine cells had, at best, a minor role. This allowed us to formulate an adaptive cascade model (ACM), similar to the one previously used to describe ganglion cell responses to motion onset. By incorporating the ON pathway into the ACM, we were able to reproduce the time-varying firing rate of fast OFF ganglion cells for all experimentally tested stimuli. Analysis of the ACM demonstrates that bipolar cell gain control is primarily responsible for generating the synchronized retinal response, as individual bipolar cells require a constant time delay before recovering from gain control.

Nonlinear spatial integration in the receptive field surround of retinal ganglion cells

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.

The projective field of retinal bipolar cells and its modulation by visual context

The receptive field of a sensory neuron spells out all the receptor inputs it receives. To understand a neuron's role in the circuit, one also needs to know its projective field, namely the outputs it sends to all downstream cells. Here we present the projective fields of the primary excitatory neurons in a sensory circuit. We stimulated single bipolar cells of the salamander retina and recorded simultaneously from a population of ganglion cells. Individual bipolar cell signals diverge through polysynaptic pathways into ganglion cells of many different types and over surprisingly large distance. However, the strength and polarity of the projection depend on the cell types involved. Furthermore, visual stimulation strongly modulates the bipolar cell projective field, in opposite direction for different cell types. In this way, the context from distant parts of the visual field can control the routing of signals in the inner retina.

Adaptation to changes in higher-order stimulus statistics in the salamander retina

Adaptation in the retina is thought to optimize the encoding of natural light signals into sequences of spikes sent to the brain. While adaptive changes in retinal processing to the variations of the mean luminance level and second-order stimulus statistics have been documented before, no such measurements have been performed when higher-order moments of the light distribution change. We therefore measured the ganglion cell responses in the tiger salamander retina to controlled changes in the second (contrast), third (skew) and fourth (kurtosis) moments of the light intensity distribution of spatially uniform temporally independent stimuli. The skew and kurtosis of the stimuli were chosen to cover the range observed in natural scenes. We quantified adaptation in ganglion cells by studying linear-nonlinear models that capture well the retinal encoding properties across all stimuli. We found that the encoding properties of retinal ganglion cells change only marginally when higher-order statistics change, compared to the changes observed in response to the variation in contrast. By analyzing optimal coding in LN-type models, we showed that neurons can maintain a high information rate without large dynamic adaptation to changes in skew or kurtosis. This is because, for uncorrelated stimuli, spatio-temporal summation within the receptive field averages away non-gaussian aspects of the light intensity distribution.

Searching for collective behavior in a large network of sensory neurons

Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such "K-pairwise" models--being systematic extensions of the previously used pairwise Ising models--provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction.

Nonlinear dynamics support a linear population code in a retinal target-tracking circuit

A basic task faced by the visual system of many organisms is to accurately track the position of moving prey. The retina is the first stage in the processing of such stimuli; the nature of the transformation here, from photons to spike trains, constrains not only the ultimate fidelity of the tracking signal but also the ease with which it can be extracted by other brain regions. Here we demonstrate that a population of fast-OFF ganglion cells in the salamander retina, whose dynamics are governed by a nonlinear circuit, serve to compute the future position of the target over hundreds of milliseconds. The extrapolated position of the target is not found by stimulus reconstruction but is instead computed by a weighted sum of ganglion cell outputs, the population vector average (PVA). The magnitude of PVA extrapolation varies systematically with target size, speed, and acceleration, such that large targets are tracked most accurately at high speeds, and small targets at low speeds, just as is seen in the motion of real prey. Tracking precision reaches the resolution of single photoreceptors, and the PVA algorithm performs more robustly than several alternative algorithms. If the salamander brain uses the fast-OFF cell circuit for target extrapolation as we suggest, the circuit dynamics should leave a microstructure on the behavior that may be measured in future experiments. Our analysis highlights the utility of simple computations that, while not globally optimal, are efficiently implemented and have close to optimal performance over a limited but ethologically relevant range of stimuli.

Differential progression of structural and functional alterations in distinct retinal ganglion cell types in a mouse model of glaucoma

Intraocular pressure (IOP) elevation is a principal risk factor for glaucoma. Using a microbead injection technique to chronically raise IOP for 15 or 30 d in mice, we identified the early changes in visual response properties of different types of retinal ganglion cells (RGCs) and correlated these changes with neuronal morphology before cell death. Microbead-injected eyes showed reduced optokinetic tracking as well as cell death. In such eyes, multielectrode array recordings revealed that four RGC types show diverse alterations in their light responses upon IOP elevation. OFF-transient RGCs exhibited a more rapid decline in both structural and functional organizations compared with other RGCs. In contrast, although the light-evoked responses of OFF-sustained RGCs were perturbed, the dendritic arbor of this cell type remained intact. ON-transient and ON-sustained RGCs had normal functional receptive field sizes but their spontaneous and light-evoked firing rates were reduced. ON- and OFF-sustained RGCs lost excitatory synapses across an otherwise structurally normal dendritic arbor. Together, our observations indicate that there are changes in spontaneous activity and light-evoked responses in RGCs before detectable dendritic loss. However, when dendrites retract, we found corresponding changes in receptive field center size. Importantly, the effects of IOP elevation are not uniformly manifested in the structure and function of diverse RGC populations, nor are distinct RGC types perturbed within the same time-frame by such a challenge.

Adaptive colour contrast coding in the salamander retina efficiently matches natural scene statistics

The visual system continually adjusts its sensitivity to the statistical properties of the environment through an adaptation process that starts in the retina. Colour perception and processing is commonly thought to occur mainly in high visual areas, and indeed most evidence for chromatic colour contrast adaptation comes from cortical studies. We show that colour contrast adaptation starts in the retina where ganglion cells adjust their responses to the spectral properties of the environment. We demonstrate that the ganglion cells match their responses to red-blue stimulus combinations according to the relative contrast of each of the input channels by rotating their functional response properties in colour space. Using measurements of the chromatic statistics of natural environments, we show that the retina balances inputs from the two (red and blue) stimulated colour channels, as would be expected from theoretical optimal behaviour. Our results suggest that colour is encoded in the retina based on the efficient processing of spectral information that matches spectral combinations in natural scenes on the colour processing level.

Local and global contrast adaptation in retinal ganglion cells

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.

Alert response to motion onset in the retina

Previous studies have shown that motion onset is very effective at capturing attention and is more salient than smooth motion. Here, we find that this salience ranking is present already in the firing rate of retinal ganglion cells. By stimulating the retina with a bar that appears, stays still, and then starts moving, we demonstrate that a subset of salamander retinal ganglion cells, fast OFF cells, responds significantly more strongly to motion onset than to smooth motion. We refer to this phenomenon as an alert response to motion onset. We develop a computational model that predicts the time-varying firing rate of ganglion cells responding to the appearance, onset, and smooth motion of a bar. This model, termed the adaptive cascade model, consists of a ganglion cell that receives input from a layer of bipolar cells, represented by individual rectified subunits. Additionally, both the bipolar and ganglion cells have separate contrast gain control mechanisms. This model captured the responses to our different motion stimuli over a wide range of contrasts, speeds, and locations. The alert response to motion onset, together with its computational model, introduces a new mechanism of sophisticated motion processing that occurs early in the visual system.

Features and functions of nonlinear spatial integration by retinal ganglion cells

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.

Mapping a complete neural population in the retina

Recording simultaneously from essentially all of the relevant neurons in a local circuit is crucial to understand how they collectively represent information. Here we show that the combination of a large, dense multielectrode array and a novel, mostly automated spike-sorting algorithm allowed us to record simultaneously from a highly overlapping population of >200 ganglion cells in the salamander retina. By combining these methods with labeling and imaging, we showed that up to 95% of the ganglion cells over the area of the array were recorded. By measuring the coverage of visual space by the receptive fields of the recorded cells, we concluded that our technique captured a neural population that forms an essentially complete representation of a region of visual space. This completeness allowed us to determine the spatial layout of different cell types as well as identify a novel group of ganglion cells that responded reliably to a set of naturalistic and artificial stimuli but had no measurable receptive field. Thus, our method allows unprecedented access to the complete neural representation of visual information, a crucial step for the understanding of population coding in sensory systems.

Ionic mechanism underlying optimal stimuli for neuronal excitation: role of Na+ channel inactivation

The ionic mechanism underlying optimal stimulus shapes that induce a neuron to fire an action potential, or spike, is relevant to understanding optimal information transmission and therapeutic stimulation in the nervous system. Here we analyze for the first time the ionic basis for stimulus optimality in the Hodgkin and Huxley model and for eliciting a spike in squid giant axons, the preparation for which the model was devised. The experimentally determined stimulus is a smoothly varying biphasic current waveform having a relatively long and shallow hyperpolarizing phase followed by a depolarizing phase of briefer duration. The hyperpolarizing phase removes a small degree of the resting level of Na⁺ channel inactivation. This result together with the subsequent depolarizing phase provides a signal that is energetically more efficient for eliciting spikes than rectangular current pulses. Sodium channel inactivation is the only variable that is changed during the stimulus waveform, other than the membrane potential, V. The activation variables for Na⁺ and K⁺ channels are unchanged throughout the stimulus. This result demonstrates how an optimal stimulus waveform relates to ionic dynamics and may have implications for energy efficiency of neural excitation in many systems including the mammalian brain.