Encoding surprise by retinal ganglion cells.

The efficient coding hypothesis posits that early sensory neurons transmit maximal information about sensory stimuli, given internal constraints. A central prediction of this theory is that neurons should preferentially encode stimuli that are most surprising. Previous studies suggest this may be the case in early visual areas, where many neurons respond strongly to rare or surprising stimuli. For example, previous research showed that when presented with a rhythmic sequence of full-field flashes, many retinal ganglion cells (RGCs) respond strongly at the instance the flash sequence stops, and when another flash would be expected. This phenomenon is called the 'omitted stimulus response'. However, it is not known whether the responses of these cells varies in a graded way depending on the level of stimulus surprise. To investigate this, we presented retinal neurons with extended sequences of stochastic flashes. With this stimulus, the surprise associated with a particular flash/silence, could be quantified analytically, and varied in a graded manner depending on the previous sequences of flashes and silences. Interestingly, we found that RGC responses could be well explained by a simple normative model, which described how they optimally combined their prior expectations and recent stimulus history, so as to encode surprise. Further, much of the diversity in RGC responses could be explained by the model, due to the different prior expectations that different neurons had about the stimulus statistics. These results suggest that even as early as the retina many cells encode surprise, relative to their own, internally generated expectations.

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.

Predicting synchronous firing of large neural populations from sequential recordings.

A major goal in neuroscience is to understand how populations of neurons code for stimuli or actions. While the number of neurons that can be recorded simultaneously is increasing at a fast pace, in most cases these recordings cannot access a complete population: some neurons that carry relevant information remain unrecorded. In particular, it is hard to simultaneously record all the neurons of the same type in a given area. Recent progress have made possible to profile each recorded neuron in a given area thanks to genetic and physiological tools, and to pool together recordings from neurons of the same type across different experimental sessions. However, it is unclear how to infer the activity of a full population of neurons of the same type from these sequential recordings. Neural networks exhibit collective behaviour, e.g. noise correlations and synchronous activity, that are not directly captured by a conditionally-independent model that would just put together the spike trains from sequential recordings. Here we show that we can infer the activity of a full population of retina ganglion cells from sequential recordings, using a novel method based on copula distributions and maximum entropy modeling. From just the spiking response of each ganglion cell to a repeated stimulus, and a few pairwise recordings, we could predict the noise correlations using copulas, and then the full activity of a large population of ganglion cells of the same type using maximum entropy modeling. Remarkably, we could generalize to predict the population responses to different stimuli with similar light conditions and even to different experiments. We could therefore use our method to construct a very large population merging cells' responses from different experiments. We predicted that synchronous activity in ganglion cell populations saturates only for patches larger than 1.5mm in radius, beyond what is today experimentally accessible.

Mice Lacking Gpr179 with Complete Congenital Stationary Night Blindness Are a Good Model for Myopia.

Mutations in GPR179 are one of the most common causes of autosomal recessive complete congenital stationary night blindness (cCSNB). This retinal disease is characterized in patients by impaired dim and night vision, associated with other ocular symptoms, including high myopia. cCSNB is caused by a complete loss of signal transmission from photoreceptors to ON-bipolar cells. In this study, we hypothesized that the lack of Gpr179 and the subsequent impaired ON-pathway could lead to myopic features in a mouse model of cCSNB. Using ultra performance liquid chromatography, we show that adult Gpr179-/- mice have a significant decrease in both retinal dopamine and 3,4-dihydroxyphenylacetic acid, compared to Gpr179+/+ mice. This alteration of the dopaminergic system is thought to be correlated with an increased susceptibility to lens-induced myopia but does not affect the natural refractive development. Altogether, our data added a novel myopia model, which could be used to identify therapeutic interventions.

Towards optogenetic vision restoration with high resolution.

In many cases of inherited retinal degenerations, ganglion cells are spared despite photoreceptor cell death, making it possible to stimulate them to restore visual function. Several studies have shown that it is possible to express an optogenetic protein in ganglion cells and make them light sensitive, a promising strategy to restore vision. However the spatial resolution of optogenetically-reactivated retinas has rarely been measured, especially in the primate. Since the optogenetic protein is also expressed in axons, it is unclear if these neurons will only be sensitive to the stimulation of a small region covering their somas and dendrites, or if they will also respond to any stimulation overlapping with their axon, dramatically impairing spatial resolution. Here we recorded responses of mouse and macaque retinas to random checkerboard patterns following an in vivo optogenetic therapy. We show that optogenetically activated ganglion cells are each sensitive to a small region of visual space. A simple model based on this small receptive field predicted accurately their responses to complex stimuli. From this model, we simulated how the entire population of light sensitive ganglion cells would respond to letters of different sizes. We then estimated the maximal acuity expected by a patient, assuming it could make an optimal use of the information delivered by this reactivated retina. The obtained acuity is above the limit of legal blindness. Our model also makes interesting predictions on how acuity might vary upon changing the therapeutic strategy, assuming an optimal use of the information present in the retinal activity. Optogenetic therapy could thus potentially lead to high resolution vision, under conditions that our model helps to determinine.

Blindfold learning of an accurate neural metric.

The brain has no direct access to physical stimuli but only to the spiking activity evoked in sensory organs. It is unclear how the brain can learn representations of the stimuli based on those noisy, correlated responses alone. Here we show how to build an accurate distance map of responses solely from the structure of the population activity of retinal ganglion cells. We introduce the Temporal Restricted Boltzmann Machine to learn the spatiotemporal structure of the population activity and use this model to define a distance between spike trains. We show that this metric outperforms existing neural distances at discriminating pairs of stimuli that are barely distinguishable. The proposed method provides a generic and biologically plausible way to learn to associate similar stimuli based on their spiking responses, without any other knowledge of these stimuli.

Toward a unified theory of efficient, predictive, and sparse coding.

A central goal in theoretical neuroscience is to predict the response properties of sensory neurons from first principles. To this end, "efficient coding" posits that sensory neurons encode maximal information about their inputs given internal constraints. There exist, however, many variants of efficient coding (e.g., redundancy reduction, different formulations of predictive coding, robust coding, sparse coding, etc.), differing in their regimes of applicability, in the relevance of signals to be encoded, and in the choice of constraints. It is unclear how these types of efficient coding relate or what is expected when different coding objectives are combined. Here we present a unified framework that encompasses previously proposed efficient coding models and extends to unique regimes. We show that optimizing neural responses to encode predictive information can lead them to either correlate or decorrelate their inputs, depending on the stimulus statistics; in contrast, at low noise, efficiently encoding the past always predicts decorrelation. Later, we investigate coding of naturalistic movies and show that qualitatively different types of visual motion tuning and levels of response sparsity are predicted, depending on whether the objective is to recover the past or predict the future. Our approach promises a way to explain the observed diversity of sensory neural responses, as due to multiple functional goals and constraints fulfilled by different cell types and/or circuits.

Modeling the Correlated Activity of Neural Populations: A Review.

The principles of neural encoding and computations are inherently collective and usually involve large populations of interacting neurons with highly correlated activities. While theories of neural function have long recognized the importance of collective effects in populations of neurons, only in the past two decades has it become possible to record from many cells simultaneously using advanced experimental techniques with single-spike resolution and to relate these correlations to function and behavior. This review focuses on the modeling and inference approaches that have been recently developed to describe the correlated spiking activity of populations of neurons. We cover a variety of models describing correlations between pairs of neurons, as well as between larger groups, synchronous or delayed in time, with or without the explicit influence of the stimulus, and including or not latent variables. We discuss the advantages and drawbacks or each method, as well as the computational challenges related to their application to recordings of ever larger populations.

Nonlinear decoding of a complex movie from the mammalian retina.

Retina is a paradigmatic system for studying sensory encoding: the transformation of light into spiking activity of ganglion cells. The inverse problem, where stimulus is reconstructed from spikes, has received less attention, especially for complex stimuli that should be reconstructed "pixel-by-pixel". We recorded around a hundred neurons from a dense patch in a rat retina and decoded movies of multiple small randomly-moving discs. We constructed nonlinear (kernelized and neural network) decoders that improved significantly over linear results. An important contribution to this was the ability of nonlinear decoders to reliably separate between neural responses driven by locally fluctuating light signals, and responses at locally constant light driven by spontaneous-like activity. This improvement crucially depended on the precise, non-Poisson temporal structure of individual spike trains, which originated in the spike-history dependence of neural responses. We propose a general principle by which downstream circuitry could discriminate between spontaneous and stimulus-driven activity based solely on higher-order statistical structure in the incoming spike trains.

A Simple Model for Low Variability in Neural Spike Trains.

Neural noise sets a limit to information transmission in sensory systems. In several areas, the spiking response (to a repeated stimulus) has shown a higher degree of regularity than predicted by a Poisson process. However, a simple model to explain this low variability is still lacking. Here we introduce a new model, with a correction to Poisson statistics, that can accurately predict the regularity of neural spike trains in response to a repeated stimulus. The model has only two parameters but can reproduce the observed variability in retinal recordings in various conditions. We show analytically why this approximation can work. In a model of the spike-emitting process where a refractory period is assumed, we derive that our simple correction can well approximate the spike train statistics over a broad range of firing rates. Our model can be easily plugged to stimulus processing models, like a linear-nonlinear model or its generalizations, to replace the Poisson spike train hypothesis that is commonly assumed. It estimates the amount of information transmitted much more accurately than Poisson models in retinal recordings. Thanks to its simplicity, this model has the potential to explain low variability in other areas.

A New Promoter Allows Optogenetic Vision Restoration with Enhanced Sensitivity in Macaque Retina.

The majority of inherited retinal degenerations converge on the phenotype of photoreceptor cell death. Second- and third-order neurons are spared in these diseases, making it possible to restore retinal light responses using optogenetics. Viral expression of channelrhodopsin in the third-order neurons under ubiquitous promoters was previously shown to restore visual function, albeit at light intensities above illumination safety thresholds. Here, we report (to our knowledge, for the first time) activation of macaque retinas, up to 6 months post-injection, using channelrhodopsin-Ca2+-permeable channelrhodopsin (CatCh) at safe light intensities. High-level CatCh expression was achieved due to a new promoter based on the regulatory region of the gamma-synuclein gene (SNCG) allowing strong expression in ganglion cells across species. Our promoter, in combination with clinically proven adeno-associated virus 2 (AAV2), provides CatCh expression in peri-foveolar ganglion cells responding robustly to light under the illumination safety thresholds for the human eye. On the contrary, the threshold of activation and the proportion of unresponsive cells were much higher when a ubiquitous promoter (cytomegalovirus [CMV]) was used to express CatCh. The results of our study suggest that the inclusion of optimized promoters is key in the path to clinical translation of optogenetics.

Predictive information in a sensory population.

Guiding behavior requires the brain to make predictions about the future values of sensory inputs. Here, we show that efficient predictive computation starts at the earliest stages of the visual system. We compute how much information groups of retinal ganglion cells carry about the future state of their visual inputs and show that nearly every cell in the retina participates in a group of cells for which this predictive information is close to the physical limit set by the statistical structure of the inputs themselves. Groups of cells in the retina carry information about the future state of their own activity, and we show that this information can be compressed further and encoded by downstream predictor neurons that exhibit feature selectivity that would support predictive computations. Efficient representation of predictive information is a candidate principle that can be applied at each stage of neural computation.

Thermodynamics and signatures of criticality in a network of neurons.

The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but, with more spikes, the number of possible patterns increases. This tradeoff between probability and numerosity is mathematically equivalent to the relationship between entropy and energy in statistical physics. We construct this relationship for populations of up to N = 160 neurons in a small patch of the vertebrate retina, using a combination of direct and model-based analyses of experiments on the response of this network to naturalistic movies. We see signs of a thermodynamic limit, where the entropy per neuron approaches a smooth function of the energy per neuron as N increases. The form of this function corresponds to the distribution of activity being poised near an unusual kind of critical point. We suggest further tests of criticality, and give a brief discussion of its functional significance.

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.

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.

Targeting channelrhodopsin-2 to ON-bipolar cells with vitreally administered AAV Restores ON and OFF visual responses in blind mice.

Most inherited retinal dystrophies display progressive photoreceptor cell degeneration leading to severe visual impairment. Optogenetic reactivation of retinal neurons mediated by adeno-associated virus (AAV) gene therapy has the potential to restore vision regardless of patient-specific mutations. The challenge for clinical translatability is to restore a vision as close to natural vision as possible, while using a surgically safe delivery route for the fragile degenerated retina. To preserve the visual processing of the inner retina, we targeted ON bipolar cells, which are still present at late stages of disease. For safe gene delivery, we used a recently engineered AAV variant that can transduce the bipolar cells after injection into the eye's easily accessible vitreous humor. We show that AAV encoding channelrhodopsin under the ON bipolar cell-specific promoter mediates long-term gene delivery restricted to ON-bipolar cells after intravitreal administration. Channelrhodopsin expression in ON bipolar cells leads to restoration of ON and OFF responses at the retinal and cortical levels. Moreover, light-induced locomotory behavior is restored in treated blind mice. Our results support the clinical relevance of a minimally invasive AAV-mediated optogenetic therapy for visual restoration.

Hidden complexity of synaptic receptive fields in cat V1.

In the primary visual cortex (V1), Simple and Complex receptive fields (RFs) are usually characterized on the basis of the linearity of the cell spiking response to stimuli of opposite contrast. Whether or not this classification reflects a functional dichotomy in the synaptic inputs to Simple and Complex cells is still an open issue. Here we combined intracellular membrane potential recordings in cat V1 with 2D dense noise stimulation to decompose the Simple-like and Complex-like components of the subthreshold RF into a parallel set of functionally distinct subunits. Results show that both Simple and Complex RFs exhibit a remarkable diversity of excitatory and inhibitory Complex-like contributions, which differ in orientation and spatial frequency selectivity from the linear RF, even in layer 4 and layer 6 Simple cells. We further show that the diversity of Complex-like contributions recovered at the subthreshold level is expressed in the cell spiking output. These results demonstrate that the Simple or Complex nature of V1 RFs does not rely on the diversity of Complex-like components received by the cell from its synaptic afferents but on the imbalance between the weights of the Simple-like and Complex-like synaptic contributions.

Dynamical criticality in the collective activity of a population of retinal neurons.

Recent experimental results based on multielectrode and imaging techniques have reinvigorated the idea that large neural networks operate near a critical point, between order and disorder. However, evidence for criticality has relied on the definition of arbitrary order parameters, or on models that do not address the dynamical nature of network activity. Here we introduce a novel approach to assess criticality that overcomes these limitations, while encompassing and generalizing previous criteria. We find a simple model to describe the global activity of large populations of ganglion cells in the rat retina, and show that their statistics are poised near a critical point. Taking into account the temporal dynamics of the activity greatly enhances the evidence for criticality, revealing it where previous methods would not. The approach is general and could be used in other biological networks.

What can neuromorphic event-driven precise timing add to spike-based pattern recognition?

This letter introduces a study to precisely measure what an increase in spike timing precision can add to spike-driven pattern recognition algorithms. The concept of generating spikes from images by converting gray levels into spike timings is currently at the basis of almost every spike-based modeling of biological visual systems. The use of images naturally leads to generating incorrect artificial and redundant spike timings and, more important, also contradicts biological findings indicating that visual processing is massively parallel, asynchronous with high temporal resolution. A new concept for acquiring visual information through pixel-individual asynchronous level-crossing sampling has been proposed in a recent generation of asynchronous neuromorphic visual sensors. Unlike conventional cameras, these sensors acquire data not at fixed points in time for the entire array but at fixed amplitude changes of their input, resulting optimally sparse in space and time-pixel individually and precisely timed only if new, (previously unknown) information is available (event based). This letter uses the high temporal resolution spiking output of neuromorphic event-based visual sensors to show that lowering time precision degrades performance on several recognition tasks specifically when reaching the conventional range of machine vision acquisition frequencies (30-60 Hz). The use of information theory to characterize separability between classes for each temporal resolution shows that high temporal acquisition provides up to 70% more information that conventional spikes generated from frame-based acquisition as used in standard artificial vision, thus drastically increasing the separability between classes of objects. Experiments on real data show that the amount of information loss is correlated with temporal precision. Our information-theoretic study highlights the potentials of neuromorphic asynchronous visual sensors for both practical applications and theoretical investigations. Moreover, it suggests that representing visual information as a precise sequence of spike times as reported in the retina offers considerable advantages for neuro-inspired visual computations.

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.