Mapping nonlinear receptive field structure in primate retina at single cone resolution

Novel color via stimulation of individual photoreceptors at population scale

We introduce a principle, Oz, for displaying color imagery: directly controlling the human eye's photoreceptor activity via cell-by-cell light delivery. Theoretically, novel colors are possible through bypassing the constraints set by the cone spectral sensitivities and activating M cone cells exclusively. In practice, we confirm a partial expansion of colorspace toward that theoretical ideal. Attempting to activate M cones exclusively is shown to elicit a color beyond the natural human gamut, formally measured with color matching by human subjects. They describe the color as blue-green of unprecedented saturation. Further experiments show that subjects perceive Oz colors in image and video form. The prototype targets laser microdoses to thousands of spectrally classified cones under fixational eye motion. These results are proof-of-principle for programmable control over individual photoreceptors at population scale.

The receptive field construction of midget ganglion cells in primate retina

The midget pathway of the primate retina provides the visual system with the foundations for high spatial resolution and color perception. An essential contributor to these properties is center-surround organization, in which responses from the central area of a cell's receptive field are antagonized by responses from a surrounding area. Two key questions about center-surround organization are unresolved. First, the surround is largely or completely due to negative feedback from horizontal cells to cones: how can this feedback be reconciled with the popular difference of Gaussians (DOG) model, which implies feedforward inhibition? Second, can the spatial extent of center and surround be predicted from the components-optics, horizontal cell receptive field, ganglion cell dendrites-that give rise to them? We address these questions with a computational model of midget pathway signal processing in macaque retina; model parameters are derived from published literature. We show that, contrary to the DOG model, the surround's effect is better treated as divisive. A simplified version of our model-a ratio of Gaussians (ROG) model-has practical advantages over the DOG, such as accounting for spatiotemporal interactions and pulse responses. The ROG model also shows that both center and surround radii can be calculated from a sum of squared radii of their components. Finally, chromatic antagonism between center and surround in the full model predicts cone opponency as a function of eccentricity. We suggest that a signal-processing model gives new insight into retinal function.NEW & NOTEWORTHY We simulated signal processing from cones to midget ganglion cells in the monkey retina and found that: 1) center/surround structure is better described as a ratio of Gaussian functions than as the traditional difference of Gaussians; 2) ganglion cell center and surround radii can be calculated from a sum of squares of radii in upstream stages; 3) the model can predict chromatic dominance in the center and surround mechanisms as a function of eccentricity.

Nonlinear receptive fields evoke redundant retinal coding of natural scenes

The role of the vertebrate retina in early vision is generally described by the efficient coding hypothesis1,2, which predicts that the retina reduces the redundancy inherent in natural scenes3 by discarding spatiotemporal correlations while preserving stimulus information4. It is unclear, however, whether the predicted decorrelation and redundancy reduction in the activity of ganglion cells, the retina's output neurons, hold under gaze shifts, which dominate the dynamics of the natural visual input5. We show here that species-specific gaze patterns in natural stimuli can drive correlated spiking responses both in and across distinct types of ganglion cells in marmoset as well as mouse retina. These concerted responses disrupt redundancy reduction to signal fixation periods with locally high spatial contrast. Model-based analyses of ganglion cell responses to natural stimuli show that the observed response correlations follow from nonlinear pooling of ganglion cell inputs. Our results indicate cell-type-specific deviations from efficient coding in retinal processing of natural gaze shifts.

Fixational eye movements enhance the precision of visual information transmitted by the primate retina

Fixational eye movements alter the number and timing of spikes transmitted from the retina to the brain, but whether these changes enhance or degrade the retinal signal is unclear. To quantify this, we developed a Bayesian method for reconstructing natural images from the recorded spikes of hundreds of retinal ganglion cells (RGCs) in the macaque retina (male), combining a likelihood model for RGC light responses with the natural image prior implicitly embedded in an artificial neural network optimized for denoising. The method matched or surpassed the performance of previous reconstruction algorithms, and provides an interpretable framework for characterizing the retinal signal. Reconstructions were improved with artificial stimulus jitter that emulated fixational eye movements, even when the eye movement trajectory was assumed to be unknown and had to be inferred from retinal spikes. Reconstructions were degraded by small artificial perturbations of spike times, revealing more precise temporal encoding than suggested by previous studies. Finally, reconstructions were substantially degraded when derived from a model that ignored cell-to-cell interactions, indicating the importance of stimulus-evoked correlations. Thus, fixational eye movements enhance the precision of the retinal representation.

Applying Super-Resolution and Tomography Concepts to Identify Receptive Field Subunits in the Retina

Spatially nonlinear stimulus integration by retinal ganglion cells lies at the heart of various computations performed by the retina. It arises from the nonlinear transmission of signals that ganglion cells receive from bipolar cells, which thereby constitute functional subunits within a ganglion cell's receptive field. Inferring these subunits from recorded ganglion cell activity promises a new avenue for studying the functional architecture of the retina. This calls for efficient methods, which leave sufficient experimental time to leverage the acquired knowledge for further investigating identified subunits. Here, we combine concepts from super-resolution microscopy and computed tomography and introduce super-resolved tomographic reconstruction (STR) as a technique to efficiently stimulate and locate receptive field subunits. Simulations demonstrate that this approach can reliably identify subunits across a wide range of model variations, and application in recordings of primate parasol ganglion cells validates the experimental feasibility. STR can potentially reveal comprehensive subunit layouts within only a few tens of minutes of recording time, making it ideal for online analysis and closed-loop investigations of receptive field substructure in retina recordings.

Optimization-Based Pairwise Interaction Point Process (O-PIPP): A Precise and Universal Retinal Mosaic Modeling Approach

Purpose

A retinal mosaic, the spatial organization of a population of homotypic neurons, is thought to sample a specific visual feature into the feedforward visual pathway. The purpose of this study was to propose a universal modeling approach for precisely generating retinal mosaics and overcoming the limitations of previous models, especially in modeling abnormal mosaic patterns under disease conditions.

Methods

Here, we developed the optimization-based pairwise interaction point process (O-PIPP). It incorporates optimization techniques into previous simulation approaches, enabling directional control of the simulation process according to the user-designed optimization target. For the convenience of the community, we implemented the O-PIPP approach into a Python package and a website application.

Results

We showed that the O-PIPP can generate more precise neural spatial patterns of healthy and diseased mosaics compared to previous phenomenological approaches. Notably, through modeling the retinal neural circuitry with O-PIPP-simulated retinitis pigmentosa cone mosaics, we elucidated how the cone mosaic rearrangement impacted the information processing of ganglion cells.

Conclusions

The O-PIPP provides a precise and universal tool to simulate realistic mosaics, which could help to investigate the function of retinal mosaics in vision.

Dynamic Nonlinear Spatial Integrations on Encoding Contrasting Stimuli of Tectal Neurons

Animals detect targets using a variety of visual cues, with the visual salience of these cues determining which environmental features receive priority attention and further processing. Surround modulation plays a crucial role in generating visual saliency, which has been extensively studied in avian tectal neurons. Recent work has reported that the suppression of tectal neurons induced by motion contrasting stimulus is stronger than that by luminance contrasting stimulus. However, the underlying mechanism remains poorly understood. In this study, we built a computational model (called Generalized Linear-Dynamic Modulation) which incorporates independent nonlinear tuning mechanisms for excitatory and inhibitory inputs. This model aims to describe how tectal neurons encode contrasting stimuli. The results showed that: (1) The dynamic nonlinear integration structure substantially improved the accuracy (significant difference (p < 0.001, paired t-test) in the goodness of fit between the two models) of the predicted responses to contrasting stimuli, verifying the nonlinear processing performed by tectal neurons. (2) The modulation difference between luminance and motion contrasting stimuli emerged from the predicted response by the full model but not by that with only excitatory synaptic input (spatial luminance: 89 ± 2.8% (GL_DM) vs. 87 ± 2.1% (GL_DMexc); motion contrasting stimuli: 87 ± 1.7% (GL_DM) vs. 83 ± 2.2% (GL_DMexc)). These results validate the proposed model and further suggest the role of dynamic nonlinear spatial integrations in contextual visual information processing, especially in spatial integration, which is important for object detection performed by birds.

Estimating receptive fields of simple and complex cells in early visual cortex: A convolutional neural network model with parameterized rectification

Neurons in the primary visual cortex respond selectively to simple features of visual stimuli, such as orientation and spatial frequency. Simple cells, which have phase-sensitive responses, can be modeled by a single receptive field filter in a linear-nonlinear model. However, it is challenging to analyze phase-invariant complex cells, which require more elaborate models having a combination of nonlinear subunits. Estimating parameters of these models is made additionally more difficult by cortical neurons' trial-to-trial response variability. We develop a simple convolutional neural network method to estimate receptive field models for both simple and complex visual cortex cells from their responses to natural images. The model consists of a spatiotemporal filter, a parameterized rectifier unit (PReLU), and a two-dimensional Gaussian "map" of the receptive field envelope. A single model parameter determines the simple vs. complex nature of the receptive field, capturing complex cell responses as a summation of homogeneous subunits, and collapsing to a linear-nonlinear model for simple type cells. The convolutional method predicts simple and complex cell responses to natural image stimuli as well as grating tuning curves. The fitted models yield a continuum of values for the PReLU parameter across the sampled neurons, showing that the simple/complex nature of cells can vary in a continuous manner. We demonstrate that complex-like cells respond less reliably than simple-like cells. However, compensation for this unreliability with noise ceiling analysis reveals predictive performance for complex cells proportionately closer to that for simple cells. Most spatial receptive field structures are well fit by Gabor functions, whose parameters confirm well-known properties of cat A17/18 receptive fields.

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.

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.

Inhibition, but not excitation, recovers from partial cone loss with greater spatiotemporal integration, synapse density, and frequency

Neural circuits function in the face of changing inputs, either caused by normal variation in stimuli or by cell death. To maintain their ability to perform essential computations with partial inputs, neural circuits make modifications. Here, we study the retinal circuit’s responses to changes in light stimuli or in photoreceptor inputs by inducing partial cone death in the mature mouse retina. Can the retina withstand or recover from input loss? We find that the excitatory pathways exhibit functional loss commensurate with cone death and with some aspects predicted by partial light stimulation. However, inhibitory pathways recover functionally from lost input by increasing spatiotemporal integration in a way that is not recapitulated by partially stimulating the control retina. Anatomically, inhibitory synapses are upregulated on secondary bipolar cells and output ganglion cells. These findings demonstrate the greater capacity for inhibition, compared with excitation, to modify spatiotemporal processing with fewer cone inputs.

Lee et al. find partial cone loss triggers inhibition, but not excitation, to increase spatiotemporal integration, recover contrast gain, and increase synaptic release onto retinal ganglion cells. Natural images filtered by cone-loss receptive fields perceptually match those of controls. Thus, inhibition compensates for fewer cones to potentially preserve perception.

Impact of Photoreceptor Loss on Retinal Circuitry

Our sense of sight relies on photoreceptors, which transduce photons into the nervous system's electrochemical interpretation of the visual world. These precious photoreceptors can be disrupted by disease, injury, and aging. Once photoreceptors start to die, but before blindness occurs, the remaining retinal circuitry can withstand, mask, or exacerbate the photoreceptor deficit and potentially be receptive to newfound therapies for vision restoration. To maximize the retina's receptivity to therapy, one must understand the conditions that influence the state of the remaining retina. In this review, we provide an overview of the retina's structure and function in health and disease. We analyze a collection of observations on photoreceptor disruption and generate a predictive model to identify parameters that influence the retina's response. Finally, we speculate on whether the retina, with its remarkable capacity to function over light levels spanning nine orders of magnitude, uses these same adaptational mechanisms to withstand and perhaps mask photoreceptor loss.

The Relationship Between Visual Sensitivity and Eccentricity, Cone Density and Outer Segment Length in the Human Foveola

Purpose

The cellular topography of the human foveola, the central 1° diameter of the fovea, is strikingly non-uniform, with a steep increase of cone photoreceptor density and outer segment (OS) length toward its center. Here, we assessed to what extent the specific cellular organization of the foveola of an individual is reflected in visual sensitivity and if sensitivity peaks at the preferred retinal locus of fixation (PRL).

Methods

Increment sensitivity to small-spot, cone-targeted visual stimuli (1 × 1 arcmin, 543-nm light) was recorded psychophysically in four human participants at 17 locations concentric within a 0.2° diameter on and around the PRL with adaptive optics scanning laser ophthalmoscopy-based microstimulation. Sensitivity test spots were aligned with cell-resolved maps of cone density and cone OS length.

Results

Peak sensitivity was at neither the PRL nor the topographical center of the cone mosaic. Within the central 0.1° diameter, a plateau-like sensitivity profile was observed. Cone density and maximal OS length differed significantly across participants, correlating with their peak sensitivity. Based on these results, biophysical simulation allowed to develop a model of visual sensitivity in the foveola, with distance from the PRL (eccentricity), cone density, and OS length as parameters.

Conclusions

Small-spot sensitivity thresholds in healthy retinas will help to establish the range of normal foveolar function in cell-targeted vision testing. Because of the high reproducibility in replicate testing, threshold variability not explained by our model is assumed to be caused by individual cone and bipolar cell weighting at the specific target locations.

Nonlinear Decoding of Natural Images From Large-Scale Primate Retinal Ganglion Recordings

Decoding sensory stimuli from neural activity can provide insight into how the nervous system might interpret the physical environment, and facilitates the development of brain-machine interfaces. Nevertheless, the neural decoding problem remains a significant open challenge. Here, we present an efficient nonlinear decoding approach for inferring natural scene stimuli from the spiking activities of retinal ganglion cells (RGCs). Our approach uses neural networks to improve on existing decoders in both accuracy and scalability. Trained and validated on real retinal spike data from more than 1000 simultaneously recorded macaque RGC units, the decoder demonstrates the necessity of nonlinear computations for accurate decoding of the fine structures of visual stimuli. Specifically, high-pass spatial features of natural images can only be decoded using nonlinear techniques, while low-pass features can be extracted equally well by linear and nonlinear methods. Together, these results advance the state of the art in decoding natural stimuli from large populations of neurons.

Interphotoreceptor coupling: an evolutionary perspective

In the vertebrate retina, signals generated by cones of different spectral preference and by highly sensitive rod photoreceptors interact at various levels to extract salient visual information. The first opportunity for such interaction is offered by electrical coupling of the photoreceptors themselves, which is mediated by gap junctions located at the contact points of specialised cellular processes: synaptic terminals, telodendria and radial fins. Here, we examine the evolutionary pressures for and against interphotoreceptor coupling, which are likely to have shaped how coupling is deployed in different species. The impact of coupling on signal to noise ratio, spatial acuity, contrast sensitivity, absolute and increment threshold, retinal signal flow and colour discrimination is discussed while emphasising available data from a variety of vertebrate models spanning from lampreys to primates. We highlight the many gaps in our knowledge, persisting discrepancies in the literature, as well as some major unanswered questions on the actual extent and physiological role of cone-cone, rod-cone and rod-rod communication. Lastly, we point toward limited but intriguing evidence suggestive of the ancestral form of coupling among ciliary photoreceptors.

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

Nonlinear Spatial Integration Underlies the Diversity of Retinal Ganglion Cell Responses to Natural Images

How neurons encode natural stimuli is a fundamental question for sensory neuroscience. In the early visual system, standard encoding models assume that neurons linearly filter incoming stimuli through their receptive fields, but artificial stimuli, such as contrast-reversing gratings, often reveal nonlinear spatial processing. We investigated to what extent such nonlinear processing is relevant for the encoding of natural images in retinal ganglion cells in mice of either sex.

How neurons encode natural stimuli is a fundamental question for sensory neuroscience. In the early visual system, standard encoding models assume that neurons linearly filter incoming stimuli through their receptive fields, but artificial stimuli, such as contrast-reversing gratings, often reveal nonlinear spatial processing. We investigated to what extent such nonlinear processing is relevant for the encoding of natural images in retinal ganglion cells in mice of either sex. We found that standard linear receptive field models yielded good predictions of responses to flashed natural images for a subset of cells but failed to capture the spiking activity for many others. Cells with poor model performance displayed pronounced sensitivity to fine spatial contrast and local signal rectification as the dominant nonlinearity. By contrast, sensitivity to high-frequency contrast-reversing gratings, a classical test for nonlinear spatial integration, was not a good predictor of model performance and thus did not capture the variability of nonlinear spatial integration under natural images. In addition, we also observed a class of nonlinear ganglion cells with inverse tuning for spatial contrast, responding more strongly to spatially homogeneous than to spatially structured stimuli. These findings highlight the diversity of receptive field nonlinearities as a crucial component for understanding early sensory encoding in the context of natural stimuli.

SIGNIFICANCE STATEMENT Experiments with artificial visual stimuli have revealed that many types of retinal ganglion cells pool spatial input signals nonlinearly. However, it is still unclear how relevant this nonlinear spatial integration is when the input signals are natural images. Here we analyze retinal responses to natural scenes in large populations of mouse ganglion cells. We show that nonlinear spatial integration strongly influences responses to natural images for some ganglion cells, but not for others. Cells with nonlinear spatial integration were sensitive to spatial structure inside their receptive fields, and a small group of cells displayed a surprising sensitivity to spatially homogeneous stimuli. Traditional analyses with contrast-reversing gratings did not predict this variability of nonlinear spatial integration under natural images.

Retinal ganglion cells and the magnocellular, parvocellular, and koniocellular subcortical visual pathways from the eye to the brain

In primates including humans, most retinal ganglion cells send signals to the lateral geniculate nucleus (LGN) of the thalamus. The anatomical and functional properties of the two major pathways through the LGN, the parvocellular (P) and magnocellular (M) pathways, are now well understood. Neurones in these pathways appear to convey a filtered version of the retinal image to primary visual cortex for further analysis. The properties of the P-pathway suggest it is important for high spatial acuity and red-green color vision, while those of the M-pathway suggest it is important for achromatic visual sensitivity and motion vision. Recent work has sharpened our understanding of how these properties are built in the retina, and described subtle but important nonlinearities that shape the signals that cortex receives. In addition to the P- and M-pathways, other retinal ganglion cells also project to the LGN. These ganglion cells are larger than those in the P- and M-pathways, have different retinal connectivity, and project to distinct regions of the LGN, together forming heterogenous koniocellular (K) pathways. Recent work has started to reveal the properties of these K-pathways, in the retina and in the LGN. The functional properties of K-pathways are more complex than those in the P- and M-pathways, and the K-pathways are likely to have a distinct contribution to vision. They provide a complementary pathway to the primary visual cortex, but can also send signals directly to extrastriate visual cortex. At the level of the LGN, many neurones in the K-pathways seem to integrate retinal with non-retinal inputs, and some may provide an early site of binocular convergence.

Reconstruction of natural images from responses of primate retinal ganglion cells

The visual message conveyed by a retinal ganglion cell (RGC) is often summarized by its spatial receptive field, but in principle also depends on the responses of other RGCs and natural image statistics. This possibility was explored by linear reconstruction of natural images from responses of the four numerically-dominant macaque RGC types. Reconstructions were highly consistent across retinas. The optimal reconstruction filter for each RGC - its visual message - reflected natural image statistics, and resembled the receptive field only when nearby, same-type cells were included. ON and OFF cells conveyed largely independent, complementary representations, and parasol and midget cells conveyed distinct features. Correlated activity and nonlinearities had statistically significant but minor effects on reconstruction. Simulated reconstructions, using linear-nonlinear cascade models of RGC light responses that incorporated measured spatial properties and nonlinearities, produced similar results. Spatiotemporal reconstructions exhibited similar spatial properties, suggesting that the results are relevant for natural vision.

Computational challenges and opportunities for a bi-directional artificial retina

A future artificial retina that can restore high acuity vision in blind people will rely on the capability to both read (observe) and write (control) the spiking activity of neurons using an adaptive, bi-directional and high-resolution device. Although current research is focused on overcoming the technical challenges of building and implanting such a device, exploiting its capabilities to achieve more acute visual perception will also require substantial computational advances. Using high-density large-scale recording and stimulation in the primate retina with an ex vivo multi-electrode array lab prototype, we frame several of the major computational problems, and describe current progress and future opportunities in solving them. First, we identify cell types and locations from spontaneous activity in the blind retina, and then efficiently estimate their visual response properties by using a low-dimensional manifold of inter-retina variability learned from a large experimental dataset. Second, we estimate retinal responses to a large collection of relevant electrical stimuli by passing current patterns through an electrode array, spike sorting the resulting recordings and using the results to develop a model of evoked responses. Third, we reproduce the desired responses for a given visual target by temporally dithering a diverse collection of electrical stimuli within the integration time of the visual system. Together, these novel approaches may substantially enhance artificial vision in a next-generation device.

Inference of nonlinear receptive field subunits with spike-triggered clustering

Responses of sensory neurons are often modeled using a weighted combination of rectified linear subunits. Since these subunits often cannot be measured directly, a flexible method is needed to infer their properties from the responses of downstream neurons. We present a method for maximum likelihood estimation of subunits by soft-clustering spike-triggered stimuli, and demonstrate its effectiveness in visual neurons. For parasol retinal ganglion cells in macaque retina, estimated subunits partitioned the receptive field into compact regions, likely representing aggregated bipolar cell inputs. Joint clustering revealed shared subunits between neighboring cells, producing a parsimonious population model. Closed-loop validation, using stimuli lying in the null space of the linear receptive field, revealed stronger nonlinearities in OFF cells than ON cells. Responses to natural images, jittered to emulate fixational eye movements, were accurately predicted by the subunit model. Finally, the generality of the approach was demonstrated in macaque V1 neurons.

Inferring synaptic inputs from spikes with a conductance-based neural encoding model

Descriptive statistical models of neural responses generally aim to characterize the mapping from stimuli to spike responses while ignoring biophysical details of the encoding process. Here, we introduce an alternative approach, the conductance-based encoding model (CBEM), which describes a mapping from stimuli to excitatory and inhibitory synaptic conductances governing the dynamics of sub-threshold membrane potential. Remarkably, we show that the CBEM can be fit to extracellular spike train data and then used to predict excitatory and inhibitory synaptic currents. We validate these predictions with intracellular recordings from macaque retinal ganglion cells. Moreover, we offer a novel quasi-biophysical interpretation of the Poisson generalized linear model (GLM) as a special case of the CBEM in which excitation and inhibition are perfectly balanced. This work forges a new link between statistical and biophysical models of neural encoding and sheds new light on the biophysical variables that underlie spiking in the early visual pathway.

Understanding the retinal basis of vision across species

The vertebrate retina first evolved some 500 million years ago in ancestral marine chordates. Since then, the eyes of different species have been tuned to best support their unique visuoecological lifestyles. Visual specializations in eye designs, large-scale inhomogeneities across the retinal surface and local circuit motifs mean that all species' retinas are unique. Computational theories, such as the efficient coding hypothesis, have come a long way towards an explanation of the basic features of retinal organization and function; however, they cannot explain the full extent of retinal diversity within and across species. To build a truly general understanding of vertebrate vision and the retina's computational purpose, it is therefore important to more quantitatively relate different species' retinal functions to their specific natural environments and behavioural requirements. Ultimately, the goal of such efforts should be to build up to a more general theory of vision.

Multiple Timescales Account for Adaptive Responses across Sensory Cortices

Sensory systems encounter remarkably diverse stimuli in the external environment. Natural stimuli exhibit timescales and amplitudes of variation that span a wide range. Mechanisms of adaptation, a ubiquitous feature of sensory systems, allow for the accommodation of this range of scales. Are there common rules of adaptation across different sensory modalities? We measured the membrane potential responses of individual neurons in the visual, somatosensory, and auditory cortices of male and female mice to discrete, punctate stimuli delivered at a wide range of fixed and nonfixed frequencies. We find that the adaptive profile of the response is largely preserved across these three areas, exhibiting attenuation and responses to the cessation of stimulation, which are signatures of response to changes in stimulus statistics. We demonstrate that these adaptive responses can emerge from a simple model based on the integration of fixed filters operating over multiple time scales.SIGNIFICANCE STATEMENT Our recent sensations affect our current expectations and perceptions of the environment. Neural correlates of this process exist throughout the brain and are loosely termed adaptation. Adaptive processes have been described across sensory cortices, but direct comparisons of these processes have not been possible because paradigms have been tailored specifically for each modality. We developed a common stimulus set that was used to characterize adaptation in somatosensory, visual, and auditory cortex. We describe here the similarities and differences in adaptation across these cortical areas and demonstrate that adaptive responses may emerge from a set of static filters that operate over a broad range of timescales.

Data-Driven Approaches to Understanding Visual Neuron Activity

With modern neurophysiological methods able to record neural activity throughout the visual pathway in the context of arbitrarily complex visual stimulation, our understanding of visual system function is becoming limited by the available models of visual neurons that can be directly related to such data. Different forms of statistical models are now being used to probe the cellular and circuit mechanisms shaping neural activity, understand how neural selectivity to complex visual features is computed, and derive the ways in which neurons contribute to systems-level visual processing. However, models that are able to more accurately reproduce observed neural activity often defy simple interpretations. As a result, rather than being used solely to connect with existing theories of visual processing, statistical modeling will increasingly drive the evolution of more sophisticated theories.

Voltage- and calcium-gated ion channels of neurons in the vertebrate retina

In this review, we summarize studies investigating the types and distribution of voltage- and calcium-gated ion channels in the different classes of retinal neurons: rods, cones, horizontal cells, bipolar cells, amacrine cells, interplexiform cells, and ganglion cells. We discuss differences among cell subtypes within these major cell classes, as well as differences among species, and consider how different ion channels shape the responses of different neurons. For example, even though second-order bipolar and horizontal cells do not typically generate fast sodium-dependent action potentials, many of these cells nevertheless possess fast sodium currents that can enhance their kinetic response capabilities. Ca2+ channel activity can also shape response kinetics as well as regulating synaptic release. The L-type Ca2+ channel subtype, CaV1.4, expressed in photoreceptor cells exhibits specific properties matching the particular needs of these cells such as limited inactivation which allows sustained channel activity and maintained synaptic release in darkness. The particular properties of K+ and Cl- channels in different retinal neurons shape resting membrane potentials, response kinetics and spiking behavior. A remaining challenge is to characterize the specific distributions of ion channels in the more than 100 individual cell types that have been identified in the retina and to describe how these particular ion channels sculpt neuronal responses to assist in the processing of visual information by the retina.

Unusual Physiological Properties of Smooth Monostratified Ganglion Cell Types in Primate Retina

The functions of the diverse retinal ganglion cell types in primates and the parallel visual pathways they initiate remain poorly understood. Here, unusual physiological and computational properties of the ON and OFF smooth monostratified ganglion cells are explored. Large-scale multi-electrode recordings from 48 macaque retinas revealed that these cells exhibit irregular receptive field structure composed of spatially segregated hotspots, quite different from the classic center-surround model of retinal receptive fields. Surprisingly, visual stimulation of different hotspots in the same cell produced spikes with subtly different spatiotemporal voltage signatures, consistent with a dendritic contribution to hotspot structure. Targeted visual stimulation and computational inference demonstrated strong nonlinear subunit properties associated with each hotspot, supporting a model in which the hotspots apply nonlinearities at a larger spatial scale than bipolar cells. These findings reveal a previously unreported nonlinear mechanism in the output of the primate retina that contributes to signaling spatial information.

Global and Multiplexed Dendritic Computations under In Vivo-like Conditions

Dendrites integrate inputs nonlinearly, but it is unclear how these nonlinearities contribute to the overall input-output transformation of single neurons. We developed statistically principled methods using a hierarchical cascade of linear-nonlinear subunits (hLN) to model the dynamically evolving somatic response of neurons receiving complex, in vivo-like spatiotemporal synaptic input patterns. We used the hLN to predict the somatic membrane potential of an in vivo-validated detailed biophysical model of a L2/3 pyramidal cell. Linear input integration with a single global dendritic nonlinearity achieved above 90% prediction accuracy. A novel hLN motif, input multiplexing into parallel processing channels, could improve predictions as much as conventionally used additional layers of local nonlinearities. We obtained similar results in two other cell types. This approach provides a data-driven characterization of a key component of cortical circuit computations: the input-output transformation of neurons during in vivo-like conditions.

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.

The spectral identity of foveal cones is preserved in hue perception

Organisms are faced with the challenge of making inferences about the physical world from incomplete incoming sensory information. One strategy to combat ambiguity in this process is to combine new information with prior experiences. We investigated the strategy of combining these information sources in color vision. Single cones in human subjects were stimulated and the associated percepts were recorded. Subjects rated each flash for brightness, hue, and saturation. Brightness ratings were proportional to stimulus intensity. Saturation was independent of intensity, but varied between cones. Hue, in contrast, was assigned in a stereotyped manner that was predicted by cone type. These experiments revealed that, near the fovea, long and middle wavelength sensitive cones produce sensations that can be reliably distinguished on the basis of hue, but not saturation or brightness. Taken together, these observations implicate the high-resolution, color-opponent parvocellular pathway in this low-level visual task.

Probing Computation in the Primate Visual System at Single-Cone Resolution

Daylight vision begins when light activates cone photoreceptors in the retina, creating spatial patterns of neural activity. These cone signals are then combined and processed in downstream neural circuits, ultimately producing visual perception. Recent technical advances have made it possible to deliver visual stimuli to the retina that probe this processing by the visual system at its elementary resolution of individual cones. Physiological recordings from nonhuman primate retinas reveal the spatial organization of cone signals in retinal ganglion cells, including how signals from cones of different types are combined to support both spatial and color vision. Psychophysical experiments with human subjects characterize the visual sensations evoked by stimulating a single cone, including the perception of color. Future combined physiological and psychophysical experiments focusing on probing the elementary visual inputs are likely to clarify how neural processing generates our perception of the visual world.

Synaptic Convergence Patterns onto Retinal Ganglion Cells Are Preserved despite Topographic Variation in Pre- and Postsynaptic Territories

Sensory processing can be tuned by a neuron's integration area, the types of inputs, and the proportion and number of connections with those inputs. Integration areas often vary topographically to sample space differentially across regions. Here, we highlight two visual circuits in which topographic changes in the postsynaptic retinal ganglion cell (RGC) dendritic territories and their presynaptic bipolar cell (BC) axonal territories are either matched or unmatched. Despite this difference, in both circuits, the proportion of inputs from each BC type, i.e., synaptic convergence between specific BCs and RGCs, remained constant across varying dendritic territory sizes. Furthermore, synapse density between BCs and RGCs was invariant across topography. Our results demonstrate a wiring design, likely engaging homotypic axonal tiling of BCs, that ensures consistency in synaptic convergence between specific BC types onto their target RGCs while enabling independent regulation of pre- and postsynaptic territory sizes and synapse number between cell pairs.

The dynamic receptive fields of retinal ganglion cells

Retinal ganglion cells (RGCs) were one of the first classes of sensory neurons to be described in terms of a receptive field (RF). Over the last six decades, our understanding of the diversity of RGC types and the nuances of their response properties has grown exponentially. We will review the current understanding of RGC RFs mostly from studies in mammals, but including work from other vertebrates as well. We will argue for a new paradigm that embraces the fluidity of RGC RFs with an eye toward the neuroethology of vision. Specifically, we will focus on (1) different methods for measuring RGC RFs, (2) RF models, (3) feature selectivity and the distinction between fluid and stable RF properties, and (4) ideas about the future of understanding RGC RFs.

Spatial summation in the human fovea: Do normal optical aberrations and fixational eye movements have an effect?

Psychophysical inferences about the neural mechanisms supporting spatial vision can be undermined by uncertainties introduced by optical aberrations and fixational eye movements, particularly in fovea where the neuronal grain of the visual system is fine. We examined the effect of these preneural factors on photopic spatial summation in the human fovea using a custom adaptive optics scanning light ophthalmoscope that provided control over optical aberrations and retinal stimulus motion. Consistent with previous results, Ricco's area of complete summation encompassed multiple photoreceptors when measured with ordinary amounts of ocular aberrations and retinal stimulus motion. When both factors were minimized experimentally, summation areas were essentially unchanged, suggesting that foveal spatial summation is limited by postreceptoral neural pooling. We compared our behavioral data to predictions generated with a physiologically-inspired front-end model of the visual system, and were able to capture the shape of the summation curves obtained with and without pre-retinal factors using a single postreceptoral summing filter of fixed spatial extent. Given our data and modeling, neurons in the magnocellular visual pathway, such as parasol ganglion cells, provide a candidate neural correlate of Ricco's area in the central fovea.

Pathway-Specific Asymmetries between ON and OFF Visual Signals

Visual processing is largely organized into ON and OFF pathways that signal stimulus increments and decrements, respectively. These pathways exhibit natural pairings based on morphological and physiological similarities, such as ON and OFF α-ganglion cells in the mammalian retina. Several studies have noted asymmetries in the properties of ON and OFF pathways. For example, the spatial receptive fields (RFs) of OFF α-cells are systematically smaller than ON α-cells. Analysis of natural scenes suggests that these asymmetries are optimal for visual encoding. To test the generality of ON/OFF asymmetries, we measured the spatiotemporal RF properties of multiple RGC types in rat retina. Through a quantitative and serial classification, we identified three functional pairs of ON and OFF RGCs. We analyzed the structure of their RFs and compared spatial integration, temporal integration, and gain across ON and OFF pairs. Similar to previous results from the cat and primate, RGC types with larger spatial RFs exhibited briefer temporal integration and higher gain. However, each pair of ON and OFF RGC types exhibited distinct asymmetric relationships between RF properties, some of which were opposite to the findings of previous reports. These results reveal the functional organization of six RGC types in the rodent retina and indicate that ON/OFF asymmetries are pathway specific.SIGNIFICANCE STATEMENT Circuits that process sensory input frequently process increments separately from decrements, so-called ON and OFF responses. Theoretical studies indicate that this separation, and associated asymmetries in ON and OFF pathways, may be beneficial for encoding natural stimuli. However, the generality of ON and OFF pathway asymmetries has not been tested. Here we compare the functional properties of three distinct pairs of ON and OFF pathways in the rodent retina and show that their asymmetries are pathway specific. These results provide a new view on the partitioning of vision across diverse ON and OFF signaling pathways.

Receptive field center-surround interactions mediate context-dependent spatial contrast encoding in the retina

Antagonistic receptive field surrounds are a near-universal property of early sensory processing. A key assumption in many models for retinal ganglion cell encoding is that receptive field surrounds are added only to the fully formed center signal. But anatomical and functional observations indicate that surrounds are added before the summation of signals across receptive field subunits that creates the center. Here, we show that this receptive field architecture has an important consequence for spatial contrast encoding in the macaque monkey retina: the surround can control sensitivity to fine spatial structure by changing the way the center integrates visual information over space. The impact of the surround is particularly prominent when center and surround signals are correlated, as they are in natural stimuli. This effect of the surround differs substantially from classic center-surround models and raises the possibility that the surround plays unappreciated roles in shaping ganglion cell sensitivity to natural inputs.

Inferring hidden structure in multilayered neural circuits

A central challenge in sensory neuroscience involves understanding how neural circuits shape computations across cascaded cell layers. Here we attempt to reconstruct the response properties of experimentally unobserved neurons in the interior of a multilayered neural circuit, using cascaded linear-nonlinear (LN-LN) models. We combine non-smooth regularization with proximal consensus algorithms to overcome difficulties in fitting such models that arise from the high dimensionality of their parameter space. We apply this framework to retinal ganglion cell processing, learning LN-LN models of retinal circuitry consisting of thousands of parameters, using 40 minutes of responses to white noise. Our models demonstrate a 53% improvement in predicting ganglion cell spikes over classical linear-nonlinear (LN) models. Internal nonlinear subunits of the model match properties of retinal bipolar cells in both receptive field structure and number. Subunits have consistently high thresholds, supressing all but a small fraction of inputs, leading to sparse activity patterns in which only one subunit drives ganglion cell spiking at any time. From the model’s parameters, we predict that the removal of visual redundancies through stimulus decorrelation across space, a central tenet of efficient coding theory, originates primarily from bipolar cell synapses. Furthermore, the composite nonlinear computation performed by retinal circuitry corresponds to a boolean OR function applied to bipolar cell feature detectors. Our methods are statistically and computationally efficient, enabling us to rapidly learn hierarchical non-linear models as well as efficiently compute widely used descriptive statistics such as the spike triggered average (STA) and covariance (STC) for high dimensional stimuli. This general computational framework may aid in extracting principles of nonlinear hierarchical sensory processing across diverse modalities from limited data.

Computation in neural circuits arises from the cascaded processing of inputs through multiple cell layers. Each of these cell layers performs operations such as filtering and thresholding in order to shape a circuit’s output. It remains a challenge to describe both the computations and the mechanisms that mediate them given limited data recorded from a neural circuit. A standard approach to describing circuit computation involves building quantitative encoding models that predict the circuit response given its input, but these often fail to map in an interpretable way onto mechanisms within the circuit. In this work, we build two layer linear-nonlinear cascade models (LN-LN) in order to describe how the retinal output is shaped by nonlinear mechanisms in the inner retina. We find that these LN-LN models, fit to ganglion cell recordings alone, identify filters and nonlinearities that are readily mapped onto individual circuit components inside the retina, namely bipolar cells and the bipolar-to-ganglion cell synaptic threshold. This work demonstrates how combining simple prior knowledge of circuit properties with partial experimental recordings of a neural circuit’s output can yield interpretable models of the entire circuit computation, including parts of the circuit that are hidden or not directly observed in neural recordings.

Modern Machine Learning as a Benchmark for Fitting Neural Responses

Neuroscience has long focused on finding encoding models that effectively ask "what predicts neural spiking?" and generalized linear models (GLMs) are a typical approach. It is often unknown how much of explainable neural activity is captured, or missed, when fitting a model. Here we compared the predictive performance of simple models to three leading machine learning methods: feedforward neural networks, gradient boosted trees (using XGBoost), and stacked ensembles that combine the predictions of several methods. We predicted spike counts in macaque motor (M1) and somatosensory (S1) cortices from standard representations of reaching kinematics, and in rat hippocampal cells from open field location and orientation. Of these methods, XGBoost and the ensemble consistently produced more accurate spike rate predictions and were less sensitive to the preprocessing of features. These methods can thus be applied quickly to detect if feature sets relate to neural activity in a manner not captured by simpler methods. Encoding models built with a machine learning approach accurately predict spike rates and can offer meaningful benchmarks for simpler models.

Sensations from a single M-cone depend on the activity of surrounding S-cones

Color vision requires the activity of cone photoreceptors to be compared in post-receptoral circuitry. Decades of psychophysical measurements have quantified the nature of these comparative interactions on a coarse scale. How such findings generalize to a cellular scale remains unclear. To answer that question, we quantified the influence of surrounding light on the appearance of spots targeted to individual cones. The eye's aberrations were corrected with adaptive optics and retinal position was precisely tracked in real-time to compensate for natural movement. Subjects reported the color appearance of each spot. A majority of L-and M-cones consistently gave rise to the sensation of white, while a smaller group repeatedly elicited hue sensations. When blue sensations were reported they were more likely mediated by M- than L-cones. Blue sensations were elicited from M-cones against a short-wavelength light that preferentially elevated the quantal catch in surrounding S-cones, while stimulation of the same cones against a white background elicited green sensations. In one of two subjects, proximity to S-cones increased the probability of blue reports when M-cones were probed. We propose that M-cone increments excited both green and blue opponent pathways, but the relative activity of neighboring cones favored one pathway over the other.

Neural Mechanisms Mediating Motion Sensitivity in Parasol Ganglion Cells of the Primate Retina

Considerable theoretical and experimental effort has been dedicated to understanding how neural circuits detect visual motion. In primates, much is known about the cortical circuits that contribute to motion processing, but the role of the retina in this fundamental neural computation is poorly understood. Here, we used a combination of extracellular and whole-cell recording to test for motion sensitivity in the two main classes of output neurons in the primate retina-midget (parvocellular-projecting) and parasol (magnocellular-projecting) ganglion cells. We report that parasol, but not midget, ganglion cells are motion sensitive. This motion sensitivity is present in synaptic excitation and disinhibition from presynaptic bipolar cells and amacrine cells, respectively. Moreover, electrical coupling between neighboring bipolar cells and the nonlinear nature of synaptic release contribute to the observed motion sensitivity. Our findings indicate that motion computations arise far earlier in the primate visual stream than previously thought.

New Frontiers and Challenges for Single-Cell Electrochemical Analysis

Previous measurements of cell populations might obscure many important cellular differences, and new strategies for single-cell analyses are urgently needed to re-examine these fundamental biological principles for better diagnosis and treatment of diseases. Electrochemistry is a robust technique for the analysis of single living cells that has the advantages of minor interruption of cellular activity and provides the capability of high spatiotemporal resolution. The achievements of the past 30 years have revealed significant information about the exocytotic events of single cells to elucidate the mechanisms of cellular activity. Currently, the rapid developments of micro/nanofabrication and optoelectronic technologies drive the development of multifunctional electrodes and novel electrochemical approaches with higher resolution for single cells. In this Perspective, three new frontiers in this field, namely, electrochemical microscopy, intracellular analysis, and single-cell analysis in a biological system (i.e., neocortex and retina), are reviewed. The unique features and remaining challenges of these techniques are discussed.

Electrical receptive fields of retinal ganglion cells: Influence of presynaptic neurons

Implantable retinal stimulators activate surviving neurons to restore a sense of vision in people who have lost their photoreceptors through degenerative diseases. Complex spatial and temporal interactions occur in the retina during multi-electrode stimulation. Due to these complexities, most existing implants activate only a few electrodes at a time, limiting the repertoire of available stimulation patterns. Measuring the spatiotemporal interactions between electrodes and retinal cells, and incorporating them into a model may lead to improved stimulation algorithms that exploit the interactions. Here, we present a computational model that accurately predicts both the spatial and temporal nonlinear interactions of multi-electrode stimulation of rat retinal ganglion cells (RGCs). The model was verified using in vitro recordings of ON, OFF, and ON-OFF RGCs in response to subretinal multi-electrode stimulation with biphasic pulses at three stimulation frequencies (10, 20, 30 Hz). The model gives an estimate of each cell’s spatiotemporal electrical receptive fields (ERFs); i.e., the pattern of stimulation leading to excitation or suppression in the neuron. All cells had excitatory ERFs and many also had suppressive sub-regions of their ERFs. We show that the nonlinearities in observed responses arise largely from activation of presynaptic interneurons. When synaptic transmission was blocked, the number of sub-regions of the ERF was reduced, usually to a single excitatory ERF. This suggests that direct cell activation can be modeled accurately by a one-dimensional model with linear interactions between electrodes, whereas indirect stimulation due to summated presynaptic responses is nonlinear.

Implantable neural stimulation devices are being widely used and clinically tested for the restoration of lost function (e.g. cochlear implants) and the treatment of neurological disorders. Smart devices that can combine sensing and stimulation will dramatically improve future patient outcomes. To this end, mathematical models that can accurately predict neural responses to electrical stimulation will be critical for the development of smart stimulation devices. Here, we demonstrate a model that predicts neural responses to simultaneous stimulation across multiple electrodes in the retina. We show that the activation of presynaptic neurons leads to nonlinearities in the responses of postsynaptic retinal ganglion cells. The model is accurate and is applicable to a wide range of neural stimulation devices.

Multiplexed computations in retinal ganglion cells of a single type

In the early visual system, cells of the same type perform the same computation in different places of the visual field. How these cells code together a complex visual scene is unclear. A common assumption is that cells of a single-type extract a single-stimulus feature to form a feature map, but this has rarely been observed directly. Using large-scale recordings in the rat retina, we show that a homogeneous population of fast OFF ganglion cells simultaneously encodes two radically different features of a visual scene. Cells close to a moving object code quasilinearly for its position, while distant cells remain largely invariant to the object's position and, instead, respond nonlinearly to changes in the object's speed. We develop a quantitative model that accounts for this effect and identify a disinhibitory circuit that mediates it. Ganglion cells of a single type thus do not code for one, but two features simultaneously. This richer, flexible neural map might also be present in other sensory systems.

A neurophysiological explanation for biases in visual localization

Observers show small but systematic deviations from equal weighting of all elements when asked to localize the center of an array of dots. Counter-intuitively, with small numbers of dots drawn from a Gaussian distribution, this bias results in subjects overweighting the influence of outlier dots - inconsistent with traditional statistical estimators of central tendency. Here we show that this apparent statistical anomaly can be explained by the observation that outlier dots also lie in regions of lower dot density. Using a standard model of V1 processing, which includes spatial integration followed by a compressive static nonlinearity, we can successfully predict the finding that dots in less dense regions of an array have a relatively greater influence on the perceived center.

Spatiochromatic Interactions between Individual Cone Photoreceptors in the Human Retina

A remarkable feature of human vision is that the retina and brain have evolved circuitry to extract useful spatial and spectral information from signals originating in a photoreceptor mosaic with trichromatic constituents that vary widely in their relative numbers and local spatial configurations. A critical early transformation applied to cone signals is horizontal-cell-mediated lateral inhibition, which imparts a spatially antagonistic surround to individual cone receptive fields, a signature inherited by downstream neurons and implicated in color signaling. In the peripheral retina, the functional connectivity of cone inputs to the circuitry that mediates lateral inhibition is not cone-type specific, but whether these wiring schemes are maintained closer to the fovea remains unsettled, in part because central retinal anatomy is not easily amenable to direct physiological assessment. Here, we demonstrate how the precise topography of the long (L)-, middle (M)-, and short (S)-wavelength-sensitive cones in the human parafovea (1.5° eccentricity) shapes perceptual sensitivity. We used adaptive optics microstimulation to measure psychophysical detection thresholds from individual cones with spectral types that had been classified independently by absorptance imaging. Measured against chromatic adapting backgrounds, the sensitivities of L and M cones were, on average, receptor-type specific, but individual cone thresholds varied systematically with the number of preferentially activated cones in the immediate neighborhood. The spatial and spectral patterns of these interactions suggest that interneurons mediating lateral inhibition in the central retina, likely horizontal cells, establish functional connections with L and M cones indiscriminately, implying that the cone-selective circuitry supporting red-green color vision emerges after the first retinal synapse.SIGNIFICANCE STATEMENT We present evidence for spatially antagonistic interactions between individual, spectrally typed cones in the central retina of human observers using adaptive optics. Using chromatic adapting fields to modulate the relative steady-state activity of long (L)- and middle (M)-wavelength-sensitive cones, we found that single-cone detection thresholds varied predictably with the spectral demographics of the surrounding cones. The spatial scale and spectral pattern of these photoreceptor interactions were consistent with lateral inhibition mediated by retinal horizontal cells that receive nonselective input from L and M cones. These results demonstrate a clear link between the neural architecture of the visual system inputs-cone photoreceptors-and visual perception and have implications for the neural locus of the cone-specific circuitry supporting color vision.

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.

Technologies for imaging neural activity in large volumes

Neural circuitry has evolved to form distributed networks that act dynamically across large volumes. Conventional microscopy collects data from individual planes and cannot sample circuitry across large volumes at the temporal resolution relevant to neural circuit function and behaviors. Here we review emerging technologies for rapid volume imaging of neural circuitry. We focus on two critical challenges: the inertia of optical systems, which limits image speed, and aberrations, which restrict the image volume. Optical sampling time must be long enough to ensure high-fidelity measurements, but optimized sampling strategies and point-spread function engineering can facilitate rapid volume imaging of neural activity within this constraint. We also discuss new computational strategies for processing and analyzing volume imaging data of increasing size and complexity. Together, optical and computational advances are providing a broader view of neural circuit dynamics and helping elucidate how brain regions work in concert to support behavior.

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.