Dynamical adaptation in photoreceptors

Predictably manipulating photoreceptor light responses to reveal their role in downstream visual responses

Computation in neural circuits relies on the judicious use of nonlinear circuit components. In many cases, multiple nonlinear components work collectively to control circuit outputs. Separating the contributions of these different components is difficult, and this limits our understanding of the mechanistic basis of many important computations. Here, we introduce a tool that permits the design of light stimuli that predictably alter rod and cone phototransduction currents - including stimuli that compensate for nonlinear properties such as light adaptation. This tool, based on well-established models for the rod and cone phototransduction cascade, permits the separation of nonlinearities in phototransduction from those in downstream circuits. This will allow, for example, direct tests of how adaptation in rod and cone phototransduction affects downstream visual signals and perception.

Biophysical neural adaptation mechanisms enable artificial neural networks to capture dynamic retinal computation

Adaptation is a universal aspect of neural systems that changes circuit computations to match prevailing inputs. These changes facilitate efficient encoding of sensory inputs while avoiding saturation. Conventional artificial neural networks (ANNs) have limited adaptive capabilities, hindering their ability to reliably predict neural output under dynamic input conditions. Can embedding neural adaptive mechanisms in ANNs improve their performance? To answer this question, we develop a new deep learning model of the retina that incorporates the biophysics of photoreceptor adaptation at the front-end of conventional convolutional neural networks (CNNs). These conventional CNNs build on 'Deep Retina,' a previously developed model of retinal ganglion cell (RGC) activity. CNNs that include this new photoreceptor layer outperform conventional CNN models at predicting male and female primate and rat RGC responses to naturalistic stimuli that include dynamic local intensity changes and large changes in the ambient illumination. These improved predictions result directly from adaptation within the phototransduction cascade. This research underscores the potential of embedding models of neural adaptation in ANNs and using them to determine how neural circuits manage the complexities of encoding natural inputs that are dynamic and span a large range of light levels.

Disparate nonlinear neural dynamics measured with different techniques in macaque and human V1

Diverse neuro-imaging techniques measure different aspects of neural responses with distinct spatial and temporal resolutions. Relating measured neural responses across different methods has been challenging. Here, we take a step towards overcoming this challenge, by comparing the nonlinearity of neural dynamics measured across methods. We used widefield voltage-sensitive dye imaging (VSDI) to measure neural population responses in macaque V1 to visual stimuli with a wide range of temporal waveforms. We found that stimulus-evoked VSDI responses are surprisingly near-additive in time. These results are qualitatively different from the strong sub-additive dynamics previously measured using fMRI and electrocorticography (ECoG) in human visual cortex with a similar set of stimuli. To test whether this discrepancy is specific to VSDI-a signal dominated by subthreshold neural activity, we repeated our measurements using widefield imaging of a genetically encoded calcium indicator (GcaMP6f)-a signal dominated by spiking activity, and found that GCaMP signals in macaque V1 are also near-additive. Therefore, the discrepancies in the extent of sub-additivity between the macaque and the human measurements are unlikely due to differences between sub- and supra-threshold neural responses. Finally, we use a simple yet flexible delayed normalization model to capture these different dynamics across measurements (with different model parameters). The model can potentially generalize to a broader set of stimuli, which aligns with previous suggestion that dynamic gain-control is a canonical computation contributing to neural processing in the brain.

A dynamical adaptation model of visual spatiotemporal processing in cones and horizontal cells

In this work, we introduce a phenomenological model for the cone-horizontal cell assembly, including spatial integration and formation of receptive field-like structures. The model extends our previous dynamical adaptation description with gain control accounting for processes in single cones, valid in severe nonlinear regimes. Here, a spatially extended feedback mechanism is introduced from horizontal cells to cones to account for experimental evidence, contributing thus to the development of a center-surround receptive field in cones and downstream bipolar cells. Feedback gain is defined on different spatial scales by weighting spatial filters: a short scale accounting for cone input to the feedback mechanism and a large scale driven by the syncytium characteristics of horizontal cells. A third spatial scale improves the description, mimicking neighboring cone-cone coupling. This overall spatial integration couples to temporal signal processing, thus obtaining a spatiotemporal model of outer retina responses capable of reproducing nonlinear features in both dimensions (space and time). The model was tested and validated using measurements on horizontal cells from different studies, with excellent performance. By its phenomenological nature, signal processing properties are inferred from model parameters. The model can be used in arrays of processing units with more complex incoming patterns of visual stimuli.

Multifaceted luminance gain control beyond photoreceptors in Drosophila

Animals navigating in natural environments must handle vast changes in their sensory input. Visual systems, for example, handle changes in luminance at many timescales, from slow changes across the day to rapid changes during active behavior. To maintain luminance-invariant perception, visual systems must adapt their sensitivity to changing luminance at different timescales. We demonstrate that luminance gain control in photoreceptors alone is insufficient to explain luminance invariance at both fast and slow timescales and reveal the algorithms that adjust gain past photoreceptors in the fly eye. We combined imaging and behavioral experiments with computational modeling to show that downstream of photoreceptors, circuitry taking input from the single luminance-sensitive neuron type L3 implements gain control at fast and slow timescales. This computation is bidirectional in that it prevents the underestimation of contrasts in low luminance and overestimation in high luminance. An algorithmic model disentangles these multifaceted contributions and shows that the bidirectional gain control occurs at both timescales. The model implements a nonlinear interaction of luminance and contrast to achieve gain correction at fast timescales and a dark-sensitive channel to improve the detection of dim stimuli at slow timescales. Together, our work demonstrates how a single neuronal channel performs diverse computations to implement gain control at multiple timescales that are together important for navigation in natural environments.

Homeostasis at different backgrounds: The roles of overlayed feedback structures in vertebrate photoadaptation

We have studied the resetting behavior of eight basic integral controller motifs with respect to different but constant backgrounds. We found that the controllers split symmetrically into two classes: one class, based on derepression of the compensatory flux, leads to more rapid resetting kinetics as backgrounds increase. The other class, which directly activates the compensatory flux, shows a slowing down in the resetting at increased backgrounds. We found a striking analogy between the resetting kinetics of vertebrate photoreceptors and controllers based on derepression, i.e. vertebrate rod or cone cells show decreased sensitivities and accelerated response kinetics as background illuminations increase. The central molecular model of vertebrate photoadaptation consists of an overlay of three negative feedback loops with cytosolic calcium ([Formula: see text]), cyclic guanosine monophosphate (cGMP) and cyclic nucleotide-gated (CNG) channels as components. While in one of the feedback loops the extrusion of [Formula: see text] by potassium-dependent sodium-calcium exchangers (NCKX) can lead to integral control with cGMP as the controlled variable, the expected robust perfect adaptation of cGMP is lost, because of the two other feedback loops. They avoid that [Formula: see text] levels become too high and toxic. Looking at psychophysical laws, we found that in all of the above mentioned basic controllers Weber's law is followed when a "just noticeable difference" (threshold) of 1% of the controlled variable's set-point was considered. Applying comparable threshold pulses or steps to the photoadaptation model we find, in agreement with experimental results, that Weber's law is followed for relatively high backgrounds, while Stephens' power law gives a better description when backgrounds are low. Limitations of our photoadaption model, in particular with respect to potassium/sodium homeostasis, are discussed. Finally, we discuss possible implication of background perturbations in biological controllers when compensatory fluxes are based on activation.

A theoretical model reveals specialized synaptic depressions and temporal frequency tuning in retinal parallel channels

In the Outer Plexiform Layer of a retina, a cone pedicle provides synaptic inputs for multiple cone bipolar cell (CBC) subtypes so that each subtype formats a parallelized processing channel to filter visual features from the environment. Due to the diversity of short-term depressions among cone-CBC contacts, these channels have different temporal frequency tunings. Here, we propose a theoretical model based on the hierarchy Linear-Nonlinear-Synapse framework to link the synaptic depression and the neural activities of the cone-CBC circuit. The model successfully captures various frequency tunings of subtype-specialized channels and infers synaptic depression recovery time constants inside circuits. Furthermore, the model can predict frequency-tuning behaviors based on synaptic activities. With the prediction of region-specialized UV cone parallel channels, we suggest the acute zone in the zebrafish retina supports detecting light-off events at high temporal frequencies.

Exploiting colour space geometry for visual stimulus design across animals

Colour vision represents a vital aspect of perception that ultimately enables a wide variety of species to thrive in the natural world. However, unified methods for constructing chromatic visual stimuli in a laboratory setting are lacking. Here, we present stimulus design methods and an accompanying programming package to efficiently probe the colour space of any species in which the photoreceptor spectral sensitivities are known. Our hardware-agnostic approach incorporates photoreceptor models within the framework of the principle of univariance. This enables experimenters to identify the most effective way to combine multiple light sources to create desired distributions of light, and thus easily construct relevant stimuli for mapping the colour space of an organism. We include methodology to handle uncertainty of photoreceptor spectral sensitivity as well as to optimally reconstruct hyperspectral images given recent hardware advances. Our methods support broad applications in colour vision science and provide a framework for uniform stimulus designs across experimental systems. This article is part of the theme issue 'Understanding colour vision: molecular, physiological, neuronal and behavioural studies in arthropods'.

Classical center-surround receptive fields facilitate novel object detection in retinal bipolar cells

Antagonistic interactions between center and surround receptive field (RF) components lie at the heart of the computations performed in the visual system. Circularly symmetric center-surround RFs are thought to enhance responses to spatial contrasts (i.e., edges), but how visual edges affect motion processing is unclear. Here, we addressed this question in retinal bipolar cells, the first visual neuron with classic center-surround interactions. We found that bipolar glutamate release emphasizes objects that emerge in the RF; their responses to continuous motion are smaller, slower, and cannot be predicted by signals elicited by stationary stimuli. In our hands, the alteration in signal dynamics induced by novel objects was more pronounced than edge enhancement and could be explained by priming of RF surround during continuous motion. These findings echo the salience of human visual perception and demonstrate an unappreciated capacity of the center-surround architecture to facilitate novel object detection and dynamic signal representation.

Excitatory and inhibitory neural dynamics jointly tune motion detection

Neurons integrate excitatory and inhibitory signals to produce their outputs, but the role of input timing in this integration remains poorly understood. Motion detection is a paradigmatic example of this integration, since theories of motion detection rely on different delays in visual signals. These delays allow circuits to compare scenes at different times to calculate the direction and speed of motion. Different motion detection circuits have different velocity sensitivity, but it remains untested how the response dynamics of individual cell types drive this tuning. Here, we sped up or slowed down specific neuron types in Drosophila's motion detection circuit by manipulating ion channel expression. Altering the dynamics of individual neuron types upstream of motion detectors increased their sensitivity to fast or slow visual motion, exposing distinct roles for excitatory and inhibitory dynamics in tuning directional signals, including a role for the amacrine cell CT1. A circuit model constrained by functional data and anatomy qualitatively reproduced the observed tuning changes. Overall, these results reveal how excitatory and inhibitory dynamics together tune a canonical circuit computation.

Suppression without inhibition: how retinal computation contributes to saccadic suppression

Visual perception remains stable across saccadic eye movements, despite the concurrent strongly disruptive visual flow. This stability is partially associated with a reduction in visual sensitivity, known as saccadic suppression, which already starts in the retina with reduced ganglion cell sensitivity. However, the retinal circuit mechanisms giving rise to such suppression remain unknown. Here, we describe these mechanisms using electrophysiology in mouse, pig, and macaque retina, 2-photon calcium imaging, computational modeling, and human psychophysics. We find that sequential stimuli, like those that naturally occur during saccades, trigger three independent suppressive mechanisms in the retina. The main mechanism is triggered by contrast-reversing sequential stimuli and originates within the receptive field center of ganglion cells. It does not involve inhibition or other known suppressive mechanisms like saturation or adaptation. Instead, it relies on temporal filtering of the inherently slow response of cone photoreceptors coupled with downstream nonlinearities. Two further mechanisms of suppression are present predominantly in ON ganglion cells and originate in the receptive field surround, highlighting another disparity between ON and OFF ganglion cells. The mechanisms uncovered here likely play a role in shaping the retinal output following eye movements and other natural viewing conditions where sequential stimulation is ubiquitous.

Retinal Encoding of Natural Scenes

An ultimate goal in retina science is to understand how the neural circuit of the retina processes natural visual scenes. Yet most studies in laboratories have long been performed with simple, artificial visual stimuli such as full-field illumination, spots of light, or gratings. The underlying assumption is that the features of the retina thus identified carry over to the more complex scenario of natural scenes. As the application of corresponding natural settings is becoming more commonplace in experimental investigations, this assumption is being put to the test and opportunities arise to discover processing features that are triggered by specific aspects of natural scenes. Here, we review how natural stimuli have been used to probe, refine, and complement knowledge accumulated under simplified stimuli, and we discuss challenges and opportunities along the way toward a comprehensive understanding of the encoding of natural scenes. Expected final online publication date for the Annual Review of Vision Science, Volume 8 is September 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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.

Predicting and Manipulating Cone Responses to Naturalistic Inputs

Primates explore their visual environment by making frequent saccades, discrete and ballistic eye movements that direct the fovea to specific regions of interest. Saccades produce large and rapid changes in input. The magnitude of these changes and the limited signaling range of visual neurons mean that effective encoding requires rapid adaptation. Here, we explore how macaque cone photoreceptors maintain sensitivity under these conditions. Adaptation makes cone responses to naturalistic stimuli highly nonlinear and dependent on stimulus history. Such responses cannot be explained by linear or linear-nonlinear models but are well explained by a biophysical model of phototransduction based on well-established biochemical interactions. The resulting model can predict cone responses to a broad range of stimuli and enables the design of stimuli that elicit specific (e.g., linear) cone photocurrents. These advances will provide a foundation for investigating the contributions of cone phototransduction and post-transduction processing to visual function.SIGNIFICANCE STATEMENT We know a great deal about adaptational mechanisms that adjust sensitivity to slow changes in visual inputs such as the rising or setting sun. We know much less about the rapid adaptational mechanisms that are essential for maintaining sensitivity as gaze shifts around a single visual scene. We characterize how phototransduction in cone photoreceptors adapts to rapid changes in input similar to those encountered during natural vision. We incorporate these measurements into a quantitative model that can predict cone responses across a broad range of stimuli. This model not only shows how cone phototransduction aids the encoding of natural inputs but also provides a tool to identify the role of the cone responses in shaping those of downstream visual neurons.

Phototransduction in retinal cones: Analysis of parameter importance

In daylight, cone photoreceptors in the retina are responsible for the bulk of visual perception, yet compared to rods, far less is known quantitatively about their biochemistry. This is partly because it is hard to isolate and purify cone proteins. The issue is also complicated by the synergistic interaction of these parameters in producing systems biology outputs, such as photoresponse. Using a 3-D resolved, finite element model of cone outer segments, here we conducted a study of parameter significance using global sensitivity analysis, by Sobol indices, which was contextualized within the uncertainty surrounding these parameters in the available literature. The analysis showed that a subset of the parameters influencing the circulating dark current, such as the turnover rate of cGMP in the dark, may be most influential for variance with experimental flash response, while the shut-off rates of photoexcited rhodopsin and phosphodiesterase also exerted sizable effect. The activation rate of transducin by rhodopsin and the light-induced hydrolysis rate of cGMP exerted measurable effects as well but were estimated as relatively less significant. The results of this study depend on experimental ranges currently described in the literature and should be revised as these become better established. To that end, these findings may be used to prioritize parameters for measurement in future investigations.

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

Multiscale 'whole-cell' models to study neural information processing - New insights from fly photoreceptor studies

Understanding a neuron's input-output relationship is a longstanding challenge. Arguably, these signalling dynamics can be better understood if studied at three levels of analysis: computational, algorithmic and implementational (Marr, 1982). But it is difficult to integrate such analyses into a single platform that can realistically simulate neural information processing. Multiscale dynamical "whole-cell" modelling, a recent systems biology approach, makes this possible. Dynamical "whole-cell" models are computational models that aim to account for the integrated function of numerous genes or molecules to behave like virtual cells in silico. However, because constructing such models is laborious, only a couple of examples have emerged since the first one, built for Mycoplasma genitalium bacterium, was reported in 2012. Here, we review dynamic "whole-cell" neuron models for fly photoreceptors and how these have been used to study neural information processing. Specifically, we review how the models have helped uncover the mechanisms and evolutionary rules of quantal light information sampling and integration, which underlie light adaptation and further improve our understanding of insect vision.

A minimal synaptic model for direction selective neurons in Drosophila

Visual motion estimation is a canonical neural computation. In Drosophila, recent advances have identified anatomic and functional circuitry underlying direction-selective computations. Models with varying levels of abstraction have been proposed to explain specific experimental results but have rarely been compared across experiments. Here we use the wealth of available anatomical and physiological data to construct a minimal, biophysically inspired synaptic model for Drosophila’s first-order direction-selective T4 cells. We show how this model relates mathematically to classical models of motion detection, including the Hassenstein-Reichardt correlator model. We used numerical simulation to test how well this synaptic model could reproduce measurements of T4 cells across many datasets and stimulus modalities. These comparisons include responses to sinusoid gratings, to apparent motion stimuli, to stochastic stimuli, and to natural scenes. Without fine-tuning this model, it sufficed to reproduce many, but not all, response properties of T4 cells. Since this model is flexible and based on straightforward biophysical properties, it provides an extensible framework for developing a mechanistic understanding of T4 neural response properties. Moreover, it can be used to assess the sufficiency of simple biophysical mechanisms to describe features of the direction-selective computation and identify where our understanding must be improved.

Object-Displacement-Sensitive Visual Neurons Drive Freezing in Drosophila

Visual systems are often equipped with neurons that detect small moving objects, which may represent prey, predators, or conspecifics. Although the processing properties of those neurons have been studied in diverse organisms, links between the proposed algorithms and animal behaviors or circuit mechanisms remain elusive. Here, we have investigated behavioral function, computational algorithm, and neurochemical mechanisms of an object-selective neuron, LC11, in Drosophila. With genetic silencing and optogenetic activation, we show that LC11 is necessary for a visual object-induced stopping behavior in walking flies, a form of short-term freezing, and its activity can promote stopping. We propose a new quantitative model for small object selectivity based on the physiology and anatomy of LC11 and its inputs. The model accurately reproduces LC11 responses by pooling fast-adapting, tightly size-tuned inputs. Direct visualization of neurotransmitter inputs to LC11 confirmed the model conjectures about upstream processing. Our results demonstrate how adaptation can enhance selectivity for behaviorally relevant, dynamic visual features.

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.

Heterogeneous Temporal Contrast Adaptation in Drosophila Direction-Selective Circuits

In visual systems, neurons adapt both to the mean light level and to the range of light levels, or the contrast. Contrast adaptation has been studied extensively, but it remains unclear how it is distributed among neurons in connected circuits, and how early adaptation affects subsequent computations. Here, we investigated temporal contrast adaptation in neurons across Drosophila's visual motion circuitry. Several ON-pathway neurons showed strong adaptation to changes in contrast over time. One of these neurons, Mi1, showed almost complete adaptation on fast timescales, and experiments ruled out several potential mechanisms for its adaptive properties. When contrast adaptation reduced the gain in ON-pathway cells, it was accompanied by decreased motion responses in downstream direction-selective cells. Simulations show that contrast adaptation can substantially improve motion estimates in natural scenes. The benefits are larger for ON-pathway adaptation, which helps explain the heterogeneous distribution of contrast adaptation in these circuits.

Temporal information loss in the macaque early visual system

Stimuli that modulate neuronal activity are not always detectable, indicating a loss of information between the modulated neurons and perception. To identify where in the macaque visual system information about periodic light modulations is lost, signal-to-noise ratios were compared across simulated cone photoreceptors, lateral geniculate nucleus (LGN) neurons, and perceptual judgements. Stimuli were drifting, threshold-contrast Gabor patterns on a photopic background. The sensitivity of LGN neurons, extrapolated to populations, was similar to the monkeys' at low temporal frequencies. At high temporal frequencies, LGN sensitivity exceeded the monkeys' and approached the upper bound set by cone photocurrents. These results confirm a loss of high-frequency information downstream of the LGN. However, this loss accounted for only about 5% of the total. Phototransduction accounted for essentially all of the rest. Together, these results show that low temporal frequency information is lost primarily between the cones and the LGN, whereas high-frequency information is lost primarily within the cones, with a small additional loss downstream of the LGN.

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.

Dynamic nonlinearities enable direction opponency in Drosophila elementary motion detectors

Direction-selective neurons respond to visual motion in a preferred direction. They are direction-opponent if they are also inhibited by motion in the opposite direction. In flies and vertebrates, direction opponency has been observed in second-order direction-selective neurons, which achieve this opponency by subtracting signals from first-order direction-selective cells with opposite directional tunings. Here, we report direction opponency in Drosophila that emerges in first-order direction-selective neurons, the elementary motion detectors T4 and T5. This opponency persists when synaptic output from these cells is blocked, suggesting that it arises from feedforward, not feedback, computations. These observations exclude a broad class of linear-nonlinear models that have been proposed to describe direction-selective computations. However, they are consistent with models that include dynamic nonlinearities. Simulations of opponent models suggest that direction opponency in first-order motion detectors improves motion discriminability by suppressing noise generated by the local structure of natural scenes.

Adaptive information processing of network modules to dynamic and spatial stimuli

BACKGROUND

Adaptation and homeostasis are basic features of information processing in cells and seen in a broad range of contexts. Much of the current understanding of adaptation in network modules/motifs is based on their response to simple stimuli. Recently, there have also been studies of adaptation in dynamic stimuli. However a broader synthesis of how different circuits of adaptation function, and which circuits enable a broader adaptive behaviour in classes of more complex and spatial stimuli is largely missing.

RESULTS

We study the response of a variety of adaptive circuits to time-varying stimuli such as ramps, periodic stimuli and static and dynamic spatial stimuli. We find that a variety of responses can be seen in ramp stimuli, making this a basis for discriminating between even similar circuits. We also find that a number of circuits adapt exactly to ramp stimuli, and dissect these circuits to pinpoint what characteristics (architecture, feedback, biochemical aspects, information processing ingredients) allow for this. These circuits include incoherent feedforward motifs, inflow-outflow motifs and transcritical circuits. We find that changes in location in such circuits where a signal acts can result in non-adaptive behaviour in ramps, even though the location was associated with exact adaptation in step stimuli. We also demonstrate that certain augmentations of basic inflow-outflow motifs can alter the behaviour of the circuit from exact adaptation to non-adaptive behaviour. When subject to periodic stimuli, some circuits (inflow-outflow motifs and transcritical circuits) are able to maintain an average output independent of the characteristics of the input. We build on this to examine the response of adaptive circuits to static and dynamic spatial stimuli. We demonstrate how certain circuits can exhibit a graded response in spatial static stimuli with an exact maintenance of the spatial mean-value. Distinct features which emerge from the consideration of dynamic spatial stimuli are also discussed. Finally, we also build on these results to show how different circuits which show any combination of presence or absence of exact adaptation in ramps, exact mainenance of time average output in periodic stimuli and exact maintenance of spatial average of output in static spatial stimuli may be realized.

CONCLUSIONS

By studying a range of network circuits/motifs on one hand and a range of stimuli on the other, we isolate characteristics of these circuits (structural) which enable different degrees of exact adaptive and homeostatic behaviour in such stimuli, how they may be combined, and also identify cases associated with non-homeostatic behaviour. We also reveal constraints associated with locations where signals may act to enable homeostatic behaviour and constraints associated with augmentations of circuits. This consideration of multiple experimentally/naturally relevant stimuli along with circuits of adaptation of relevance in natural and engineered biology, provides a platform for deepening our understanding of adaptive and homeostatic behaviour in natural systems, bridging the gap between models of adaptation and experiments and in engineering homeostatic synthetic circuits.

Functional Diversity in the Retina Improves the Population Code

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

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.

How Diverse Retinal Functions Arise from Feedback at the First Visual Synapse

Many brain regions contain local interneurons of distinct types. How does an interneuron type contribute to the input-output transformations of a given brain region? We addressed this question in the mouse retina by chemogenetically perturbing horizontal cells, an interneuron type providing feedback at the first visual synapse, while monitoring the light-driven spiking activity in thousands of ganglion cells, the retinal output neurons. We uncovered six reversible perturbation-induced effects in the response dynamics and response range of ganglion cells. The effects were enhancing or suppressive, occurred in different response epochs, and depended on the ganglion cell type. A computational model of the retinal circuitry reproduced all perturbation-induced effects and led us to assign specific functions to horizontal cells with respect to different ganglion cell types. Our combined experimental and theoretical work reveals how a single interneuron type can differentially shape the dynamical properties of distinct output channels of a brain region.

Effects of phase correlations in naturalistic stimuli on quantitative information coding by fly photoreceptors

Natural visual scenes are rarely random. Instead, intensity and wavelength change slowly in time and space over many regions of the scene, so that neighboring temporal and spatial visual inputs are more correlated and contain less information than truly random signals. It has been suggested that sensory optimization to match these higher order correlations (HOC) occurs at the earliest visual stages, and that photoreceptors can process temporal natural signals more efficiently than random signals. We tested this early-stage hypothesis by comparing the information content of Calliphora vicina photoreceptor responses to naturalistic inputs before and after removing HOC by randomizing phase. Forty different, 60-s long, naturalistic sequences (NS) were used, together with randomized-phase versions of the same sequences to give pink noise (PN) so that each input pair had identical means, variances, mean contrasts, and power spectra. We measured the information content of inputs and membrane potential responses by three different methods: coherence, mutual information, and compression entropy. We also used entropy and phase statistics of each pair as measures of HOC. Responses to randomized signals generally had higher gain, signal-to-noise ratio, and information rates than responses to NS. Information rate increased with a strong, positive, linear correlation to phase randomization within sequence pairs. This was confirmed by varying the degree of phase randomization. Our data indicate that individual photoreceptors encode input information by Weber's law, with HOC within natural sequences reducing information transfer by decreasing the number of local contrast events that exceed the noise-imposed threshold. NEW & NOTEWORTHY Natural visual scenes feature statistical regularities, or higher order correlations (HOC), both in time and space, to encode surfaces, textures, and object boundaries. Visual systems rely on this information; however, it remains controversial whether individual photoreceptors can discriminate and enhance information encoded in HOC. Here we show that the more HOC the stimulus contains, the lower the information transfer rate of photoreceptors. We explain our findings by applying the Weber's paradigm of differential signal perception.

Parallel Computations in Insect and Mammalian Visual Motion Processing

Sensory systems use receptors to extract information from the environment and neural circuits to perform subsequent computations. These computations may be described as algorithms composed of sequential mathematical operations. Comparing these operations across taxa reveals how different neural circuits have evolved to solve the same problem, even when using different mechanisms to implement the underlying math. In this review, we compare how insect and mammalian neural circuits have solved the problem of motion estimation, focusing on the fruit fly Drosophila and the mouse retina. Although the two systems implement computations with grossly different anatomy and molecular mechanisms, the underlying circuits transform light into motion signals with strikingly similar processing steps. These similarities run from photoreceptor gain control and spatiotemporal tuning to ON and OFF pathway structures, motion detection, and computed motion signals. The parallels between the two systems suggest that a limited set of algorithms for estimating motion satisfies both the needs of sighted creatures and the constraints imposed on them by metabolism, anatomy, and the structure and regularities of the visual world.

Olfactory receptor neurons use gain control and complementary kinetics to encode intermittent odorant stimuli

Insects find food and mates by navigating odorant plumes that can be highly intermittent, with intensities and durations that vary rapidly over orders of magnitude. Much is known about olfactory responses to pulses and steps, but it remains unclear how olfactory receptor neurons (ORNs) detect the intensity and timing of natural stimuli, where the absence of scale in the signal makes detection a formidable olfactory task. By stimulating Drosophila ORNs in vivo with naturalistic and Gaussian stimuli, we show that ORNs adapt to stimulus mean and variance, and that adaptation and saturation contribute to naturalistic sensing. Mean-dependent gain control followed the Weber-Fechner relation and occurred primarily at odor transduction, while variance-dependent gain control occurred at both transduction and spiking. Transduction and spike generation possessed complementary kinetic properties, that together preserved the timing of odorant encounters in ORN spiking, regardless of intensity. Such scale-invariance could be critical during odor plume navigation.

A biomimetic fly photoreceptor model elucidates how stochastic adaptive quantal sampling provides a large dynamic range

Light intensities (photons s^-1  μm^-2 ) in a natural scene vary over several orders of magnitude from shady woods to direct sunlight. A major challenge facing the visual system is how to map such a large dynamic input range into its limited output range, so that a signal is neither buried in noise in darkness nor saturated in brightness. A fly photoreceptor has achieved such a large dynamic range; it can encode intensity changes from single to billions of photons, outperforming man-made light sensors. This performance requires powerful light adaptation, the neural implementation of which has only become clear recently. A computational fly photoreceptor model, which mimics the real phototransduction processes, has elucidated how light adaptation happens dynamically through stochastic adaptive quantal information sampling. A Drosophila R1-R6 photoreceptor's light sensor, the rhabdomere, has 30,000 microvilli, each of which stochastically samples incoming photons. Each microvillus employs a full G-protein-coupled receptor signalling pathway to adaptively transduce photons into quantum bumps (QBs, or samples). QBs then sum the macroscopic photoreceptor responses, governed by four quantal sampling factors (limitations): (i) the number of photon sampling units in the cell structure (microvilli), (ii) sample size (QB waveform), (iii) latency distribution (time delay between photon arrival and emergence of a QB), and (iv) refractory period distribution (time for a microvillus to recover after a QB). Here, we review how these factors jointly orchestrate light adaptation over a large dynamic range.

A novel mechanism of cone photoreceptor adaptation

An animal’s ability to survive depends on its sensory systems being able to adapt to a wide range of environmental conditions, by maximizing the information extracted and reducing the noise transmitted. The visual system does this by adapting to luminance and contrast. While luminance adaptation can begin at the retinal photoreceptors, contrast adaptation has been shown to start at later stages in the retina. Photoreceptors adapt to changes in luminance over multiple time scales ranging from tens of milliseconds to minutes, with the adaptive changes arising from processes within the phototransduction cascade. Here we show a new form of adaptation in cones that is independent of the phototransduction process. Rather, it is mediated by voltage-gated ion channels in the cone membrane and acts by changing the frequency response of cones such that their responses speed up as the membrane potential modulation depth increases and slow down as the membrane potential modulation depth decreases. This mechanism is effectively activated by high-contrast stimuli dominated by low frequencies such as natural stimuli. However, the more generally used Gaussian white noise stimuli were not effective since they did not modulate the cone membrane potential to the same extent. This new adaptive process had a time constant of less than a second. A critical component of the underlying mechanism is the hyperpolarization-activated current, I_h, as pharmacologically blocking it prevented the long- and mid- wavelength sensitive cone photoreceptors (L- and M-cones) from adapting. Consistent with this, short- wavelength sensitive cone photoreceptors (S-cones) did not show the adaptive response, and we found they also lacked a prominent I_h. The adaptive filtering mechanism identified here improves the information flow by removing higher-frequency noise during lower signal-to-noise ratio conditions, as occurs when contrast levels are low. Although this new adaptive mechanism can be driven by contrast, it is not a contrast adaptation mechanism in its strictest sense, as will be argued in the Discussion.

An animal’s ability to survive depends on its ability to adapt to a wide range of light conditions, by maximizing the information flow through the retina. Here, we show a new form of adaptation in cone photoreceptors that helps them optimize the information they transmit by adjusting their response kinetics to better match the visual conditions. The adaptive mechanism we describe is independent of the cone phototransduction process and is instead mediated by membrane processes in which the hyperpolarization-activated current, I_h, plays a critical role. Consistent with the critical role of this current, we also found that cones sensitive to short wavelengths lacked a prominent I_h current and did not show this new form of adaptation. As voltage-dependent processes underlie the adaptational mechanism, it is only apparent when the stimuli are able to sufficiently modulate the membrane potential of cones. This happens with natural stimuli, which are able to deliver high levels of “effective” contrast. However, even though this new adaptive mechanism can be driven by contrast, we argue in the Discussion that in its strictest sense it is not a contrast adaptation mechanism per se.

A Computational Framework for Realistic Retina Modeling

Computational simulations of the retina have led to valuable insights about the biophysics of its neuronal activity and processing principles. A great number of retina models have been proposed to reproduce the behavioral diversity of the different visual processing pathways. While many of these models share common computational stages, previous efforts have been more focused on fitting specific retina functions rather than generalizing them beyond a particular model. Here, we define a set of computational retinal microcircuits that can be used as basic building blocks for the modeling of different retina mechanisms. To validate the hypothesis that similar processing structures may be repeatedly found in different retina functions, we implemented a series of retina models simply by combining these computational retinal microcircuits. Accuracy of the retina models for capturing neural behavior was assessed by fitting published electrophysiological recordings that characterize some of the best-known phenomena observed in the retina: adaptation to the mean light intensity and temporal contrast, and differential motion sensitivity. The retinal microcircuits are part of a new software platform for efficient computational retina modeling from single-cell to large-scale levels. It includes an interface with spiking neural networks that allows simulation of the spiking response of ganglion cells and integration with models of higher visual areas.

Rods in daylight act as relay cells for cone-driven horizontal cell-mediated surround inhibition

Vertebrate vision relies on two types of photoreceptors, rods and cones, which signal increments in light intensity with graded hyperpolarizations. Rods operate in the lower range of light intensities while cones operate at brighter intensities. The receptive fields of both photoreceptors exhibit antagonistic center-surround organization. Here we show that at bright light levels, mouse rods act as relay cells for cone-driven horizontal cell-mediated surround inhibition. In response to large, bright stimuli that activate their surrounds, rods depolarize. Rod depolarization increases with stimulus size, and its action spectrum matches that of cones. Rod responses at high light levels are abolished in mice with nonfunctional cones and when horizontal cells are reversibly inactivated. Rod depolarization is conveyed to the inner retina via postsynaptic circuit elements, namely the rod bipolar cells. Our results show that the retinal circuitry repurposes rods, when they are not directly sensing light, to relay cone-driven surround inhibition.