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A simple white noise analysis of neuronal light responses
Abstract
A white noise technique is presented for estimating the response properties of spiking visual system neurons. The technique is simple, robust, efficient and well suited to simultaneous recordings from multiple neurons. It provides a complete and easily interpretable model of light responses even for neurons that display a common form of response nonlinearity that precludes classical linear systems analysis. A theoretical justification of the technique is presented that relies only on elementary linear algebra and statistics. Implementation is described with examples. The technique and the underlying model of neural responses are validated using recordings from retinal ganglion cells, and in principle are applicable to other neurons. Advantages and disadvantages of the technique relative to classical approaches are discussed.
... with preferred direction-response R P and null ( = opposite) direction response R N . For the white noise stimulus (protocol e), we used the linearnon-linear (LN) cascade model described earlier (Chichilnisky, 2001;Kim and Rieke, 2001;Baccus and Meister, 2002;Field et al., 2010;Wang et al., 2011) to interpret RGC responses. This model consists of a linear filter that determines the cell's temporal, chromatic and spatial sensitivities, as well as a "static" non-linearity that converts the filtered stimulus into a firing rate. ...
... This model consists of a linear filter that determines the cell's temporal, chromatic and spatial sensitivities, as well as a "static" non-linearity that converts the filtered stimulus into a firing rate. In the time domain, the linear filter is proportional to the spiketriggered average stimulus (STA, the average stimulus preceding each spike) (Chichilnisky, 2001). Therefore, for LN models with identical linear filter but different non-linearities, spike-triggered average stimuli are identical up to a scale factor. ...
... In brief, the linear temporal filter was estimated by computing the spike-triggered average (STA). The inner product between the STA and the actual stimuli yielded a generator signal, and the relationship between the actual response and the generator signal was used to estimate the static nonlinearity (Chichilnisky, 2001). I e was computed by first convolving the light stimuli with the linear filter and then passing the results through the non-linearity. ...
In the vertebrate retina, several dozens of parallel channels relay information about the visual world to the brain. These channels are represented by the different types of retinal ganglion cells (RGCs), whose responses are rendered selective for distinct sets of visual features by various mechanisms. These mechanisms can be roughly grouped into synaptic interactions and cell-intrinsic mechanisms, with the latter including dendritic morphology as well as ion channel complement and distribution. Here, we investigate how strongly ion channel complement can shape RGC output by comparing two mouse RGC types, the well-described ON alpha cell and a little-studied ON cell that is EGFP-labelled in the Igfbp5 mouse line and displays an unusual selectivity for stimuli with high contrast. Using patch-clamp recordings and computational modelling, we show that a higher activation threshold and a pronounced slow inactivation of the voltage-gated Na⁺ channels contribute to the distinct contrast tuning and transient responses in ON Igfbp5 RGCs, respectively. In contrast, such a mechanism could not be observed in ON alpha cells. This study provides an example for the powerful role that the last stage of retinal processing can play in shaping RGC responses.
... In a typical experiment, we measured the responses of 250-430 RGCs simultaneously. Spatiotemporal receptive fields were estimated by computing the spike-triggered average to the checkerboard stimulus 27 . This provides an estimate of the linear component of the spatiotemporal receptive field. ...
... We next examined the contrast response functions of the RGCs. Also referred to as static nonlinearities in reverse correlation analyses 27 , the contrast response functions capture how many spikes an RGC tends to produce for a given similarity (correlation) between the stimulus and the receptive field. In untreated retinas, there was a diminished gain between 4 and 7 M relative to WT retinas (Fig. 4C, gray distributions). ...
... 85% of space-time separable STAs met this criterion. Static nonlinearities were calculated for RGCs with space-time separable STAs by mapping the convolution of the linear filter and checkerboard stimulus with their response 27 . These static nonlinearities were used to characterize the contrast response function of individual RGCs and their response gain. ...
Retinitis pigmentosa is an inherited photoreceptor degeneration that begins with rod loss followed by cone loss. This cell loss greatly diminishes vision, with most patients becoming legally blind. Gene therapies are being developed, but it is unknown how retinal function depends on the time of intervention. To uncover this dependence, we utilize a mouse model of retinitis pigmentosa capable of artificial genetic rescue. This model enables a benchmark of best-case gene therapy by removing variables that complicate answering this question. Complete genetic rescue was performed at 25%, 50%, and 70% rod loss (early, mid and late, respectively). Early and mid treatment restore retinal output to near wild-type levels. Late treatment retinas exhibit continued, albeit slowed, loss of sensitivity and signal fidelity among retinal ganglion cells, as well as persistent gliosis. We conclude that gene replacement therapies delivered after 50% rod loss are unlikely to restore visual function to normal. This is critical information for administering gene therapies to rescue vision.
... To address these questions, we first introduced the information theory framework and modeled the primary visual channel as a communication channel. Based on the framework and related studies, we estimated the average channel capacity to be 63 bit per second (bps) using the broadband stimulus modulated by spatially uniformed White Noise (WN) [14]. Consequently, we observe that the JFPM SSVEP paradigm, which stimulates frequencies between 8-15.8 ...
... To estimate the information transfer in this process, we define the dynamic stimulus sequence as information source, the primary visual pathway as the information channel, and the noninvasive sensors as the information receiver. Consistent with prior research [7,[14][15][16], our proposed model for the information channel adopts the additive Gaussian channel hypothesis (Fig. 2b). This hypothesis assumes that the signal is subject to interference from independent colored noise. ...
... The alpha band (filtered to[8][9][10][11][12][13][14][15][16][17][18][19][20] Hz, background gray line) and gamma band (filtered to 20-100Hz, red line) TRF h(τ ) of a representative participant, replicated from Zhigalov et al.[23] b, the same as c, calculated from sweep-2 MEG (unpublish) with blue line represents the gamma component of TRF h(τ ). c, The frequency response H(f ) (right blue y-axis) and the spectral representation of evoked response (each peak represents a stimulation frequency, 6-75 Hz) d, Upper panel, the classification accuracy based on full, linear and linear temporal templates (preliminary experiment data, n=10, mean, error bar is 95% CI), the linear templates are obtained through linear encoder. ...
The mission of visual brain-computer interfaces (BCIs) is to enhance information transfer rate (ITR) to reach high speed towards real-life communication. Despite notable progress, noninvasive visual BCIs have encountered a plateau in ITRs, leaving it uncertain whether higher ITRs are achievable. In this study, we investigate the information rate limits of the primary visual channel to explore whether we can and how we should build visual BCI with higher information rate. Using information theory, we estimate a maximum achievable ITR of approximately 63 bits per second (bps) with a uniformly-distributed White Noise (WN) stimulus. Based on this discovery, we propose a broadband WN BCI approach that expands the utilization of stimulus bandwidth, in contrast to the current state-of-the-art visual BCI methods based on steady-state visual evoked potentials (SSVEPs). Through experimental validation, our broadband BCI outperforms the SSVEP BCI by an impressive margin of 7 bps, setting a new record of 50 bps. This achievement demonstrates the possibility of decoding 40 classes of noninvasive neural responses within a short duration of only 0.1 seconds. The information-theoretical framework introduced in this study provides valuable insights applicable to all sensory-evoked BCIs, making a significant step towards the development of next-generation human-machine interaction systems.
... We took a model-based approach to ask how spatiotemporal patterns of inhibition we observed in relay cells might arise from the output of the types of interneurons we sampled; these analyses were implemented in Julia (Bezanson et al., 2017). First, we used standard linear-nonlinear-Poisson (LNP) models (Chichilnisky, 2001) to describe the spatiotemporal response of On and Off interneurons to sparse-noise stimuli of different sizes and at half contrast: ...
... We began by building linear-nonlinear Poisson models (LNP) (Chichilnisky, 2001;Paninski, 2004) fitted to visual responses recorded from different types of interneurons. The receptive field of an On or Off cell was described as the product of two linear kernels, one spatial and one temporal (Chichilnisky, 2001), and the nonlinearity was estimated using standard techniques (Karklin and Simoncelli, 2011;Zoltowski and Pillow, 2018). ...
... We began by building linear-nonlinear Poisson models (LNP) (Chichilnisky, 2001;Paninski, 2004) fitted to visual responses recorded from different types of interneurons. The receptive field of an On or Off cell was described as the product of two linear kernels, one spatial and one temporal (Chichilnisky, 2001), and the nonlinearity was estimated using standard techniques (Karklin and Simoncelli, 2011;Zoltowski and Pillow, 2018). The only nonstandard approach we took was to separate the analysis of On and Off responses for On-Off cells. ...
By influencing the type and quality of information that relay cells transmit, local interneurons in thalamus have a powerful impact on cortex. To define the sensory features that these inhibitory neurons encode, we mapped receptive fields of optogenetically identified cells in the murine dorsolateral geniculate nucleus. Although few in number, local interneurons had diverse types of receptive fields, like their counterpart relay cells. This result differs markedly from visual cortex, where inhibitory cells are typically less selective than excitatory cells. To explore how thalamic interneurons might converge on relay cells, we took a computational approach. Using an evolutionary algorithm to search through a library of interneuron models generated from our results, we show that aggregated output from different groups of local interneurons can simulate the inhibitory component of the relay cell′s receptive field. Thus, our work provides proof-of-concept that groups of diverse interneurons can supply feature-specific inhibition to relay cells.
... We get twelve reliably recorded RGCs [Papadopoulos et al., 2021, through Spike Triggered Average (STA) analysis [Chichilnisky, 2001]. Errors in raw data processing (e.g. in spike sorting) and/or at the retina preparation may corrupt the biological recordings. ...
... Errors in raw data processing (e.g. in spike sorting) and/or at the retina preparation may corrupt the biological recordings. We trained a Convolutional Neural Network (CNN) model [McIntosh et al., 2016] on the set and then fed white noise sequences to the model to get an unbiased Receptive Field (RF) estimate through STA [Chichilnisky, 2001]. Reliable cells were selected based on spatial (center surround antagonism) and temporal (biphasic response) STA characteristics. ...
... Reliable cells were selected based on spatial (center surround antagonism) and temporal (biphasic response) STA characteristics. The STA properties of RGCs have been documented in the literature [Chichilnisky, 2001]. ...
Visual attention forms the basis of understanding the visual world. In this work we follow a computational approach to investigate the biological basis of visual attention. We analyze retinal and cortical electrophysiological data from mouse. Visual Stimuli are Natural Images depicting real world scenes. Our results show that in primary visual cortex (V1), a subset of around $10\%$ of the neurons responds differently to salient versus non-salient visual regions. Visual attention information was not traced in retinal response. It appears that the retina remains naive concerning visual attention; cortical response gets modulated to interpret visual attention information. Experimental animal studies may be designed to further explore the biological basis of visual attention we traced in this study. In applied and translational science, our study contributes to the design of improved visual prostheses systems -- systems that create artificial visual percepts to visually impaired individuals by electronic implants placed on either the retina or the cortex.
... As a consequence, neural system identification (SI) approaches have flourished (Fig 1a top). They empirically fit the stimulusresponse (transfer) function of neurons based on experimentally recorded data [2][3][4]. A classic example is the generalized linear model (GLM, [2,5]), which consists of a linear filter as a first order approximation of a neuron's response function (i.e., its receptive field; [6]), followed by a point-wise nonlinear function for the neuron's output. ...
... They empirically fit the stimulusresponse (transfer) function of neurons based on experimentally recorded data [2][3][4]. A classic example is the generalized linear model (GLM, [2,5]), which consists of a linear filter as a first order approximation of a neuron's response function (i.e., its receptive field; [6]), followed by a point-wise nonlinear function for the neuron's output. To account for additional non-linearities (e.g., [7,8]), several extensions, such as linear-nonlinear cascades [9,10], have been proposed. ...
... To confirm that our hybrid models capture the properties of the recorded cells, we estimated their RFs (Fig 3b and S1(f) Fig; Methods). Indeed, we found that the models learned antagonistic center-surround RFs with biphasic temporal kernels, reminiscent of RGC RFs found in other studies [2,47]. To get insights to which degree our models resembled biological vision systems, we next investigated the internal representations by analyzing the filters of the models' subunits [18,61]. ...
Neural system identification aims at learning the response function of neurons to arbitrary stimuli using experimentally recorded data, but typically does not leverage normative principles such as efficient coding of natural environments. Visual systems, however, have evolved to efficiently process input from the natural environment. Here, we present a normative network regularization for system identification models by incorporating, as a regularizer, the efficient coding hypothesis, which states that neural response properties of sensory representations are strongly shaped by the need to preserve most of the stimulus information with limited resources. Using this approach, we explored if a system identification model can be improved by sharing its convolutional filters with those of an autoencoder which aims to efficiently encode natural stimuli. To this end, we built a hybrid model to predict the responses of retinal neurons to noise stimuli. This approach did not only yield a higher performance than the "stand-alone" system identification model, it also produced more biologically plausible filters, meaning that they more closely resembled neural representation in early visual systems. We found these results applied to retinal responses to different artificial stimuli and across model architectures. Moreover, our normatively regularized model performed particularly well in predicting responses of direction-of-motion sensitive retinal neurons. The benefit of natural scene statistics became marginal, however, for predicting the responses to natural movies. In summary, our results indicate that efficiently encoding environmental inputs can improve system identification models, at least for noise stimuli, and point to the benefit of probing the visual system with naturalistic stimuli.
... In the present study, a linear-nonlinear (LN) model was applied to estimate the average light sensitivity of individual RGC under the sustained Gaussian contrast stimulation, with the structure and function of LN model being described previously (Chichilnisky 2001;Dai and Liang 2020). Specifically, the input signal of the LN model, s (t), indicates the intensity of light striking at the surface of the photoreceptor layer and the output signal r (t) represents the instantaneous firing rate of an RGC. ...
... Functionally, the linear part of LN model, L (t), characterizes how the retinal network presynaptic to RGC integrates light inputs, and was set as a normalized linear kernel estimated from the STA algorithm (Chichilnisky 2001). The intermediate variable g (t), which indicates the integrated outputs of the linear part, was then computed by convolution of the linear part L (t) and the input signal s (t). ...
... The changes of RGC's firing rate in exposure to sustained contrast stimulations were considered as the result of responsiveness changes, which are related to response latency and light sensitivity (Baccus and Meister 2002;Chichilnisky 2001;Kastner and Baccus 2011). Previous study has shown that light sensitivity was oppositely modulated in adaptation and sensitization processes: during sustained high-contrast period, light sensitivity was decreased for adapting RGCs while was increased for sensitizing RGCs; but the modulation of response latency showed no differences between adaptation and sensitization (Dai and Liang 2020). ...
Two coordinated dynamic properties (adaptation and sensitization) are observed in retinal ganglion cells (RGCs) under the contrast stimulation. During sustained high-contrast period, adaptation decreases RGCs’ responses while sensitization increases RGCs’ responses. In mouse retina, adaptation and sensitization respectively show OFF- and ON-pathway-dominance. However, the mechanisms which drive the differentiation between adaptation and sensitization remain unclear. In the present study, multi-electrode recordings were conducted on isolated mouse retina under full-field contrast stimulation. Dynamic property was quantified based on the trend of RGC’s firing rate during high-contrast period, light sensitivity was estimated by linear-nonlinear analysis and coding ability was estimated through stimulus reconstruction algorism. γ-Aminobutyric acid (GABA) receptors were pharmacologically blocked to explore the relation between RGCs’ dynamic property and the activity of GABA receptors. It was found that GABAA and GABAC receptors respectively mediated the adaptation and sensitization processes in RGCs’ responses. RGCs’ dynamic property changes occurred after the blockage of GABA receptors were related to the modulation of the cells’ light sensitivity. Further, the blockage of GABAA (GABAC) receptor significantly decreased RGCs’ overall coding ability and eliminated the functional benefits of adaptation (sensitization). Our work suggests that the dynamic property of individual RGC is related to the balance between its GABAA-receptor-mediated inputs and GABAC-receptor-mediated inputs. Blockage of GABA receptors breaks the balance of retinal circuitry for signal processing, and down-regulates the visual information coding ability.
... Although patients with BPD were not compared with a control group, their patterns were randomly shuffled to create a synthetic control group for comparison, as in Chichilnisky (6); the methodology is detailed in Section 2.5.2. As stated by Staebler et al. (3), patients with BPD exhibited more blended facial expressions (displaying features of mixed and different emotions) and masking of emotions (covering a negative emotion with smiling) than healthy controls; likewise, even when masking was not statistically significant between conditions, this behavior was remarked during exclusion compared to inclusion. ...
... The patterns of both conditions were tested against their respective random-shuffled data sets created by randomly shuffling the frequencies of the original data sets, as shown in Algorithm 1. White noise is inherently random; furthermore, each white noise sample is statistically independent of the others, and there is no correlation between successive samples. This randomness property makes white noise useful in various applications, such as modeling stochastic processes, simulating random events, and providing a baseline for comparison in statistical analyses (6,(17)(18)(19)(20). ...
Borderline Personality Disorder (BPD) symptoms include inappropriate control of anger and severe emotional dysregulation after rejection in daily life. Nevertheless, when using the Cyberball paradigm, a tossing game to simulate social exclusion, the seven basic emotions (happiness, sadness, anger, surprise, fear, disgust, and contempt) have not been exhaustively tracked out. It was hypothesized that these patients would show anger, contempt, and disgust during the condition of exclusion versus the condition of inclusion. When facial emotions are automatically detected by Artificial Intelligence, “blending”, -or a mixture of at least two emotions- and “masking”, -or showing happiness while expressing negative emotions- may be most easily traced expecting higher percentages during exclusion rather than inclusion. Therefore, face videos of fourteen patients diagnosed with BPD (26 ± 6 years old), recorded while playing the tossing game, were analyzed by the FaceReader software. The comparison of conditions highlighted an interaction for anger: it increased during inclusion and decreased during exclusion. During exclusion, the masking of surprise; i.e., displaying happiness while feeling surprised, was significantly more expressed. Furthermore, disgust and contempt were inversely correlated with greater difficulties in emotion regulation and symptomatology, respectively. Therefore, the automatic detection of emotional expressions during both conditions could be useful in rendering diagnostic guidelines in clinical scenarios.
... ; https://doi.org/10. 1101/2024 We summarized the response of each ON-T and ON-S RGC by computing the average stimulus 134 preceding each recorded spike (the spike-triggered average or STA stimulus) when presenting 135 a non-repeated Gaussian noise stimulus (Fig. 1D) (Chichilnisky, 2001) and we quantified 136 response kinetics from these STA waveforms by measuring the time of zero-crossing (between 137 trough and peak) as well as the ratio of amplitudes of the trough and peak (biphasic index). ON- ...
... The linear filter captures the kinetics of the RGC response and is analogous to the time-reversed 174 STA derived from spike responses (Chichilnisky, 2001). As with the STAs in Figure 1D . ...
Parallel processing is a fundamental organizing principle in the nervous system, and understanding how parallel neural circuits generate distinct outputs from common inputs is a key goal of neuroscience. In the mammalian retina, divergence of cone signals into multiple feed-forward bipolar cell pathways forms the initial basis for parallel retinal circuits dedicated to specific visual functions. Here, we used patch-clamp electrophysiology, electron microscopy and two photon imaging of a fluorescent glutamate sensor to examine how kinetically distinct responses arise in transient versus sustained ON alpha RGCs (ON-T and ON-S RGCs) of the mouse retina. We directly compared the visual response properties of these RGCs with their presynaptic bipolar cell partners, which we identified using 3D electron microscopy reconstruction. Different ON bipolar cell subtypes (type 5i, type 6 and type 7) had indistinguishable light-driven responses whereas extracellular glutamate signals around RGC dendrites and postsynaptic excitatory currents measured in ON-T and ON-S RGCs in response to the identical stimuli used to probe bipolar cells were kinetically distinct. Anatomical examination of the bipolar cell axon terminals presynaptic to ON-T and ON-S RGCs suggests bipolar subtype-specific differences in the size of synaptic ribbon-associated vesicle pools may contribute to transient versus sustained kinetics. Our findings indicate bipolar cell synapses are a primary point of divergence in kinetically distinct visual pathways.
... STNMF is a type of spike-triggered analysis that aims at extracting spatial subunits from the structure of spike-eliciting stimulus segments under white-noise stimulation. Spike-triggered analyses have long been used for assessing receptive fields via computation of the spike-triggered average (STA; Bryant and Segundo 1976;Chichilnisky 2001;De Boer and Kuyper 1968) as well as for obtaining multiple (typically temporal) stimulus filters via spike-triggered covariance (STC) analysis (Cantrell et al. 2010;Fairhall et al. 2006;Gollisch and Meister 2008;Samengo and Gollisch 2013;Schwartz et al. 2006). As an extension of these approaches, STNMF can identify localized subunits, based on the statistical structure (e.g. ...
... The receptive field of a given ganglion cell was estimated using reverse correlation to obtain the spiketriggered average (STA; Chichilnisky 2001). The stimulus frames within the 700 ms time window preceding a spike were collected and averaged across all spikes. ...
A standard circuit motif in sensory systems is the pooling of sensory information from an upstream neuronal layer. A downstream neuron thereby collects signals across different locations in stimulus space, which together compose the neuron’s receptive field. In addition, nonlinear transformations in the signal transfer between the layers give rise to functional subunits inside the receptive field. For ganglion cells in the vertebrate retina, for example, receptive field subunits are thought to correspond to presynaptic bipolar cells. Identifying the number and locations of subunits from the stimulus–response relationship of a recorded ganglion cell has been an ongoing challenge in order to characterize the retina’s functional circuitry and to build computational models that capture nonlinear signal pooling. Here we present a novel version of spike-triggered non-negative matrix factorization (STNMF), which can extract localized subunits in ganglion-cell receptive fields from recorded spiking responses under spatiotemporal white-noise stimulation. The method provides a more than 100-fold speed increase compared to a previous implementation, which can be harnessed for systematic screening of hyperparameters, such as sparsity regularization. We demonstrate the power and flexibility of this approach by analyzing populations of ganglion cells from salamander and primate retina. We find that subunits of midget as well as parasol ganglion cells in the marmoset retina form separate mosaics that tile visual space. Moreover, subunit mosaics show alignment with each other for ON and OFF midget as well as for ON and OFF parasol cells, indicating a spatial coordination of ON and OFF signals at the bipolar-cell level. Thus, STNMF can reveal organizational principles of signal transmission between successive neural layers, which are not easily accessible by other means.
... Linear-nonlinear (LN) analysis was performed as previously described (Chichilnisky, 2001;Jarsky et al., 2011;PoNackal et al., 2021). Firing of AlphaONS RGCs was evoked by a series of quasi-white-noise (WN) stimuli. ...
... We further examined the temporal tuning of AlphaONS RGCs by recording APs generated in response to a 300µm diameter flickering white noise stimulus. The stimulus contains a wide-range of temporal frequencies, and the response can be quantified with a linear-nonlinear (LN) analysis; the linear filter represents temporal integration, and the nonlinearity represents the input-output relationship of the spiking mechanism ( Figure 3H-M) (Chichilnisky, 2001;Demb, 2008). Linear filters were similar between control and 7dpc conditions. ...
Retinal ganglion cells (RGCs) are the sole output neurons of the retina and convey visual information to the brain via their axons in the optic nerve. Following an injury to the optic nerve, RGCs axons degenerate and many cells die. For example, a surgical model of compressive axon injury, the optic nerve crush (ONC), kills ∼80% of RGCs after two weeks. Surviving cells are biased towards certain ‘resilient’ types, including several types that originally produced sustained firing to light stimulation. RGC survival may depend on activity level, and there is a limited understanding of how or why activity changes following optic nerve injury. Here we quantified the electrophysiological properties of a highly resilient RGC type, the sustained ON-Alpha RGC, seven days post-ONC with extracellular and whole-cell patch clamp recording. Both light- and current-driven firing were reduced after ONC, but synaptic inputs were largely intact. Resting membrane potential and input resistance were relatively unchanged, while voltage-gated currents were impaired, including a reduction in voltage-gated sodium channel density in the axon initial segment and function. Hyperpolarization or chelation of intracellular calcium partially rescued firing rates. These data suggest that an injured resilient RGC reduces its activity by a combination of reduced voltage-gated channel expression and function and downregulation of intrinsic excitability via a Ca ²⁺ -dependent mechanism without substantial changes in synaptic input. Reduced excitability may be due to degradation of the axon but could also be energetically beneficial for injured RGCs, preserving cellular energy for survival and regeneration.
Graphical Abstract
Schematic view of the effects of axon injury (optic nerve crush) on the physiology of an sustained ON-Alpha (AlphaONS) retinal ganglion cell. These cells are highly resilient to axon injury and survive for several weeks while other retinal ganglion cell types perish. At one week after injury, the AlphaONS RGC has diminished spontaneous and light-evoked action potential firing. Reduced firing depends not on changes in synaptic inputs but rather on reductions in intrinsic excitability. Reduced excitability is explained by a Ca ²⁺ -dependent mechanism and by a reduction in sodium channel density and function.
Key Points Summary
1) Retinal ganglion cell (RGC) types show diverse rates of survival after axon injury.
2) A resilient RGC type maintains its synaptic inputs one week post-injury.
3) The resilient RGC type shows diminished firing and reduced expression of axon initial segment (AIS) genes following injury
4) Activity deficits arise from intrinsic dysfunction (Na ⁺ channels, intracellular Ca ²⁺ ), not from loss of excitation or enhanced inhibition.
... In the actor-model framework, artificial image encoding depends on two components: the forward model (digital twin of the retina) and the actor network (artificial image encoding). Much research has been previously dedicated to deriving a forward model of the retina 32,35,36,[43][44][45][46][47] . Selecting a suitable forward model plays a crucial role in this study. ...
... Manual inspection was performed using Phy software (version 2.0b5) 61 , including verification of gaussian distribution in the amplitudes, waveforms present in multiple channels, presence of a dip in autocorrelogram, and merging/separating clusters as necessary. To assess the reliability of the recorded neurons and account for experimental drift, random binary checkerboard stimuli was presented at the start of the experiment, and then redisplayed roughly every half an hour 43 . The check size was 50 µm, the refresh rate was 33 Hz and the presentation time was 5 min. ...
A fundamental challenge in neuroengineering is determining a proper artificial input to a sensory system that yields the desired perception. In neuroprosthetics, this process is known as artificial sensory encoding, and it holds a crucial role in prosthetic devices restoring sensory perception in individuals with disabilities. For example, in visual prostheses, one key aspect of artificial image encoding is to downsample images captured by a camera to a size matching the number of inputs and resolution of the prosthesis. Here, we show that downsampling an image using the inherent computation of the retinal network yields better performance compared to learning-free downsampling methods. We have validated a learning-based approach (actor-model framework) that exploits the signal transformation from photoreceptors to retinal ganglion cells measured in explanted mouse retinas. The actor-model framework generates downsampled images eliciting a neuronal response in-silico and ex-vivo with higher neuronal reliability than the one produced by a learning-free approach. During the learning process, the actor network learns to optimize contrast and the kernel’s weights. This methodological approach might guide future artificial image encoding strategies for visual prostheses. Ultimately, this framework could be applicable for encoding strategies in other sensory prostheses such as cochlear or limb.
... Retinal ganglion cells, the output neurons of the retina, are classically modelled with a linearnonlinear (LN) model (Chichilnisky, 2001). This can take the center-surround structure of their receptive fields into account, but indiscriminately considers luminance signals inside the receptive field to be integrated linearly and passed through a nonlinearity only afterwards, at the model's output stage. ...
... We estimated the receptive fields of cells by computing the spike-triggered average (STA) from responses to a spatiotemporal binary white-noise stimulus on a checkerboard grid (Meister et al., 1994;Chichilnisky, 2001). Each stimulus field had a size of 15 µm by 15 µm and was randomly updated every four frames (i.e., 47 ms) to either black or white with 100% Michelson contrast. ...
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. 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 less than an hour of recording time, making it ideal for online analysis and closed-loop investigations of receptive field substructure in retina recordings.
... Kilosort 2 was used for spike sorting [Pachitariu 2023]. RGC light response properties, including receptive fields, were characterized with reverse correlation using a white noise checkerboard stimulus [Chichilnisky 2001]. Ground truth cell type classification was performed manually by clustering over features computed from the light response properties and spiking auto-correlation functions, according to previously described procedures [Field 2007, Rhoades 2019]. ...
... Receptive field centers were computed from the spike-triggered averages (STAs) characterized with white noise reverse correlation [Chichilnisky 2001]. The time component of the STA was estimated by computing a mean over statistically-significant pixels, and a 2D intensity map was constructed by regressing the STA with that time component. ...
Identifying neuronal cell types and their biophysical properties based on their extracellular electrical features is a major challenge for experimental neuroscience and the development of high-resolution brain-machine interfaces. One example is identification of retinal ganglion cell (RGC) types and their visual response properties, which is fundamental for developing future electronic implants that can restore vision. The electrical image (EI) of a RGC, or the mean spatio-temporal voltage footprint of its recorded spikes on a high-density electrode array, contains substantial information about its anatomical, morphological, and functional properties. However, the analysis of these properties is complex because of the high-dimensional nature of the EI. We present a novel optimization-based algorithm to decompose electrical image into a low-dimensional, biophysically-based representation: the temporally-shifted superposition of three learned basis waveforms corresponding to spike waveforms produced in the somatic, dendritic and axonal cellular compartments. Large-scale multi-electrode recordings from the macaque retina were used to test the effectiveness of the decomposition. The decomposition accurately localized the somatic and dendritic compartments of the cell. The imputed dendritic fields of RGCs correctly predicted the location and shape of their visual receptive fields. The inferred waveform amplitudes and shapes accurately identified the four major primate RGC types (ON and OFF midget and parasol cells), a substantial advance. Together, these findings may contribute to more accurate inference of RGC types and their original light responses in the degenerated retina, with possible implications for other electrical imaging applications.
... The method of reverse correlation has been widely used to measure response transfer functions -that is, the relationship of outputs to inputs in a dynamical system. In experimental neuroscience, white noise stimuli and reverse correlation have long been used to map receptive fields of sensory neurons 4,5 . For visual neurons, spikes are recorded while a checkerboard-like spatial and temporal white noise stimulus is repeatedly presented. ...
... After thousands of spikes have been recorded, the average history of the visual noise stimulus that preceded each spike -the spike-triggered average, a first order reverse correlation -reveals the location and timing of light intensities that most effectively drive spiking, the spatiotemporal visual receptive field (Figure 1, top and lower left). Higher-order reverse correlation with spike-triggered covariance can be used to characterize neurons with more complex non-linear response properties 5,6 . ...
A novel approach to studying attention in mice reveals processes similar to those in humans and lays out an efficient way to explore its neuronal correlates in a genetically tractable animal model.
... Each of these RGC types exhibits highly stereotyped responses and feature selectivity while forming a mosaic of receptive fields that approximately tiles space [96,30,36]. To test whether clusters of cells on the encoding manifold corresponded to individual RGC types, we examined the spatial receptive field locations of RGCs within each cluster and from individual retinas by calculating the spike-triggered average to a checkerboard noise stimulus [19]; this revealed that RGCs in a given cluster, when sampled by the MEA at sufficient density, exhibited a mosaic-like organization (Figs. 3d-g and S3). ...
... Custom software was used to present drifting gratings and flow stimuli at 60 Hz refresh rate, described in section 1.3 below. RGC responses to checkerboard noise were used to estimate the spatial and temporal components of the spike-triggered average (STA) [19]. The STA estimates the spatial and temporal integration of visual stimuli by the receptive field. ...
The retina and primary visual cortex (V1) both exhibit diverse neural populations sensitive to diverse visual features. Yet it remains unclear how neural populations in each area partition stimulus space to span these features. One possibility is that neural populations are organized into discrete groups of neurons, with each group signaling a particular constellation of features. Alternatively, neurons could be continuously distributed across feature-encoding space. To distinguish these possibilities, we presented a battery of visual stimuli to mouse retina and V1 while measuring neural responses with multi-electrode arrays. Using machine learning approaches, we developed a manifold embedding technique that captures how neural populations partition feature space and how visual responses correlate with physiological and anatomical properties of individual neurons. We show that retinal populations discretely encode features, while V1 populations provide a more continuous representation. Applying the same analysis approach to convolutional neural networks that model visual processing, we demonstrate that they partition features much more similarly to the retina, indicating they are more like big retinas than little brains.
... We simulated a population of vestibular nuclei neurons using linear-nonlinear cascade models [50,108]. The firing rate response of the neuron is given by rðtÞ ¼ Tðr lin ðtÞÞ in which r lin (t) is the linear estimation neural response, and T(�) is the nonlinear relation that relates r lin (t) to actual firing rate calculated from data. ...
How the activities of large neural populations are integrated in the brain to ensure accurate perception and behavior remains a central problem in systems neuroscience. Here, we investigated population coding of naturalistic self-motion by neurons within early vestibular pathways in rhesus macaques (Macacca mulatta). While vestibular neurons displayed similar dynamic tuning to self-motion, inspection of their spike trains revealed significant heterogeneity. Further analysis revealed that, during natural but not artificial stimulation, heterogeneity resulted primarily from variability across neurons as opposed to trial-to-trial variability. Interestingly, vestibular neurons displayed different correlation structures during naturalistic and artificial self-motion. Specifically, while correlations due to the stimulus (i.e., signal correlations) did not differ, correlations between the trial-to-trial variabilities of neural responses (i.e., noise correlations) were instead significantly positive during naturalistic but not artificial stimulation. Using computational modeling, we show that positive noise correlations during naturalistic stimulation benefits information transmission by heterogeneous vestibular neural populations. Taken together, our results provide evidence that neurons within early vestibular pathways are adapted to the statistics of natural self-motion stimuli at the population level. We suggest that similar adaptations will be found in other systems and species.
... A custom spike sorting procedure [14] was applied to the recordings to identify and segregate spikes from individual RGCs. The spike-triggered average (STA) stimulus was then computed for each RGC to classify functionally-distinct cell types [35][36][37][38]. For each cell, the electrical image (EI), or the average spatiotemporal pattern of activity associated with a cell's spike, was computed by averaging the voltage traces during the time of each cell's spike [14,39]. ...
Background: Bi-directional electronic neural interfaces, capable of both electrical recording and stimulation, communicate with the nervous system to permit precise calibration of electrical inputs by capturing the evoked neural responses. However, one significant challenge is that stimulation artifacts often mask the actual neural signals. To address this issue, we introduce a novel approach that employs dynamical control systems to detect and decipher electrically evoked neural activity despite the presence of electrical artifacts.
Methods: Our proposed method leverages the unique spatiotemporal patterns of neural activity and electrical artifacts to distinguish and identify individual neural spikes. We designed distinctive dynamical models for both the stimulation artifact and each neuron observed during spontaneous neural activity. We can estimate which neurons were active by analyzing the recorded voltage responses across multiple electrodes post-stimulation. This technique also allows us to exclude signals from electrodes heavily affected by stimulation artifacts, such as the stimulating electrode itself, yet still accurately differentiate between evoked spikes and electrical artifacts.
Results: We applied our method to high-density multi-electrode recordings from the primate retina in an ex vivo setup, using a grid of 512 electrodes. Through repeated electrical stimulations at varying amplitudes, we were able to construct activation curves for each neuron. The curves obtained with our method closely resembled those derived from manual spike sorting. Additionally, the stimulation thresholds we estimated strongly agreed with those determined through manual analysis, demonstrating high reliability (R^2 = 0.951 for human 1 and R^2 = 0.944 for human 2).
Conclusion: Our method can effectively separate evoked neural spikes from stimulation artifacts by exploiting the distinct spatiotemporal propagation patterns captured by a dense, large-scale multi-electrode array. This technique holds promise for future applications in real-time closed-loop stimulation systems and for managing multi-channel stimulation strategies.
... Although these investigations provide thorough insight into the retina's structure and function, their development is slow and difficult. Another standard approach is the Linear-nonlinear (LN) model [18] which combines a linear spatiotemporal filter with a single static nonlinearity. These models have been used to describe the retinal responses to artificial stimuli; however, they fail to generalize to natural stimuli [19]. ...
It is a popular hypothesis in neuroscience that ganglion cells in the retina are activated by selectively detecting visual features in an observed scene. While ganglion cell firings can be predicted via data-trained deep neural nets, the networks remain indecipherable, thus providing little understanding of the cells' underlying operations. To extract knowledge from the cell firings, in this paper we learn an interpretable graph-based classifier from data to predict the firings of ganglion cells in response to visual stimuli. Specifically, we learn a positive semi-definite (PSD) metric matrix
$ M ≥ 0 $
that defines Mahalanobis distances between graph nodes (visual events) endowed with pre-computed feature vectors; the computed inter-node distances lead to edge weights and a combinatorial graph that is amenable to binary classification. Mathematically, we define the objective of metric matrix
$ \rm{M} $
optimization using a graph adaptation of large margin nearest neighbor (LMNN), which is rewritten as a semi-definite programming (SDP) problem. We solve it efficiently via a fast approximation called Gershgorin disc perfect alignment (GDPA) linearization. The learned metric matrix
$ \rm{M} $
provides interpretability: important features are identified along
$ \rm{M} $
's diagonal, and their mutual relationships are inferred from off-diagonal terms. Our fast metric learning framework can be applied to other biological systems with pre-chosen features that require interpretation.
... The receptive fields (RFs) of the identified RGC axon patches or SC somata were estimated by reverse-correlation methods using the random checkerboard stimuli 37 . Specifically, we calculated the response-weighted average of the stimulus waveform (0.5 s window; 16.7 ms bin width) and characterized its spatial profile by the twodimensional (2D) Gaussian curve fit at the peak latency (e.g., Fig. 2e and Supplementary Figs. ...
Retinotopy, like all long-range projections, can arise from the axons themselves or their targets. The underlying connectivity pattern, however, remains elusive at the fine scale in the mammalian brain. To address this question, we functionally mapped the spatial organization of the input axons and target neurons in the female mouse retinocollicular pathway at single-cell resolution using in vivo two-photon calcium imaging. We found a near-perfect retinotopic tiling of retinal ganglion cell axon terminals, with an average error below 30 μm or 2° of visual angle. The precision of retinotopy was relatively lower for local neurons in the superior colliculus. Subsequent data-driven modeling ascribed it to a low input convergence, on average 5.5 retinal ganglion cell inputs per postsynaptic cell in the superior colliculus. These results indicate that retinotopy arises largely from topographically precise input from presynaptic cells, rather than elaborating local circuitry to reconstruct the topography by postsynaptic cells.
... The analysis results made qualitative sense and was consistent with previous work 53 as the turn probability increases when the spike rate or the stimulus decreases ( Figure S9). However, because the spike distribution was non-Gaussian, this approach cannot be employed to analyze the data collected in this study quantitatively as the resulting filter would be erroneous, a well-known limitation of reverse-correlation approaches 54 . Next, we tried another approach that was successful in describing behavior in larvae 55 where a logistic Generalized Linear Model (GLM) was employed to predict the relationship between ORN responses and behavior. ...
Most real-world behaviors – such as odor-guided locomotion - are performed with incomplete information. Activity in olfactory receptor neuron (ORN) classes provides information about odor identity but not the location of its source. In this study, we investigate the sensorimotor transformation that relates ORN activation to locomotion changes in Drosophila by optogenetically activating different combinations of ORN classes and measuring the resulting changes in locomotion. Three features describe this sensorimotor transformation: First, locomotion depends on both the instantaneous firing frequency ( f ) and its change ( df ); the two together serve as a short-term memory that allows the fly to adapt its motor program to sensory context automatically. Second, the mapping between ( f, df ) and locomotor parameters such as speed or curvature is distinct for each pattern of activated ORNs. Finally, the sensorimotor mapping changes with time after odor exposure, allowing information integration over a longer timescale.
... This work builds on previous research on modeling neural responses to visual scenes. Early attempts included Linear-nonlinear (LN) [68,69] and Generalized Linear Models (GLMs) [2,7]. However, these models have limited capabilities and fail when faced with more complex stimuli [8,9]. ...
Developing computational models of neural response is crucial for understanding sensory processing and neural computations. Current state-of-the-art neural network methods use temporal filters to handle temporal dependencies, resulting in an unrealistic and inflexible processing paradigm. Meanwhile, these methods target trial-averaged firing rates and fail to capture important features in spike trains. This work presents the temporal conditioning spiking latent variable models (TeCoS-LVM) to simulate the neural response to natural visual stimuli. We use spiking neurons to produce spike outputs that directly match the recorded trains. This approach helps to avoid losing information embedded in the original spike trains. We exclude the temporal dimension from the model parameter space and introduce a temporal conditioning operation to allow the model to adaptively explore and exploit temporal dependencies in stimuli sequences in a natural paradigm. We show that TeCoS-LVM models can produce more realistic spike activities and accurately fit spike statistics than powerful alternatives. Additionally, learned TeCoS-LVM models can generalize well to longer time scales. Overall, while remaining computationally tractable, our model effectively captures key features of neural coding systems. It thus provides a useful tool for building accurate predictive computational accounts for various sensory perception circuits.
... Neural system identification methods are a standard approach for RF estimation [reviewed in Wu et al., 2006]. They estimate response functions of neurons using the recorded activities to external stimuli such as white noise and natural images [Rust andMovshon, 2005, Qiu et al., 2021], classically with a linear-nonlinear-Poisson model or its variants [Chichilnisky, 2001, Huang et al., 2021, Karamanlis and Gollisch, 2021. More recently, deep neural networks (DNNs) with hierarchical non-linear processing have shown great success for learning the stimulus-response functions of neurons along the ventral visual stages from retina [McIntosh et al., 2016, Batty et al., 2016, Qiu et al., 2023 and primary visual cortex [Klindt et al., 2017, Ecker et al., 2018 to higher visual areas [Yamins et al., 2014, Güçlü andvan Gerven, 2015]. ...
Neural population responses in sensory systems are driven by external physical stimuli. This stimulus-response relationship is typically characterized by receptive fields with the assumption of identical and independent Gaussian or Poisson distributions through the loss function. However, responses to repeated presentations of the same stimulus vary, complicating the understanding of neural coding in a stochastic manner. Therefore, to appreciate neural information processing, it is critical to identify stimulus-response function in the presence of trial-to-trial variability. Here, we present a Bayesian system identification approach to predict neural responses to visual stimuli with uncertainties, and explore whether incorporating response fluctuations by using synaptic variability can be beneficial for identifying neural response properties. To this end, we build a neural network model using variational inference to estimate the distribution of each model weight. Tests with different neural datasets demonstrate that this method can achieve higher or comparable performance on neural prediction compared to Monte Carlo dropout methods and traditional models using point estimates of the model parameters. At the same time, our variational method allows to estimate the uncertainty of neural transfer function, which we have found to be negatively correlated with the predictive performance. Finally, our model enables a highly challenging task, i.e., the prediction of noise correlations for unseen stimuli, albeit to a moderate degree. Together, we provide a probabilistic approach as a starting point for simultaneously estimating neuronal receptive fields and analyzing trial-to-trial co-variability for a population of neurons, which may help to uncover the underpinning of stochastic biological computation.
... There is concern about whether the GLM model can be applied to analyze different subtypes of αRGCs in the same way. However, based on a normal and intact circuit, the GLM model can be applied to predict the responses of subtypes of αRGCs to visual stimuli (Chichilnisky, 2001;Pillow et al., 2005;Shapley, 2009). If the myopic retina encodes visual information differently from the normal retina, then the predicted results from GLM model would reflect these differences. ...
The etiology of myopia remains unclear. This study investigated whether retinal ganglion cells (RGCs) in the myopic retina encode visual information differently from the normal retina and to determine the role of Connexin (Cx) 36 in this process. Generalized linear models (GLMs), which can capture stimulus-dependent changes in real neurons with spike timing precision and reliability, were used to predict RGCs responses to focused and defocused images in the retinas of wild-type (normal) and Lens-Induced Myopia (LIM) mice. As the predominant subunit of gap junctions in the mouse retina and a plausible modulator in myopia development, Cx36 knockout (KO) mice were used as a control for an intact retinal circuit. The kinetics of excitatory postsynaptic currents (EPSCs) of a single αRGC could reflect projection of both focused and defocused images in the retinas of normal and LIM, but not in the Cx36 knockout mice. Poisson GLMs revealed that RGC encoding of visual stimuli in the LIM retina was similar to that of the normal retina. In the LIM retinas, the linear-Gaussian GLM model with offset was a better fit for predicting the spike count under a focused image than the defocused image. Akaike information criterion (AIC) indicated that nonparametric GLM (np-GLM) model predicted focused/defocused images better in both LIM and normal retinas. However, the spike counts in 33% of αRGCs in LIM retinas were better fitted by exponential GLM (exp-GLM) under defocus, compared to only 13% αRGCs in normal retinas. The difference in encoding performance between LIM and normal retinas indicated the possible amendment and plasticity of the retinal circuit in myopic retinas. The absence of a similar response between Cx36 KO mice and normal/LIM mice might suggest that Cx36, which is associated with myopia development, play a role in encoding focused and defocused images.
... 10 However, it is unclear how to interpret these models in terms of their contribution to neural computation or relationship to individual biological neurons. Simple linear-nonlinear (LN) models, 11 generalized linear models (GLMs), 6 or two-layer LN-LN models with nonlinear subunits, [12][13][14][15][16] show higher computational interpretability-the ability to understand the mathematical components of the model-yet an LN model's single spatiotemporal filter, or the two sequential stages of an LN-LN model, are inadequate to capture the complex visual processing of natural stimuli. ...
Understanding the circuit mechanisms of the visual code for natural scenes is a central goal of sensory neuroscience. We show that a three-layer network model predicts retinal natural scene responses with an accuracy nearing experimental limits. The model's internal structure is interpretable, as interneurons recorded separately and not modeled directly are highly correlated with model interneurons. Models fitted only to natural scenes reproduce a diverse set of phenomena related to motion encoding, adaptation, and predictive coding, establishing their ethological relevance to natural visual computation. A new approach decomposes the computations of model ganglion cells into the contributions of model interneurons, allowing automatic generation of new hypotheses for how interneurons with different spatiotemporal responses are combined to generate retinal computations, including predictive phenomena currently lacking an explanation. Our results demonstrate a unified and general approach to study the circuit mechanisms of ethological retinal computations under natural visual scenes.
... This work builds on previous research on modeling neural responses to visual scenes. Early attempts included Linear-nonlinear (LN) [68,69] and Generalized Linear Models (GLMs) [2,7]. However, these models have limited capabilities and fail when faced with more complex stimuli [8,9]. ...
Developing computational models of neural response is crucial for understanding sensory processing and neural computations. Current state-of-the-art neural network methods use temporal filters to handle temporal dependencies, resulting in an unrealistic and inflexible processing flow. Meanwhile, these methods target trial-averaged firing rates and fail to capture important features in spike trains. This work presents the temporal conditioning spiking latent variable models (TeCoS-LVM) to simulate the neural response to natural visual stimuli. We use spiking neurons to produce spike outputs that directly match the recorded trains. This approach helps to avoid losing information embedded in the original spike trains. We exclude the temporal dimension from the model parameter space and introduce a temporal conditioning operation to allow the model to adaptively explore and exploit temporal dependencies in stimuli sequences in a natural paradigm. We show that TeCoS-LVM models can produce more realistic spike activities and accurately fit spike statistics than powerful alternatives. Additionally, learned TeCoS-LVM models can generalize well to longer time scales. Overall, while remaining computationally tractable, our model effectively captures key features of neural coding systems. It thus provides a useful tool for building accurate predictive computational accounts for various sensory perception circuits.
... Visual stimulation and cell type classification. To identify the type of each recorded cell, as well as the location and shape of the visual receptive field, the retina was visually stimulated with a dynamic, binary white noise stimulus, and the spike-triggered average (STA) stimulus was computed for each RGC (Chichilnisky, 2001;Chichilnisky and Kalmar, 2002). The STA summarizes the spatial, temporal, and chromatic structure of the light response. ...
High-fidelity electronic implants can in principle restore the function of neural circuits by precisely activating neurons via extracellular stimulation. However, direct characterization of the individual electrical sensitivity of a large population of target neurons, in order to precisely control their activity, can be difficult or impossible. A potential solution is to leverage biophysical principles to infer sensitivity to electrical stimulation from features of spontaneous electrical activity, which can be recorded relatively easily. Here, this approach is developed and its potential value for vision restoration is tested quantitatively using large-scale multi-electrode stimulation and recording from male and female macaque retinal ganglion cells (RGCs) ex vivo . Electrodes recording larger spikes from a given cell exhibited lower stimulation thresholds across cell types, retinas, and eccentricities, with systematic and distinct trends for somas and axons. Thresholds for somatic stimulation increased with distance from the axon initial segment. The dependence of spike probability on injected current was inversely related to threshold, and was substantially steeper for axonal than somatic compartments, which could be identified by their recorded electrical signatures. Dendritic stimulation was largely ineffective for eliciting spikes. These trends were quantitatively reproduced with biophysical simulations. Results from human RGCs were broadly consistent. The inference of stimulation sensitivity from recorded electrical features was tested in a data-driven simulation of visual reconstruction, revealing that the approach could significantly improve the function of future high-fidelity retinal implants.
Significance Statement:
This study demonstrates that individual in situ primate retinal ganglion cells of different types respond to artificially generated, external electrical fields in a systematic manner, in accordance with theoretical predictions, that allows for prediction of electrical stimulus sensitivity from recorded spontaneous activity. It also provides evidence that such an approach could be immensely helpful in the calibration of clinical retinal implants.
... The introduction of these latencies into the averaging enables the characterization of spatio-temporal receptive fields (STRF). The averaging of the snapshots of the environment, delayed relative to the spike times, is called spike-triggered averaging (STA) or 'reverse correlation' and is widely used in estimating the STRF [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. When the stimulus patterns of interest are sound frequencies, as in the exploration of the response properties of auditory neurons, the same method is used for constructing spectro-temporal receptive fields, which are also abbreviated as STRF [11]. ...
Spatio-temporal receptive fields (STRF) of visual neurons are often estimated using spike-triggered averaging of binary pseudo-random stimulus sequences. The spike train of a visual neuron is recorded simultaneously with the stimulus presentation. The neuron’s STRF is estimated by averaging the stimulus frames that coincide with spikes at fixed latencies. Although this is a widely used technique, an analytical method for determining the statistical significance of the estimated value of the STRF pixels seems to be lacking. Such a significance test would be useful for identifying the significant features of the STRF and investigating their relationship with experimental variables. Here, the distribution of the estimated STRF pixel values is derived for given spike trains, under the null hypothesis that spike occurrences and stimulus values are statistically independent. This distribution is then used for computing amplitude thresholds to determine the STRF pixels where the null hypothesis can be rejected at a desired two-tailed significance level. It is also proposed that the size of the receptive field may be inferred from the significant pixels. The application of the proposed method is illustrated on spike trains collected from individual mouse retinal ganglion cells.
... Early stochastic encoding models of the retina were primarily developed for artificial stimuli [21,22,23], and their results cannot be directly generalized to natural scenes due to the stimulusdependent nature of noise in the retina. Here our fitted model was evaluated by comparing with neural data various commonly used second-order statistics including correlation measures and single-cell variability measures (Figure 3). ...
The ability to discriminate visual stimuli is constrained by their retinal representations. Previous studies of visual discriminability were limited to either low-dimensional artificial stimuli or theoretical considerations without a realistic model. Here we propose a novel framework for understanding stimulus discriminability achieved by retinal representations of naturalistic stimuli with the method of information geometry. To model the joint probability distribution of neural responses conditioned on the stimulus, we created a stochastic encoding model of a population of salamander retinal ganglion cells based on a three-layer convolutional neural network model. This model not only accurately captured the mean response to natural scenes but also a variety of second-order statistics. With the model and the proposed theory, we are able to compute the Fisher information metric over stimuli and study the most discriminable stimulus directions. We found that the most discriminable stimulus varied substantially, allowing an examination of the relationship between the most discriminable stimulus and the current stimulus. We found that the most discriminative response mode is often aligned with the most stochastic mode. This finding carries the important implication that under natural scenes noise correlations in the retina are information-limiting rather than aiding in increasing information transmission as has been previously speculated. We observed that sensitivity saturates less in the population than for single cells and also that Fisher information varies less than sensitivity as a function of firing rate. We conclude that under natural scenes, population coding benefits from complementary coding and helps to equalize the information carried by different firing rates, which may facilitate decoding of the stimulus under principles of information maximization.
... In a typical experiment, we measured the responses of 250-430 RGCs simultaneously. Spatiotemporal receptive fields were estimated by computing the spiketriggered average to the checkerboard stimulus 26 . This provides an estimate of the linear component of the spatiotemporal receptive field. ...
Retinitis pigmentosa is an inherited photoreceptor degeneration that begins with rod loss followed by cone loss and eventual blindness. Gene therapies are being developed, but it is unknown how retinal function depends on the time of intervention. To uncover this dependence, we utilized a mouse model of retinitis pigmentosa capable of artificial genetic rescue. This model enables a benchmark of best-case gene therapy by removing the variables that complicate the ability to answer this vital question. Complete genetic rescue was performed at 25%, 50%, and 70% rod loss (early, mid and late, respectively). Early and mid treatment restored retinal function to near wild-type levels, specifically the sensitivity and signal fidelity of retinal ganglion cells (RGCs), the 'output' neurons of the retina. However, some anatomical defects persisted. Late treatment retinas exhibited continued, albeit slowed, loss of sensitivity and signal fidelity among RGCs, as well as persistent gliosis. We conclude that gene replacement therapies delivered after 50% rod loss are unlikely to restore visual function to normal. This is critical information for administering gene therapies to rescue vision.
... These model neurons reflect observed properties of sensory neurons innervating campaniform sensilla, strainsensitive structures arrayed over wing veins [30]. At each node across the 25 × 50 grid of elements (corresponding to every 1 mm), strain is converted to a series of temporally sparse all-ornone sensing events using a linear-nonlinear model, a common model of neural responses [31]. In this model, strain is first convolved with a feature that represents the temporal pattern of strain to which the sensor is most sensitive. ...
Sensory feedback is essential to both animals and robotic systems for achieving coordinated, precise movements. Mechanosensory feedback, which provides information about body deformation, depends not only on the properties of sensors but also on the structure in which they are embedded. In insects, wing structure plays a particularly important role in flapping flight: in addition to generating aerodynamic forces, wings provide mechanosensory feedback necessary for guiding flight while undergoing dramatic deformations during each wingbeat. However, the role that wing structure plays in determining mechanosensory information is relatively unexplored. Insect wings exhibit characteristic stiffness gradients and are subject to both aerodynamic and structural damping. Here we examine how both of these properties impact sensory performance, using finite element analysis combined with sensor placement optimization approaches. We show that wings with nonuniform stiffness exhibit several advantages over uniform stiffness wings, resulting in higher accuracy of rotation detection and lower sensitivity to the placement of sensors on the wing. Moreover, we show that higher damping generally improves the accuracy with which body rotations can be detected. These results contribute to our understanding of the evolution of the nonuniform stiffness patterns in insect wings, as well as suggest design principles for robotic systems.
... To study whether dopamine differentially modulates the light responses of different RGC subtypes, we performed MEA recordings from adult dark-adapted mouse retinas. We used a white noise stimulus to determine the cells' receptive field (Chichilnisky, 2001), and both full-field spots (1200 μm diameter) and smaller square stimuli (75 and 150 μm square size presented at multiple locations, Fig. 1B) to estimate the surround strength. In order to study effects of dopamine in a more systematic manner, we clustered RGCs into functional subtypes using the SPIKY algorithm to calculate a pairwise dissimilarity matrix between spike trains of RGCs and a subsequent hierarchical clustering method (Jouty et al., 2018;Kreuz et al., 2013Kreuz et al., , 2015. ...
Dopamine has long been reported to enhance antagonistic surrounds of retinal ganglion cells (RGCs). Yet, the retina contains many different RGC subtypes and the effects of dopamine can be subtype‐specific. Using multielectrode array (MEA) recordings we investigated how dopamine shapes the receptive fields of RGCs in the mouse retina. We found that the non‐selective dopamine receptor agonist apomorphine can either increase or decrease RGCs’ surround strength, depending on their subtype. We then used two‐photon targeted patch‐clamp to target a specific RGC subtype, the transient‐Off‐αRGC. In line with our MEA recordings, apomorphine did not increase the antagonistic surround of transient‐Off‐αRGCs but enhanced their responses to Off stimuli in the centre receptive field. Both D1‐ and D2‐like family receptor (D1‐R and D2‐R) blockers had the opposite effect and reduced centre‐mediated responses, but differently affected transient‐Off‐αRGC's surround. While D2‐R blocker reduced surround antagonism, D1‐R blocker led to surround activation, revealing On responses to large stimuli. Using voltage‐clamp recordings we separated excitatory inputs from Off cone bipolar cells and inhibitory inputs from the primary rod pathway. In control conditions, cone inputs displayed strong surround antagonism, while inputs from the primary rod pathway showed no surround. Yet, the surround activation in the D1‐R blockade originated from the primary rod pathway. Our findings demonstrate that dopamine differentially affects RGC subtypes via distinct pathways, suggesting that dopamine has a more complex role in shaping the retinal code than previously reported. image
Key points
Receptive fields of retinal ganglion cells (RGCs) have a centre–surround organisation, and previous work has shown that this organisation can be modulated by dopamine in a light‐intensity‐dependent manner.
Dopamine is thought to enhance RGCs’ antagonistic surround, but a detailed understanding of how different RGC subtypes are affected is missing.
Using a multielectrode array recordings, clustering analysis and pharmacological manipulations, we found that dopamine can either enhance or weaken antagonistic surrounds, and also change response kinetics, of RGCs in a subtype‐specific manner.
We performed targeted patch‐clamp recordings of one RGC subtype, the transient‐Off‐αRGC, and identified the underlying circuits by which dopamine shapes its receptive field.
Our findings demonstrate that dopamine acts in a subtype‐specific manner and can have complex effects, which has implications for other retinal computations that rely on receptive field structure.
... In this type of receptive field measurement, a neuron is presented with a reference image, and many patterns of white noise superimposed onto the reference (e.g. Sakai et al. [1988], Chichilnisky [2001]). Averaging across the noise patterns that trigger extra spikes from the neuron (as compared to when the reference is presented alone), we obtain a pattern, or a distortion to the reference image that is effective in increasing neuronal spiking responses. ...
Perception is an outcome of neuronal computations. Our perception changes only when the underlying neuronal responses change. Because visual neurons preferentially respond to adjustments in some pixel values of an image more than others, our perception has greater sensitivity in detecting change to some pixel combinations more than others. Here, we examined how perceptual discriminability varies to arbitrary image perturbations assuming different models of neuronal responses. In particular, we investigated that under the assumption of different neuronal computations, how perceptual discriminability relates to neuronal receptive fields - the change in pixel combinations that invokes the largest increase in neuronal responses. We assumed that perceptual discriminability reflects the magnitude of change (the L2 norm) in neuronal responses, and the L2 norm assumption gained empirical support. We examined how perceptual discriminability relates to deterministic and stochastic neuronal computations. In the case of deterministic neuronal computations, perceptual discriminability is completely determined by neuronal receptive fields. For multiple layers of canonical linear-nonlinear (LN) computations in particular (which is a feed-forward neural network), neuronal receptive fields are linear transforms of the first-layer neurons' image filters. When one image is presented to the neural network, the first layer neurons' filters and the linear transform completely determine neuronal receptive fields across all layers, and perceptual discriminability to arbitrary distortions to the image. We expanded our analysis to examine stochastic neuronal computations, in which case perceptual discriminability can be summarized as the magnitude of change in stochastic neuronal responses, with the L2 norm being replaced by a Fisher-information computation. Using a practical lower bound on Fisher information, we showed that for stochastic neuronal computations, perceptual discriminability is completely determined by neuronal receptive fields, together with how responses co-variate across neurons.
... Linear-nonlinear-Poisson models (LNP) take a step forward from LIF models, addressing the aforementioned issues in an effective way. The first LNP model was introduced by (Chichilnisky 2001). These models represent the behaviour of spikes using inhomogeneous Poisson processes depending on the membrane potential. ...
This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of sparse interactions: each firing neuron triggers an instantaneous increase in electric potential to a fixed number of randomly chosen neurons. We prove that, as the number of neurons approaches infinity, the finite network converges to a nonlinear mean-field process characterised by a jump-type stochastic differential equation. We show that this process displays a phase transition: the activity of a typical neuron in the infinite network either rapidly dies out, or persists forever, depending on the global parameters describing the intensity of interconnection. This provides a way to understand the emergence of persistent activity triggered by weak input signals in large neural networks.
... Stimuli with white noise temporal profiles are more closely to natural stimuli as they have less regular statistics than most stimuli used in experimental procedures. Although used in other types of vision research (Chichilnisky, 2001;Chichilnisky and Rachel, 2002) they were, until recently, rarely employed in ERG recordings (Saul and Still, 2016;Zele et al., 2017;Adhikari et al., 2019;Wang et al., 2019;Kremers et al., 2022). Temporal white noise (TWN) stimuli have several advantages in comparison with flashes. ...
Purpose
To record and analyse electroretinograms (ERGs) to luminance stimuli with white noise temporal profiles in mice. White noise stimuli are expected to keep the retina in a physiologically more natural state than, e.g., flashes. The influence of mean luminance (ML) was studied.
Methods
Electroretinograms to luminance temporal white noise (TWN) modulation (wnERGs) were measured. The white noise stimuli contained all frequencies up to 20 Hz with equal amplitudes and random phases. Responses were recorded at 7 MLs between −0.7 and 1.2 log cd/m². Impulse response functions (IRFs) were calculated by cross correlating the averaged white noise electroretinogram (wnERG) responses with the stimulus. Amplitudes and latencies of the initial trough and subsequent peak in the IRFs were measured at each ML. Fourier transforms of the IRFs resulted in modulation transfer functions (MTFs). wnERGs were averaged across different animals. They were measured twice and the responses at identical instances in the 1st and 2nd recordings were plotted against each other. The correlation coefficient (r²repr) of the linear regression quantified the reproducibility. The results of the first and second measurement were further averaged. To study the underlying ERG mechanisms, the ERG potentials at the different MLs were plotted against those at the lowest and highest ML. The correlation coefficients (r²ML) were used to quantify their similarities.
Results
The amplitudes of the initial (a-wave-like) trough of the IRFs increased with increasing ML. The following positive (b-wave-like) peak showed a minimum at −0.4 log cd/m² above which there was a positive correlation between amplitude and ML. Their latencies decreased monotonously with increasing ML. In none of the IRFs, oscillatory potential (OP)-like components were observed. r²repr values were minimal at a ML of −0.1 log cd/m², where the MTFs changed from low-pass to band-pass. r²ML values increased and decreased with increasing ML when correlated with responses obtained at the highest or the lowest ML, respectively.
Conclusion
White noise electroretinograms can be reliably recorded in mice with luminance stimuli. IRFs resemble flash ERGs superficially, but they offer a novel procedure to study retinal physiology. New components can be described in the IRFs. The wnERGs are either rod- or cone-driven with little overlap.
... Fitting LN models is quite easy. It has been shown that for spherically symmetric stimuli (for example, white noise), spike-triggered averages provide optimal solutions to the linear filters [Chichilnisky, 2001]. For more general stimuli, parameters can be inferred maximizing their likelihood [Paninski, 2004]. ...
The retina is the first processing step of our visual system. Retinal ganglion cells constitute the output of this system, and feature complex nonlinear responses. A typical example is their antagonistic surround modulation: stimuli outside the receptive field center might evoke responses in ganglion cells. Recent studies have suggested that a specific circuit, the rod bipolar cell pathway, might contribute to surround modulation. We used optogenetic stimulation to isolate and model the contribution to the retinal output of the interneurons composing this pathway. We show that these contributions can be well described by a linear-nonlinear model. We then tested whether this circuit plays a role in the formation of the antagonistic surround responses of retinal ganglion cells. To this end, we expressed an inhibitory opsin, gtACR, in AII amacrine cells, and recorded surround responses of ganglion cells to visual stimuli while inhibiting the AIIs. In the perturbed condition we observed a significant decrease of response in OFF retinal ganglion cells, confirming our hypothesis that the rod bipolar cell pathway contributes to the antagonistic surround of OFF retinal ganglion cells.
Synaptic short-term plasticity and EPSP summation determine the processing of visual information by dLGN relay cells. In vitro studies suggested that desensitization of AMPA receptor results in pronounced short-term depression in retinogeniculate synapses thereby influencing activation of relay cells by retinal ganglion cell spikes. However, whether retinogeniculate synapses depress and whether AMPA receptors desensitize in vivo is controversial. We here tested the role of AMPA receptor desensitization in processing of visual information by generating a computational model of a dLGN relay cell containing AMPA receptors with different levels of desensitization. In addition, we investigated the in vivo activity of dLGN relay cells in wildtype and CKAMP44-/- mice. CKAMP44 is an auxiliary subunit that increases desensitization of AMPA receptors in retinogeniculate synapses. The comparison of responses of relay cells in the two genotypes therefore allowed us to obtain information about the contribution of AMPA receptor desensitization in processing of visual information. The simulations and the in vivo data show that AMPA receptor desensitization affects relay cell activity by decreasing input gain and response gain. In addition, desensitization sharpens the response of relay neurons to moving gratings in the temporal domain by decreasing the firing rate when the non-preferred stimulus is presented. Altogether, we uncover a complex role of CKAMP44 and AMPA receptor desensitization in information processing of dLGN relay neurons in vivo.
Retinal ganglion cells, the output neurons of the vertebrate retina, often display nonlinear summation of visual signals over their receptive fields. This creates sensitivity to spatial contrast, letting the cells respond to spatially structured visual stimuli, such as a contrast-reversing grating, even when no net change in overall illumination of the receptive field occurs. Yet, computational models of ganglion cell responses are often based on linear receptive fields. Nonlinear extensions, on the other hand, such as subunit models, which separate receptive fields into smaller, nonlinearly combined subfields, are often cumbersome to fit to experimental data, in particular when natural stimuli are considered. Previous work in the salamander retina has shown that sensitivity to spatial contrast in response to flashed images can be partly captured by a model that combines signals from the mean and variance of luminance signals inside the receptive field. Here, we extend this spatial contrast model for application to spatiotemporal stimulation and explore its performance on spiking responses that we recorded from retinas of marmosets under artificial and natural movies. We show how the model can be fitted to experimental data and that it outperforms common models with linear spatial integration, in particular for parasol ganglion cells. Finally, we use the model framework to infer the cells' spatial scale of nonlinear spatial integration and contrast sensitivity. Our work shows that the spatial contrast model provides a simple approach to capturing aspects of nonlinear spatial integration with only few free parameters, which can be used to assess the cells' functional properties under natural stimulation and which provides a simple-to-obtain benchmark for comparison with more detailed nonlinear encoding models.
The diverse nature of visual environments demands that the retina, the first stage of the visual system, encodes a vast range of stimuli with various statistics. The retina adapts its computations to some specific features of the input, such as brightness, contrast or motion. However, it is less clear whether it also adapts to the statistics of natural scenes compared to white noise, the latter of which is often used to infer models of retinal computation. To address this question, we analyzed neural activity of retinal ganglion cells (RGCs) in response to both white noise and naturalistic movie stimuli. We performed a systematic comparative analysis of traditional linear-nonlinear (LN) and recent convolutional neural network (CNN) models and tested their generalization across stimulus domains. We found that no model type trained on one stimulus ensemble was able to accurately predict neural activity on the other, suggesting that retinal processing depends on the stimulus statistics. Under white noise stimulation, the receptive fields of the neurons were mostly lowpass, while under natural image statistics they exhibited a more pronounced surround resembling the whitening filters predicted by efficient coding. Together, hese results suggest that retinal processing dynamically adapts to the stimulus statistics.
The retina and primary visual cortex (V1) both exhibit diverse neural populations sensitive to diverse visual features. Yet it remains unclear how neural populations in each area partition stimulus space to span these features. One possibility is that neural populations are organized into discrete groups of neurons, with each group signaling a particular constellation of features. Alternatively, neurons could be continuously distributed across feature-encoding space. To distinguish these possibilities, we presented a battery of visual stimuli to the mouse retina and V1 while measuring neural responses with multi-electrode arrays. Using machine learning approaches, we developed a manifold embedding technique that captures how neural populations partition feature space and how visual responses correlate with physiological and anatomical properties of individual neurons. We show that retinal populations discretely encode features, while V1 populations provide a more continuous representation. Applying the same analysis approach to convolutional neural networks that model visual processing, we demonstrate that they partition features much more similarly to the retina, indicating they are more like big retinas than little brains.
Neuromodulators have major influences on the regulation of neural circuit activity across the nervous system. Nitric oxide (NO) is a prominent neuromodulator in many circuits, and has been extensively studied in the retina across species. NO has been associated with the regulation of light adaptation, gain control, and gap junction coupling, but its effect on the retinal output, specifically on the different types of retinal ganglion cells (RGCs), is still poorly understood. Here, we used two-photon Ca2+ imaging to record RGC responses to visual stimuli to investigate the neuromodulatory effects of NO on the cell type-level in the ex vivo mouse retina. We found that about one third of the RGC types displayed highly reproducible and cell type-specific response changes during the course of an experiment, even in the absence of NO. Accounting for these adaptational changes allowed us to isolate NO effects on RGC responses. This revealed that NO affected only a few RGC types, which typically became more active due to a reduction of their response suppression. Notably, NO had no discernible effect on their spatial receptive field size and surround strength. Together, our data suggest that NO specifically modulates suppression of the temporal response in a distinct group of contrast-suppressed RGC types. Finally, our study demonstrates the need for recording paradigms that takes adaptational, non-drug-related response changes into account when analysing potentially subtle pharmacological effects.
Since the Nobel-winning discovery of simple cells and complex cells in cat's primary visual cortex (V1) by Hubel and Wiesel, many experimental studies of the visual system of the brain have been conducted. Experimental data of V1 cells from animal recordings show spatio-temporal properties, namely that they display both spatial and temporal response properties. For spatial properties, each V1 cell responds to a specific feature (such as bars, blobs, etc.) in the visual space, which is called the receptive field of this cell. The receptive fields of different V1 cells are typically different in size, orientation, spatial frequencies, etc. Furthermore, V1 cells also display temporal properties, namely that the receptive fields of V1 cells can change over time, and there is a great variety of ways in which they change over time. For example, the population of V1 cells show a great diversity from monophasic response to biphasic response, and some V1 cells are selective to a preferred direction. However, given many computational learning models that explain how spatial properties of V1 cells can be learnt, how temporal properties emerge is still not well understood. In this paper, we use a simple learning model based on sparse coding to show that spatio-temporal V1 cells, such as biphasic and direction selective cell, can emerge via synaptic plasticity when diverse spatio-temporal LGN cells are used as upstream input to V1 cells. This work suggests that temporal along with spatial properties of V1 cells may simply come from a learning process that aims to encode upstream input with spatio-temporal properties, which greatly enhances our understanding of V1 cells.
ELife digest
When light enters the eyes, it is focused onto the retina, a thin layer of brain tissue at the back of the eye. The retina converts light information into electrical signals that are transmitted to the rest of the brain to perceive vision. Unlike the rest of the brain, this light-processing tissue can continue working even when removed from an animal, making it easier for scientists to study how the retina works. This has helped it become one of the best-understood parts of the brain.
Most knowledge of retinal signal processing comes from studies of isolated retinas. However, it was still unclear if these samples behave the same way as they do in live animals, and whether findings in isolated retinas apply to natural visual processing in an awake state.
To determine this, Boissonnet et al. compared the visual responses of the retina in awake mice, anesthetised mice and when isolated from mice. Measurements of retinal electrical signals showed that awake mice responded to light substantially more quickly and strongly than the others. Computational analysis suggested that the amount of information carried to the brain was largely comparable across the different subjects, but the retina in awake mice used more energy.
The findings indicate that further studies are needed to better understand how the retina processes visual information in awake animals, rather than just in isolated conditions. Progressing this understanding could ultimately help to develop prosthetic devices that can act as a retina in the future.
The prevailing hierarchical view of the visual system consists of parallel circuits that begin in the retina, which then sum effects across sequential levels, increasing in complexity. Yet a separate type of interaction, whereby one visual pattern changes the influence of another, known as modulation, has received much less attention in terms of its circuit mechanisms. Retinal amacrine cells are a diverse class of inhibitory interneurons that are thought to have modulatory effects, but we lack a general understanding of their functional types. Using dynamic causal experiments in the salamander retina perturbing amacrine cells along with an unsupervised computational framework, we find that amacrine cell modulatory effects cluster into two distinct types. One type controls ganglion cell sensitivity to individual visual features, and a second type controls the ganglion cell’s output gain, acting to gate all features. These results establish three separate general roles of amacrine cells – to generate primary visual features, to use context to select specific visual features and to gate retinal output.
Background: Finding appropriate model parameters for multi-compartmental neuron models can be challenging. Parameters such as the leak and axial conductance are not always directly derivable from neuron observations but are crucial for replicating desired observations. The objective of this study is to replicate the attenuation behavior of an excitatory postsynaptic potential (EPSP) traveling along a linear chain of compartments on the analog BrainScaleS-2 neuromorphic hardware platform.
Methods: In the present publication we use genetic algorithms to find suitable model parameters. They promise parameterization without domain knowledge of the neuromorphic substrate or underlying neuron model. To validate the results of the genetic algorithms, a comprehensive grid search was conducted. Trial-to-trial variations in the analog system are counteracted utilizing spike-triggered averaging.
Results and conclusions: The algorithm successfully replicated the desired EPSP attenuation behavior in both single and multi-objective searches illustrating the applicability of genetic algorithms to parameterize analog neuromorphic hardware.
In vertebrate vision, early retinal circuits divide incoming visual information into functionally opposite elementary signals: On and Off, transient and sustained, chromatic and achromatic. Together these signals can yield an efficient representation of the scene for transmission to the brain via the optic nerve. However, this long-standing interpretation of retinal function is based on mammals, and it is unclear whether this functional arrangement is common to all vertebrates. Here we show that male poultry chicks use a fundamentally different strategy to communicate information from the eye to the brain. Rather than using functionally opposite pairs of retinal output channels, chicks encode the polarity, timing, and spectral composition of visual stimuli in a highly correlated manner: fast achromatic information is encoded by Off-circuits, and slow chromatic information overwhelmingly by On-circuits. Moreover, most retinal output channels combine On- and Off-circuits to simultaneously encode, or multiplex, both achromatic and chromatic information. Our results from birds conform to evidence from fish, amphibians, and reptiles which retain the full ancestral complement of four spectral types of cone photoreceptors.
A fundamental challenge in neuroengineering is determining a proper input to a sensory system that yields the desired functional output. In neuroprosthetics, this process is known as sensory encoding, and it holds a crucial role in prosthetic devices restoring sensory perception in individuals with disabilities. For example, in visual prostheses, one key aspect of image encoding is to down-sample the images captured by a camera to a size matching the number of inputs and resolution of the prosthesis. Here, we show that down-sampling an image using the inherent computation of the retinal network yields better performance compared to a learning-free down-sampling encoding. We validated a learning-based approach (actor model framework) that exploits the signal transformation from photoreceptors to retinal ganglion cells measured in explanted retinas. The actor-model framework generates down-sampled images eliciting a neuronal response in-silico and ex-vivo with higher neuronal reliability to the one produced by original images compared to a learning-free approach (i.e. pixel averaging). In addition, the actor-model learned that contrast is a crucial feature for effective down-sampling. This methodological approach could serve as a template for future image encoding strategies. Ultimately, it can be exploited to improve encoding strategies in visual prostheses or other sensory prostheses such as cochlear or limb.
Saccades are a fundamental part of natural vision. They interrupt fixations of the visual gaze and rapidly shift the image that falls onto the retina. These stimulus dynamics can cause activation or suppression of different retinal ganglion cells, but how they affect the encoding of visual information in different types of ganglion cells is largely unknown. Here, we recorded spiking responses to saccade-like shifts of luminance gratings from ganglion cells in isolated marmoset retinas and investigated how the activity depended on the combination of pre- and post-saccadic images. All identified cell types, On and Off parasol and midget cells as well as a type of Large Off cells, displayed distinct response patterns, including particular sensitivity to either the pre- or the post-saccadic image or combinations thereof. In addition, Off parasol and Large Off cells, but not On cells, showed pronounced sensitivity to whether the image changed across the transition. Stimulus sensitivity of On cells could be explained based on their responses to step changes in light intensity, whereas Off cells, in particular, parasol and the Large Off cells, seem to be affected by additional interactions that are not triggered during simple light-intensity flashes. Together, our data show that ganglion cells in the primate retina are sensitive to different combinations of pre- and post-saccadic visual stimuli. This contributes to the functional diversity of the retina’s output signals and to asymmetries between On and Off pathways and provides evidence of signal processing beyond what is triggered by isolated steps in light intensity.
Significance Statement:
Sudden eye movements (saccades) shift our direction of gaze, bringing new images in focus on our retinas. To study how retinal neurons deal with these rapid image transitions, we recorded spiking activity from ganglion cells, the retina's output neurons, in isolated retinas of marmoset monkeys while shifting a projected image in a saccade-like fashion across the retina. We found that the cells do not just respond to the newly fixated image, but that different types of ganglion cells display different sensitivities to the pre- and post-saccadic stimulus patterns. Certain Off cells, for example, are sensitive to changes in the image across transitions, which contributes to differences between On and Off information channels and extends the range of encoded stimulus features.
Electrical stimulation of retinal ganglion cells (RGCs) with electronic implants provides rudimentary artificial vision to people blinded by retinal degeneration. However, current devices stimulate indiscriminately and therefore cannot reproduce the intricate neural code of the retina. Recent work has demonstrated more precise activation of RGCs using focal electrical stimulation with multi-electrode arrays in the peripheral macaque retina, but it is unclear how effective this can be in the central retina, which is required for high-resolution vision. This work probes the neural code and effectiveness of focal epiretinal stimulation in the central macaque retina, using large-scale electrical recording and stimulation ex vivo . The functional organization, light response properties, and electrical properties of the major RGC types in the central retina were mostly similar to the peripheral retina, with some notable differences in density, kinetics, linearity, spiking statistics and correlations. The major RGC types could be distinguished by their intrinsic electrical properties. Electrical stimulation targeting parasol cells revealed similar activation thresholds and reduced axon bundle activation in the central retina, but lower stimulation selectivity. Quantitative evaluation of the potential for image reconstruction from electrically-evoked parasol cell signals revealed higher overall expected image quality in the central retina. An exploration of inadvertent midget cell activation suggested that it could contribute high spatial frequency noise to the visual signal carried by parasol cells. These results support the possibility of reproducing high-acuity visual signals in the central retina with an epiretinal implant.
SIGNIFICANCE STATEMENT:
Artificial restoration of vision with retinal implants is a major treatment for blindness. However, present-day implants do not provide high-resolution visual perception, in part because they do not reproduce the natural neural code of the retina. Here we demonstrate the level of visual signal reproduction that is possible with a future implant by examining how accurately responses to electrical stimulation of parasol retinal ganglion cells (RGCs) can convey visual signals. Although the precision of electrical stimulation in the central retina was diminished relative to the peripheral retina, the quality of expected visual signal reconstruction in parasol cells was greater. These findings suggest that visual signals could be restored with high fidelity in the central retina using a future retinal implant.
A new discrete-time reverse-correlation scheme for the study of visual neurons is proposed. The visual stimulus is generated by drawing with uniform probability, at each refresh time, an image from a finite set S of orthonormal images. We show that if the neuron can be modeled as a spatiotemporal linear filter followed by a static nonlinearity, the cross-correlation between the input image sequence and the cell's spike train output gives the projection of the receptive field onto the subspace spanned by S. The technique has been applied to the analysis of simple cells in the primary visual cortex of cats and macaque monkeys. Experimental results are presented where S spans a subspace of spatially low-pass signals. Adbantages of the proposed scheme over standard white-noise techniques include improved signal to noise ratios, increased spatial resolution, and the possibility to restrict the study to particular subspaces of interest.
Systems that can be represented by a cascade of a dynamic linear subsystem preceded (Hammerstein cascade model) or followed (Wiener cascade model) by a static nonlinearity are considered. Various identification schemes that have been proposed for the Hammerstein and Wiener systems are critically reviewed with reference to the special problems that arise in the identification of nonlinear biological systems. Examples of Wiener and Hammerstein systems are identified from limited duration input-output data using an iterative identification scheme.
Systems that can be represented by a cascade of a dynamic linear (L), a static nonlinear (N) and a dynamic linear (L) subsystem are considered. Various identification schemes that have been proposed for these LNL systems are critically reviewed with reference to the special problems that arise in the identification of nonlinear biological systems. A simulated LNL system is identified from limited duration input-output data using an iterative identification scheme.
Sensory areas of adult cerebral cortex can reorganize in response to long-term alterations in patterns of afferent signals. This long-term plasticity is thought to play a crucial role in recovery from injury and in some forms of learning. However, the degree to which sensory representations in primary cortical areas depend on short-term (i.e., minute to minute) stimulus variations remains unclear. A traditional view is that each neuron in the mature cortex has a fixed receptive field structure. An alternative view, with fundamentally different implications for understanding cortical function, is that each cell's receptive field is highly malleable, changing according to the recent history of the sensory environment. Consistent with the latter view, it has been reported that selective stimulation of regions surrounding the receptive field induces a dramatic short-term increase in receptive field size for neurons in the visual cortex [Pettet, M. W. & Gilbert, C. D. (1992) Proc. Natl. Acad. Sci. USA 89, 8366-8370]. In contrast, we report here that there is no change in either the size or the internal structure of the receptive field following several minutes of surround stimulation. However, for some cells, overall responsiveness increases. These results suggest that dynamic alterations of receptive field structure do not underlie short-term plasticity in the mature primary visual cortex. However, some degree of short-term adaptability could be mediated by changes in responsiveness.
1. We have tested the hypothesis that simple cells in the cat's visual cortex perform a linear spatiotemporal filtering of the visual image. To conduct this study we note that a visual neuron behaves linearly if the responses to small, brief flashes of light are mathematically related, via the Fourier transform, to the responses elicited by sinusoidal grating stimuli. 2. We have evaluated the linearity of temporal and spatial summation for 118 simple cells recorded from the striate cortex (area 17) of adult cats and kittens at ages 4 and 8 wk postnatal. These neurons represent a subset of the population of cells for which we have described the postnatal development of spatiotemporal receptive-field structure in the preceding paper. Spatiotemporal receptive-field profiles are constructed, with the use of a reverse correlation technique, from the responses to random sequences of small bar stimuli that are brighter or darker than the background. Fourier analysis of spatiotemporal receptive-field profiles yields linear predictions of the cells' spatial and temporal frequency tuning. These predicted responses are compared with spatial and temporal frequency tuning curves measured by the use of drifting, sinusoidal-luminance grating stimuli. 3. For most simple cells, there is good agreement between spatial and temporal frequency tuning curves predicted from the receptive-field profile and those measured by the use of sinusoidal gratings. These results suggest that both spatial and temporal summation within simple cells are approximately linear. There is a tendency for predicted tuning curves to be slightly broader than measured tuning curves, a finding that is consistent with the effects of a threshold nonlinearity at the output of these neurons. In some cases, however, predicted tuning curves deviate from measured responses only at low spatial and temporal frequencies. This cannot be explained by a simple threshold nonlinearity. 4. If linearity is assumed, it should be possible to predict the direction selectivity of simple cells from the structure of their spatiotemporal receptive-field profiles. For virtually all cells, linear predictions correctly determine the preferred direction of motion of a visual stimulus. However, the strength of the directional bias is typically underestimated by a factor of about two on the basis of linear predictions. Consideration of the expansive exponential nonlinearity revealed in the contrast-response function permits a reconciliation of the discrepancy between measured and predicted direction selectivity indexes. 5. Overall, these findings show that spatiotemporal receptive-field profiles obtained with the use of reverse correlation may be used to predict a variety of response properties for simple cells.(ABSTRACT TRUNCATED AT 400 WORDS)
Assessing the reliability of neuronal spike trains is fundamental to an understanding of the neural code. We measured the reproducibility of retinal responses to repeated visual stimuli. In both tiger salamander and rabbit, the retinal ganglion cells responded to random flicker with discrete, brief periods of firing. For any given cell, these firing events covered only a small fraction of the total stimulus time, often less than 5%. Firing events were very reproducible from trial to trial: the timing jitter of individual spikes was as low as 1 msec, and the standard deviation in spike count was often less than 0.5 spikes. Comparing the precision of spike timing to that of the spike count showed that the timing of a firing event conveyed several times more visual information than its spike count. This sparseness and precision were general characteristics of ganglion cell responses, maintained over the broad ensemble of stimulus waveforms produced by random flicker, and over a range of contrasts. Thus, the responses of retinal ganglion cells are not properly described by a firing probability that varies continuously with the stimulus. Instead, these neurons elicit discrete firing events that may be the fundamental coding symbols in retinal spike trains.
We have used Sutter's (1987) spatiotemporal m-sequence method to map the receptive fields of neurons in the visual system of the cat. The stimulus consisted of a grid of 16 x 16 square regions, each of which was modulated in time by a pseudorandom binary signal, known as an m-sequence. Several strategies for displaying the m-sequence stimulus are presented. The results of the method are illustrated with two examples. For both geniculate neurons and cortical simple cells, the measurement of first-order response properties with the m-sequence method provided a detailed characterization of classical receptive-field structures. First, we measured a spatiotemporal map of both the center and surround of a Y-cell in the lateral geniculate nucleus (LGN). The time courses of the center responses was biphasic: OFF at short latencies, ON at longer latencies. The surround was also biphasic--ON then OFF--but somewhat slower. Second, we mapped the response properties of an area 17 directional simple cell. The response dynamics of the ON and OFF subregions varied considerably; the time to peak ranged over more than a factor of two. This spatiotemporal inseparability is related to the cell's directional selectivity (Reid et al., 1987, 1991; McLean & Palmer, 1989; McLean et al., 1994). The detail with which the time course of response can be measured at many different positions is one of the strengths of the m-sequence method.
We examined the functional microcircuitry of cone inputs to blue-ON/yellow-OFF (BY) ganglion cells in the macaque retina using multielectrode recording. BY cells were identified by their ON responses to blue light and OFF responses to red or green light. Cone-isolating stimulation indicated that ON responses originated in short (S) wavelength-sensitive cones, whereas OFF responses originated in both long (L) and middle (M) wavelength-sensitive cones. Stimulation with fine spatial patterns revealed locations of individual S cones in BY cell receptive fields. Neighboring BY cells received common but unequal inputs from one or more S cones. Inputs from individual S cones differed in strength, indicating different synaptic weights, and summed approximately linearly to control BY cell firing.
The Gaussian white noise and the sum-of-sinusoids methods of systems analysis provide equivalent descriptions of nearly linear and strongly nonlinear transductions in the cat retina. Smoothness in the frequency domain is a common characteristic of biological transductions. This permits a substantial improvement in the signal-to-noise ratio by using the sum-of-sinusoids method, as is demonstrated for the transductions of the cat retina.
1. We have examined the responses of simple cells in the cat's atriate cortex to visual patterns that were designed to reveal the extent to which these cells may be considered to sum light-evoked influences linearly across their receptive fields. We used one-dimensional luminance-modulated bars and grating as stimuli; their orientation was always the same as the preferred orientation of the neurone under study. The stimuli were presented on an oscilloscope screen by a digital computer, which also accumulated neuronal responses and controlled a randomized sequence of stimulus presentations. 2. The majority of simple cells respond to sinusoidal gratings that are moving or whose contrast is modulated in time in a manner consistent with the hypothesis that they have linear spatial summation. Their responses to moving gratings of all spatial frequencies are modulated in synchrony with the passage of the gratings' bars across their receptive fields, and they do not produce unmodulated responses even at the highest spatial frequencies. Many of these cells respond to temporally modulated stationary gratings simply by changing their response amplitude sinusoidally as the spatial phase of the grating the grating is varied. Nonetheless, their behavior appears to indicate linear spatial summation, since we show in an Appendix that the absence of a 'null' phase in a visual neurone need not indicate non-linear spatial summation, and further that a linear neurone lacking a 'null' phase should give responses of the form that we have observed in this type of simple cell. 3. A minority of simple cells appears to have significant non-linearities of spatial summation. These neurones respond to moving gratings of high spatial frequency with a partially or totally unmodulated elevation of firing rate. They have no 'null' phases when tested with stationary gratings, and reveal their non-linearity by giving responses to gratings of some spatial phases that are composed partly or wholly of even harmonics of the stimulus frequency ('on-off' responses). 4. We compared simple receptive fields with their sensitivity to sinusoidal gratings of different spatial frequencies. Qualitatively, the most sensitive subregions of simple cells' receptive fields are roughly the same width as the individual bars of the gratings to which they are most sensitive. Quantitatively, their receptive field profiles measured with thin stationary lines, agree well with predicted profiles derived by Fourier synthesis of their spatial frequency tuning curves.
Complex cells in the cat's visual cortex show nonlinearities in processing of image luminance and movement. To study mechanisms, initially we have represented the chain of neurons from retina to cortex as a black-box model. Independent information about the visual system has helped us cast this "Wiener-kernel" model into a dynamic-linear/static-nonlinear/dynamic-linear (LNL) cascade. We then use system identification techniques to define the nature of these transformations directly from responses of the neuron to a single presentation of a stimulus composed of a sequence of white-noise-modulated luminance values. The two dynamic linear filters are mainly low-pass, and the static nonlinearity is mainly of even polynomial degree. This approximate squaring function may be effected in the animal by soft-thresholding each of the linear ON- and OFF-channel signals and then summing them, which account for "ON-OFF" responses and for the squaring operation needed for computation of "motion energy", both observed in these neurons.
1. Three independent sets of evidence have been obtained to show that similar first- and second-order light-evoked kernels are computed for the ganglion cell when the system output is taken to be either the spike train (discrete signal) or the postsynaptic potential (analog signal). In this paper we show that the similarity of postsynaptic potential (PSP) kernels and spike kernels is readily explained by assuming an underlying cascade structure for the neural information processing. The cascade structure enables spike kernels to be mathematically related very simply to the process of generating the postsynaptic potentials of ganglion cells. 2. Mathematical analysis of the cascade structure also suggests why spike kernels appear to differ slightly from PSP kernels. The relation between the two sets of kernels predicted from our analysis is substantiated here by experiment and reveals an interconnection between several of the signals measured. 3. Our experimental results, in particular, suggest that the neuronal circuitry leading from the light stimulus to the generation of ganglion cell spike discharges can be represented as follows: either a Wiener (LN) or a dynamic linear-static nonlinear-dynamic linear (LNL) structure is followed by a highly nonlinear process [static or brief-memory Hammerstein static-nonlinear dynamic-linear (NL) structure] of spike generation. Cross-correlation between the analog input and spike output enables identification of these structures.
The Wiener theory of nonlinear system identification was applied to a three-stage neuron chain in the catfish retina in order
to determine the functional relationship between the artificial polarization of the horizontal cell membrane potential and
the resulting discharge of the ganglion cell. A mathematical model was obtained that can predict quantitatively, with reasonable
accuracy, the nonlinear, dynamic behavior of the neuron chain. The applicability of the method is discussed. We conclude that
this is a very powerful method in the analysis of information transfer in the central nervous system.
We studied spatiotemporal interactions in cat cortical receptive fields by presenting a stimulus composed of 16 narrow bars whose luminances were randomly modulated. Conventional stimuli were also presented to classify receptive field properties. A white noise estimate of the cell's response to a stepwise moving bar stimulus was calculated from responses to the spatiotemporal random stimulus. The white noise estimate captured the most important feature of the receptive field demonstrated by conventional stimuli, i.e. directional selectivity. In addition, the white noise analysis; (1) made visible inhibitory response phases that are usually below threshold; (2) subdivided the response into its linear and non-linear estimates; (3) further subdivided the non-linear estimate into spatial and temporal interactions; and (4) allowed estimation of responses to stimuli that were never explicitly presented.
To analyze the rules that govern communication between eye and brain, visual responses were recorded from an intact salamander
retina. Parallel observation of many retinal ganglion cells with a microelectrode array showed that nearby neurons often fired
synchronously, with spike delays of less than 10 milliseconds. The frequency of such synchronous spikes exceeded the correlation
expected from a shared visual stimulus up to 20-fold. Synchronous firing persisted under a variety of visual stimuli and accounted
for the majority of action potentials recorded. Analysis of receptive fields showed that concerted spikes encoded information
not carried by individual cells; they may represent symbols in a multineuronal code for vision.
We studied the receptive field organization and contrast sensitivity of ganglion cells located within the central 80 (radius of 40) deg of the macaque retina. Ganglion cell activity was monitored as synaptic (S) potentials recorded extracellularly in the lateral geniculate nuclei of anesthetized and paralyzed monkeys. Receptive field center and surround regions of magnocellularly-projecting (M) and parvocellularly-projecting (P) cells increase in area with distance from the fovea, with the center radii of M cells being about twice those of neighboring P cells. Peak sensitivities of center and surround regions are inversely proportional to the regions' areas, so that integrated contrast sensitivities (contrast gains) are constant across the visual field, with the gain of M cells being, on average, six times that of P cells. For both M and P cells, the average ratio of surround/center gain is 0.55. Constant gain of P cells across the visual field is achieved by increasing sensitivity to stimuli falling on the peripheral retina to an extent that counteracts the aberrations introduced by the eye's optics.
The visual system integrates information from the left and right eyes and constructs a visual world that is perceived as single and three dimensional. To understand neural mechanisms underlying this process, it is important to learn about how signals from the two eyes interact at the level of single neurons. Using a sophisticated receptive field (RF) mapping technique that employs binary m-sequences, we have determined the rules of binocular interactions exhibited by simple cells in the cat's striate cortex in relation to the structure of their monocular RFs. We find that binocular interaction RFs of most simple cells are well described as the product of left and right eye RFs. Therefore the binocular interactions depend not only on binocular disparity but also on monocular stimulus position or phase. The binocular interaction RF is consistent with that predicted by a model of a linear binocular filter followed by a static nonlinearity. The static nonlinearity is shown to have a shape of a half-power function with an average exponent of approximately 2. Although the initial binocular convergence of signals is linear, the static nonlinearity makes binocular interaction multiplicative at the output of simple cells. This multiplicative binocular interaction is a key ingredient for the computation of interocular cross-correlation, an algorithm for solving the stereo correspondence problem. Therefore simple cells may perform initial computations necessary to solve this problem.
We studied the fine spatial structure of the receptive fields of retinal ganglion cells and its relationship to the dendritic geometry of these cells. Cells from which recordings had been made were microinjected with Lucifer yellow, so that responses generated at precise locations within the receptive field center could be directly compared with that cell's dendritic structure. While many cells with small receptive fields had domeshaped sensitivity profiles, the majority of large receptive fields were composed of multiple regions of high sensitivity. The density of dendritic branches at any one location did not predict the regions of high sensitivity. Instead, the interactions between a ganglion cell's dendritic tree and the local mosaic of bipolar cell axons seem to define the fine structure of the receptive field center.