Loss of sensitivity in an analog neural circuit

Identification of Multiple Noise Sources Improves Estimation of Neural Responses across Stimulus Conditions

Most models of neural responses are constructed to reproduce the average response to inputs but lack the flexibility to capture observed variability in responses. The origins and structure of this variability have significant implications for how information is encoded and processed in the nervous system, both by limiting information that can be conveyed and by determining processing strategies that are favorable for minimizing its negative effects. Here, we present a new modeling framework that incorporates multiple sources of noise to better capture observed features of neural response variability across stimulus conditions. We apply this model to retinal ganglion cells at two different ambient light levels and demonstrate that it captures the full distribution of responses. Further, the model reveals light level-dependent changes that could not be seen with previous models, showing both large changes in rectification of nonlinear circuit elements and systematic differences in the contributions of different noise sources under different conditions.

Temporal information loss in the macaque early visual system

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

Photoreceptive retinal ganglion cells control the information rate of the optic nerve

Noise in the visual signal falls as ambient light increases, allowing the retina to extract more information from the scene. We show here that a measure of ambient light produced by the small number of inner retinal photoreceptors [intrinsically photosensitive retinal ganglion cells (ipRGCs)] regulates intrinsic rates of spike firing across the population of retinal ganglion cells that form the optic nerve. Increased firing at higher irradiance allows the ganglion cells to convey more information. Our findings reveal a potential mechanism for increasing visual performance at high ambient light and show that changes in maintained activity can be used to provide proactive control over rates of information flow in the CNS.

Information transfer in the brain relies upon energetically expensive spiking activity of neurons. Rates of information flow should therefore be carefully optimized, but mechanisms to control this parameter are poorly understood. We address this deficit in the visual system, where ambient light (irradiance) is predictive of the amount of information reaching the eye and ask whether a neural measure of irradiance can therefore be used to proactively control information flow along the optic nerve. We first show that firing rates for the retina’s output neurons [retinal ganglion cells (RGCs)] scale with irradiance and are positively correlated with rates of information and the gain of visual responses. Irradiance modulates firing in the absence of any other visual signal confirming that this is a genuine response to changing ambient light. Irradiance-driven changes in firing are observed across the population of RGCs (including in both ON and OFF units) but are disrupted in mice lacking melanopsin [the photopigment of irradiance-coding intrinsically photosensitive RGCs (ipRGCs)] and can be induced under steady light exposure by chemogenetic activation of ipRGCs. Artificially elevating firing by chemogenetic excitation of ipRGCs is sufficient to increase information flow by increasing the gain of visual responses, indicating that enhanced firing is a cause of increased information transfer at higher irradiance. Our results establish a retinal circuitry driving changes in RGC firing as an active response to alterations in ambient light to adjust the amount of visual information transmitted to the brain.

Impact of light-adaptive mechanisms on mammalian retinal visual encoding at high light levels

A persistent change in illumination causes light-adaptive changes in retinal neurons. Light adaptation improves visual encoding by preventing saturation and by adjusting spatiotemporal integration to increase the signal-to-noise ratio (SNR) and utilize signaling bandwidth efficiently. In dim light, the visual input contains a greater relative amount of quantal noise, and vertebrate receptive fields are extended in space and time to increase SNR. Whereas in bright light, SNR of the visual input is high, the rate of synaptic vesicle release from the photoreceptors is low so that quantal noise in synaptic output may limit SNR postsynaptically. Whether and how reduced synaptic SNR impacts spatiotemporal integration in postsynaptic neurons remains unclear. To address this, we measured spatiotemporal integration in retinal horizontal cells and ganglion cells in the guinea pig retina across a broad illumination range, from low to high photopic levels. In both cell types, the extent of spatial and temporal integration changed according to an inverted U-shaped function consistent with adaptation to low SNR at both low and high light levels. We show how a simple mechanistic model with interacting, opponent filters can generate the observed changes in ganglion cell spatiotemporal receptive fields across light-adaptive states and postulate that retinal neurons postsynaptic to the cones in bright light adopt low-pass spatiotemporal response characteristics to improve visual encoding under conditions of low synaptic SNR.

Optimal Information Transmission by Overlapping Retinal Cell Mosaics

The retina provides an excellent system for understanding the trade-offs that influence distributed information processing across multiple neuron types. We focus here on the problem faced by the visual system of allocating a limited number neurons to encode different visual features at different spatial locations. The retina needs to solve three competing goals: 1) encode different visual features, 2) maximize spatial resolution for each feature, and 3) maximize accuracy with which each feature is encoded at each location. There is no current understanding of how these goals are optimized together. While information theory provides a platform for theoretically solving these problems, evaluating information provided by the responses of large neuronal arrays is in general challenging. Here we present a solution to this problem in the case where multi-dimensional stimuli can be decomposed into approximately independent components that are subsequently coupled by neural responses. Using this approach we quantify information transmission by multiple overlapping retinal ganglion cell mosaics. In the retina, translation invariance of input signals makes it possible to use Fourier basis as a set of independent components. The results reveal a transition where one high-density mosaic becomes less informative than two or more overlapping lower-density mosaics. The results explain differences in the fractions of multiple cell types, predict the existence of new retinal ganglion cell subtypes, relative distribution of neurons among cell types and differences in their nonlinear and dynamical response properties.

Asymmetry between ON and OFF α ganglion cells of mouse retina: integration of signal and noise from synaptic inputs

KEY POINTS

Bipolar and amacrine cells presynaptic to the ON sustained α cell of mouse retina provide currents with a higher signal-to-noise power ratio (SNR) than those presynaptic to the OFF sustained α cell. Yet the ON cell loses proportionately more SNR from synaptic inputs to spike output than the OFF cell does. The higher SNR of ON bipolar cells at the beginning of the ON pathway compensates for losses incurred by the ON ganglion cell, and improves the processing of positive contrasts.

ABSTRACT

ON and OFF pathways in the retina include functional pairs of neurons that, at first glance, appear to have symmetrically similar responses to brightening and darkening, respectively. Upon careful examination, however, functional pairs exhibit asymmetries in receptive field size and response kinetics. Until now, descriptions of how light-adapted retinal circuitry maintains a preponderance of signal over the noise have not distinguished between ON and OFF pathways. Here I present evidence of marked asymmetries between members of a functional pair of sustained α ganglion cells in the mouse retina. The ON cell exhibited a proportionately greater loss of signal-to-noise power ratio (SNR) from its presynaptic arrays to its postsynaptic currents. Thus the ON cell combines signal and noise from its presynaptic arrays of bipolar and amacrine cells less efficiently than the OFF cell does. Yet the inefficiency of the ON cell is compensated by its presynaptic arrays providing a higher SNR than the arrays presynaptic to the OFF cell, apparently to improve visual processing of positive contrasts. Dynamic clamp experiments were performed that introduced synaptic conductances into ON and OFF cells. When the amacrine-modulated conductance was removed, the ON cell's spike train exhibited an increase in SNR. The OFF cell, however, showed the opposite effect of removing amacrine input, which was a decrease in SNR. Thus ON and OFF cells have different modes of synaptic integration with direct effects on the SNR of the spike output.

How Do Efficient Coding Strategies Depend on Origins of Noise in Neural Circuits?

Neural circuits reliably encode and transmit signals despite the presence of noise at multiple stages of processing. The efficient coding hypothesis, a guiding principle in computational neuroscience, suggests that a neuron or population of neurons allocates its limited range of responses as efficiently as possible to best encode inputs while mitigating the effects of noise. Previous work on this question relies on specific assumptions about where noise enters a circuit, limiting the generality of the resulting conclusions. Here we systematically investigate how noise introduced at different stages of neural processing impacts optimal coding strategies. Using simulations and a flexible analytical approach, we show how these strategies depend on the strength of each noise source, revealing under what conditions the different noise sources have competing or complementary effects. We draw two primary conclusions: (1) differences in encoding strategies between sensory systems-or even adaptational changes in encoding properties within a given system-may be produced by changes in the structure or location of neural noise, and (2) characterization of both circuit nonlinearities as well as noise are necessary to evaluate whether a circuit is performing efficiently.

Synaptic noise is an information bottleneck in the inner retina during dynamic visual stimulation

In daylight, noise generated by cones determines the fidelity with which visual signals are initially encoded. Subsequent stages of visual processing require synapses from bipolar cells to ganglion cells, but whether these synapses generate a significant amount of noise was unknown. To characterize noise generated by these synapses, we recorded excitatory postsynaptic currents from mammalian retinal ganglion cells and subjected them to a computational noise analysis. The release of transmitter quanta at bipolar cell synapses contributed substantially to the noise variance found in the ganglion cell, causing a significant loss of fidelity from bipolar cell array to postsynaptic ganglion cell. Virtually all the remaining noise variance originated in the presynaptic circuit. Circuit noise had a frequency content similar to noise shared by ganglion cells but a very different frequency content from noise from bipolar cell synapses, indicating that these synapses constitute a source of independent noise not shared by ganglion cells. These findings contribute a picture of daylight retinal circuits where noise from cones and noise generated by synaptic transmission of cone signals significantly limit visual fidelity.

Origin and effect of phototransduction noise in primate cone photoreceptors

Noise in the responses of cone photoreceptors sets a fundamental limit to visual sensitivity, yet the origin of noise in mammalian cones and its relation to behavioral sensitivity are poorly understood. Our work here on primate cones improves understanding of these issues in three ways. First, we find that cone noise is not dominated by spontaneous photopigment activation or by quantal fluctuations in photon absorption but instead by other sources, namely channel noise and fluctuations in cGMP. Second, we find that adaptation in cones, unlike that in rods, affects signals and noise differently. This difference helps explain why thresholds for rod- and cone-mediated signals have different dependencies on background light level. Third, past estimates of noise in mammalian cones are too high to explain behavioral sensitivity. Our measurements indicate a lower level of cone noise, and thus help reconcile physiological and behavioral estimates of cone noise and sensitivity.

Independent control of reciprocal and lateral inhibition at the axon terminal of retinal bipolar cells

Bipolar cells (BCs), the second order neurons in the vertebrate retina, receive two types of GABAergic feedback inhibition at their axon terminal: reciprocal and lateral inhibition. It has been suggested that two types of inhibition may be mediated by different pathways. However, how each inhibition is controlled by excitatory BC output remains to be clarified. Here, we applied single/dual whole cell recording techniques to the axon terminal of electrically coupled BCs in slice preparation of the goldfish retina, and found that each inhibition was regulated independently. Activation voltage of each inhibition was different: strong output from a single BC activated reciprocal inhibition, but could not activate lateral inhibition. Outputs from multiple BCs were essential for activation of lateral inhibition. Pharmacological examinations revealed that composition of transmitter receptors and localization of Na(+) channels were different between two inhibitory pathways, suggesting that different amacrine cells may mediate each inhibition. Depending on visual inputs, each inhibition could be driven independently. Model simulation showed that reciprocal and lateral inhibition cooperatively reduced BC outputs as well as background noise, thereby preserving high signal-to-noise ratio. Therefore, we conclude that excitatory BC output is efficiently regulated by the dual operating mechanisms of feedback inhibition without deteriorating the quality of visual signals.

Impact and sources of neuronal variability in the fly's motion vision pathway

Nervous systems encode information about dynamically changing sensory input by changes in neuronal activity. Neuronal activity changes, however, also arise from noise sources within and outside the nervous system or from changes of the animal's behavioral state. The resulting variability of neuronal responses in representing sensory stimuli limits the reliability with which animals can respond to stimuli and may thus even affect the chances for survival in certain situations. Relevant sources of noise arising at different stages along the motion vision pathway have been investigated from the sensory input to the initiation of behavioral reactions. Here, we concentrate on the reliability of processing visual motion information in flies. Flies rely on visual motion information to guide their locomotion. They are among the best established model systems for the processing of visual motion information allowing us to bridge the gap between behavioral performance and underlying neuronal computations. It has been possible to directly assess the consequences of noise at major stages of the fly's visual motion processing system on the reliability of neuronal signals. Responses of motion sensitive neurons and their variability have been related to optomotor movements as indicators for the overall performance of visual motion computation. We address whether and how noise already inherent in the stimulus, e.g. photon noise for the visual system, influences later processing stages and to what extent variability at the output level of the sensory system limits behavioral performance. Recent advances in circuit analysis and the progress in monitoring neuronal activity in behaving animals should now be applied to understand how the animal meets the requirements of fast and reliable manoeuvres in naturalistic situations.

Why do axons differ in caliber?

CNS axons differ in diameter (d) by nearly 100-fold (∼0.1-10 μm); therefore, they differ in cross-sectional area (d(2)) and volume by nearly 10,000-fold. If, as found for optic nerve, mitochondrial volume fraction is constant with axon diameter, energy capacity would rise with axon volume, also as d(2). We asked, given constraints on space and energy, what functional requirements set an axon's diameter? Surveying 16 fiber groups spanning nearly the full range of diameters in five species (guinea pig, rat, monkey, locust, octopus), we found the following: (1) thin axons are most numerous; (2) mean firing frequencies, estimated for nine of the identified axon classes, are low for thin fibers and high for thick ones, ranging from ∼1 to >100 Hz; (3) a tract's distribution of fiber diameters, whether narrow or broad, and whether symmetric or skewed, reflects heterogeneity of information rates conveyed by its individual fibers; and (4) mitochondrial volume/axon length rises ≥d(2). To explain the pressure toward thin diameters, we note an established law of diminishing returns: an axon, to double its information rate, must more than double its firing rate. Since diameter is apparently linear with firing rate, doubling information rate would more than quadruple an axon's volume and energy use. Thicker axons may be needed to encode features that cannot be efficiently decoded if their information is spread over several low-rate channels. Thus, information rate may be the main variable that sets axon caliber, with axons constrained to deliver information at the lowest acceptable rate.

Impact of neural noise on a sensory-motor pathway signaling impending collision

Noise is a major concern in circuits processing electrical signals, including neural circuits. There are many factors that influence how noise propagates through neural circuits, and there are few systems in which noise levels have been studied throughout a processing pathway. We recorded intracellularly from multiple stages of a sensory-motor pathway in the locust that detects approaching objects. We found that responses are more variable and that signal-to-noise ratios (SNRs) are lower further from the sensory periphery. SNRs remain low even with the use of stimuli for which the pathway is most selective and for which the neuron representing its final sensory level must integrate many synaptic inputs. Modeling of this neuron shows that variability in the strength of individual synaptic inputs within a large population has little effect on the variability of the spiking output. In contrast, jitter in the timing of individual inputs and spontaneous variability is important for shaping the responses to preferred stimuli. These results suggest that neural noise is inherent to the processing of visual stimuli signaling impending collision and contributes to shaping neural responses along this sensory-motor pathway.

Cone photoreceptor contributions to noise and correlations in the retinal output

Transduction and synaptic noise generated in retinal cone photoreceptors determine the fidelity with which light inputs are encoded, and the readout of cone signals by downstream circuits determines whether this fidelity is used for vision. We examined the effect of cone noise on visual signals by measuring its contribution to correlated noise in primate retinal ganglion cells. Correlated noise was strong in the responses of dissimilar cell types with shared cone inputs. The dynamics of cone noise could account for rapid correlations in ganglion cell activity, and the extent of shared cone input could explain correlation strength. Furthermore, correlated noise limited the fidelity with which visual signals were encoded by populations of ganglion cells. Thus, a simple picture emerges: cone noise, traversing the retina through diverse pathways, accounts for most of the noise and correlations in the retinal output and constrains how higher centers exploit signals carried by parallel visual pathways.

Trigger features and excitation in the retina

This review focuses on recent advances in our understanding of how neural divergence and convergence give rise to complex encoding properties of retinal ganglion cells. We describe the apparent mismatch between the number of cone bipolar cell types, and the diversity of excitatory input to retinal ganglion cells, and outline two possible solutions. One proposal is for diversity in the excitatory pathways to be generated within axon terminals of cone bipolar cells, and the second invokes narrow-field glycinergic amacrine cells that can apparently act like bipolar cells by providing excitatory drive to ganglion cells. Finally we highlight two advances in technique that promise to provide future insights; automation of electron microscope data collection and analysis, and the use of the ideal observer to quantitatively compare neural performance at all levels.

The absolute threshold of cone vision

We report measurements of the absolute threshold of cone vision, which has been previously underestimated due to suboptimal conditions or overly strict subjective response criteria. We avoided these limitations by using optimized stimuli and experimental conditions while having subjects respond within a rating scale framework. Small (1' fwhm), brief (34 ms), monochromatic (550 nm) stimuli were foveally presented at multiple intensities in dark-adapted retina for 5 subjects. For comparison, 4 subjects underwent similar testing with rod-optimized stimuli. Cone absolute threshold, that is, the minimum light energy for which subjects were just able to detect a visual stimulus with any response criterion, was 203 ± 38 photons at the cornea, ~0.47 log unit lower than previously reported. Two-alternative forced-choice measurements in a subset of subjects yielded consistent results. Cone thresholds were less responsive to criterion changes than rod thresholds, suggesting a limit to the stimulus information recoverable from the cone mosaic in addition to the limit imposed by Poisson noise. Results were consistent with expectations for detection in the face of stimulus uncertainty. We discuss implications of these findings for modeling the first stages of human cone vision and interpreting psychophysical data acquired with adaptive optics at the spatial scale of the receptor mosaic.

Retina is structured to process an excess of darkness in natural scenes

Retinal ganglion cells that respond selectively to a dark spot on a brighter background (OFF cells) have smaller dendritic fields than their ON counterparts and are more numerous. OFF cells also branch more densely, and thus collect more synapses per visual angle. That the retina devotes more resources to processing dark contrasts predicts that natural images contain more dark information. We confirm this across a range of spatial scales and trace the origin of this phenomenon to the statistical structure of natural scenes. We show that the optimal mosaics for encoding natural images are also asymmetric, with OFF elements smaller and more numerous, matching retinal structure. Finally, the concentration of synapses within a dendritic field matches the information content, suggesting a simple principle to connect a concrete fact of neuroanatomy with the abstract concept of information: equal synapses for equal bits.

Maximizing contrast resolution in the outer retina of mammals

The outer retina removes the first-order correlation, the background light level, and thus more efficiently transmits contrast. This removal is accomplished by negative feedback from horizontal cell to photoreceptors. However, the optimal feedback gain to maximize the contrast sensitivity and spatial resolution is not known. The objective of this study was to determine, from the known structure of the outer retina, the synaptic gains that optimize the response to spatial and temporal contrast within natural images. We modeled the outer retina as a continuous 2D extension of the discrete 1D model of Yagi et al. (Proc Int Joint Conf Neural Netw 1: 787-789, 1989). We determined the spatio-temporal impulse response of the model using small-signal analysis, assuming that the stimulus did not perturb the resting state of the feedback system. In order to maximize the efficiency of the feedback system, we derived the relationships between time constants, space constants, and synaptic gains that give the fastest temporal adaptation and the highest spatial resolution of the photoreceptor input to bipolar cells. We found that feedback which directly modulated photoreceptor calcium channel activation, as opposed to changing photoreceptor voltage, provides faster adaptation to light onset and higher spatial resolution. The optimal solution suggests that the feedback gain from horizontal cells to photoreceptors should be approximately 0.5. The model can be extended to retinas that have two or more horizontal cell networks with different space constants. The theoretical predictions closely match experimental observations of outer retinal function.

Reliability and frequency response of excitatory signals transmitted to different types of retinal ganglion cell

The same visual stimulus evokes a different pattern of neural signals each time the stimulus is presented. Because this unreliability reduces visual performance, it is important to understand how it arises from neural circuitry. We asked whether different types of ganglion cell receive excitatory signals with different reliability and frequency content and, if so, how retinal circuitry contributes to these differences. If transmitter release is governed by Poisson statistics, the SNR of the postsynaptic currents (ratio of signal power to noise power) should grow linearly with quantal rate (qr), a prediction that we confirmed experimentally. Yet ganglion cells of the same type receive quanta at different rates. Thus to obtain a measure of reliability independent of quantal rate, we calculated the ratio SNR/qr, and found this measure to be type-specific. We also found type-specific differences in the frequency content of postsynaptic currents, although types whose dendrites branched at nearby levels of the inner plexiform layer (IPL) had similar frequency content. As a result, there was an orderly distribution of frequency response through the depth of the IPL, with alternating layers of broadband and high-pass signals. Different types of bipolar cell end at different depths of the IPL and provide excitatory synapses to ganglion cell dendrites there. Thus these findings indicate that a bipolar cell synapse conveys signals whose temporal message and reliability (SNR/qr) are determined by neuronal type. The final SNR of postsynaptic currents is set by the dendritic membrane area of a ganglion cell, which sets the numbers of bipolar cell synapses and thus the rate at which it receives quanta [SNR = qr x (SNR/qr)].

The challenges natural images pose for visual adaptation

Advances in our understanding of natural image statistics and of gain control within the retinal circuitry are leading to new insights into the classic problem of retinal light adaptation. Here we review what we know about how rapid adaptation occurs during active exploration of the visual scene. Adaptational mechanisms must balance the competing demands of adapting quickly, locally, and reliably, and this balance must be maintained as lighting conditions change. Multiple adaptational mechanisms in different locations within the retina act in concert to accomplish this task, with lighting conditions dictating which mechanisms dominate.

Receptive fields and functional architecture in the retina

Functional architecture of the striate cortex is known mostly at the tissue level--how neurons of different function distribute across its depth and surface on a scale of millimetres. But explanations for its design--why it is just so--need to be addressed at the synaptic level, a much finer scale where the basic description is still lacking. Functional architecture of the retina is known from the scale of millimetres down to nanometres, so we have sought explanations for various aspects of its design. Here we review several aspects of the retina's functional architecture and find that all seem governed by a single principle: represent the most information for the least cost in space and energy. Specifically: (i) why are OFF ganglion cells more numerous than ON cells? Because natural scenes contain more negative than positive contrasts, and the retina matches its neural resources to represent them equally well; (ii) why do ganglion cells of a given type overlap their dendrites to achieve 3-fold coverage? Because this maximizes total information represented by the array--balancing signal-to-noise improvement against increased redundancy; (iii) why do ganglion cells form multiple arrays? Because this allows most information to be sent at lower rates, decreasing the space and energy costs for sending a given amount of information. This broad principle, operating at higher levels, probably contributes to the brain's immense computational efficiency.

Ideal observer analysis of signal quality in retinal circuits

The function of the retina is crucial, for it must encode visual signals so the brain can detect objects in the visual world. However, the biological mechanisms of the retina add noise to the visual signal and therefore reduce its quality and capacity to inform about the world. Because an organism's survival depends on its ability to unambiguously detect visual stimuli in the presence of noise, its retinal circuits must have evolved to maximize signal quality, suggesting that each retinal circuit has a specific functional role. Here we explain how an ideal observer can measure signal quality to determine the functional roles of retinal circuits. In a visual discrimination task the ideal observer can measure from a neural response the increment threshold, the number of distinguishable response levels, and the neural code, which are fundamental measures of signal quality relevant to behavior. It can compare the signal quality in stimulus and response to determine the optimal stimulus, and can measure the specific loss of signal quality by a neuron's receptive field for non-optimal stimuli. Taking into account noise correlations, the ideal observer can track the signal-to-noise ratio available from one stage to the next, allowing one to determine each stage's role in preserving signal quality. A comparison between the ideal performance of the photon flux absorbed from the stimulus and actual performance of a retinal ganglion cell shows that in daylight a ganglion cell and its presynaptic circuit loses a factor of approximately 10-fold in contrast sensitivity, suggesting specific signal-processing roles for synaptic connections and other neural circuit elements. The ideal observer is a powerful tool for characterizing signal processing in single neurons and arrays along a neural pathway.