Quantal Encoding of Information in a Retinal Ganglion Cell

Diurnal changes in the efficiency of information transmission at a sensory synapse

Neuromodulators adapt sensory circuits to changes in the external world or the animal’s internal state and synapses are key control sites for such plasticity. Less clear is how neuromodulation alters the amount of information transmitted through the circuit. We investigated this question in the context of the diurnal regulation of visual processing in the retina of zebrafish, focusing on ribbon synapses of bipolar cells. We demonstrate that contrast-sensitivity peaks in the afternoon accompanied by a four-fold increase in the average Shannon information transmitted from an active zone. This increase reflects higher synaptic gain, lower spontaneous “noise” and reduced variability of evoked responses. Simultaneously, an increase in the probability of multivesicular events with larger information content increases the efficiency of transmission (bits per vesicle) by factors of 1.5-2.7. This study demonstrates the multiplicity of mechanisms by which a neuromodulator can adjust the synaptic transfer of sensory information.

Neuromodulators can adjust how sensory signals are processed. In this study, the authors demonstrate how time of day affects the way information is transmitted in the zebrafish retina.

A Mammalian Retinal Ganglion Cell Implements a Neuronal Computation That Maximizes the SNR of Its Postsynaptic Currents

Neurons perform computations by integrating excitatory and inhibitory synaptic inputs. Yet, it is rarely understood what computation is being performed, or how much excitation or inhibition this computation requires. Here we present evidence for a neuronal computation that maximizes the signal-to-noise power ratio (SNR). We recorded from OFF delta retinal ganglion cells in the guinea pig retina and monitored synaptic currents that were evoked by visual stimulation (flashing dark spots). These synaptic currents were mediated by a decrease in an outward current from inhibitory synapses (disinhibition) combined with an increase in an inward current from excitatory synapses. We found that the SNR of combined excitatory and disinhibitory currents was voltage sensitive, peaking at membrane potentials near resting potential. At the membrane potential for maximal SNR, the amplitude of each current, either excitatory or disinhibitory, was proportional to its SNR. Such proportionate scaling is the theoretically best strategy for combining excitatory and disinhibitory currents to maximize the SNR of their combined current. Moreover, as spot size or contrast changed, the amplitudes of excitatory and disinhibitory currents also changed but remained in proportion to their SNRs, indicating a dynamic rebalancing of excitatory and inhibitory currents to maximize SNR.SIGNIFICANCE STATEMENT We present evidence that the balance of excitatory and disinhibitory inputs to a type of retinal ganglion cell maximizes the signal-to-noise ratio power ratio (SNR) of its postsynaptic currents. This is significant because chemical synapses on a retinal ganglion cell require the probabilistic release of transmitter. Consequently, when the same visual stimulus is presented repeatedly, postsynaptic currents vary in amplitude. Thus, maximizing SNR may be a strategy for producing the most reliable signal possible given the inherent unreliability of synaptic transmission.

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.

Cross inhibition from ON to OFF pathway improves the efficiency of contrast encoding in the mammalian retina

The retina is divided into parallel and mostly independent ON and OFF pathways, but the ON pathway "cross" inhibits the OFF pathway. Cross inhibition was thought to improve signal processing by the OFF pathway, but its effect on contrast encoding had not been tested experimentally. To quantify the effect of cross inhibition on the encoding of contrast, we presented a dark flash to an in vitro preparation of the mammalian retina. We then recorded excitatory currents, inhibitory currents, membrane voltages, and spikes from OFF α-ganglion cells. The recordings were subjected to an ideal observer analysis that used Bayesian methods to determine how accurately the recordings detected the dark flash. We found that cross inhibition increases the detection accuracy of currents and membrane voltages. Yet these improvements in encoding do not fully reach the spike train, because cross inhibition also hyperpolarizes the OFF α-cell below spike threshold, preventing small signals in the membrane voltages at low contrast from reaching the spike train. The ultimate effect of cross inhibition is to increase the accuracy with which the spike train detects moderate contrast, but reduce the accuracy with which it detects low contrast. In apparent compensation for the loss of accuracy at low contrast, cross inhibition, by hyperpolarizing the OFF α-cell, reduces the number of spikes required to detect the dark flash and thereby increases encoding efficiency.

The faithful copy neuron

Theoretical and experimental evidence is presented for the presence in nervous tissue of neurons whose firing rate faithfully follow their input stimulus. Such neurons are shown to deliver their spikes with minimum dissipation per spike. This optimal performance is likely accomplished by use of local circuitry that adjusts conductances to match input currents so that the neuron operates near the threshold for firing. This results in an unusual mechanism for neuronal firing that uses background noise to achieve the desired firing rate. This framework takes place dynamically, and the present deliberations apply under time varying conditions. It is shown that an analytically explicit probability distribution function, which depends on one dimensionless parameter, can account for the interspike interval statistics under general time varying conditions. An innovative analysis based on the unsteady firing rate fits data to the appropriate probability distribution function.

Spiking Neurons and the First Passage Problem

We derive a model of a neuron’s interspike interval probability density through analysis of the first passage problem. The fit of our expression to retinal ganglion cell laboratory data extracts three physiologically relevant parameters, with which our model yields input-output features that conform to laboratory results. Preliminary analysis suggests that under common circumstances, local circuitry readjusts these parameters with changes in firing rate and so endeavors to faithfully replicate an input signal. Further results suggest that the so-called principle of sloppy workmanship also plays a role in evolution’s choice of these parameters.

The ON pathway rectifies the OFF pathway of the mammalian retina

In the vertebrate visual system, ON cells respond to positive contrasts and OFF cells respond to negative contrasts, and thus both ON and OFF cells exhibit rectification. We investigated the retinal circuits by which the ON pathway rectifies the OFF pathway. White noise was projected onto an in vitro preparation of the mammalian retina and excitatory currents were recorded from retinal ganglion cells under whole-cell voltage clamp. Currents in OFF cells were more rectified than those in ON cells: thus, currents in ON cells were able to signal both positive and negative contrasts, but currents in OFF cells were virtually restricted to negative contrasts. Blocking signals in the ON pathway derectified currents in OFF ganglion cells, thus allowing them to be modulated by positive contrasts, indicating that the ON pathway normally rectifies currents in OFF ganglion cells. Such cross-rectification from ON to OFF pathways required intact glycinergic inhibition, indicating that a glycinergic amacrine cell, most likely the AII amacrine cell, allows the ON bipolar cell to hyperpolarize the OFF bipolar cell close to the threshold for transmitter release, thus rectifying excitatory currents in the OFF ganglion cell. Asymmetrical rectification of ON and OFF cells may be an adaptation to natural scenes that have more contrast levels below the mean than above. Thus, in order for ON and OFF pathways to encode an equal number of contrast levels, the ON cells must signal some negative contrasts.

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)].

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.

The maintained discharge of rat retinal ganglion cells

Action potentials were recorded from rat retinal ganglion cell fibers in the presence of a uniform field, and the maintained discharge pattern was characterized. Spike trains recorded under ketaminexylazine. The majority of cells had multimodal interval distributions, with the first peak in the range of 25.00.97). Both ON and OFF cells show serial correlations between adjacent interspike intervals, while ON cells also showed second-order correlations. Cells with multimodal interval distribution showed a strong peak at high frequencies in the power spectra in the range of 28.9-41.4 Hz. Oscillations were present under both anesthetic conditions and persisted in the dark at a slightly lower frequency, implying that the oscillations are generated independent of any light stimulus but can be modulated by light level. The oscillation frequency varied slightly between cells of the same type and in the same eye, suggesting that multiple oscillatory generating mechanisms exist within the retina. Cells with high-frequency oscillations were described well by an integrate-and-fire model with the input consisting of Gaussian noise plus a sinusoid where the phase was jittered randomly to account for the bandwidth present in the oscillations.

Populations of Tightly Coupled Neurons: The RGC/LGN System

A mathematical model, of general character for the dynamic description of coupled neural oscillators is presented. The population approach that is employed applies equally to coupled cells as to populations of such coupled cells. The formulation includes stochasticity and preserves details of precisely firing neurons. Based on the generally accepted view of cortical wiring, this formulation is applied to the retinal ganglion cell (RGC)/lateral geniculate nucleus (LGN) relay cell system, of the early mammalian visual system. The smallness of quantal voltage jumps at the retinal level permits a Fokker-Planck approximation for the RGC contribution; however, the LGN description requires the use of finite jumps, which for fast synaptic dynamics appears as finite jumps in the membrane potential.

Analyses of equilibrium spiking behavior for both the deterministic and stochastic cases are presented. Green's function methods form the basis for the asymptotic and exact results that are presented. This determines the spiking ratio (i.e., the number of RGC arrivals per LGN spike), which is the reciprocal of the transfer ratio, under wide circumstances. Criteria for spiking regimes, in terms of the relatively few parameters of the model, are presented.

Under reasonable hypotheses, it is shown that the transfer ratio is ≤1/2, in the absence of input from other areas. Thus, the model suggests that the LGN/RGC system may be a relatively unsophisticated spike editor. In the absence of other input, the system is designed to fire an LGN spike only when two or more RGC spikes appear in a relatively short time. Transfer ratios that briefly exceed 1/2 (but are less than 1) have been recorded in the laboratory. Inclusion of brain stem input has been shown to provide a signal that elevates the transfer ratio (Ozaki & Kaplan, 2006). A model that includes this contribution is also presented.

How robust is a neural circuit?

Design in engineering begins with the problem of robustness-by what factor should intrinsic capacity exceed normal demand? Here we consider robustness for a neural circuit that crosses the retina from cones to ganglion cells. The circuit's task is to represent the visual scene at many successive stages, each time by modulating a stream of stochastic events: photoisomerizations, then transmitter quanta, then spikes. At early stages, the event rates are high to achieve some critical signal-to-noise ratio and temporal bandwidth, which together set the information rate. Then neural circuits concentrate the information and repackage it, so that nearly the same total information can be represented by modulating far lower event rates. This is important for spiking because of its high metabolic cost. Considering various measurements at the outer and inner retina, we conclude that the "safety factors" are about 2-10, similar to other tissues.

Benefits of contrast normalization demonstrated in neurons and model cells

The large dynamic range of natural stimuli poses a challenge for neural coding: how is a neuron to encode large differences at high contrast while remaining sensitive to small differences at low contrast? Many sensory neurons exhibit contrast normalization: gain depends on the range of stimuli presented, such that firing-rate modulation is not proportional to contrast. However, coding depends strongly on the precision of spike timing and the reliability of spike number, neither of which can be predicted from neural gain. The presumption that contrast normalization is associated with maintained coding efficiency remained untested. We report that, as contrast decreases, responses are more variable and encode less information, as expected. Nevertheless, these changes can be small, and information transmission is even better preserved across contrasts than rate modulation. The extent of contrast normalization is correlated with the extent to which information transmission is preserved across contrasts. Specifically, normalization is associated with maintaining the bits of information per spike rather than bits per second. Finally, we show that a nonadapting model can exhibit both contrast normalization and the associated information preservation.

Different mechanisms generate maintained activity in ON and OFF retinal ganglion cells

Neuronal discharge is driven by either synaptic input or cell-autonomous intrinsic pacemaker activity. It is commonly assumed that the resting spike activity of retinal ganglion cells (RGCs), the output cells of the retina, is driven synaptically, because retinal photoreceptors and second-order cells tonically release neurotransmitter. Here we show that ON and OFF RGCs generate maintained activity through different mechanisms: ON cells depend on tonic excitatory input to drive resting activity, whereas OFF cells continue to fire in the absence of synaptic input. In addition to spontaneous activity, OFF cells exhibit other properties of pacemaker neurons, including subthreshold oscillations, burst firing, and rebound excitation. Thus, variable weighting of synaptic mechanisms and intrinsic properties underlies differences in the generation of maintained activity in these parallel retinal pathways.