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

Abstract

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)].

Fig. 1.

Ten types of ganglion cell whose excitatory postsynaptic currents were recorded. Cells are shown as projections from optical sections (methods). Some show a patch pipette in place (bright triangles, top left). Cell bodies appear larger because of fluorescent flare. A: 5 types of ganglion cell whose excitatory postsynaptic currents were measured for reliability and frequency response. B: 5 additional types of ganglion cells whose excitatory postsynaptic currents were measured for frequency response. Note that the scale bar in this figure is smaller than that in A; thus these cells have larger dendritic arbors (>250 μm, in this and subsequent figures: α, alpha; β, beta; δ, delta; LE, local edge).

Fig. 2.

Measuring signal to noise ratio (SNR). A: an interval of the white noise stimulus (temporal contrast: mean/SD = 0.2). B: excitatory postsynaptic currents (EPSCs) evoked by repeated presentation of the stimulus (on LE cell). C: signal was EPSCs averaged over repeats. D: noise was the difference between the average EPSC and the EPSC evoked by a stimulus repeat. E: the power spectrum of signal-to-noise ratio, SNR(f), was integrated between 0 and 100 Hz to give the ratio of signal power to noise power (SNR).

Fig. 3.

Charge transfer from spontaneous (s)EPSCs. A: sEPSCs were detected by their onset (), peak (✚), and exponential decay (solid lines). B: sEPSCs were averaged and then integrated to give quantal charge q′. C: average quantal charge for 6 types of retinal ganglion cell.

Fig. 4.

Reliability of excitatory signals to different types of retinal ganglion cell. Each graph shows SNR vs. quantal rate for cells of the same type; each symbol and the associated regression fit represent a cell. The histogram (bottom right) is a summary of the reliability of each cell type, where reliability is measured as the ratio of SNR to quantal rate, taken from the regression fits in the graphs.

Fig. 5.

Verifying quantal charge with ensemble noise analysis. A: EPSCs were detected in currents evoked by white noise (same cell as in Fig. 3). B: each point represents a detected EPSC. The charge variance across stimulus repetitions σ_Q² is proportional to the average charge 〈Q〉, consistent with Poisson statistics. Substituting variance and average into the equation of ensemble analysis (Eq. 3) provides an estimate of quantal charge q*. C: each point represents a ganglion cell. The points fall along the line q* = q′, indicating that light-evoked EPSCs are composed of quanta with the same average charge as that calculated from the sEPSCs.

Fig. 6.

SNR of excitatory input to different types of ganglion cell plotted against contrast. Contrast of white-noise stimulus was varied from mean/SD = 0.1 to 0.3. Each symbol and associated regression line are from a single cell. Note that ganglion cells of the same type have different slopes, indicating different SNR/contrast ratios.

Fig. 7.

SNR/contrast ratio is correlated with number of synapses. A: tracings of cells were made from optical sections. B: the ratio SNR/contrast was taken from the regression fits of Fig. 6 and plotted against total dendritic length taken from the tracing in A.

Fig. 8.

SNR spectrum scales with quantal rate. A: SNR spectra normalized by divided by the quantal rate. Note that resulting normalized spectra b(f) are similar, indicating that the spectrum retains a constant shape as it scales with quantal rate. B: plotting peak frequency (Fpeak) and upper cutoff frequency (Fhi) at one quantal rate (F[i]) against the same measure at the next highest quantal rate (F[i+1]) gives data points that follow the diagonal (F[i] = F[i+1]), indicating no consistent change in the shape of the spectrum. C: plotting the amplitude of the SNR spectrum at 1 Hz (Vlow) and at 20 Hz (Vhi) at one quantal rate (V[i]) against the next highest quantal rate (V[i+1]) gives data points that follow the diagonal, confirming no consistent change in shape. D: bandwidth: the difference between the low-frequency cutoff (Flow) and the high-frequency cutoff (Fhi) for the different ganglion cells types. There were no statistically significant differences in bandwidth.

Fig. 9.

Stratification of frequency responses through the depth of the inner plexiform layer (IPL). To the left are the dendritic stratifications of identified types of ganglion cell, showing SE as error bars. Small bistratified cells are represented by 2 filled circles connected by a dotted line. To the right are the impulse spectra from the same cell types, showing SE as confidence bands (gray). Impulse spectra from the small bistratified cell are from recordings during which on bipolar cells were blocked with L-AP4.