Article Figures & Data
Figures
- Figure 1.
Stimulus–response relationships for cells in the rod bipolar pathway. A, Schematic of the mammalian rod bipolar pathway and estimates of convergence [cat (Sterling et al., 1988); mouse (Tsukamoto et al., 2001)]. Most synapses are glutamatergic, with the exceptions of electrical coupling between the AII amacrine and on cone bipolar, and a glycinergic synapse between the AII amacrine and off cone bipolar (Strettoi et al., 1992) (for review, see Bloomfield and Dacheux, 2001). B, Stimulus–response relationships for cells across the rod bipolar pathway in mouse retina. Points plot average responses (mean ± SEM) to a 10 ms flash delivered in darkness. The rod stimulus–response relationship was fit with a saturating exponential with φhalf = 9.6 ± 0.2 Rh* (N = 22). Stimulus–response relationships for on α ganglion cells, AII amacrine cells, and rod bipolar cells were fit with a Hill curve (Eq. 1). Half-saturating flash strengths, φhalf, and the exponent, n, were φhalf = 1.83 ± 0.06 Rh*/rod and n = 1.6 ± 0.04 for rod bipolar cells (N = 43), φhalf = 0.12 ± 0.01 Rh*/rod and n = 1.20 ± 0.06 for AII amacrine cells (N = 12), and φhalf = 0.11 ± 0.01 Rh*/rod and n = 1.01 ± 0.06 for ganglion cells (N = 9).
- Figure 2.
Procedure for measuring signal and noise. A, Four current responses of a mouse on α ganglion cell to a flash producing on average 0.02 Rh*/rod delivered at time 0 with no background. Template (thick trace) is the average of 28 responses. Holding potential was −60 mV. Filtered at 100 Hz. B, Four responses to a flash producing on average 0.06 Rh*/rod with a background of 0.6 Rh*/rod/s. Template (thick trace) is the average of 28 responses. C, Distribution of correlations between the template and responses to a flash producing on average 1 Rh*/rod in darkness (N = 39). Thick trace is a Gaussian fit (mean ± SD, 1.09 ± 0.52). D, Noise trials in darkness. E, Noise trials on the same background in B. F, Distribution of the correlations between the noise trials with no background (N = 39) and the template. Thick trace is a Gaussian fit (SD of 0.0089). The SD of the noise distribution defines the flash-independent noise.
- Figure 3.
Gain, noise, and threshold for a single mouse ganglion cell. A, Gain estimated from consecutive responses to three flash strengths (open symbols) and averaged across flash strengths and repeated measurements (filled circles) for several background intensities. Gain was defined as the mean of the response trial correlations (see Fig. 2C). B, Flash-independent noise for several backgrounds. Flash-independent noise was defined as the SD of correlations between noise trials and the template (see Fig. 2F). C, Flash-dependent noise for several backgrounds. Flash-dependent noise measures the variability attributable to the flash itself (i.e., the variability remaining after subtracting flash-independent noise). Flash-dependent noise was estimated for a flash strength equal to detection threshold (see D and Materials and Methods). D, Threshold for several backgrounds, calculated according to Equation 4. The threshold represents the flash strength (Rh* per rod) at which the signal-to-noise ratio for a flash/no-flash two-interval forced-choice experiment is 1 (see Materials and Methods).
- Figure 4.
Gain, noise, and threshold of primate ganglion cells. A, Dependence of gain on background. Collected current responses (mean ± SEM) from eight primate on ganglion cells. Smooth fit from Equation 5 with exponent m = −0.53 ± 0.06 (mean ± SD), a = 0.01, b fixed at 1.3, c = 7.1, and d fixed at 1. Error bars represent SEM. Measurements at backgrounds that differed by <30% were averaged together. Voltage clamped at −60 mV. B, Dependence of flash-independent noise on background. Smooth fit from Equation 5 with parameters a = 4.4, b = 3.7, c fixed at 1, d = 0.004, and m fixed at 0. C, Dependence of flash-dependent noise on background. Smooth fit from Equation 5 with parameters a = 23, b = 27, c = 0.56, d = 0.01, and m = −0.67. D, Dependence of threshold on background. Smooth fit from Equation 6 with M = 0.6 ± 0.1 (mean ± SD), ID = 0.16, and K = 0.02.
- Figure 5.
Gain, noise, and threshold of mouse on α ganglion cells. A, Dependence of gain on background. Collected current responses (mean ± SEM) from mouse on α ganglion cells in slice (N = 16; filled circles) and in flat-mount (N = 13; open circles) preparations. Smooth fit from Equation 5: exponent m = −0.78 ± 0.05 for slice, −0.62 ± 0.05 for flat mount (mean ± SD); a = 0.01 for slice and 0.19 for flat mount; b fixed at 1.3; c = 2.91 for slice and 2.44 for flat mount; and d fixed at 1. Voltage clamped at −60 mV. B, Dependence of flash-independent noise on background. Smooth fit from Equation 5 with a fixed at 10, b fixed at 1.6, c = 0.003, d = 0.007, and m fixed at −1. C, Dependence of flash-dependent noise on background. Smooth fit from Equation 5 with a = 0.74, b fixed at 1.3, c = 0.68, d = 0.09, and m = −0.54. D, Dependence of threshold on background for mouse (black) and primate (gray). Smooth fit to the mouse data from Equation 6 increased with M = 0.76 ± 0.08 (mean ± SD), ID = 0.29, and K = 0.02.
- Figure 6.
Rod photoreceptor gain and flash-independent noise. A, Outer segment current responses of a mouse rod photoreceptor to flashes producing an average of 2.4 Rh*/rod with no background. Flash was delivered at time 0 and was 10 ms in duration. Template (thick trace) is the average of 40 responses. Noise records were taken from the 400 ms period before the flash, and response trials were taken from the 400 ms period after. Filtered at 30 Hz. B, Responses to flashes producing an average of 2.4 Rh*/rod with a background of 0.71 Rh*/rod/s. Template (thick trace) is the average of 40 responses. C, Background dependence of gain for 17 mouse rod photoreceptors. Smooth fit from Equation 5 with m = −0.75 ± 0.04 (mean ± SEM), a = 0.64, b fixed at 1.3, c = 0.31, and d fixed at 1. Superimposed in gray is the gain plot from mouse ganglion cells from Figure 5A. Error bars are SEM. D, Background dependence of flash-independent noise. Smooth fit from Equation 5 with a = 1.20, b fixed at 4, c = 0.07, d = 0.56, and m = −0.39.
- Figure 7.
Rod bipolar cell gain and flash-independent noise. A, Current responses of a mouse rod bipolar cell to flashes producing an average of 0.1 Rh*/rod with no background. Flash was delivered at time 0 and was 10 ms in duration. Noise trials were taken from the 300 ms period before the flash, and response trials were taken from the 300 ms period after. Template (thick trace) is the average of 20 responses. Holding potential was −60 mV. Filtered at 100 Hz. B, Responses to flashes producing an average of 0.1 Rh*/rod with a background of 1.3 Rh*/rod/s. Template (thick trace) is the average of 10 responses. C, Dependence of rod bipolar gain on background collected from current (filled circles; N = 23) and voltage (open circles; N = 17) responses. Smooth fit from Equation 5 with m = −1.2 ± 1.3, a = 3.9, b fixed at 3, c = 0.01, and d fixed at 1. Superimposed in gray is the mouse ganglion cell gain. Error bars are SEM. D, Dependence of flash-independent noise on background. Smooth fit from Equation 5 with m fixed at −0.7, a fixed at 16, b fixed at 15, c = 0.07, and d fixed at 0.13.
- Figure 8.
AII amacrine cell gain and flash-independent noise. A, Current responses of a mouse AII amacrine cell to a flash producing an average of 0.16 Rh*/rod with no background. Flash was delivered at time 0 and was 10 ms in duration. Noise trials were taken from the 200 ms period before the flash, and response trials were from the 200 ms period after. Template (thick trace) was the average of 28 responses. Holding potential was −60 mV. Filtered at 100 Hz. B, Responses to a flash producing an average of 2.6 Rh*/rod with a background of 1.0 Rh*/rod/s. Template (thick trace) was the average of 26 responses. C, Dependence of AII amacrine cell gain on background. Black circles plot gain for 13 wild-type AII amacrine cells, fit with Equation 5 with exponent m = −0.54 ± 0.04 (mean ± SD), a = 0.001, b fixed at 1.3, c = 21.9, and d fixed at 1. White circles plot gain for 12 connexin36−/− AII amacrine cells, fit with Equation 5 with m = −0.65 ± 0.15 (mean ± SD), a = 0.04, b fixed at 1.3, c = 4.9, and d fixed at 1. Gray circles plot mouse ganglion cell gain. Error bars are SEM. D, Dependence of flash-independent noise on background for AII amacrine cells from wild-type (filled circles) and connexin36−/− (open circles) mice. Smooth fit from Equation 5 with m = −0.21, a = 0.13, b fixed at 3, c = 5.8, and d = 0.01.
- Figure 9.
Comparison of experiment with ideal-observer predictions. A, Noise and threshold were predicted by passing simulated rod responses through a nonlinearity, summing N signals, and applying a gain change. Location 1 represents the signal before the gain change, and location 2 represents the signal after. The nonlinearity was a cumulative Gaussian (midpoint of 1.3; SD of 0.1). N was 4096 for α ganglion cell predictions. B, Response gain before (1) and after (2) the gain control site. Gray region shows fits to upper (measured + SEM) and lower (measured − SEM) limits to the measured gain from Figure 5A. Gain in the model was chosen to match that measured and scaled with background as (0.3 + IB)−0.8. C, Total flash-independent and flash-dependent noise at threshold of the model before (1) and after (2) the gain change. Gray region shows fits to upper (measured + SEM) and lower (measured − SEM) limits to the measured total noise from Figure 5, B and C. D, Threshold of the ideal-observer model (black) compared with fits to the upper (measured + SEM) and lower (measured − SEM) limits to the measured threshold from Figure 5D (gray region).
