We measured spike responses (Figure 2A) and excitatory synaptic inputs (Figure 2B) of On parasol ganglion cells in response to brief flashes superimposed on a range of backgrounds (see also ‘Materials and methods’ and Figures 10 and 11). We focused specifically on backgrounds near the onset of changes in human behavioral threshold (0.01–0.2 isomerizations/rod/s or R*/rod/s). Flash strengths (0.001–0.006 R*/rod) were chosen to elicit responses well below saturation. Both individual responses (Figure 2A,B) and averages (Figure 2C) had a clear dependence on background. Furthermore, a cell’s excitatory synaptic input and its spike response changed similarly with changes in background (Figure 2C). To quantify the effect of background on a cell’s response, we determined the response gain by dividing the response amplitude (spike count or integrated current) by the flash strength; the gain measures the response per R*/rod. The gain of spike responses and excitatory input had a similar dependence on background (Figure 2D).

Figure 2

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Figure 2C,D suggest that the effect of changes in background on a cell’s spike output is dominated by the changes in excitatory input. To further test this conclusion, we defined a detection threshold as the strength of the flash (in R*/rod) eliciting a response with a signal-to-noise ratio of 1 (see ‘Materials and methods’). Noise was measured from sections of recording prior to the flash. Detection thresholds for spike responses and excitatory synaptic inputs measured in the same cell were near identical across a range of backgrounds (Figure 2E). Consistent with the similarity of the spike responses and excitatory inputs, inhibitory synaptic inputs to the same stimuli were three to four times smaller than the excitatory inputs, and hence unlikely to contribute strongly to spike output (data not shown).

Figure 2 indicates the changes in the gain of an On parasol cell's spike output are dominated by changes in the cell's excitatory synaptic inputs. Below, we focus on how gain of the excitatory synaptic inputs is controlled.

Changes in human behavioral threshold with background show several characteristic regions (reviewed by Barlow, 1965; Donner, 1992; Rieke and Rudd, 2009): (1) a ‘dark light’ region extending to ∼0.01 R*/rod/s in which threshold is independent of background, (2) a ‘Rose–deVries’ region in which threshold increases with the square root of the background (de Vries, 1943; Rose, 1948), and (3) a ‘Weber’ region in which threshold increases proportionally with the background. Since threshold depends on both signal and noise, the relationship between these behavioral measurements and gain control is unclear. Hence, the experiments below characterize gain, noise, and threshold of the On parasol responses across a range of background intensities spanning these behaviorally defined regions.

We extended experiments like those in Figure 2 to span a wide range of backgrounds (Figure 3). In this and all subsequent experiments, we adjusted the flash strength to elicit similar responses across backgrounds because the change in gain exceeded the cell’s linear response range (see ‘Materials and methods’ and Figures 10 and 11). Adjusting flash strength (and dividing the response by the flash strength to measure gain) allowed us to probe a ∼10,000-fold range of backgrounds. Across the entire range tested, the dependence of gain on background (Figure 3A) was well described by a modified Weber function:

where G is the gain and G_D is its maximum value, I_B is the background, and I₀ is the background required to reduce the gain by 50%. Gain in Equation 1 is constant when I_B << I₀, begins to decrease when I_B nears I₀, and scales inversely with background when I_B >> I₀. For the cell in Figure 3A, I₀ was 0.076 R*/rod/s (marked by the arrowhead); across cells, I₀ was 0.08 ± 0.03 R*/rod/s (mean ± SD, n = 6). We observed a small but consistent reduction in gain in darkness relative to its maximal value at backgrounds ∼0.01 R*/rod/s. The reduced gain in darkness was highly dependent on the history of light exposure, and hence is only partially captured in Figure 3A because we returned to the dark condition after exposure to several backgrounds (see ‘Recordings and light stimulation’). The low dark gain reflects a nonlinear processing step that is engaged in the dark but relieved for backgrounds producing 0.005–0.01 R*/rod/s; this nonlinearity and its impact on visual sensitivity is the subject of another study (P Ala-Laurila and F Rieke, unpublished).

Figure 3

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Two features of Figure 3A are notable. First, over a ∼1000-fold range of backgrounds gain closely followed Weber law behavior, even though multiple mechanisms contribute to gain control across this range. This indicates an orderly coordination of gain control mechanisms (see ‘Discussion’). Second, gain began to decrease for backgrounds near 0.01 or 0.02 R*/rod/s—close to the onset of changes in human behavioral threshold. We summarized the onset of gain changes across cells by choosing three regions spanning equal ranges of background intensities centered below, on, or above I₀ (horizontal colored lines in Figure 3A). Figure 3D plots the exponent describing the dependence of gain on background (i.e., the slope on a log–log scale as in Figure 3A) in each region. Gain scaled inversely with background above 0.3 R*/rod/s, and more gradually at lower background intensities. Consistent with the ability of Equation 1 to describe the data, we did not see evidence for an extended region where gain scaled inversely with the square root of the background (see ‘Discussion’).

We quantified noise at each background by projecting the current prior to the flash along the same template used to measure signal (see ‘Analysis’). Noise also changed with background, but such changes were modest across those backgrounds near the onset of changes in behavioral threshold (Figure 3B,E); specifically, noise changed <10-fold over a range of backgrounds that produced an ∼10,000-fold change in gain. These changes in noise with background were much less than expected from Poisson fluctuations in photon absorption and no changes in gain. If Poisson fluctuations dominated noise and gain remained constant, the standard deviation of the current should increase as the square root of the background—that is, with slope 0.5—since the variance of a Poisson process is proportional to the mean. Noise changed much less with background than this prediction (Figure 3B,E). The largest increases in noise occurred between darkness and backgrounds <0.01 R*/rod/s. These changes are produced by a nonlinear processing step that reduces gain in the dark (see above; P Ala-Laurila and F Rieke, unpublished). The reduction in noise at backgrounds higher than 0.1 R*/rod/s likely reflects the stronger decrease in gain at these backgrounds, which more than compensates the increase in Poisson fluctuations.

Changes in noise, although modest, had a noticeable effect on detection threshold—defined as the strength of the flash eliciting a response with a signal-to-noise ratio of 1 (Figure 3C,F; see ‘Analysis’). This measure of threshold assumes a linear scaling of response with flash strength, which fails in the dark but holds for backgrounds exceeding 0.01 R*/rod/s (P Ala-Laurila and F Rieke, preprint). The threshold in Figure 3C,F corresponds to the threshold of an ideal observer of the ganglion cell's output, assuming that signal and noise are independent and additive. Thus, the threshold defined here provides a point of comparison to human behavioral threshold vs intensity curves. The threshold for On parasol responses increased for backgrounds as low as 0.02 R*/rod/s, in close correspondence with backgrounds that produce changes in behavioral threshold (Donner, 1992). Threshold increased with a slope <1 for backgrounds between 0.02 and 5 R*/rod/s (Figure 3F). The extended region over which the slope was less than unity reflected the increase in noise at backgrounds lower than those required to produce gain changes, a region near the onset of gain changes where noise was near constant, and the decrease in noise at backgrounds where gain began to decrease proportionally with background.

The experiments described above indicate that the gain of retinal signals begins to decline at backgrounds producing ∼0.02 R*/rod/s. Gain control under these conditions is challenging because photons arrive rarely at individual rod photoreceptors; retinal responses at these backgrounds are noisy, and hence changes in background will be difficult to discern without a large degree of spatial and/or temporal averaging. At the same time, left unabated, the high gain associated with fully dark-adapted vision would cause a parasol ganglion cell to generate hundreds of spikes per second for backgrounds producing ∼0.02 R*/rod/s. The experiments described in this section characterize several key properties of how gain is controlled—particularly the statistical feature of the input that sets gain and how the mechanism integrates over space and time.

Changes in the mean background necessarily also change the magnitude of the fluctuations about the mean because of the division of light into discrete photons and the resulting statistical fluctuations in photon arrival. Such Poisson fluctuations in photon absorption are particularly large relative to the mean absorption rate at low backgrounds. Because these statistical fluctuations increase with the square root of the background, a gain control that directly depends on the magnitude of the noise would cause gain to scale inversely with the square root of the background (Brown and Rudd, 1998). The experiments below, however, indicate that gain at low backgrounds is controlled by the mean photon absorption rate and not by the magnitude of the fluctuations about the mean rate.

To isolate the potential effects of fluctuations about the mean on gain, we delivered a series of flashes before, during, and after a high contrast fluctuating stimulus while maintaining a constant mean background (Figure 4A). A Rose–deVries gain control mechanism based on the fluctuations about the mean predicts that gain should decrease linearly with standard deviation (dashed line in Figure 4B). Instead, contrast stimuli that substantially increased the variance of a ganglion cell’s excitatory synaptic inputs tended to increase, rather than decrease, the gain of the flash response. In nine cells, stimuli that increased the standard deviation of the baseline excitatory synaptic inputs by 43 ± 17% (mean ± SD) produced a 18 ± 11% increase in gain (Figure 4B). These data argue directly against noise controlling gain at low backgrounds, indicating instead that gain is controlled by the mean photon flux.

Figure 4

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Gain control at low backgrounds requires averaging across rods and/or time to obtain a sufficient photon count to determine that the mean background has changed (Rushton, 1965). Too much spatial or temporal averaging could limit the effectiveness of gain control: spatial averaging across regions of a scene with different backgrounds could fail to protect retinal signals from local saturation, and temporal averaging could be ineffective if it introduces too long a delay between changes in input and changes in gain. What strategy, then, does the circuit adopt? We start by describing the kinetics of gain changes.

To test for slow changes in gain that would reflect extensive temporal averaging, we switched the background periodically between two levels while delivering flashes every second to monitor gain. The baseline firing rate and mean excitatory input changed slowly following a change in background, and had not reached an obvious steady-state level even after 200 s. Gain changes, however, occurred within a few seconds following a change in background—for example, in Figure 5—figure supplement 1, the ∼twofold change in gain between panels B and C is largely complete by the time of the first flash response (1 s after the background change). Gain did not change noticeably in the subsequent 60–200 s (Figure 5—figure supplement 1; see also Figures 10 and 11).

To resolve the initial rapid change in gain, we delivered flashes at times ranging from 0.1 to 2 s following either an increase or a decrease in background while measuring a cell’s excitatory synaptic inputs. We adjusted the flash strength to generate a near-constant response at the two backgrounds. Subtracting the response to the background step alone isolated responses to the flashes (Figure 5A, bottom). Following an increase in background, gain fell with a time constant of 0.10 ± 0.02 s (mean ± SEM, n = 5); following a decrease in background, gain increased with a time constant of 0.4 ± 0.1 s (n = 6). The decrease in gain at light onset tracked the development of the step response, with apparently little delay due to the gain control mechanism itself. Recovery of gain following a decrease in background took more time, as indicated by the slower kinetics at light offset.

Figure 5 with 1 supplement see all

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The rapid kinetics of gain changes at both light onset and offset indicate a need for considerable integration of signals across rods. For example, in the 0.1 s following an increase in background from 0.02 to 0.08 R*/rod/s, <1 in 100 rods absorbs a photon. Thus, the observed gain changes cannot be explained by a mechanism operating on a small collection of rods; for example, a mechanism operating in single rods would only be engaged in 1 out of 100 rods, and hence could reduce overall gain at most by 1%. The halving of gain produced by this step in background requires a mechanism that integrates over at least 50 rods even if a single absorbed photon reduces gain to 0 (Figure 6). In this section, we describe experiments that probed the spatial scale of the gain control mechanism by measuring the extent to which a decrease in gain in one region of space transferred to neighboring regions.

Figure 6

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We adapted subregions within the ganglion cell receptive field while probing the gain of responses elicited at distinct locations (Figure 7A). In the ‘baseline’ phase of the experiment, we flashed two different probe patterns consisting of a set of bars on a weak spatially uniform adapting background (0.02 R*/rod/s). In the ‘adaptation’ phase of the experiment, we presented a steady adapting bar pattern (bar intensity = 0.2 R*/rod/s) that overlapped exactly with one of the probe patterns (‘adapted’ location) and had no overlap with the other probe pattern (‘unadapted’ location). We then repeated measurements of the responses to the two probe patterns to determine the extent to which the adapting pattern affected gain in the adapted and unadapted locations.

Figure 7

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By exploring a range of widths for the adapting bars, we were able to measure the distance over which gain changes from the adapted location transferred to the unadapted location. Figure 7B illustrates the logic of the experiment. Adapting bars that are narrow compared to the adapting subregions (circles in Figure 7B) should produce near-identical gain changes in each subregion since the total adapting pattern will vary little between subregions. In this case, the ganglion cell should respond similarly to probes at the adapted and unadapted locations, indicating complete or near-complete transfer of gain changes. Adapting bars that are wide compared to the size of the adapting subregions should produce variable changes in gain across subregions; in this case, the ganglion cell should respond more strongly at the unadapted location, indicating incomplete transfer of gain changes.

Figure 8A shows results from one such experiment. Gain changes at the adapted and unadapted location were measured by dividing responses to probes during the adaptation phase (gray traces) by those during the baseline phase (black traces). Adaptation transfer was defined as the gain change at the unadapted location divided by the gain change at the adapted location. For the cell in Figure 8A, the narrow bars produced considerably greater adaptation transfer than the wide bars.

Figure 8

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Figure 8B collects results across bar sizes and cells. Gain changes transferred completely or near completely for bar widths up to 50 µm. Near-complete adaptation transfer at this bar width requires that the receptive field of the adapting mechanism have a diameter of at least 100 µm—so that the mechanism always samples both the bright and dark bars (see Figure 7B). A receptive field of this size would contain at least 500 rods given the rod density of ∼0.1/µm² (Osterberg, 1935). Bar widths of 100 µm and larger produced incomplete adaptation transfer, proving an upper bound on the extent of spatial integration.

The experiments of Figures 7 and 8 indicate that gain control is mediated by a mechanism that has access to signals from hundreds of rods. This degree of spatial pooling is required to support the rapid kinetics described in Figure 5 and is present only downstream of the synapse between rod bipolar cells and AII amacrine cells (Figure 1).

To further constrain the possible sites of gain control, we looked for transfer of gain changes from rod- to cone-mediated signals (Figure 9). The rod bipolar pathway shares the cone bipolar cell and its synapse onto the ganglion cell with the pathways that convey signals transduced in cones to the ganglion cells (Figure 1A). Transfer of gain changes from the rod bipolar pathway to the cone pathway would indicate that gain is controlled in a circuit element shared between the two pathways—most likely the cone bipolar cell itself. Failure of gain changes to transfer would indicate that the mechanism is located at a circuit element providing input only to the rod bipolar pathway.

Figure 9

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The spectral separation of the photopigments in rods and long-wavelength (L) cones and the considerably higher gain of rod-mediated signals allowed separation of rod- and cone-mediated inputs to a ganglion cell (Figure 9A; Dunn et al., 2007). Long-wavelength light stimuli produced a rapid L-cone–mediated response superimposed on a slower rod-mediated response (purple trace in Figure 9A). This reflects the ∼600-fold greater sensitivity of the L-cones compared to the rods for long wavelength light and a roughly equal compensating factor for the higher gain of rod-mediated signals. Stimulation with dim short-wavelength light (<0.1 R*/rod and <0.03 R*/cone) generated a nearly pure rod-mediated response (blue trace in Figure 9A). Appropriate scaling of the strengths of the two flashes produced matched rod responses to long- and short-wavelength stimuli. Subtracting the rod-mediated response from the mixed response isolated the cone-mediated response (red trace in Figure 9A).

We separated rod- and cone-mediated responses as in Figure 9A across a range of dim backgrounds (Figure 9B,C). Backgrounds that produced substantial reductions in gain of the rod-mediated signals failed to reduce the gain of the cone-mediated signals (Figure 9B–E). Thus, gain changes do not transfer from the rod pathway to the cone pathway, indicating that gain is controlled at a site prior to mixing of rod and cone signals in the cone bipolar cell. The lack of transfer from rod to cone pathways, together with the requirement that the gain control mechanism have access to signals from hundreds of rods (Figure 8), makes the AII amacrine cell and/or its gap junction with On cone bipolar cells likely sites.

How do the properties of gain controls at low backgrounds in primate retina relate to human behavioral threshold verses intensity (TVI) measurements in humans? The region of the TVI curve in which threshold is unaffected by background light has long been associated with the intrinsic noise of the visual system (Fechner, 1860; Barlow, 1956). Threshold is increased only by backgrounds that produce a sufficient rate of photon absorption to exceed intrinsic noise. Human behavioral threshold begins to increase for backgrounds near 0.01 R*/rod/s, similar to the backgrounds (∼0.02 R*/rod/s) at which primate ganglion cell thresholds began to increase. Both of these are considerably higher than the rate at which spontaneous activation of rhodopsin generates photon-like noise events in primate rods (0.003–0.004 R*/rod/s) (GD Field and F Rieke, unpublished). They are, however, consistent with measures of the total noise (i.e., both discrete and continuous) generated by macaque rods (Schneeweis and Schnapf, 2000).

The Rose–deVries region of the TVI curve has long been assumed to reflect an increase in noise without a reduction in gain (Barlow, 1957). Consistent with this view, the gain of retinal signals measured via electroretinograms begins to decline only at backgrounds ∼fivefold higher than those that increase behavioral threshold (Frishman et al., 1996). Several other previous experiments, however, suggest that gain is reduced in the Rose–deVries range. First, behavioral brightness matching experiments, which should be sensitive to changes in neural gain but not noise, show a robust Rose–deVries region (Brown and Rudd, 1998). Second, the spike responses of toad ganglion cells exhibit an ∼10-fold range of backgrounds over which the threshold required to reach a criterion spike rate increases in proportion to the square root of the background (Donner et al., 1990). Experiments in cat (Barlow and Levick, 1969; Enroth-Cugell and Shapley, 1973) and mouse (Dunn et al., 2006) also find adaptation at dim backgrounds, but with an exponent >0.5.

Our measurements of how gain control mechanisms affect both the signal and noise of the responses of On parasol ganglion cells provide a direct comparison to human psychophysics. The gain of signals in the rod pathway indeed decreased at low backgrounds, and noise increased much more slowly with increasing background than expected from Poisson fluctuations in photon absorption. The region of the ganglion cell TVI curve with slope 0.5 was limited to a narrow range of backgrounds. This suggests that post-retinal mechanisms contribute substantially to the more extended Rose–deVries region measured in behavioral studies.

Our results place a number of constraints on the neural gain control mechanism that is engaged at the lowest backgrounds—for example, in starlight. The mechanism estimates the mean photon flux rather than its variance (Figure 4), it is rapid (Figure 5), it has access to signals from hundreds of rods (Figure 8), and it acts on rod-mediated but not cone-mediated signals (Figure 9). Previously described gain control mechanisms are sensitive to variance (reviewed by Demb, 2008), act at locations with insufficient rod convergence (Dunn et al., 2006; Dunn and Rieke, 2008), or affect cone signals (Dunn et al., 2007). The constraints above suggest a novel mechanism located in the AII amacrine cell or the synaptic connections it makes with cone bipolar cells (Figure 5). Recordings from these cells as well as the On cone bipolar cells to which they make gap junctions could uncover more mechanistic details.

Although we focused on gain changes in the inputs to On parasol ganglion cells, a location of the site of adaptation in the rod bipolar pathway indicates that it should be shared across ganglion cell types. Consistent with this prediction, On midget ganglion cells adapted very similarly to On parasol ganglion cells (data not shown).

The mechanism we identify here adds to a long list of gain controls in the retinal circuitry. Considering luminance alone, retinal ganglion cells encode stimuli over 10 log units of background, far exceeding the dynamic range of any single mechanism. In the rod pathway, there are at least three gain control mechanisms engaged across backgrounds, each matched to the rod convergence at the adapting location. Backgrounds producing approximately 10–20 R*/rod/s halve the gain of the phototransduction cascade in primate rods (Schneeweis and Schnapf, 2000). Backgrounds producing ∼0.4 R*/rod/s halve the gain of the rod bipolar to AII synapse by reducing the number of releasable vesicles (Dunn et al., 2006; Dunn and Rieke, 2008; Oesch and Diamond, 2011). And, as shown here, backgrounds ∼0.08 R*/rod/s engage a mechanism located downstream of the rod bipolar–AII synapse; the light levels at which this mechanism is engaged are consistent with backgrounds that are just detectable given the total noise generated by macaque rods (Schneeweis and Schnapf, 2000). Impressively, these mechanisms act in concert to create a smooth dependence of gain on background in the ganglion cell (e.g., Figure 3A), even extending to backgrounds at which signaling begins to switch from rods to cones and gain control mechanisms in the cone pathway become active (Dunn et al., 2007). At least five separate gain control mechanisms that contribute to a single smooth function relating background to gain over >5 log units on each axis (Figure 3A) suggest that this particular functional form for adaptation was a target of selective pressure in primate evolution.

Adapting at low backgrounds is inherently dangerous as statistical fluctuations in photon absorption introduce substantial noise into the neural signals accessible to a gain control mechanism; such noise would be expected to cause gain to vary widely. The impact of noise in the signals controlling gain could be mitigated by not adapting until backgrounds increase enough to make more photons available, or by integrating over time and/or rods to reduce noise. Surprisingly, retinal gain controls appear to operate at the lowest backgrounds physically possible—that is, each absorbed photon within the pool of rods providing input to an adaptational mechanism lowers gain.

Adaptation at the rod bipolar to AII synapse approaches the sensitivity limit imposed by convergence and integration time (Dunn and Rieke, 2008; see Figure 1B). That is, a single absorbed photon reduces the gain of the next single photon response. Rod convergence onto AII amacrine cells is not known precisely in primate, but the onset of adaptation is consistent with a single photon absorption in the AII receptive field reducing gain. Assuming a 0.1 s integration time (Figure 5), a mechanism operating on a pool of 200 rods would have to reduce gain by 40% for each photon absorbed for the gain to be halved at 0.08 R*/rod/s; a pool of 800 rods could achieve this level of gain control with a 11% gain reduction per photon (see ‘Modeling’).

Vision in the dark requires high gain of the retinal circuitry conveying rod-mediated signals to ganglion cells. This high gain could easily lead to saturation of retinal signals as backgrounds increase. Indeed, the onset of retinal gain control coincides with the dimmest detectable backgrounds given the intrinsic noise of the rods. These considerations help explain why retinal gain controls are engaged by each absorbed photon, even when adaptation under these conditions is necessarily noisy.

All recordings were from On parasol ganglion cells in peripheral (eccentricity typically >30°; ∼15° to 20° for the experiments of Figure 9) primate retina (Macaca nemestrina, fascicularis, and mulatta). Retina was obtained through the Tissue Distribution Program of the Regional Primate Center at the University of Washington. The retina was dark adapted for 1 hr while attached to the pigment epithelium and stored for up to 24 hr in a light-tight container at 32°C in Ames solution equilibrated with 95% O₂/5% CO₂. All subsequent procedures were performed under infrared light (>900 nm) using infrared-visible converters.

For recording, a roughly 4 × 4-mm piece of retina was removed from the pigment epithelium and mounted photoreceptor side down on a polylysine-coated glass coverslip forming the bottom of the recording chamber. The retina was secured by nylon wires stretched across a platinum ring. The retina was continuously superfused (8–10 ml/min) with warmed (32–34°C) Ames solution equilibrated with 95% O₂/5% CO₂. Calibrated light stimuli were delivered from LEDs focused on the retina by the microscope condenser. Spatial stimuli for Figures 7 and 8 were delivered using an OLED array (eMagin, Bellevue, WA). Stimulus intensities are given in terms of isomerizations per rod per second (R*/rod/s), based on the measured LED spectral output, the rod spectral sensitivity, and an assumed collecting area of 1 μm².

Spike responses were measured in the cell-attached configuration using pipettes filled with Ames solution. Whole-cell voltage clamp recordings were made using patch pipettes filled with 105 mM CsCH₃SO₃, 10 mM TEA-Cl, 20 mM HEPES, 10 mM EGTA, 5 mM Mg-ATP, 0.5 mM Tris-GTP, and 2 mM QX-314 (pH ∼7.3 with CsOH, ∼280 mOsm). Reported holding voltages have been corrected for the ∼10 mV junction potential associated with this internal solution. Series resistance was typically 6–10 MΩ, and was compensated 50%.

All data came from parasol ganglion cells exhibiting high sensitivity when fully dark adapted. Recordings followed previous procedures (Trong and Rieke, 2008). We first used cell-attached recordings to test the spike response to a brief flash producing 0.001–0.002 R*/rod, and collected data only from cells that responded to these flashes with an average of 4–5 spikes. During experiments monitoring adaptation across a range of light levels (e.g., Figures 2, 3 and 9), we periodically returned to a ‘reference’ background near 0.05 R*/rod/s to check for slow changes in sensitivity. Figures 10 and 11 illustrate the basic timeline of such experiments for cell-attached recordings of spike responses (Figures 10) and whole-cell recordings of excitatory synaptic inputs (Figures 11). Figures 10B and 11B show the changes in flash strength (gray line and right axes) used to generate near-equal responses across backgrounds. The figures also illustrate, based on raw data, some of the key features quantified in the ‘Results’: (1) the sensitivity of gain to weak backgrounds (Figures 10A–C and 11A–C); (2) the rapid changes in gain following changes in background (Figure 10C and 11C); (3) the slow changes in baseline firing rate (Figure 10D) and excitatory synaptic input (Figure 11D) following changes in background; and (4) the changes in noise following changes in background (Figure 11E).

Figure 10

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Figure 11

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A time window containing the flash response was chosen for each background and flash intensity by selecting the time points at which the average response exceeded 20% of its maximal value. The response amplitude was computed as the integrated current during this time window minus a baseline current recorded before the flash. Using a fixed time window across backgrounds and flash strengths yielded similar results. Gain values in Figures 2, 3, 10, and 11 and Figure 5—figure supplement 1 are the response amplitude divided by the flash strength.

We projected flash responses along a template to compute flash detection thresholds (Figures 2 and 3). The template was the average current trace in the time window described above. For each trial, we defined the signal γ as the projection of the measured current along the template divided by the flash strength, and the noise ν as the projection of the current during a time window before the flash. Detection threshold θ was defined as the flash strength required to give a signal-to-noise ratio of 1 according to the following equation:

Gain and threshold of spike responses were computed analogously using the peristimulus time histogram to define the response time window for spike counts (Figure 2).

Probabilities of photon absorptions depending on background, integration time, and rod convergence (Figure 6) were computed from a Poisson distribution as follows. For a given background (μ) in units of R*/rod/s, an integration time (τ), and a rod convergence (C) per neural element, the probability of a neural element collecting a particular number (k) of photons follows Poisson statistics.

Figure 6 plots the combination of values of μ, τ, and C required for half of the neural elements to collect at least one photon.

In the ‘Discussion’, we compute the gain reduction achieved for several size pools of converging rods. If each photon (k) collected by a neural element reduces the gain for the next photon response by a constant factor (α), the gain as a function of k and α can be computed as follows.

Therefore, the gain of a collection of neural elements (Γ) collecting photons according to Poisson statistics (normalized to Γ = 1 for maximal gain) is computed as follows.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

We thank Petri Ala-Laurila, Juan Angueyra, Jeff Diamond, and Michael Rudd for helpful comments, and Mark Cafaro and Paul Newman for technical assistance.

Animal experimentation: Primate (Macaca fascicularis, fascicularis and mulatta) retinas were obtained through the Tissue Distribution Program of the Regional Primate Research Center at the University of Washington. All procedures were approved by the institutional animal care and use committee (protocol 4140-01).

© 2013, Schwartz and Rieke

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