Symmetry breakdown in the ON and OFF pathways of the retina at night: functional implications

Abstract

Several recent studies have shown that the ON and OFF channels of the visual system are not simple mirror images of each other, that their response characteristics are asymmetric (Chichilnisky and Kalmar, 2002; Sagdullaev and McCall, 2005). How the asymmetries bear on visual processing is not well understood. Here, we show that ON and OFF ganglion cells show a strong asymmetry in their temporal adaptation to photopic (day) and scotopic (night) conditions and that the asymmetry confers a functional advantage. Under photopic conditions, the ON and OFF ganglion cells show similar temporal characteristics. Under scotopic conditions, the two cell classes diverge-ON cells shift their tuning to low temporal frequencies, whereas OFF cells continue to respond to high. This difference in processing corresponds to an asymmetry in the natural world, one produced by the Poisson nature of photon capture and persists over a broad range of light levels. This work characterizes a previously unknown divergence in the ON and OFF pathways and its utility to visual processing. Furthermore, the results have implications for downstream circuitry and thus offer new constraints for models of downstream processing, since ganglion cells serve as building blocks for circuits in higher brain areas. For example, if simple cells in visual cortex rely on complementary interactions between the two pathways, such as push-pull interactions (Alonso et al., 2001; Hirsch, 2003), their receptive fields may be radically different under scotopic conditions, when the ON and OFF pathways are out of sync.

Figure 1.

ON and OFF cells show similar temporal frequency tuning in response to sine wave gratings under photopic conditions. A, Representative responses for four ON and four OFF ganglion cells to drifting sine wave gratings of increasing temporal frequency. Each segment of the traces shows the average firing rate over one period of the drifting grating for a given frequency. B, Average tuning curves (mean ± SEM) for all ON and OFF cells, normalized to the peak (n = 20 ON cells, 31 OFF cells). Temporal tuning curves were calculated by Fourier analyzing the responses and extracting the amplitude of the first harmonic response at each frequency. ON and OFF cells respond to a similar range of temporal frequencies (p > 0.05, Student's t test, comparing the mean center of mass of the ON cell tuning curves with that of the OFF cells).

Figure 2.

Frequency tuning of ON and OFF cells diverges under scotopic conditions. A, Representative responses of four ON and four OFF ganglion cells to drifting sine wave gratings of increasing temporal frequency. B, Average tuning curves (mean ± SEM) for all ON and OFF cells, normalized to the peak (n = 20 ON cells, 31 OFF cells). On average, the ON cells shifted to low frequencies, whereas the OFF cells continued to respond to high frequencies (p < 10⁻³, Student's t test, comparing the mean center of mass of the two populations). Note that, under scotopic conditions, both ON and OFF cells fail to respond to the extreme high frequencies.

Figure 3.

ON and OFF cells show similar temporal response properties to white noise under photopic conditions. A, Representative STA time courses for four ON and four OFF ganglion cells in response to a white noise (random checkerboard) stimulus. Note that OFF STAs are inverted so that the similarity of the short peaks is easy to observe. B, Average temporal frequency responses (mean ± SEM) for all ON and OFF cells (n = 20 ON cells, n = 31 OFF cells), normalized to the peak. Temporal frequency responses were calculated by Fourier analyzing the STA at the checkerboard square that produced the largest response for each cell. ON and OFF cells showed similar temporal response profiles (p > 0.05, Student's t test, comparing the mean center of mass of ON cell temporal frequency responses with that of the OFF cells).

Figure 4.

The divergence under scotopic conditions was also observed for the white noise stimulus. A, Representative STA time courses for four ON and four OFF ganglion cells in response to a white noise (random checkerboard) stimulus. B, Average temporal frequency responses (mean ± SEM), normalized to the peak (n = 20 ON cells, n = 31 OFF cells). As with the grating stimulus, the ON cells shifted to low frequencies, whereas the OFF cells continued to respond to high frequencies (p < 10⁻³, Student's t test, comparing the mean center of mass the two populations).

Figure 5.

Under photopic conditions, it is possible to decode across the entire range of temporal frequencies using responses of ON or OFF cells. A, Representative confusion matrices for 16 ON and 16 OFF cells calculated using responses to drifting gratings. The vertical axis gives the presented stimulus (i), and the horizontal axis gives the decoded stimulus (j). Each element of a confusion matrix plots the probability of decoding stimulus j when presented with stimulus i (see text). Decoders based on both ON and OFF responses show little confusion over the range of temporal frequencies, as indicated by the prominent diagonal lines in the confusion matrices. B, Average confusion matrices over all ON and OFF cells (n = 20 ON cells; n = 31 OFF cells). C, The average of the diagonals of the matrices (mean ± SEM) for all ON (red) and OFF (blue) cells (n = 20 ON cells; n = 31 OFF cells). ON and OFF cells perform equally well over the full range of temporal frequencies (p > 0.1 for all frequencies, Student's t test, adjusted for multiple comparisons).

Figure 6.

Under scotopic conditions, there is a divergence in performance—ON cells perform better at low frequencies, whereas OFF cells perform better at high. A, Representative confusion matrices calculated using the responses of 16 ON and 16 OFF cells to drifting gratings. ON cells show better performance at low frequencies, as indicated by the bright squares along the diagonal at low frequencies, which break down at middle and high frequencies. In contrast, for OFF cells, performance is shifted toward high frequencies. B, Average confusion matrices over all ON and OFF cells show the same trend (n = 20 ON cells; n = 31 OFF cells). C, The average of the diagonals of the matrices (mean ± SEM) for ON (red) and OFF (blue) populations (n = 20 ON cells; n = 31 OFF cells). ON cells perform significantly better at the lowest two frequencies tested (p < 0.01), whereas OFF cells perform significantly better at the highest frequency (p < 0.01, Student's t test, adjusted for multiple comparisons).

Figure 7.

At low light levels, increments become harder to discriminate than decrements of equal magnitude, because of asymmetries in the Poisson distribution. A, Distributions of photon counts are shown for increments (gray) and decrements (black) in steps of 10% contrast around a mean rate (dotted line). For increments, the distributions are broader and show much greater overlap than for decrements, making increments harder to detect. B, Performance for an ideal observer in the discrimination task for increments (gray) or decrements (black) over a range of mean photon counts. For each mean photon count, stimuli at steps of ±10% contrast around the mean are simulated (as in A), and the observer chooses stimuli based on the maximum a posteriori probability over the set of stimuli. Over a broad range of photon counts, performance is better for decrements than for increments. The arrows indicate separation between increment and decrement performance (i.e., the factor by which an increment detector needs to observe more photons to match the performance of the decrement detector). The dotted line indicates performance at chance. We note that this aspect of Poisson processes—that it is more difficult to detect increments than to detect decrements—might seem counterintuitive, since signal-to-noise ratio (SNR) increases with mean rate increases. But SNR is not the relevant statistic here. An increase in SNR means that it is easier to detect the same fractional change around a high mean rate than around a low mean rate. In our case, we are asking whether, given a constant mean rate (e.g., the rate under night conditions), it is easier to detect an increment or a decrement. Since the variability of a Poisson process is proportional to its rate, an increment leads to a more variable signal than a decrement and, therefore, is harder to detect. The suggestion in this paper, then, is that ON cells compensate for the higher variability by integrating their input over a longer period of time (i.e., by shifting toward low temporal frequencies).

Figure 8.

Decrements can be detected more readily than increments, and the asymmetry is an accelerating function of contrast. To compare intrinsic discriminability, we use the ratio of Kullback–Leibler distances between a baseline Poisson process, and one whose rate changes by a factor of (1 + c) or (1 − c). This ratio (Eq. 10) has a value of 1 for equal discriminability. Values >1 indicate that decrements are more readily discriminated.