Symmetry Breakdown in the ON and OFF Pathways of the Retina at Night: Functional Implications

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.

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).

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).

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).

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).

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).