< Back to Article

Dynamical Adaptation in Photoreceptors

Figure 6

Analyses of salamander cone data with a Linear-Non-linear (LN) model and with the DA model.

(A) A white-noise flickering light stimulus (top) is presented to a salamander cone while its membrane potential (bottom) is measured. (B) Enlarged cone response trace and comparison of the experimental curve, the LN model prediction, and the DA model prediction. The LN model prediction deviates from the recorded trace with a RMS residual of 0.277 (in units of response s.d., or 0.533 mV); equivalently, a value of 0.927. The DA model has a RMS residual of 0.243 (in units of response s.d., or 0.468 mV); equivalently, a value of 0.943. The DA model follows the experimental output more closely, especially at peaks and troughs where discrepancies with the LN model are most prominent (signaled by black triangles). (C) Schematic illustration of the LN model. The stimulus is convolved with a best-fit linear filter, obtained by reverse correlation of the response to the stimulus. A static, non-linear function is then evaluated, with the output of the convolution as its argument, to produce the predicted response. (D–F) Scatter plots of the experimental cone response against the model predictions. In (D), the cone outut is compared to a linear prediction (denoted in panel C). The LN non-linearity is read off from this plot. In (E), the cone output is compared to the full LN model prediction. In (F), the cone output is compared to the DA model prediction. Low intensity (green) and high intensity (red) points are highlighted as those for which the preceding 300 ms of stimulus is in the brightest and dimmest 10%, respectively. The slope obtained from all points taken together is 1 (black line), and tick marks are 1 s. d. For the linear prediction, the slopes of the two subsets of points are 1.36 (green line, low light) and 0.76 (orange line, bright light). For the LN predictions, the slopes of the green and orange lines are 1.18 and 0.87, respectively. These differences are statistically significant (0.01, see Methods). For the DA predictions, the slopes of the green and orange lines are 0.98 and 0.94, respectively. This discrepancy is not statistically significant (0.1, see Methods). Thus, the DA model prediction replicates the experimental output more precisely than the LN model prediction. Overall values in the three cases (D), (E), and (F) are 0.918, 0.927, and 0.943, respectively; thus, the LN non-linearity accounts for 11% of the missing variance, while the DA model accounts for 30% of the missing variance. (G) Plot of the instantaneous gain as a function of the average light intensity in the preceding 300 ms. The instantaneous gain was calculated, at each time, as the slope of the linear fit in an experimental response-versus-linear prediction scatter plot. (H) Variation of the response time scale as a function of the preceding light intensity. Instantaneous gain values along the time trace were split into ten percentile groups and, for each group, the time of maximum cross-correlation between input and experimental response was calculated (see Methods). The resulting value is plotted against the instantaneous gain value of the percentile. The slope of the best linear fit is 9.6±3.6 ms. (I) Variation of the shape and, specifically, time scale of the instantaneous best linear filter as a function of the preceding light intensity. Three linear filters, computed for the highest, middle, and lowest 10% of instantaneous gain values, are plotted. The data show that both the gain and time scale vary dynamically with light intensity.

doi: https://doi.org/10.1371/journal.pcbi.1003289.g006