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Dynamical Adaptation in Photoreceptors

Figure 12

Illustration of the non-linear transformation of fluctuating inputs.

(A) A concave functional form, as that of the gain prefactor in the flash response (Eq. (49)), increases the mean in the transformation. That is, downward fluctuations in contribute more to increasing than upward fluctuations to decreasing it. Therefore, . The flash response gain in the presence of a fluctuating background is thus larger than that in the presence of a constant, mean-matched background. (B) A convex functional form decreases the mean in the transformation, so that . Depending upon the strength of the background, , and the relative structure of the two kernels, and , the mean response to a fluctuating input may be either suppressed or enhanced compared to the flicker-free case. The DA model (see, e. g., Eq. (55)) takes on the convex form shown here as in the case with (and ), thus decreasing the mean response relative to that in the presence of a constant input. In the case in which and differ in their timing, the functional form becomes concave as in (A) and the mean response to a fluctuating input is enhanced. The modulation of the mean response therefore depends sensitively upon stimulus and kernels parameters.

doi: https://doi.org/10.1371/journal.pcbi.1003289.g012