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Dynamical Adaptation in Photoreceptors

Figure 11

Behavior of DA model responses in the presence of Gaussian fluctuating inputs. All calculations in this figure use parameter set B.

(A) Top: A sample Gaussian input with correlation time of 200 ms. Middle: Model responses for three different contrasts of the fluctuating input. The mean input intensity is given by . Bottom: After normalization of the response by the input's standard deviation, one can see signatures of the model's non-linearity as the curves do not collapse unto a single curve. (B) Mean response of a model photoreceptor presented with Gaussian flickers with three different contrasts: analytical and numerical results. Larger contrasts yield less hyperpolarized responses, on average. Black dots: numerical result; red curve: analytical result. (C) Mean flash responses of a model photoreceptor in the presence of Gaussian flickering backgrounds with different variances. Top: Average flash responses were calculated numerically by running simulations with two different stimuli: one with Gaussian flicker only, the other with Gaussian flicker and superimposed flashes. The average flash response was obtained as the difference between the two outcomes, averaged over flicker instantiations. Bottom: The fractional difference between flash responses in the presence of Gaussian flicker with three different contrasts. Solid lines: numerical result (±1 SEM error bars); dotted lines: analytical result. (D) Fractional change in average flash response as a function of flicker correlation time. From Eqs. (44, 45, 46), the magnitude of the average flash response depends upon the correlation time of the random flicker. Black dots: numerical result; red curve: analytical result. (E) Responses of a model photoreceptor in the presence of flicker with time-varying contrast. We fed the DA model Gaussian flicker with standard deviation alternating between 35% and 5%, with a 1 second period (top). Average flash responses were calculated at different times during the period (middle), as was done in (C). Sample average flash responses are displayed in the inset panel, while the main panel shows the variation of the flash response amplitude across one period. Black curve: numerical result (±1 SEM error bars); red curve: analytical result. The average response (bottom) was also calculated numerically (black, ±1 SEM) and analytically (red). Note the overshoots of the average response following contrast switches (see the text for an explanation).

doi: https://doi.org/10.1371/journal.pcbi.1003289.g011