Response and dynamical adaptation with respect to natural fluctuating inputs—DA model fit and predictions.

<p>(A) <i>Top</i>: Sample of a light intensity trace, from the natural time series in Ref. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003289#pcbi.1003289-vanHateren4" target="_blank">[50]</a>. <i>Bottom</i>: The corresponding DA model response trace (red), superimposed upon goldfish cone recording (black) from Ref. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003289#pcbi.1003289-Endeman1" target="_blank">[49]</a>. The agreement between the two traces is quantified by an values of 0.934. The parameters , , and were fitted to the data; otherwise parameters from set B were used (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003289#pcbi-1003289-t002" target="_blank">Table 2</a>).(B) <i>Top</i>: Different clip from the same light intensity trace as in (A), from the natural time series in Ref. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003289#pcbi.1003289-vanHateren4" target="_blank">[50]</a>. <i>Bottom</i>: The corresponding model response trace. (C) DA model predictions of responses to small (100-photon) flashes superimposed on the fluctuating natural light intensity. The flash is presented at time . Thin pink curves represent individual flash responses, while the thick red curve is the average over all such responses. The weakest (1st percentile) and strongest (99th percentile) peak responses are measured as −0.0238 mV and −0.5524 mV, respectively, <i>i. e.</i>, they differ by a factor greater than 20. The dotted thick red curve is the flash response in the presence of a constant background matched to the mean of the fluctuating input. The dotted red curve peaks at 0.081 mV, while the solid red curve peaks at 0.135 mV. Thus, individual flash responses vary greatly as a function of background history, and their mean is offset with respect to the constant-background case. (D) Response to a fluctuating input with time-varying contrast. <i>Top</i>: Superimposition of several input traces. The standard deviation of the flicker switches, suddenly and periodically, from its natural value to zero, with a period of 2 s, while its mean remains constant. <i>Bottom</i>: Trace of the mean DA model response to the time-varying flicker. (The thick red line represents an average over multiple natural stimuli. The pink area represents the standard error of this average.) Each switch is signaled by an over- or under-shoot in the mean response, depending upon the direction of the switch. The ‘steady-state’ mean response is greater (more hyperpolarized) in the constant-background half-period than in the fluctuating-background half-period. Parameter set B was used for all theory curves in (B), (C), and (D) (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003289#pcbi-1003289-t002" target="_blank">Table 2</a>).