Computational analysis of vertebrate phototransduction: Combined quantitative and qualitative modeling of dark- and light-adapted responses in amphibian rods

Abstract

We evaluated the generality of two models of vertebrate phototransduction. The approach was to quantitatively optimize each model to the full waveform of high-quality, dark-adapted (DA), salamander rod flash responses. With the optimal parameters, each model was then used to account for signature, qualitative features of rod responses from three experimental paradigms (stimulus/response, “S/R suite”): (1) step responses; (2) the intensity dependence of the period of photocurrent saturation (T_satvs. ln(I)); and (3) light-adapted (LA) incremental flash sensitivity as a function of background intensity. The first model was the recent successful model of Nikonov et al. (1998). The second model replaced the instantaneous Ca²⁺ buffering used in the Nikonov et al. model with a dynamic buffer. The results showed that, in the absence of the dynamic Ca²⁺ buffer, the Nikonov et al. model does not have sufficient flexibility to provide a good fit to the flash responses, and, using the same parameters, reproduce the salient features of the S/R suite—critical features at step onset and offset are absent; the T_sat function has too shallow a slope; and the model cannot generate the empirically observed I-range of Weber–Fechner LA behavior. Some features could be recovered by changing parameters, but only at the expense of the fit to the reference (Ref) data. When the dynamic buffer is added, the model is able to achieve an acceptable fit to the Ref data while reproducing several features of the S/R suite, including an empirically observed T_sat function, and an extended range of LA flash sensitivity adhering to Weber's law. The overall improved behavior of the model with a dynamic Ca²⁺ buffer indicates that it is an important mechanism to include in a working model of phototransduction, and that, despite the slow kinetics of amphibian rods, Ca²⁺ buffering should not be simulated as an instantaneous process. However, neither model was able to capture all the features with the same parameters yielding the optimal fit to the Ref data. In addition, neither model could maintain a good fit to the Ref data when five key biochemical parameters were held at their current known values. Moreover, even after optimization, a number of important parameters remained outside their empirical estimates. We conclude that other mechanisms will need to be added, including additional Ca²⁺-feedback mechanisms. The present research illustrates the importance of a hybrid qualitative/quantitative approach to model development, and the limitations of modeling restricted sets of data.