Phototransduction in rods: A theoretical analysis of inactivation kinetics, saturation and noise

Purpose. The time course of recovery of rod photocurrent from a saturating flash and noise in the single-photon response are intimately related. A single model should account for both. In the case of lower vertebrate rods, a plot of the recovery function which gives the time required for the in ward photocurrent, to increase by a criterion amount from saturation at zero as a function of the number of photoisomerizations, is well described by a single straight line on linear vs. log coordinates. One interpretation, that the random lifetime of a single activated rhodopsin (R*) is exponentially distributed, leads to a well-known theoretical problem. If the time course of activated phosphodiesterase (PDE*) were controlled by that of R*., predicted single-photon responses would be too noisy. If, instead, the time course of PDE* were uncoupled from that of R*, responses would not be noisy enough. Methods. We explored a model for R* in which complete inactivation requires multiple phosphorylation steps and a final "capping" reaction. This scheme was coupled to a phototransduction model which extends the model of Lamb and Pugh to include inactivation reactions and feedback control of guanylate cyclase activity by Ca²⁺ Results. One choice of parameters gives computed single-photon responses, noise and recovery function like those reported for lower vertebrates. Another gives single-photon responses and noise like those reported for primate rods; it also gives a recovery function with two branches like that inferred from human ERG recordings. Mathematical analysis shows why this behavior obtains. Conclusions. A single model for transduction accounts for characteristics of rod responses to single photons and to super-saturating flashes.