Single-photon responses (SPRs) in vertebrate rods are considerably less variable than expected if isomerized rhodopsin (R*) inactivated in a single, memoryless step, and no other variability-reducing mechanisms were available. We present a new stochastic model, the core of which is the successive ratcheting down of R* activity, and a concomitant increase in the probability of quenching of R* by arrestin (Arr), with each phosphorylation of R* (Gibson, S.K., J.H. Parkes, and P.A. Liebman. 2000. Biochemistry. 39:5738–5749.). We evaluated the model by means of Monte-Carlo simulations of dim-flash responses, and compared the response statistics derived from them with those obtained from empirical dim-flash data (Whitlock, G.G., and T.D. Lamb. 1999. Neuron. 23:337–351.). The model accounts for four quantitative measures of SPR reproducibility. It also reproduces qualitative features of rod responses obtained with altered nucleotide levels, and thus contradicts the conclusion that such responses imply that phosphorylation cannot dominate R* inactivation (Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836–1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733–747.). Moreover, the model is able to reproduce the salient qualitative features of SPRs obtained from mouse rods that had been genetically modified with specific pathways of R* inactivation or Ca2+ feedback disabled. We present a theoretical analysis showing that the variability of the area under the SPR estimates the variability of integrated R* activity, and can provide a valid gauge of the number of R* inactivation steps. We show that there is a heretofore unappreciated tradeoff between variability of SPR amplitude and SPR duration that depends critically on the kinetics of inactivation of R* relative to the net kinetics of the downstream reactions in the cascade. Because of this dependence, neither the variability of SPR amplitude nor duration provides a reliable estimate of the underlying variability of integrated R* activity, and cannot be used to estimate the minimum number of R* inactivation steps. We conclude that multiple phosphorylation-dependent decrements in R* activity (with Arr-quench) can confer the observed reproducibility of rod SPRs; there is no compelling need to invoke a long series of non-phosphorylation dependent state changes in R* (as in Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836–1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733–747.). Our analyses, plus data and modeling of others (Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836–1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733–747.), also argue strongly against either feedback (including Ca2+-feedback) or depletion of any molecular species downstream to R* as the dominant cause of SPR reproducibility.

Recently, we introduced a phototransduction model that was able to account for the reproducibility of vertebrate rod single-photon responses (SPRs) (Hamer et al., 2003). The model was able to reproduce SPR statistics by means of stochastic activation and inactivation of rhodopsin (R*), transducin (G α ), and phosphodiesterase (PDE). The features needed to capture the SPR statistics were (1) multiple steps of R* inactivation by means of multiple phosphorylations (followed by arrestin capping) and (2) phosphorylation dependence of the affinity between R* and the three molecules competing to bind with R* (G α , arrestin, and rhodopsin kinase). The model was also able to account for several other rod response features in the dim-flash regime, including SPRs obtained from rods in which various elements of the cascade have been genetically disabled or disrupted. However, the model was not tested under high light-level conditions. We sought to evaluate the extent to which the multiple phosphorylation model could simultaneously account for single-photon response behavior, as well as responses to high light levels causing complete response saturation and/or significant light adaptation (LA). To date no single model, with one set of parameters, has been able to do this. Dim-flash responses and statistics were simulated using a hybrid stochastic/ deterministic model and Monte-Carlo methods as in Hamer et al. (2003). A dark-adapted flash series, and stimulus paradigms from the literature eliciting various degrees of light adaptation (LA), were simulated using a full differential equation version of the model that included the addition of Ca 2+ -feedback onto rhodopsin kinase via recoverin. With this model, using a single set of parameters, we attempted to account for (1) SPR waveforms and statistics (as in Hamer et al., 2003); (2) a full darkadapted flash-response series, from dim flash to saturating, bright flash levels, from a toad rod; (3) steady-state LA responses, including LA circulating current (as in Koutalos et al., 1995) and LA flash sensitivity measured in rods from four species; (4) step responses from newt rods (Forti et al., 1989) over a large dynamic range; (5) dynamic LA responses, such as the step-flash paradigm of Fain et al. (1989), and the two-flash paradigm of Murnick and Lamb (1996); and (6) the salient response features from four knockout rod preparations. The model was able to meet this stringent test, accounting for almost all the salient qualitative, and many quantitative features, of the responses across this broad array of stimulus conditions, including SPR reproducibility. The model promises to be useful in testing hypotheses regarding both normal and abnormal photoreceptor function, and is a good starting point for development of a full-range model of cone phototransduction. Informative limitations of the model are also discussed.

In order to account for the multi-phasic dynamics of photopigment regeneration in human rods, we developed a new model of the retinoid cycle. We first examined the relative roles of the classical and channeling mechanisms of metarhodopsin decay in establishing these dynamics. We showed that neither of these mechanisms alone, nor a linear combination of the two, can adequately account for the dynamics of rhodopsin regeneration at all bleach levels. Our new model adds novel inhibitory interactions in the cycle of regeneration of rhodopsin that are consistent with the 3D structure of rhodopsin. Our analyses show that the dynamics of human rod photopigment regeneration can be accounted for by end-product regulation of the channeling mechanism where all-trans retinal (tral) inhibits the binding of 11-cis retinal to the opsin.tral complex.

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