Multiple Steps of Phosphorylation of Activated Rhodopsin Can Account for the Reproducibility of Vertebrate Rod Single-photon Responses

Abstract

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.

Toward a unified model of vertebrate rod phototransduction

“…In the absence of other variability reducing mechanisms, this highly variable R* lifetime would perforce be reflected, to one degree or another, in the variability of the SPR amplitude and/or kinetics. Yet, empirically, rod single-photon responses are substantially less variable than predicted from a pure single-step inactivation mechanism (Baylor et al, 1979;Schnapf, 1983;Schneeweis & Schnapf, 1995;Rieke & Baylor, 1998a,b;Whitlock & Lamb, 1999;Field & Rieke, 2002;Hamer et al, 2003). Thus, the relative reproducibility of singlephoton responses, despite the inherent variability of the underlying individual biochemical reactions, must place strong constraints on any model of phototransduction.…”

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AbstractRecently, 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).

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“…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.…”

“…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.…”

A neurociência computacional no estudo dos processos cognitivos

“…In this sense, computational neuroscience can help understanding the visual system at all three levels of Marr, by presenting models that contribute to the comprehension of visual measurement. For example, many studies use computational models to understand the absorption of photons by photoreceptors at very low light levels (Hamer, Nicholas, Tranchina, Liebman, & Lamb, 2003;Lamb & Pugh, 2006;Lyubarsky & Pugh, 1996), or to analyze the integration of these absorptions by post-receptoral neurons (Berntson, Smith, & Taylor, 2004;Lipin, Smith, & Taylor, 2010).…”