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.
Multiple Steps of Phosphorylation of Activated Rhodopsin Can Account for the Reproducibility of Vertebrate Rod Single-photon Responses
Abbreviations used in this paper: Arr, arrestin; PDE, phosphodiesterase; RK, rhodopsin kinase; SPR, single-photon response.
The choice to place all the phosphorylation dependence in the first of the RK reactions (kRK1, Eqs. 2a and 6) was made for computational simplicity. It is possible that other phosphorylation rate constants in Eqs.
Thus, in our formulation, activated G-protein cannot be inactivated unless it is bound to PDE.
Heck and Hofmann (2001) reported a higher rate (∼600 G*/s per R*) in bovine tissue. Their value was an extrapolated maximal rate under optimized conditions in vitro, with a high density of G-protein, a high concentration of GTP, and a low concentration of GDP. Arshavsky et al. (2002) have argued that, with reasonable assumptions about cellular conditions, the rate calculated from the results of Heck and Hofmann (2001) would correspond to around 220 G*/s per R* in amphibian rods in vivo, close to the value of Leskov et al. (2000) that we adopted for the simulations. In additional simulations (unpublished data), we found that changing the rate of G* activation from 150 to 600 G*/s/R* had no effect on the four measures of reproducibility, and only reduced the fine-structure of noise in the rising phase of the response by a modest amount.
The mechanisms underlying the slow R* inactivation under CSM, RK−/−, and Arr−/− are not known. For Arr−/−, the slow recovery may reflect thermal inactivation of R* (Ebrey, 1968; Cone and Cobbs, 1969; Xu et al., 1997). The recovery in CSM and RK−/− is much faster than expected for thermal R* inactivation, but is still very slow compared to the rate-limiting time constant of inactivation of WT mouse rods (∼200 ms; e.g., Chen et al., 2000). Mendez et al. (2000) hypothesized that some form of slow Arr-binding that is able proceed in the absence of six phosphorylation sites on the carboxy terminus might be shutting off R* in the CSM rods. If so, perhaps the same mechanism is operating in the RK−/− rods. In our simulations, we did not build in alternate pathways of R* inactivation (although this is certainly feasible for future research). In our model, without phosphorylation, R* activity plateaus at a fixed level. In the absence of Arr binding, R* activity can still be ratcheted down by phosphorylation, but will never shut off completely. See Fig. 5.
As noted by Felber et al. (1996), the distribution of R* lifetimes will not be exactly exponential when the inactivation reaction is competitive with other species. In this case, RK and G-protein compete, with the G-bound states of R* representing timeouts from the inactivation reaction. In practice, for the parameters we used, the distribution of R* lifetimes was indistinguishable from exponential. However, in order to acknowledge the theoretical influence of the competitive nature of the reaction with R*, we will refer to the distributions as approximately exponential, and to the theoretical CVs as ∼1.
R.D. Hamer, S.C. Nicholas, D. Tranchina, P.A. Liebman, T.D. Lamb; Multiple Steps of Phosphorylation of Activated Rhodopsin Can Account for the Reproducibility of Vertebrate Rod Single-photon Responses . J Gen Physiol 1 October 2003; 122 (4): 419–444. doi: https://doi.org/10.1085/jgp.200308832
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