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Figure 1.

Comparing the CVs of the total activated effectors at time with the CVs of the total relative charge up to time .

All simulations assume both the sojourn time and the number of shutoff steps as random (Case 3 of Test Cases). The CVs of both and stabilize asymptotically for three or more phosphorylation sites (3P–6P). A CV of about for at times past the peak time is reduced to a CV of about for the corresponding photocurrent . This points to an intrinsic variability reduction effect of the diffusion part of the process.

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Table 1.

Coefficients of variation, ms.

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Figure 2.

Simulations SPR for mutant phosphorylation sites of , or with Arr knockout.

Panel A: Simulated SPRs for rhodopsin with a number of available phosphorylation sites (thus sites are mutant); Panel B: Reproduction of data from [3] showing SPRs from mutant mice with different phosphorylation sites. CSM: completely substituted mutant (0P); STM: serine triple mutant (3P); S338A: mutant lacking S338 (5P); S343A: mutant lacking residue S343 (5P); S338/CSM: one site (S338) was restored in the CSM (1P); S334/S338/CSM: two sites (S334 and S338) were restored in the CSM (2P); Mutant rhodopsins bearing zero, one (S338), or two (S334/S338) phosphorylation sites generated single-photon responses with greatly prolonged durations. Responses from rods expressing mutant rhodopsins bearing more than two phosphorylation sites declined along smooth, reproducible time courses; the rate of recovery increased with increasing numbers of phosphorylation sites; Panel C: Simulated SPRs with no phosphorylation site (0P), lacking arrestin (–/–), and wild type (WT); Panel D: Reproduction of the SPRs from rod with C terminal truncation, lacking arrestin (–/–), and wild type (+/+) [24] rescaled to exhibit the same proportional amplitude as the wild type SPR. The simulated curves were rescaled accordingly. With arrestin absent, the flash response displayed a rapid partial recovery followed by a prolonged final phase. This behavior indicates that an arrestin-independent mechanism initiates the quench of rhodopsin's catalytic activity and that arrestin completes the quench. Analogous simulations for the faster dynamics and are in Figure S2 of the supplementary material.

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Table 2.

Characteristics of SPRs, ms and ms.

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Table 3.

The sequences for the dynamics of ms and .

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Figure 3.

State diagram of CTMC model for rhodopsin deactivation.

States 1 to n are active states and state n+1 is the inactive state. The phosphorylation rates and arrestin binding rates are denoted respectively by and .

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Figure 4.

Mouse SPRs by simulation (black) and experiment (red).

The simulation is conducted with the parameters shown in Table S2 for the dynamics and (left), and the dynamics suggested in [28], [30], [31](right). Left: Dynamics of and . The WT SPR exhibits a maximum of , decrease of current at after activation. Experimental data is an average of sets of SPRs kindly provided by C. Makino. Right: Same experimental (red) and simulated (black) WT response with and . Experimental data kindly provided by C. Makino.

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Table 4.

CTMC model parameters.

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Table 4 Expand