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Quantitative modeling of the molecular steps underlying shut-off of rhodopsin activity in rod phototransduction.

Lamb TD, Kraft TW - Mol. Vis. (2016)

Bottom Line: We analyze the transitions that an activated R* molecule undergoes as a result of successive phosphorylation steps and arrestin binding.We conclude that the conventional model of graded reduction in R* activity through successive phosphorylation steps appears to be inconsistent with experimental results.Instead, we find that two variants of a model in which R* activity initially remains high and then declines abruptly after several phosphorylation steps appears capable of providing a better description of experimentally measured SPRs.

View Article: PubMed Central - PubMed

Affiliation: Department of Optometry and Vision Science, University of Alabama at Birmingham, Birmingham, AL.

ABSTRACT

Purpose: To examine the predictions of alternative models for the stochastic shut-off of activated rhodopsin (R*) and their implications for the interpretation of experimentally recorded single-photon responses (SPRs) in mammalian rods.

Theory: We analyze the transitions that an activated R* molecule undergoes as a result of successive phosphorylation steps and arrestin binding. We consider certain simplifying cases for the relative magnitudes of the reaction rate constants and derive the probability distributions for the time to arrestin binding. In addition to the conventional model in which R* catalytic activity declines in a graded manner with successive phosphorylations, we analyze two cases in which the activity is assumed to occur not via multiple small steps upon each phosphorylation but via a single large step. We refer to these latter two cases as the binary R* shut-off and three-state R* shut-off models.

Methods: We simulate R*'s stochastic reactions numerically for the three models. In the simplifying cases for the ratio of rate constants in the binary and three-state models, we show that the probability distribution of the time to arrestin binding is accurately predicted. To simulate SPRs, we then integrate the differential equations for the downstream reactions using a standard model of the rod outer segment that includes longitudinal diffusion of cGMP and Ca(2+).

Results: Our simulations of SPRs in the conventional model of graded shut-off of R* conform closely to the simulations in a recent study. However, the gain factor required to account for the observed mean SPR amplitude is higher than can be accounted for from biochemical experiments. In addition, a substantial minority of the simulated SPRs exhibit features that have not been reported in published experiments. Our simulations of SPRs using the model of binary R* shut-off appear to conform closely to experimental results for wild type (WT) mouse rods, and the required gain factor conforms to biochemical expectations. However, for the arrestin knockout (Arr(-/-)) phenotype, the predictions deviated from experimental findings and led us to invoke a low-activity state that R* enters before arrestin binding. Our simulations of this three-state R* shut-off model are very similar to those of the binary model in the WT case but are preferred because they appear to accurately predict the mean SPRs for four mutant phenotypes, Arr(+/-), Arr(-/-), GRK1(+/-), and GRK1(-/-), in addition to the WT phenotype. When we additionally treated the formation and shut-off of activated phosphodiesterase (E*) as stochastic, the simulated SPRs appeared even more similar to real SPRs, and there was very little change in the ensemble mean and standard deviation or in the amplitude distribution.

Conclusions: We conclude that the conventional model of graded reduction in R* activity through successive phosphorylation steps appears to be inconsistent with experimental results. Instead, we find that two variants of a model in which R* activity initially remains high and then declines abruptly after several phosphorylation steps appears capable of providing a better description of experimentally measured SPRs.

No MeSH data available.


Related in: MedlinePlus

Results of simulation of Model 3 (Three-state model). The equations for Model 3 were simulated numerically using M = 3 and ν = κ = μ = 60 s−1 for the stochastic parameters (Table 1) and with the downstream parameters from Table 2; the flash duration was set to zero. The number of simulations of R* activity in panels A and B was 106, while for the subsequent panels the downstream reactions were integrated using the first 50 R* simulations (panel C) or the first 105 R* simulations (panels E and F). A: Distribution of times to the low-activity state (left) and to Arr binding (right) for the 106 simulations. Blue traces are simulations, and red curves are theoretical predictions. B: Mean R*(t) time-course, for the 106 simulations (dashed blue trace). The overlying dashed red trace is the prediction of Equation (3.5). For comparison, the dotted red trace shows the predicted response for the binary model using the same values of ν and μ; thus it plots the dashed red trace from Figure 3B. The similarity of these traces shows that inclusion of the low-activity state made little difference to the mean time-course of the simulated and predicted R*(t) responses. C: The first 50 simulated SPRs. D: SPRs for a set of defined times to the low-activity state. Rather than being simulated stochastically, the interval until low activity was instead set to 5, 10, 20, 30, 45, 60, 80, 100, 130, 200, 300, 400, 500, 600, or 800 ms. The subsequent delay to arrestin binding was fixed at its mean value of 1/μ. Red circles indicate the peaks. These measurements were fit by a spline function and used to predict the expected distribution in panel F. E: Time course of the mean (blue) and SD (red) for the ensemble of 105 simulated SPRs. F: Probability distribution of the peak amplitudes for the 105 simulated SPRs (blue). The smooth red trace plots the predicted distribution obtained using the approach described in the Theory section using Equation (3.6) and the measurements of peak amplitude from panel D.
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f4: Results of simulation of Model 3 (Three-state model). The equations for Model 3 were simulated numerically using M = 3 and ν = κ = μ = 60 s−1 for the stochastic parameters (Table 1) and with the downstream parameters from Table 2; the flash duration was set to zero. The number of simulations of R* activity in panels A and B was 106, while for the subsequent panels the downstream reactions were integrated using the first 50 R* simulations (panel C) or the first 105 R* simulations (panels E and F). A: Distribution of times to the low-activity state (left) and to Arr binding (right) for the 106 simulations. Blue traces are simulations, and red curves are theoretical predictions. B: Mean R*(t) time-course, for the 106 simulations (dashed blue trace). The overlying dashed red trace is the prediction of Equation (3.5). For comparison, the dotted red trace shows the predicted response for the binary model using the same values of ν and μ; thus it plots the dashed red trace from Figure 3B. The similarity of these traces shows that inclusion of the low-activity state made little difference to the mean time-course of the simulated and predicted R*(t) responses. C: The first 50 simulated SPRs. D: SPRs for a set of defined times to the low-activity state. Rather than being simulated stochastically, the interval until low activity was instead set to 5, 10, 20, 30, 45, 60, 80, 100, 130, 200, 300, 400, 500, 600, or 800 ms. The subsequent delay to arrestin binding was fixed at its mean value of 1/μ. Red circles indicate the peaks. These measurements were fit by a spline function and used to predict the expected distribution in panel F. E: Time course of the mean (blue) and SD (red) for the ensemble of 105 simulated SPRs. F: Probability distribution of the peak amplitudes for the 105 simulated SPRs (blue). The smooth red trace plots the predicted distribution obtained using the approach described in the Theory section using Equation (3.6) and the measurements of peak amplitude from panel D.

Mentions: The results of our simulations for this three-state model are collected in Figure 4, where the organization of panels follows that in Figure 3. The top pair of panels summarize the simulated activity of the R* molecule in 106 repetitions; the middle pair show a selection of responses; and the bottom pair plot the ensemble behavior for SPRs in 105 simulations.


Quantitative modeling of the molecular steps underlying shut-off of rhodopsin activity in rod phototransduction.

Lamb TD, Kraft TW - Mol. Vis. (2016)

Results of simulation of Model 3 (Three-state model). The equations for Model 3 were simulated numerically using M = 3 and ν = κ = μ = 60 s−1 for the stochastic parameters (Table 1) and with the downstream parameters from Table 2; the flash duration was set to zero. The number of simulations of R* activity in panels A and B was 106, while for the subsequent panels the downstream reactions were integrated using the first 50 R* simulations (panel C) or the first 105 R* simulations (panels E and F). A: Distribution of times to the low-activity state (left) and to Arr binding (right) for the 106 simulations. Blue traces are simulations, and red curves are theoretical predictions. B: Mean R*(t) time-course, for the 106 simulations (dashed blue trace). The overlying dashed red trace is the prediction of Equation (3.5). For comparison, the dotted red trace shows the predicted response for the binary model using the same values of ν and μ; thus it plots the dashed red trace from Figure 3B. The similarity of these traces shows that inclusion of the low-activity state made little difference to the mean time-course of the simulated and predicted R*(t) responses. C: The first 50 simulated SPRs. D: SPRs for a set of defined times to the low-activity state. Rather than being simulated stochastically, the interval until low activity was instead set to 5, 10, 20, 30, 45, 60, 80, 100, 130, 200, 300, 400, 500, 600, or 800 ms. The subsequent delay to arrestin binding was fixed at its mean value of 1/μ. Red circles indicate the peaks. These measurements were fit by a spline function and used to predict the expected distribution in panel F. E: Time course of the mean (blue) and SD (red) for the ensemble of 105 simulated SPRs. F: Probability distribution of the peak amplitudes for the 105 simulated SPRs (blue). The smooth red trace plots the predicted distribution obtained using the approach described in the Theory section using Equation (3.6) and the measurements of peak amplitude from panel D.
© Copyright Policy - open-access
Related In: Results  -  Collection

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f4: Results of simulation of Model 3 (Three-state model). The equations for Model 3 were simulated numerically using M = 3 and ν = κ = μ = 60 s−1 for the stochastic parameters (Table 1) and with the downstream parameters from Table 2; the flash duration was set to zero. The number of simulations of R* activity in panels A and B was 106, while for the subsequent panels the downstream reactions were integrated using the first 50 R* simulations (panel C) or the first 105 R* simulations (panels E and F). A: Distribution of times to the low-activity state (left) and to Arr binding (right) for the 106 simulations. Blue traces are simulations, and red curves are theoretical predictions. B: Mean R*(t) time-course, for the 106 simulations (dashed blue trace). The overlying dashed red trace is the prediction of Equation (3.5). For comparison, the dotted red trace shows the predicted response for the binary model using the same values of ν and μ; thus it plots the dashed red trace from Figure 3B. The similarity of these traces shows that inclusion of the low-activity state made little difference to the mean time-course of the simulated and predicted R*(t) responses. C: The first 50 simulated SPRs. D: SPRs for a set of defined times to the low-activity state. Rather than being simulated stochastically, the interval until low activity was instead set to 5, 10, 20, 30, 45, 60, 80, 100, 130, 200, 300, 400, 500, 600, or 800 ms. The subsequent delay to arrestin binding was fixed at its mean value of 1/μ. Red circles indicate the peaks. These measurements were fit by a spline function and used to predict the expected distribution in panel F. E: Time course of the mean (blue) and SD (red) for the ensemble of 105 simulated SPRs. F: Probability distribution of the peak amplitudes for the 105 simulated SPRs (blue). The smooth red trace plots the predicted distribution obtained using the approach described in the Theory section using Equation (3.6) and the measurements of peak amplitude from panel D.
Mentions: The results of our simulations for this three-state model are collected in Figure 4, where the organization of panels follows that in Figure 3. The top pair of panels summarize the simulated activity of the R* molecule in 106 repetitions; the middle pair show a selection of responses; and the bottom pair plot the ensemble behavior for SPRs in 105 simulations.

Bottom Line: We analyze the transitions that an activated R* molecule undergoes as a result of successive phosphorylation steps and arrestin binding.We conclude that the conventional model of graded reduction in R* activity through successive phosphorylation steps appears to be inconsistent with experimental results.Instead, we find that two variants of a model in which R* activity initially remains high and then declines abruptly after several phosphorylation steps appears capable of providing a better description of experimentally measured SPRs.

View Article: PubMed Central - PubMed

Affiliation: Department of Optometry and Vision Science, University of Alabama at Birmingham, Birmingham, AL.

ABSTRACT

Purpose: To examine the predictions of alternative models for the stochastic shut-off of activated rhodopsin (R*) and their implications for the interpretation of experimentally recorded single-photon responses (SPRs) in mammalian rods.

Theory: We analyze the transitions that an activated R* molecule undergoes as a result of successive phosphorylation steps and arrestin binding. We consider certain simplifying cases for the relative magnitudes of the reaction rate constants and derive the probability distributions for the time to arrestin binding. In addition to the conventional model in which R* catalytic activity declines in a graded manner with successive phosphorylations, we analyze two cases in which the activity is assumed to occur not via multiple small steps upon each phosphorylation but via a single large step. We refer to these latter two cases as the binary R* shut-off and three-state R* shut-off models.

Methods: We simulate R*'s stochastic reactions numerically for the three models. In the simplifying cases for the ratio of rate constants in the binary and three-state models, we show that the probability distribution of the time to arrestin binding is accurately predicted. To simulate SPRs, we then integrate the differential equations for the downstream reactions using a standard model of the rod outer segment that includes longitudinal diffusion of cGMP and Ca(2+).

Results: Our simulations of SPRs in the conventional model of graded shut-off of R* conform closely to the simulations in a recent study. However, the gain factor required to account for the observed mean SPR amplitude is higher than can be accounted for from biochemical experiments. In addition, a substantial minority of the simulated SPRs exhibit features that have not been reported in published experiments. Our simulations of SPRs using the model of binary R* shut-off appear to conform closely to experimental results for wild type (WT) mouse rods, and the required gain factor conforms to biochemical expectations. However, for the arrestin knockout (Arr(-/-)) phenotype, the predictions deviated from experimental findings and led us to invoke a low-activity state that R* enters before arrestin binding. Our simulations of this three-state R* shut-off model are very similar to those of the binary model in the WT case but are preferred because they appear to accurately predict the mean SPRs for four mutant phenotypes, Arr(+/-), Arr(-/-), GRK1(+/-), and GRK1(-/-), in addition to the WT phenotype. When we additionally treated the formation and shut-off of activated phosphodiesterase (E*) as stochastic, the simulated SPRs appeared even more similar to real SPRs, and there was very little change in the ensemble mean and standard deviation or in the amplitude distribution.

Conclusions: We conclude that the conventional model of graded reduction in R* activity through successive phosphorylation steps appears to be inconsistent with experimental results. Instead, we find that two variants of a model in which R* activity initially remains high and then declines abruptly after several phosphorylation steps appears capable of providing a better description of experimentally measured SPRs.

No MeSH data available.


Related in: MedlinePlus