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

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. 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. 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+). 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 tr