Stochastic simulation of the transducin GTPase cycle.

On rod disc membranes, single photoactivated rhodopsin (R*) molecules catalytically activate many copies of the G-protein (Gt), which in turn binds and activates the effector (phosphodiesterase). We have performed master equation simulations of the underlying diffusional protein interactions on a rectangular 1-micron2 model membrane, divided into 15 x 15 cells. Mono- and bimolecular reactions occur within cells, and diffusional transitions occur between (neighboring) cells. Reaction and diffusion constants yield the related probabilities for the stochastic transitions. The calculated kinetics of active effector form a response that is essentially determined by the stochastic lifetime distribution of R* (with characteristic time tau R*) and the reaction constants of Gt activation. Only a short tau R* (approximately 0.3 s) and a high catalytic rate (3000-4000 Gt s-1 R*-1) are consistent with electrophysiological data. Although R* shut-off limits the rise of the response, the lifetime distribution of free R* is not translated into a corresponding variability of the response peaks, because 1) the lifetime distribution of catalytically engaged R* is distorted, 2) small responses are enlarged by an overshoot of active effector, and 3) larger responses tend to undergo saturation. Comparison of these results to published photocurrent waveforms may open ways to understand the relative uniformity of the rod response.