We present a quantitative kinetic model for the transient velocity (microM of cGMP hydrolyzed/s) response of retinal rod outer segment (ROS) cGMP phosphodiesterase (v(t) versus t) to a stimulating light pulse in the linear response range. The model gives an excellent fit to experimental v(t) versus t data for ROS suspensions at different concentrations of GTP and GDP and clarifies experimental results which are difficult to understand in the absence of such a model. It contains the minimum number of steps required to fit our experimental data and consists of one rate-limiting step with specific rate kL for the production of active phosphodiesterase (PDE), PDE*, by photoactivated rhodopsin, R*, and deactivation processes for R* and PDE* with lifetimes tau R and tau P, respectively. The experimental graphs of v(t) versus t at each concentration of GTP and GDP are characterized by a fast rise to a peak value, vpeak, followed by a slow decay to zero level. The minimal kinetic model allows us to characterized completely the effects of GTP and GDP, and any other pertinent species, in terms of their effects on the parameters kL, tau R, and tau P. Our kinetic model indicates that for "washed" ROS preparations (a) the risetime of v(t) is determined by tau P which has a value of about 2 s and is insensitive to [GTP]. (b) The decay of v(t) is determined by tau R which decreases with [GTP] and has a value greater than 300 s at low [GTP] and a limiting value of 50 s at high [GTP]. We attribute the greater than 300 s lifetime to the complex R*G (where G is ROS G protein) and the 50-s lifetime to free R*. (c) The rate kL increases hyperbolically with [GTP] with a half-maximal value of 56 microM and kL.max = 22-45 s-1. (d) Peak velocity is given by the expression vpeak alpha kL tau P which is consistent with the dependence of kL on [GTP] and the experimental finding that vpeak varies hyperbolically with [GTP]. The minimal model has also allowed us to (a) develop clear definitions of amplification for the light-triggered enzymatic cascade and (b) clarify experimental methods for measuring gain.(ABSTRACT TRUNCATED AT 400 WORDS)