FIG. 1. Schematic diagram of activation in the G-protein cascade of phototransduction in the vertebrate photoreceptor. Receptor protein rhodopsin (R; gray) is an integral membrane protein with characteristic 7-transmembrane segment structure; it is activated to R* (metarhodopsin II; white) within a few milliseconds of photon absorption. The G-protein transducin (G; green) is a heterotrimer, which in the quiescent state has a molecule of GDP bound to its α subunit. Upon diffusional contact between R* and G (open arrows) the two proteins bind, and the Gα is enabled to release the bound GDP. Provided that GTP is present in the cytoplasm, a molecule of GTP binds to the vacant nucleotide binding site, creating the activated G·GTP. The two protein molecules then separate, with the R* unaltered; by analogy with other cascades, the G protein is thought to split, with the a-subunit Gα·GTP representing the active form G* (yellow). The PDE effector protein E (blue) is tetrameric, comprising two closely similar hydrolytic α and β subunits each with an attached inhibitory γ subunit. Upon contact between G* and E, the G* binds to the γ subunit and relieves its inhibitory influence, thereby activating E to E* (red). Because of its double-unit structure, the PDE can bind two G*s, but the two units appear to act independently. The activated PDE, E*, hydrolyzes cGMP in the cytoplasm, reducing the concentration of cGMP and thereby causing closure of cGMP-gated channels in the plasma membrane.

zymatic gain, permitting the attainment of very high overall amplification.

Inactivation. The subsequent steps involved in response inactivation and recovery are less well understood than the activation steps outlined above. Although qualitative information is available on rhodopsin phosphorylation, on the Gprotein's GTPase activity, on the decline in cytoplasmic Ca2+ concentration, and on calcium's role in activating guanylyl cyclase, there is not as yet a quantitative understanding of the way in which all these factors fit together. For this reason, the following analysis is restricted to the activation steps in phototransduction, and it therefore provides a description only of the onset phase of the response to light.

Simulation of the Diffusional Interactions Underlying Activation

The diffusional interactions of the proteins have been simulated by Monte-Carlo techniques (8), and an example is presented in Fig. 2. The molecular species are identified (Inset), and the four panels depict areas of membrane at successive times after activation of a single molecule of R*. Initially, the molecules were distributed randomly (Fig. 2A), with the G protein (green) and the effector protein (blue) present at mean concentrations of 2500 and 250 molecules per µm2, respectively, and with a single R* (white) at the center of the region.

For t > 0, the molecules underwent two-dimensional diffusion, according to the estimated lateral diffusion coefficients of the respective molecular species (see Fig. 2 legend). After 0.2 ms (Fig. 2B), the R* had contacted and activated three molecules of G protein to the excited form, G* (yellow); of these three G*s, one had contacted and bound to an effector molecule, to produce an E* (red). Subsequently, at 0.4 ms (Fig. 2C), five G*s had been activated, of which four had contacted effectors to produce E*s. Finally, after 1 ms, a total of 10 G*s and 5 E*s had been generated (Fig. 2D, illustrating the whole area of the simulation).

Although the stochastic nature of the activation reactions is evident in Fig. 2, this randomness may be appreciated more intuitively by viewing a dynamic simulation. A computer program (WALK) that provides such a simulation is available on the Internet (for details, see ref. 8 or legend to Fig. 2).

Predicted Gain and Kinetics

The simulation in Fig. 2 suffers a significant limitation due to the small number of molecules present, and already at 1 ms the activated molecules have traversed a significant fraction of the area under consideration. To extend the maximum time to 100

FIG. 2. Simulation of the activation of G* and E* in the G-protein cascade of phototransduction. Each panel depicts an area of membrane at successive times after activation of a single molecule of R*. (A) Time zero. (B) 0.2 ms. (C) 0.4 ms. (D) 1.0 ms. (Inset) Molecular species are identified. Single white R* was initially placed at the center of the region, and the green Gs and blue Es were randomly distributed, with mean concentrations 2500 and 250 µm−2. At time 0, the molecules began undergoing lateral diffusion, simulated by Monte-Carlo methods (8), using the estimated lateral diffusion coefficients for R*, G, G*, and E of 0.7, 1.2, 1.5, and 0.8 µm−2·s−1, respectively (4,78). Scale: region of simulation was ≈200 nm2, with nonabsorbing boundaries, and diameters of the R*, G, and E molecules were 3, 6, and 7 nm; pixel size, 0.4 nm; simulation time increment, 0.02 µs. Simulation was performed on an i486 machine using the program WALK (8), which is available on the Internet by anonymous FTP from the Biophysics server at; for instructions, begin with the file “ReadMe.1st” in the directory pub/biophysics/Computer_Programs/ WALK. A Windows version (95 or 3.x) is now available on the World Wide Web, from the site

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