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The Dynamics of Phosphodiesterase Activation in Rods and Cones

Jürgen Reingruber ^* and David Holcman ^* 

^* Département de Biologie, Ecole Normale Supérieure, Paris, France; and Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel

Correspondence: Address reprint requests to David Holcman, E-mail: holcman{at}biologie.ens.fr.

Phototransduction starts with the activation of a rhodopsin (respectively, coneopsin) molecule, located in the outer segment of rod (respectively, cone) photoreceptors. The subsequent amplification pathway proceeds via the G-protein transducin to the activation of phosphodiesterase (PDE), a G-protein coupled effector enzyme. In this article, we study the dynamics of PDE activation by constructing a Markov model that is based on the underlying chemical reactions including multiple rhodopsin phosphorylations. We derive explicit equations for the mean and the variance of activated PDE. Our analysis reveals that a low rhodopsin lifetime variance is neither necessary nor sufficient to achieve reliable PDE activation. The numerical simulations show that during the rising phase the variability of PDE activation is much lower compared to the recovery phase, and this property depends crucially on the transducin activation rates. Furthermore, we find that the dynamics of the activation process greatly differs depending on whether rhodopsin or PDE deactivation limits the recovery of the photoresponse. Finally, our simulations for cones show that only very few PDEs are activated by an excited photopigment, which might explain why in S-cones no single photon response can be observed.