Diffusion in narrow domains and application to phototransduction.

The mean time for a Brownian particle to find a small target inside a narrow domain is a key parameter for many chemical reactions occurring in cellular microstructures. Although current estimations are given for a large class of domains, they cannot be used for narrow domains often encountered in cellular biology, such as the synaptic cleft, narrow compartments in the outer segment of vertebrate photoreceptors, or neuron-glia contact. We compute here the mean time for a Brownian particle to hit a small target placed on the surface of a narrow cylinder. We then use this result to estimate the rate constant of cyclic-GMP (cGMP) hydrolysis by the activated enzyme phosphodiesterase (PDE) in the narrow microdomains that build up the outer segment of a rod photoreceptor. By controlling the cGMP concentration, PDE activity is at the basis of the early photoresponse chemical reaction cascade. Our approach allows us to compute the cGMP rate constant as a function of biophysical parameters.