Diffusion-limited binding to a site on the wall of a membrane channel

The authors develop a theory of diffusion-controlled reactions with a site located on the wall of a cylindrical membrane channel that connects two reservoirs containing diffusing particles which are trapped by the site at the first contact. An expression for the Laplace transform of the rate coefficient, kt, is derived assuming that the size of the site is small compared to the channel radius. The expression is used to find the stationary value of the rate coefficient, kinfinity, as a function of the length and radius of the channel, the radius of the site, and its position inside the channel (distances from the two ends of the channel) as well as the particle diffusion constants in the bulk and in the channel. Their derivation is based on the one-dimensional description of the particle motion in the channel, which is generalized to include binding to the site into consideration. The validity of the approximate one-dimensional description of diffusion and binding was checked by three-dimensional Brownian dynamics simulations. They found that the one-dimensional description works reasonably well when the size of the site does not exceed 0.2 of the channel radius.