Narrow escape time to a structured target located on the boundary of a microdomain.

The forward binding rate of chemical reactions is the reciprocal of the mean time for a Brownian molecule to hit its molecular target. When the target is embedded in the surface of a microdomain, this time is known as the narrow escape time, and it has been computed for various geometries. However, for large targets that extend from the surface far into the cytosol the classical computations do not apply and new ones are needed. In this work we generalize the narrow escape time formula to a three-dimensional spine attached to the boundary. We treat in detail the case of an ellipsoidal spine and validate our analysis by Brownian simulations. Finally, we compute the narrow escape time when the spine is uniformly covered by small partially absorbing disks and estimate the homogenized trapping rate of such a patchy surface.