Boundary homogenization for spherical surfaces randomly covered with nonoverlapping partially absorbing disks

A common signaling mechanism used by cells involves producing soluble extracellular ligands, which diffuse and bind to specific receptors covering the cell surface. This mechanism can be modeled with point particles (ligands) diffusing in a medium containing reflective spheres (cells) randomly covered by nonoverlapping partially absorbing disks (receptors). In order to simplify the modeling, it is desirable to replace the patchy cell surface with a spherical surface where absorption is uniform. In this Note, we use a Brownian dynamics model to test an approximating formula reported by Berezhkovkii et al. [J. Chem. Phys.121, 11390 (2004)] designed for boundary homogenization problems. We also use the model to solve the more general problem of diffusion to reactive spherical sinks.