Ligand binding in a spherical region randomly crowded by receptors

This paper reports on some results concerning the binding of diffusing ligands in a spherical 3D region randomly filled by free receptors. It is shown that commonly accepted mean-field theory which is successfully used for bulk diffusion-controlled reactions cannot describe the behavior of ligand concentration in the diffusion layer close to the region boundary. To eliminate this drawback of the theory, we introduce a new complementary diffusion equation in the boundary layer with an appropriate matching condition. Using this equation, we find the characteristic ligand penetration length and total time-dependent flux of ligand binding to free receptors randomly distributed in a spherical region. (paper)