Time-dependent ligand current into a saturating cell performing chemoreception

We determine the ligand current into a single spherical cell whose receptors become permanently blocked after binding ligands. Initially the cell is placed in a medium which contains ligands at uniform concentration. The analytical solution for the ligand distribution is obtained in terms of an integral over the solution at the cell surface. For the solution at the cell surface a nonlinear integral equation is derived which is solved numerically. We determine the time-dependent ligand current into the cell and the average number of free receptors in the cell surface as a function of time.