Time-dependent ligand current into a single cell performing chemoreception

We determine the ligand current into a single spherical cell which carries a large number of receptors on its surface. Initially, this cell is placed into a medium which contains ligands at uniform concentration. The time-dependent ligand distribution is calculated, from which the time-dependent ligand current into the cell is derived. If the ligand concentration is kept constant at distances comparable to the radius of the cell the stationary state sets in at times comparable to the time T1 necessary for ligands to travel a distance of the order of the radius of the cell. If the ligand concentration is kept constant at infinity the stationary state sets in at a time which is about 1000T1 for typical values of the parameters.