Chemoreception by a cell with age-dependent receptor binding sites

The authors determine the time-dependent ligand current into a spherical cell that is covered with a large number of age-dependent receptors. These receptor can be either of two states: active (i.e., available for ligand binding) or inactive. An active receptor turns inactive upon binding a ligand, and it can reappear as active at some later time. The transition inactive → active is treated as a probabilistic process. The ligand distribution around the cell is determined analytically in terms of this distribution at the cell surface. A set of nonlinear integral equations is derived for the distribution at the cell surface, which is solved numerically. In this way the time-dependent ligand current into the cell as well as the average active receptor population at the cell surface are determined.