Diffusion model for growth factors - Cell receptors interaction

A theoretical model describing the interaction between growth factor molecules and their receptors from the cell surface within an 'off-centre' diffusion approximation is developed in this paper. It is assumed that a number of non interacting particles (growth-factor molecules) move diffusively in the presence of traps (specific receptors) which are located at the surfaces of a number of cells uniformly distributed in space. The diffusion equations system is solved by a perturbative method. The model predicts a nonlinear dependence of the receptor occupation and of the time needed to reach a threshold value of receptor occupation on the total number of cell receptors. An autocrine binding, when the ligand is secreted by the responsive cells accounts for the interaction between IL-2 and helper T-cells.