Calculations of distance distributions and probabilities of binding by ligands between parallel plane membranes comprising receptors

Cell communication through biochemical signaling pathways is a key determinant of tissue responses to radiation. Several molecules, such as the transforming growth factor β (TGFβ), are implicated in radiation-induced signaling between cells. Brownian Dynamics (BD) algorithms have recently been used to simulate the interaction of ligands with receptors and to elucidate signal transduction and autocrine loops in ligand-receptors systems. In this paper, we discuss the simulation of particle diffusion and binding kinetics in a space bounded by two parallel plane membranes, using an exact algorithm to sample the propagator (Green's function) of a particle located between 2 membranes. We also show that the simulation results are independent of the number of time steps used, in accordance with time discretization equations. These simulations could be used to simulate the motion and binding of ligand molecules in a cell culture, and possibly in neuronal synapses.