The most probable dynamics of receptor-ligand binding on cell membrane

We devise a method for predicting certain receptor-ligand binding behaviors, based on stochastic dynamical modelling. We consider the dynamics of a receptor binding to a ligand on the cell membrane, where the receptor and ligand perform different motions and are thus modeled by stochastic differential equations with Gaussian noise or non-Gaussian noise. We use neural networks based on Onsager-Machlup function to compute the probability $P_1$ of the unbounded receptor diffusing to the cell membrane. Meanwhile, we compute the probability $P_2$ of extracellular ligand arriving at the cell membrane by solving the associated Fokker-Planck equation. Then, we could predict the most probable binding probability by combining $P_1$ and $P_2$. In this way, we conclude with some indication about where the ligand will most probably encounter the receptor, contributing to better understanding of cell's response to external stimuli and communication with other cells.