Reconstructing wells from high density regions extracted from super-resolution single particle trajectories

Large amount of super-resolution single particle trajectories has revealed that the cellular environment is enriched in heterogenous regions of high density, which remain unexplained. The biophysical properties of these regions are characterized by a drift and their extension (a basin of attraction) that can be estimated from an ensemble of trajectories. We develop here two statistical methods to recover the dynamics and local potential wells (field of force and boundary) using as a model a truncated Ornstein-Ulhenbeck process. The first method uses the empirical distribution of points, which differs inside and outside the potential well, while the second focuses on recovering the drift field. Finally, we apply these two methods to voltage-gated calcium channels and phospholipids moving on the surface of neuronal cells and recover the energy and size of these high-density regions with nanometer precision.