Abstract
A large number (tens of thousands) of single molecular trajectories on a cell membrane can now be collected by superresolution methods. The data contains information about the diffusive motion of molecule, proteins, or receptors and here we review methods for its recovery by statistical analysis of the data. The information includes the forces, organization of the membrane, the diffusion tensor, the long-time behavior of the trajectories, and more. To recover the long-time behavior and statistics of long trajectories, a stochastic model of their nonequilibrium motion is required. Modeling and data analysis serve extracting novel biophysical features at an unprecedented spatiotemporal resolution. The review presents data analysis, modeling, and stochastic simulations applied in particular on surface receptors evolving in neuronal cells.