Statistical Methods for Large Ensembles of Super-Resolution Stochastic Single Particle Trajectories in Cell Biology

Abstract

Following recent progress in super-resolution microscopy in the past decade, massive amounts of redundant single stochastic trajectories are now available for statistical analysis. Flows of trajectories of molecules or proteins sample the cell membrane or its interior at very high time and space resolution. Several statistical analyses were developed to extract information contained in these data, such as the biophysical parameters of the underlying stochastic motion to reveal the cellular organization. These trajectories can further reveal hidden subcellular organization. We review here the statistical analysis of these trajectories based on the classical Langevin equation, which serves as a model of trajectories. Parametric and nonparametric estimators are constructed by discretizing the stochastic equations, and they allow the recovery of tethering forces, diffusion tensors, or membrane organization from measured trajectories that differ from physical ones by a localization noise. Modeling, data analysis, and automatic detection algorithms serve to extract novel biophysical features such as potential wells and other substructures, such as rings, at an unprecedented spatiotemporal resolution. It is also possible to reconstruct the surface membrane of a biological cell from the statistics of projected random trajectories.