Statistical methods for large ensemble of super-resolution stochastic single particle trajectories

Abstract

Following recent progresses in super-resolution microscopy obtained in the last decade, massive amount of redundant single stochastic trajectories are now available for statistical analysis. Flows of trajectories of molecules or proteins are sampling the cell membrane or its interior at a very high time and space resolution. Several statistical analysis 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 present here the statistical analysis of these trajectories based on the classical Langevin equation, which serves as a model of trajectories. Parametric and non-parametric estimators are constructed by discretizing the stochastic equations and they allow recovering tethering forces, diffusion tensor or membrane organization from measured trajectories, that differ from physical ones by a localization noise. Modeling, data analysis and automatic detection algorithms serve extracting novel biophysical features such as potential wells and other sub-structures, 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.

Chromatin phase separated nanoregions explored by polymer cross-linker models and reconstructed from single particle trajectories

“…where a(X) is the drift field and B(X) is a matrix and _ W is a random noise. The drift in Eq 1 can be recovered from SPTs acquired at any infinitesimal time step Δt by estimating the conditional moments of the trajectory displacements ΔX = X(t + Δt) − X(t) [52][53][54][55] aðxÞ ¼ lim…”