Abstract

Co-author: David Holcman (ENS Paris)

Recovering a stochastic process from noisy ensembles of single particle trajectories is resolved here using the Langevin equation as a model. The massive redundancy contained in single particle trajectories allows recovering local parameters of the underlying physical model. However, point localization is perturbed by instrumental noise, which, although of the order of ~10 nanometers, affects the estimation of biophysical parameters such as the drift and diffusion of the motion. Moreover, even if the acquisition frequency of modern tracking algorithm is very high, it is not instantaneous, and this biases parameter estimation. Here, we use several parametric and non-parametric estimators to compute the first and second moment of the process and to recover the local drift, its derivative and the diffusion tensor, in diffusion processes whose observation is perturbed by instrumental noise and non-instantaneous sampling rate. Using a local asymptotic expansion of the estimators and computing the empirical transition probability function, we develop here a method to deconvolve the instrumental from the physical noise. We use numerical simulations to explore the range of validity for the estimators. The present analysis allows characterizing what can exactly be recovered from the statistics of super-resolution microscopy trajectories used in molecular tracking and underlying cellular function.