Recovering a stochastic process from noisy ensembles of many single particle trajectories

TL;DR

This paper presents a method to recover the parameters of a stochastic process from noisy single particle trajectories using the Langevin model, enabling analysis of molecular trafficking in cells.

Contribution

It introduces a novel approach combining parametric and non-parametric estimators with local asymptotic expansion to deconvolve physical and instrumental noise in trajectory data.

Findings

Effective recovery of local drift and diffusion tensor.

Validation of estimators through numerical simulations.

Characterization of recoverable information from microscopy trajectories.

Abstract

Recovering a stochastic process from noisy ensembles of single particle trajectories (SPTs) is resolved here using the Langevin equation as a model. The massive redundancy contained in SPTs data allows recovering local parameters of the underlying physical model. 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. 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 trafficking and underlying cellular function.