Vincent Briane | Searcharxiv

arXiv2018

A Sequential Algorithm to Detect Diffusion Switching along Intracellular Particle Trajectories

Single-particle tracking allows to infer the motion of single molecules in living cells. When we observe a long trajectory (more than 100 points), it is possible that the particle switches mode of motion over time. Then, fitting a single model to the trajectory can be misleading. In this paper, we propose a method to detect the temporal change points : the times at which a change of dynamics occurs. More specifically, we consider that the particle switches between three main modes of motion : Brownian motion, subdiffusion and superdiffusion. We use an algorithm based on a statistic (Briane et al. 2016) computed on local windows along the trajectory. The method is non parametric as the statistic is not related to any particular model. This algorithm controls the number of false change point detections in the case where the trajectory is fully Brownian. A Monte Carlo study is proposed to demonstrate the performances of the method and also to compare the procedure to two competitive algorithms. At the end, we illustrate the utility of the method on real data depicting the motion of mRNA complexes (called mRNP) in neuronal dendrites.

stat.ME↗

arXiv2017

A statistical analysis of particle trajectories in living cells

Recent advances in molecular biology and fluorescence microscopy imaging have made possible the inference of the dynamics of single molecules in living cells. Such inference allows to determine the organization and function of the cell. The trajectories of particles in the cells, computed with tracking algorithms, can be modelled with diffusion processes. Three types of diffusion are considered : (i) free diffusion; (ii) subdiffusion or (iii) superdiffusion. The Mean Square Displacement (MSD) is generally used to determine the different types of dynamics of the particles in living cells (Qian, Sheetz and Elson 1991). We propose here a non-parametric three-decision test as an alternative to the MSD method. The rejection of the null hypothesis -- free diffusion -- is accompanied by claims of the direction of the alternative (subdiffusion or a superdiffusion). We study the asymptotic behaviour of the test statistic under the null hypothesis, and under parametric alternatives which are currently considered in the biophysics literature, (Monnier et al,2012) for example. In addition, we adapt the procedure of Benjamini and Hochberg (2000) to fit with the three-decision test setting, in order to apply the test procedure to a collection of independent trajectories. The performance of our procedure is much better than the MSD method as confirmed by Monte Carlo experiments. The method is demonstrated on real data sets corresponding to protein dynamics observed in fluorescence microscopy.

stat.AP↗