A Statistical Analysis of Particle Trajectories in Living Cells

Vincent Briane (1) , Charles Kervrann (1) , Myriam Vimond (2)

1 SERPICO - Space-timE RePresentation, Imaging and cellular dynamics of molecular COmplexes
2 CREST - Centre de Recherche en Economie et Statistique [Bruz]

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 asymp-totic behaviour of the test statistic under the null hypothesis, and under parametric alternatives. 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.

Mots clés: Intracellular trafficking; Diffusion processes; Multiple hypothesis testing; Three-decision test

Domaines: Applications [stat.AP]

Vincent Briane, Charles Kervrann, Myriam Vimond. A Statistical Analysis of Particle Trajectories in Living Cells. 2017. ⟨hal-01557705v2⟩