An overview of diffusion models for intracellular dynamics analysis

We present an overview of diffusion models commonly used for quantifying the dynamics of intracellular particles (e.g. biomolecules) inside eukaryotic living cells. It is established that inference on the modes of mobility of molecules is central in cell biology since it reflects interactions between structures and determines functions of biomolecules in the cell. In that context, Brownian motion is a key component in short distance transportation (e.g. connectivity for signal transduction). Another dynamical process that has been heavily studied in the past decade is the motor-mediated transport (e.g. dynein, kinesin and myosin) of molecules. Primarily supported by actin filament and microtubule network, it ensures spatial organization and temporal synchronization in the intracellular mechanisms and structures. Nevertheless, the complexity of internal structures and molecular processes in the living cell influence the molecular dynamics and prevent the systematic application of pure Brownian or directed motion modeling. On the one hand, cytoskeleton density will hinder the free displacement of the particle, a phenomenon called subdiffusion. On the other hand, the cytoskeleton elasticity combined with thermal bending can contribute a phenomenon called superdiffusion. This paper discusses the basics of diffusion modes observed in eukariotic cells, by introducing the essential properties of these processes. Applications of diffusion models include protein trafficking and transport and membrane diffusion.

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 molecules in living cells. Such inference allows us to understand and determine the organization and function of the cell. The trajectories of particles (e.g., biomolecules) in living cells, computed with the help of object tracking methods, can be modeled with diffusion processes. Three types of diffusion are considered: (i) free diffusion, (ii) subdiffusion, and (iii) superdiffusion. The mean-square displacement (MSD) is generally used to discriminate the three types of particle dynamics. We propose here a nonparametric three-decision test as an alternative to the MSD method. The rejection of the null hypothesis, i.e., free diffusion, is accompanied by claims of the direction of the alternative (subdiffusion or superdiffusion). We study the asymptotic behavior of the test statistic under the null hypothesis and under parametric alternatives which are currently considered in the biophysics literature. In addition, we adapt the multiple-testing procedure of Benjamini and Hochberg 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.