The analysis of experimental random walks aims at identifying the process(es) that generate(s) them. It is in general a difficult task, because statistical dispersion within an experimental set of random walks is a complex combination of the stochastic nature of the generating process, and the possibility to have more than one simple process. In this paper, we study by numerical simulations how the statistical distribution of various geometric descriptors such as the second, third and fourth order moments of two-dimensional random walks depends on the stochastic process that generates that set. From these observations, we derive a method to classify complex sets of random walks, and resolve the generating process(es) by the systematic comparison of experimental moment distributions with those numerically obtained for candidate processes. In particular, various processes such as Brownian diffusion combined with convection, noise, confinement, anisotropy, or intermittency, can be resolved by using high order moment distributions. In addition, finite-size effects are observed that are useful for treating short random walks. As an illustration, we describe how the present method can be used to study the motile behavior of epithelial microvilli. The present work should be of interest in biology for all possible types of single particle tracking experiments.
The present work takes advantage of the intrinsic localisation of two-photon fluorescence excitation to develop two-photon fluorescence recovery after photobleaching -TP-FRAP -as a method to assess fluorophore dynamics with microscopic resolution. Numerical simulations are proposed to improve data interpretation beyond the usual frame of FRAP data analysis. This work was developed for measuring the dynamics of cytoskeleton proteins.The apical face of epithelial cells is covered with a dense set of microvilli, the main components of which have been identified and localized at the ultrastructural level, but their dynamic organisation remains largely unknown. To understand the apical morphogenesis and to assess the dynamics of cytoskeleton proteins that might underlie the steadystate morphology, GFP-fusion proteins were expressed. Using TP-FRAP, fluorophore dynamics could be resolved between the plasma membrane and the cytosol, and interpreted in terms of diffusive mobility or exchange rates within and between these two compartments. This is applied in particular to ezrin, a membrane-actin linker protein localized in the cytosol and at the plasma membrane, which plays a key role in coupling signal transduction to cortical morphogenesis. TP-FRAP experiments in conjunction with ezrin mutaganesis and numerical modelling strongly suggest a fast cyclic renewal dynamics with three sequential membrane binding states with distinct mobilities and biochemical reactivities.This paper presents a detailed account of the instrumental design and the numerical method developed to interpret recovery data. This approach should be more generally useful to locally assess the dynamics of protein turnover in submicroscopic structures, and resolve its molecular basis.
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