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.Comment: Revised introduction. A clearer and shorter description of the model (section 2

PEWA: Patch-Based Exponentially Weighted Aggregation for Image Denoising

International audienceWe present a statistical aggregation method, which combines image patches denoised with conventional algorithms. We evaluate the SURE estimator of each denoised candidate image patch to compute the exponential weighted aggregation (EWA) estimator. The PEWA algorithm has an interpretation with Gibbs distribution, is based on a MCMC sampling and is able to produce results that are comparable to the current state-of-the-art

Biomolecule Trafficking and Network Tomography-based Simulations

International audienceDuring the past two decades many groundbreaking technologies, including Green Fluorescent Protein (GFP)-tagging and super-resolution microscopy, emerged and allowed the visualization of protein dynamics and molecular interactions at different levels of spatial and temporal resolution. In the meantime, the automated quantification of microscopy images depicting moving biomolecules has become of major importance in cell biology since it offers a better understanding of fundamental mechanisms including membrane transport, cell signaling, cell division and motility. Consequently, dedicated image analysis methods have been developed to process challenging temporal series of 2D-3D images and to estimate individual trajectories of biomolecules. Nevertheless, the current tracking methods cannot provide global information about biomolecule trafficking. This motivated the development of simulation techniques able to generate realistic fluorescence microscopy image sequences depicting trafficking of small moving particles in interaction, with variable velocities within the cell. In this chapter, we describe a simulation approach based on the concept of Network Tomography (NT) which is generally used in network communications and transport to infer the main routes of communication between origins and destinations. The trafficking model, scaled down for microscopy, is combined with real 2D-3D image sequences to generate artificial videos depicting fluorescently tagged moving proteins within cells. Simulation in bioimaging is timely since it has become essential to build ground truth datasets for image processing algorithm evaluation such as biomolecule detectors and trackers, as well as to generate training datasets for deep learning algorithms

Statistical and computational methods for intracellular trajectory analysis in fluorescence microscopy

International audienceThe characterization of molecule dynamics in living cells is essential to decipher biological mechanisms and processes. This topic is usually addressed in fluorescent video-microscopy from particle trajectories computed by object tracking algorithms. However, classifying individual trajectories into predefined diffusion classes (e.g. sub-diffusion, free diffusion (or Brownian motion), super-diffusion), estimating diffusion model parameters, or detecting diffusion regime changes, is a difficult task in most cases. To address this challenging issue, we propose a computational framework based on statistical tests (with the Brownian motion as the null hypothesis) to analyze short and long trajectories, and derive spatial diffusion maps. The methodological approach is well-grounded in statistics and is more robust than previous techniques, including the Mean Square Displacement (MSD) method and variants. In this talk, I will present the concepts and methods and focus on dynamics of biomolecules involved in exocytosis and endocytosis mechanisms, observed in total internal reflection fluorescence (TIRF) and lattice light sheet microscopy. The algorithms, dedicated to short or long trajectories, are flexible in most cases, with a minimal number of control parameters to be tuned (p-values). They can be applied to a large range of problems in cell imaging and can be integrated in generic image-based workflows, including for high content screeningapplications

DCT2net: an interpretable shallow CNN for image denoising

International audienceThis work tackles the issue of noise removal from images, focusing on the well-known DCT image denoising algorithm. The latter, stemming from signal processing, has been well studied over the years. Though very simple, it is still used in crucial parts of state-of-the-art "traditional" denoising algorithms such as BM3D. Since a few years however, deep convolutional neural networks (CNN) have outperformed their traditional counterparts, making signal processing methods less attractive. In this paper, we demonstrate that a DCT denoiser can be seen as a shallow CNN and thereby its original linear transform can be tuned through gradient descent in a supervised manner, improving considerably its performance. This gives birth to a fully interpretable CNN called DCT2net. To deal with remaining artifacts induced by DCT2net, an original hybrid solution between DCT and DCT2net is proposed combining the best that these two methods can offer; DCT2net is selected to process non-stationary image patches while DCT is optimal for piecewise smooth patches. Experiments on artificially noisy images demonstrate that two-layer DCT2net provides comparable results to BM3D and is as fast as DnCNN algorithm composed of more than a dozen of layers

NETWORK TOMOGRAPHY AND MINIMAL PATHS FOR TRAFFIC FLOWESTIMATION IN MOLECULAR IMAGING

International audienceGreen Fluorescent Protein (GFP)-tagging and time-lapse fluorescence microscopy enable to observe molecular dynamics and interactions in live cells. Original image analysis methods are then required to process challenging 2D or 3D image sequences. To address the tracking problem of several hundreds of objects, we propose an original framework that provides general information about molecule transport, that is about traffic flows between origin and destination regions detected in the image sequence. Traffic estimation can be accomplished by adapting the recent advances in Network Tomography commonly used in network communications. In this paper, we address image partition given vesicle stocking areas and multipaths routing for vesicle transport. This approach has been developed for real image sequences and Rab proteins