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Revealing the transport mechanisms from a single trajectory in living cells

Abstract : This thesis is dedicated to the analysis and modeling of experiments where the position of a tracer in the cellular medium is recorded over time. The goal is to be able to extract as much information as possible from a single experimentally observed trajectory. The main challenge is to identify the transport mechanisms underlying the observed movement. The difficulty of this task lies in the analysis of individual trajectories, which requires the development of new statistical analysis tools. In the first chapter, an overview is given of the wide variety of dynamics that can be observed in the cellular medium. In particular, a review of different models of anomalous and non-Gaussian diffusion is carried out. In the second chapter, a test is proposed to reveal weak ergodicity breaking from a single trajectory. This is a generalization of the approach of M. Magdziarz and A. Weron based on the time-averaged characteristic function of the process. This new estimator is able to identify the ergodicity breaking of continuous random walking where waiting times are power law distributed. By calculating the average of the estimator for several subdiffusion models, the applicability of the method is demonstrated. In the third chapter, an algorithm is proposed to recognize the different phases of an intermittent process from a single trajectory (e.g. active/passive transport within cells, etc.).This test assumes that the process alternates between two distinct phases but does not require any hypothesis on the dynamics of each phase. Phase changes are captured by calculating quantities associated with the local convex hull (volume, diameter) evaluated along the trajectory. It is shown that this algorithm is effective in distinguishing states from a large class of intermittent processes (6 models tested). In addition, this algorithm is robust at high noise levels due to the integral nature of the convex hull. In the fourth chapter, a diffusion model in a heterogeneous medium where the diffusion coefficient evolves randomly is introduced and solved analytically. The probability density function of the displacements presents exponential tails and converges towards a Gaussian one at long time. This model generalizes previous approaches and thus makes it possible to study dynamic heterogeneities in detail. In particular, it is shown that these heterogeneities can drastically affect the accuracy of measurements made by time averages along a trajectory. In the last chapter, single-trajectory based methods are used for the analysis of two experiments. The first analysis carried out shows that the tracers exploring the cytoplasm show that the probability density of displacements has exponential tails over periods of time longer than the second. This behavior is independent of the presence of both microtubules and the actin network in the cell. The trajectories observed therefore show fluctuations in diffusivity, indicating for the first time the presence of dynamic heterogeneities within the cytoplasm. The second analysis deals with an experiment in which a set of 4mm diameter discs was vibrated vertically on a plate, inducing random motion of the disks. Through an in-depth statistical analysis, it is demonstrated that this experiment is close to a macroscopic realization of a Brownian movement. However, the probability densities of disks’ displacements show deviations from Gaussian which are interpreted as the result of inter-disk shocks. In the conclusion, the limits of the approaches adopted as well as the future research orientation opened by this thesis are discussed in detail.
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Yann Lanoiselée. Revealing the transport mechanisms from a single trajectory in living cells. Statistical Mechanics [cond-mat.stat-mech]. Université Paris Saclay (COmUE), 2018. English. ⟨NNT : 2018SACLX081⟩. ⟨tel-01997530⟩



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