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

Test statistique pour détecter les diffusions non browniennes

National audienceLa modélisation de la dynamique des particules intracellulaires permet de répondre à des problèmes biologiques. Dans ce travail, nous supposons que le mouvement de ces particules est décrit à l'aide de processus stochastiques particuliers: les processus de diffusion. Nous développons ici un test statistique permettant de classer les trajectoires observées en trois groupes: la diffusion confinée, dirigée et libre (ou mouvement Brownien). Cette méthode est une alternative à la l'analyse du déplacement carré moyen (Mean Square Displacement) utilisé dans la littérature biophysique. Notre procédure est évaluée sur des simulations et des cas réels

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 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

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 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 have been heavily studied in the past decade is the motor-mediated transport (e.g., dynein, kinesin, 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 cells, by introducing the essential properties of these processes. Applications of diffusion models include protein trafficking and transport, and membrane diffusion

Preschool children's vision screening in New Zealand: a retrospective evaluation of referral accuracy

Langeslag-Smith MA, Vandal AC, Briane V, et al. Preschool children's vision screening in New Zealand: a retrospective evaluation of referral accuracy. BMJ Open 2015;5:e009207. doi: 10.1136/bmjopen-2015-009207Objectives To assess the accuracy of preschool vision screening in a large, ethnically diverse, urban population in South Auckland, New Zealand. Design Retrospective longitudinal study. Methods B4 School Check vision screening records (n=5572) were compared with hospital eye department data for children referred from screening due to impaired acuity in one or both eyes who attended a referral appointment (n=556). False positive screens were identified by comparing screening data from the eyes that failed screening with hospital data. Estimation of false negative screening rates relied on data from eyes that passed screening. Data were analysed using logistic regression modelling accounting for the high correlation between results for the two eyes of each child. Primary outcome measure Positive predictive value of the preschool vision screening programme. Results Screening produced high numbers of false positive referrals, resulting in poor positive predictive value (PPV=31%, 95% CI 26% to 38%). High estimated negative predictive value (NPV=92%, 95% CI 88% to 95%) suggested most children with a vision disorder were identified at screening. Relaxing the referral criteria for acuity from worse than 6/9 to worse than 6/12 improved PPV without adversely affecting NPV. Conclusions The B4 School Check generated numerous false positive referrals and consequently had a low PPV. There is scope for reducing costs by altering the visual acuity criterion for referral.This work was supported by the Arthur D Bronlund Trust, CCRep and University of Auckland Faculty Research Development Fund Grants (3704420)

Phenology of marine turtle nesting revealed by statistical model of the nesting season

BACKGROUND: Marine turtles deposit their eggs on tropical or subtropical beaches during discrete nesting seasons that span several months. The number and distribution of nests laid during a nesting season provide vital information on various aspects of marine turtle ecology and conservation. RESULTS: In the case of leatherback sea turtles nesting in French Guiana, we developed a mathematical model to explore the phenology of their nesting season, derived from an incomplete nest count dataset. We detected 3 primary components in the nest distribution of leatherbacks: an overall shape that corresponds to the arrival and departure of leatherback females in the Guianas region, a sinusoidal pattern with a period of approximately 10 days that is related to physiological constraints of nesting female leatherbacks, and a sinusoidal pattern with a period of approximately 15 days that likely reflects the influence of spring high tides on nesting female turtles. CONCLUSION: The model proposed here offers a variety of uses for both marine turtles and also other taxa when individuals are observed in a particular location for only part of the year

A sequential algorithm to detect diffusion switching along intracellular particle trajectories

Recent advances in molecular biology and fluorescence microscopy imaging have made possible the inference of the dynamics of single molecules in living cells. When we observe a long trajectory (more than 100 points), it is possible that the particle switches mode of motion over time. Then, an issue is to estimate the temporal change-points that is the times at which a change of dynamics occurs. We propose a non-parametric procedure based on test statistics [Briane et al., 2018] computed on local windows along the trajectory to detect the change-points. This algorithm controls the number of false change-point detections in the case where the trajectory is fully Brownian. A Monte Carlo study is proposed to demonstrate the performances of the method and also to compare the procedure to two competitive algorithms. At the end, we illustrate the efficacy of the method on real data in 2D and 3D, depicting the motion of mRNA complexes-called mRNP-in neuronal dendrites, Galectin-3 endocytosis and trafficking within the cell. A user-friendly Matlab package containing examples and the code of the simulations used in the paper is available at http://serpico.rennes.inria.fr/doku.php?id=software:cpanalysis: index

Statistical tests for analysing particle trajectories : application to intracellular imaging

L'objet de cette thèse est l'étude quantitative du mouvement des particules intracellulaires, comme les protéines ou les molécules. L'estimation du mouvement des particules au sein de la cellule est en effet d'un intérêt majeur en biologie cellulaire puisqu'il permet de comprendre les interactions entre les différents composants de la cellule. Dans cette thèse, nous modélisons les trajectoires des particules avec des processus stochastiques puisque le milieu intra-cellulaire est soumis à de nombreux aléas. Les diffusions, des processus à trajectoires continues, permettent de modéliser un large panel de mouvements intra-cellulaires. Les biophysiciens distinguent trois principaux types de diffusion: le mouvement brownien, la super-diffusion et la sous-diffusion. Ces différents types de mouvement correspondent à des scénarios biologiques distincts. Le déplacement d'une particule évoluant sans contrainte dans le cytosol ou dans le plasma membranaire est modélisée par un mouvement brownien; la particule ne se déplace pas dans une direction précise et atteint sa destination en un temps long en moyenne. Les particules peuvent aussi être propulsées par des moteurs moléculaires le long des microtubules et filaments d'actine du cytosquelette de la cellule. Leur mouvement est alors modélisé par des super-diffusions. Enfin, la sous-diffusion peut être observée dans deux situations: i/ lorsque la particule est confinée dans un micro domaine, ii/ lorsqu’elle est ralentie par l'encombrement moléculaire et doit se frayer un chemin parmi des obstacles mobiles ou immobiles. Nous présentons un test statistique pour effectuer la classification des trajectoires en trois groupes: brownien, super-diffusif et sous-diffusif. Nous développons également un algorithme pour détecter les ruptures de mouvement le long d’une trajectoire. Nous définissons les temps de rupture comme les instants où la particule change de régime de diffusion (brownien, sous-diffusif ou super-diffusif). Enfin, nous associons une méthode de regroupement avec notre procédure de test pour identifier les micro domaines dans lesquels des particules sont confinées. De telles zones correspondent à des lieux d’interactions moléculaires dans la cellule.In this thesis, we are interested in quantifying the dynamics of intracellular particles, as proteins or molecules, inside living cells. In fact, inference on the modes of mobility of molecules is central in cell biology since it reflects the interactions between the structures of the cell. We model the particle trajectories with stochastic processes as the interior of a living cell is a fluctuating environment. Diffusions are stochastic processes with continuous paths and can model a large range of intracellular movements. Biophysicists distinguish three main types of diffusions, namely Brownian motion, superdiffusion and subdiffusion. These different diffusion processes correspond to distinct biological scenarios. A particle evolving freely inside the cytosol or along the plasma membrane is modelled by Brownian motion; the particle does not travel along any particular direction and can take a very long time to go to a precise area in the cell. Active intracellular transport can overcome this difficulty so that motion is faster and direct specific. In this case, particles are carried by molecular motors along microtubular filament networks and their motion is modelled with superdiffusions. Subdiffusion can be observed in two cases i/ when the particle is confined in a microdomain, ii/ when the particle is hindered by molecular crowding and encounters dynamic or fixed obstacles. We develop a statistical test for classifying the observed trajectories into the three groups of diffusion of interest namely Brownian motion, super-diffusion and subdiffusion. We also design an algorithm to detect the changes of dynamics along a single trajectory. We define the change points as the times at which the particle switches from one diffusion type (Brownian motion, superdiffusion or subdiffusion) to another. Finally, we combine a clustering algorithm with our test procedure to identify micro domains that is zones where the particles are confined. Molecular interactions of great importance for the functioning of the cell take place in such areas

Tests statistiques pour l’analyse de trajectoires de particules : application à l’imagerie intracellulaire

In this thesis, we are interested in quantifying the dynamics of intracellular particles, as proteins or molecules, inside living cells. In fact, inference on the modes of mobility of molecules is central in cell biology since it reflects the interactions between the structures of the cell. We model the particle trajectories with stochastic processes as the interior of a living cell is a fluctuating environment. Diffusions are stochastic processes with continuous paths and can model a large range of intracellular movements. Biophysicists distinguish three main types of diffusions, namely Brownian motion, superdiffusion and subdiffusion. These different diffusion processes correspond to distinct biological scenarios. A particle evolving freely inside the cytosol or along the plasma membrane is modelled by Brownian motion; the particle does not travel along any particular direction and can take a very long time to go to a precise area in the cell. Active intracellular transport can overcome this difficulty so that motion is faster and direct specific. In this case, particles are carried by molecular motors along microtubular filament networks and their motion is modelled with superdiffusions. Subdiffusion can be observed in two cases i/ when the particle is confined in a microdomain, ii/ when the particle is hindered by molecular crowding and encounters dynamic or fixed obstacles. We develop a statistical test for classifying the observed trajectories into the three groups of diffusion of interest namely Brownian motion, super-diffusion and subdiffusion. We also design an algorithm to detect the changes of dynamics along a single trajectory. We define the change points as the times at which the particle switches from one diffusion type (Brownian motion, superdiffusion or subdiffusion) to another. Finally, we combine a clustering algorithm with our test procedure to identify micro domains that is zones where the particles are confined. Molecular interactions of great importance for the functioning of the cell take place in such areas.L'objet de cette thèse est l'étude quantitative du mouvement des particules intracellulaires, comme les protéines ou les molécules. L'estimation du mouvement des particules au sein de la cellule est en effet d'un intérêt majeur en biologie cellulaire puisqu'il permet de comprendre les interactions entre les différents composants de la cellule. Dans cette thèse, nous modélisons les trajectoires des particules avec des processus stochastiques puisque le milieu intra-cellulaire est soumis à de nombreux aléas. Les diffusions, des processus à trajectoires continues, permettent de modéliser un large panel de mouvements intra-cellulaires. Les biophysiciens distinguent trois principaux types de diffusion: le mouvement brownien, la super-diffusion et la sous-diffusion. Ces différents types de mouvement correspondent à des scénarios biologiques distincts. Le déplacement d'une particule évoluant sans contrainte dans le cytosol ou dans le plasma membranaire est modélisée par un mouvement brownien; la particule ne se déplace pas dans une direction précise et atteint sa destination en un temps long en moyenne. Les particules peuvent aussi être propulsées par des moteurs moléculaires le long des microtubules et filaments d'actine du cytosquelette de la cellule. Leur mouvement est alors modélisé par des super-diffusions. Enfin, la sous-diffusion peut être observée dans deux situations: i/ lorsque la particule est confinée dans un micro domaine, ii/ lorsqu’elle est ralentie par l'encombrement moléculaire et doit se frayer un chemin parmi des obstacles mobiles ou immobiles. Nous présentons un test statistique pour effectuer la classification des trajectoires en trois groupes: brownien, super-diffusif et sous-diffusif. Nous développons également un algorithme pour détecter les ruptures de mouvement le long d’une trajectoire. Nous définissons les temps de rupture comme les instants où la particule change de régime de diffusion (brownien, sous-diffusif ou super-diffusif). Enfin, nous associons une méthode de regroupement avec notre procédure de test pour identifier les micro domaines dans lesquels des particules sont confinées. De telles zones correspondent à des lieux d’interactions moléculaires dans la cellule