Exclusion processes: short range correlations induced by adhesion and contact interactions

We analyze the out-of-equilibrium behavior of exclusion processes where agents interact with their nearest neighbors, and we study the short-range correlations which develop because of the exclusion and other contact interactions. The form of interactions we focus on, including adhesion and contact-preserving interactions, is especially relevant for migration processes of living cells. We show the local agent density and nearest-neighbor two-point correlations resulting from simulations on two dimensional lattices in the transient regime where agents invade an initially empty space from a source and in the stationary regime between a source and a sink. We compare the results of simulations with the corresponding quantities derived from the master equation of the exclusion processes, and in both cases, we show that, during the invasion of space by agents, a wave of correlations travels with velocity v(t) ~ t^(-1/2). The relative placement of this wave to the agent density front and the time dependence of its height may be used to discriminate between different forms of contact interactions or to quantitatively estimate the intensity of interactions. We discuss, in the stationary density profile between a full and an empty reservoir of agents, the presence of a discontinuity close to the empty reservoir. Then, we develop a method for deriving approximate hydrodynamic limits of the processes. From the resulting systems of partial differential equations, we recover the self-similar behavior of the agent density and correlations during space invasion

Automatic quantification of the microvascular density on whole slide images, applied to paediatric brain tumours

Angiogenesis is a key phenomenon for tumour progression, diagnosis and treatment in brain tumours and more generally in oncology. Presently, its precise, direct quantitative assessment can only be done on whole tissue sections immunostained to reveal vascular endothelial cells. But this is a tremendous task for the pathologist and a challenge for the computer since digitised whole tissue sections, whole slide images (WSI), contain typically around ten gigapixels. We define and implement an algorithm that determines automatically, on a WSI at objective magnification $40\times$, the regions of tissue, the regions without blur and the regions of large puddles of red blood cells, and constructs the mask of blur-free, significant tissue on the WSI. Then it calibrates automatically the optical density ratios of the immunostaining of the vessel walls and of the counterstaining, performs a colour deconvolution inside the regions of blur-free tissue, and finds the vessel walls inside these regions by selecting, on the image resulting from the colour deconvolution, zones which satisfy a double-threshold criterion. A mask of vessel wall regions on the WSI is produced. The density of microvessels is finally computed as the fraction of the area of significant tissue which is occupied by vessel walls. We apply this algorithm to a set of 186 WSI of paediatric brain tumours from World Health Organisation grades I to IV. The segmentations are of very good quality although the set of slides is very heterogeneous. The computation time is of the order of a fraction of an hour for each WSI on a modest computer. The computed microvascular density is found to be robust and strongly correlates with the tumour grade. This method requires no training and can easily be applied to other tumour types and other stainings

Modeling tumor cell migration: from microscopic to macroscopic

It has been shown experimentally that contact interactions may influence the migration of cancer cells. Previous works have modelized this thanks to stochastic, discrete models (cellular automata) at the cell level. However, for the study of the growth of real-size tumors with several millions of cells, it is best to use a macroscopic model having the form of a partial differential equation (PDE) for the density of cells. The difficulty is to predict the effect, at the macroscopic scale, of contact interactions that take place at the microscopic scale. To address this we use a multiscale approach: starting from a very simple, yet experimentally validated, microscopic model of migration with contact interactions, we derive a macroscopic model. We show that a diffusion equation arises, as is often postulated in the field of glioma modeling, but it is nonlinear because of the interactions. We give the explicit dependence of diffusivity on the cell density and on a parameter governing cell-cell interactions. We discuss in details the conditions of validity of the approximations used in the derivation and we compare analytic results from our PDE to numerical simulations and to some in vitro experiments. We notice that the family of microscopic models we started from includes as special cases some kinetically constrained models that were introduced for the study of the physics of glasses, supercooled liquids and jamming systems.Comment: Final published version; 14 pages, 7 figure

Modeling origin, natural evolution and response to radiotherapy of gliomas

Diffuse low-grade gliomas are slowly growing tumors. After tens of years, they transform inexorably into more aggressive forms, jeopardizing the patientâ s life. Mathematical modeling could help clinicians to have a better understanding of the natural history of these tumors and their response to treatments. We present here different models of these tumors: the first one is discrete and describes the appearance of the first glioma cells and the genesis of a tumor. The second model is continuous and consists in a PDE that describes the evolution of the cell density. This model can describe the natural evolution of gliomas, their response to treatments such as radiotherapy and the changes in their dynamics in pregnant women. The discrete and the continuous models are designed to be close to the biological reality. The results are quantitatively compared with either biological data or clinical data, at the cellular level (histological samples) and at the tissue level (MRI scans).Non UBCUnreviewedAuthor affiliation: Paris Diderot UniversityFacult

ETUDE THEORIQUE ET EXPERIMENTALE DU COMPORTEMENT COLECTIF ET INDIVIDUEL DE MOTEURS MOLECULAIRES

LES MOTEURS MOLECULAIRES, ENZYMES UTILISANT L'HYDROLYSE DE L'ATP POUR SE DEPLACER LE LONG DE BIOFILAMENTS, SONT DES COMPOSANTS INDISPENSABLES A LA VIE DE LA CELLULE. ILS PARTICIPENT EN PARTICULIER ACTIVEMENT AU TRANSPORT INTRA-CELLULAIRE. CETTE THESE EST CONSACREE A L'ETUDE DE CES MOTEURS, SOUS DIFFERENTS ASPECTS, THEORIQUES ET EXPERIMENTAUX. DANS UN PREMIER TEMPS, LE COMPORTEMENT COLLECTIF DE CES MOTEURS A FAIT L'OBJET D'UNE ETUDE THEORIQUE : DANS LE CADRE D'UN MODELE SIMPLE A DEUX ETATS, NOUS AVONS ETUDIE L'INFLUENCE DU NOMBRE FINI DE MOTEURS SUR DES TRANSITIONS DYNAMIQUES PREVUES PRECEDEMMENT POUR UN NOMBRE INFINI DE MOTEURS. DES COMPORTEMENTS OBSERVES RECEMMENT EXPERIMENTALEMENT ONT PU ETRE EXPLIQUES DANS CE CADRE, ET RETROUVES DANS DES SIMULATIONS. NOUS AVONS D'AUTRE PART ETUDIE LE COMPORTEMENT INDIVIDUEL DE CES MOTEURS. TOUT D'ABORD, DANS LE CADRE DU MEME MODELE A DEUX ETATS, NOUS AVONS MONTRE QUE LA VITESSE DES KINESINES DIMERIQUES ETAIT PLUS ELEVEE QUE CELLE DES MOTEURS MONOMERIQUES, TANDIS QUE LEUR COEFFICIENT DE DIFFUSION ETAIT PLUS FAIBLE, REJOIGNANT AINSI DE RECENTS RESULTATS EXPERIMENTAUX. CE MODELE RESTE APPLICABLE AUX DEUX TYPES DE MOTEURS, CONTRAIREMENT AU MODELE DE MARCHE CLASSIQUE DES KINESINES A DEUX TETES. D'AUTRE PART, AFIN D'OBSERVER EXPERIMENTALEMENT LA DYNAMIQUE D'UN MOTEUR AUX ECHELLES DE TEMPS COURTS, NOUS AVONS MIS AU POINT UNE METHODE OPTIQUE ORIGINALE. POUR LA PREMIERE FOIS, AUCUNE FORCE N'EST APPLIQUEE SUR LA PROTEINE ET LA RESOLUTION TEMPORELLE EST TRES ELEVEE. NOUS AVONS AINSI CONFIRME LA VALEUR DU PAS DE LA KINESINE ET OUVERT DE LARGES PERSPECTIVES DANS L'ETUDE DES TEMPS COURTS, POUR LA KINESINE ET D'AUTRES MOTEURS.PARIS7-Bibliothèque centrale (751132105) / SudocSudocFranceF