Migration of breast cancer cells : understanding the roles of volume exclusion and cell-to-cell adhesion

We study MCF-7 breast cancer cell movement in a transwell apparatus. Various experimental conditions lead to a variety of monotone and nonmonotone responses which are difficult to interpret. We anticipate that the experimental results could be caused by cell-to-cell adhesion or volume exclusion. Without any modeling, it is impossible to understand the relative roles played by these two mechanisms. A lattice-based exclusion process random-walk model incorporating agent-to-agent adhesion is applied to the experimental system. Our combined experimental and modeling approach shows that a low value of cell-to-cell adhesion strength provides the best explanation of the experimental data suggesting that volume exclusion plays a more important role than cell-to-cell adhesion. This combined experimental and modeling study gives insight into the cell-level details and design of transwell assays.

Les littératies multiples et le devenir plurilingue (Keynote)

Cette présentation met en avant la Théorie des Littératies Multiples (TLM) et l’importance de lire, lire le monde et se lire, dans le but de se transformer en contexte plurilingue. La première partie de cette communication sera consacrée à la présentation des principes fondamentaux de la TLM. Il est vrai que la littératie valorisée par l’école est souvent celle qui est la plus prisée dans la recherche et l’enseignement. La TLM enlève la littératie scolaire de sa place privilégiée et l’insère dans un agencement de littératies au foyer, à l’école et dans la communauté. Les littératies, en tant que construit renvoient aux mots, aux gestes, aux attitudes, ou plus exactement, aux façons de parler, de lire, d’écrire et de valoriser les réalités de la vie. Elles sont une façon de devenir avec le monde. Les littératies constituent des textes au sens large (comme par exemple, la musique, l’art, la physique et les athématiques) qui peuvent être visuels,oraux, écrits, tactiles,olfactifs ou numériques. Elles se fusionnent aux contextes sociopolitiques, culturels, économiques, genrés et racialisés, qui de par leur caractère mobile et fluide transforment les littératies génératrices de locuteurs, de scripteurs, d’artistes, d’ava tars et de communautés. Les littératies prennent leur sens en contexte, dans le temps et l’espace où on se trouve De ce fait, leur actualisation n’est pas prédéterminée et est imprévisible. La TLM s’intéresse aux rôles joués par les littératies. Lire, lire le monde et se lire a pour fonction importante entre autres de transformer une vie, une communauté et une société. La deuxième partie de cette communication sera consacrée à un projet de recherche ayant pour objectif d’explorer la façon dont des enfants acquièrent simultanément deux ou plusieurs systèmes d’écriture. Des enfants âgés de 5 à 8 ans ont participé à des activités filmées en salle de classe, au foyer et dans leur quartier. Puis des entretiens ont été menés avec les enfants, leurs parents et leurs enseignants. Ce projet nous permet de mieux saisir ce que signifient en contexte plurilingue les littératies en tant que processus. Le projet s’intéresse à ce qu’implique lire, lire le monde et se lire à l’école, au foyer et dans la communauté. Dans une société pluraliste, nous sommes plus que jamais ensibilisés aux contextes particuliers dans lesquels lire, lire le monde et se lire s’actualisent, qu’il s’agisse d’un nouvel arrivant ou d’une personne vivant en milieu minoritaire.

Tactically-driven nonmonotone travelling waves

Models of cell invasion incorporating directed cell movement up a gradient of an external substance and carrying capacity-limited proliferation give rise to travelling wave solutions. Travelling wave profiles with various shapes, including smooth monotonically decreasing, shock-fronted monotonically decreasing and shock-fronted nonmonotone shapes, have been reported previously in the literature. The existence of tacticallydriven shock-fronted nonmonotone travelling wave solutions is analysed for the first time. We develop a necessary condition for nonmonotone shock-fronted solutions. This condition shows that some of the previously reported shock-fronted nonmonotone solutions are genuine while others are a consequence of numerical error. Our results demonstrate that, for certain conditions, travelling wave solutions can be either smooth and monotone, smooth and nonmonotone or discontinuous and nonmonotone. These different shapes correspond to different invasion speeds. A necessary and sufficient condition for the travelling wave with minimum wave speed to be nonmonotone is presented. Several common forms of the tactic sensitivity function have the potential to satisfy the newly developed condition for nonmonotone shock-fronted solutions developed in this work.

Travelling waves for a velocity–jump model of cell migration and proliferation

Cell invasion, characterised by moving fronts of cells, is an essential aspect of development, repair and disease. Typically, mathematical models of cell invasion are based on the Fisher–Kolmogorov equation. These traditional parabolic models can not be used to represent experimental measurements of individual cell velocities within the invading population since they imply that information propagates with infinite speed. To overcome this limitation we study combined cell motility and proliferation based on a velocity–jump process where information propagates with finite speed. The model treats the total population of cells as two interacting subpopulations: a subpopulation of left–moving cells, $L(x,t)$, and a subpopulation of right–moving cells, $R(x,t)$. This leads to a system of hyperbolic partial differential equations that includes a turning rate, $\Lambda \ge 0$, describing the rate at which individuals in the population change direction of movement. We present exact travelling wave solutions of the system of partial differential equations for the special case where $\Lambda = 0$ and in the limit that $\Lambda \to \infty$. For intermediate turning rates, $0 < \Lambda < \infty$, we analyse the travelling waves using the phase plane and we demonstrate a transition from smooth monotone travelling waves to smooth nonmonotone travelling waves as $\Lambda$ decreases through a critical value $\Lambda_{crit}$. We conclude by providing a qualitative comparison between the travelling wave solutions of our model and experimental observations of cell invasion. This comparison indicates that the small $\Lambda$ limit produces results that are consistent with experimental observations.

Induced smoothing for rank regression with censored survival times

Adaptions of weighted rank regression to the accelerated failure time model for censored survival data have been successful in yielding asymptotically normal estimates and flexible weighting schemes to increase statistical efficiencies. However, for only one simple weighting scheme, Gehan or Wilcoxon weights, are estimating equations guaranteed to be monotone in parameter components, and even in this case are step functions, requiring the equivalent of linear programming for computation. The lack of smoothness makes standard error or covariance matrix estimation even more difficult. An induced smoothing technique overcame these difficulties in various problems involving monotone but pure jump estimating equations, including conventional rank regression. The present paper applies induced smoothing to the Gehan-Wilcoxon weighted rank regression for the accelerated failure time model, for the more difficult case of survival time data subject to censoring, where the inapplicability of permutation arguments necessitates a new method of estimating null variance of estimating functions. Smooth monotone parameter estimation and rapid, reliable standard error or covariance matrix estimation is obtained.