Speaker: Pascal Laurent

Title: A few mathematical studies beyond a work of simulation of cell motility in melanoma cancer


In a first part we outline the main features of the modeling work.

Melanoblast migration is important for embryogenesis and is a key featureof melanoma metastasis. Many studies have characterized melanoblast movement, focusing on statistical properties and have highlighted basic mechanisms of melanoblast motility. We took a slightly different and complementary approach: we developed a mathematical model of melanoblast motion that enables the testing of biological assumptions about the displacement of melanoblasts and we created tests to analyze the geometric features of cell trajectories and the issue of trajectory interactions. Within this model, we performed simulations and compared the results with experimental data using geometric tests. The main focus is to study the crossings between trajectories with new theoretical results about the variation of number of intersection points with respect to the crossing times. Using these results it is possible to study the random nature of displacements and the interactions between trajectories. This analysis has raised new questions, leading to the generation of strong arguments in favour of a trail left behind each moving melanoblast.

In a second part we focus on two mathematical  subjects linked to this work :

  - around the use of SVD:  the   (approximate) embedding of metric spaces into euclidean space.

  - beyond the Buffon's needle problem: numbe r of intersections between curves randomly dropped onto a plane.