Models and numerical simulations of collective cellular motion
Models and numerical simulations of collective cellular motion
"Models and numerical simulations of collective cellular motion", organizado por CITMAga. Será impartido por Luis Francisco López Bonilla. Universidad Carlos III de Madrid.
Data: 7 de marzo de 2025.
Hora: 10:00 h.
Duración: 1 hora
Lugar: Aula Magna da Facultade de Matemáticas (USC) e online por MS Teams a través do enlace Teams Meeting.
Abstract:
The cells of incipient cancer tumors need oxygen to grow in tissues. They issue growth factors that are felt in nearby blood vessels and stimulate the formation of new blood vessels (angiogenesis) that carry the needed oxygen and nutrients to the tumor. Epithelial cells move collectively to close a wound or collectively push an epithelial monolayer of a different tissue. Aspects of these multiscale processes in biomedicine can be studied by mathematical and computational models. We discuss angiogenesis at supracellular scales by stochastic differential equations and birth-death processes, derive continuum descriptions of the density of moving blood vessels and analyse a soliton-like attractor. Numerical simulations of a cellular Potts model including Notch signaling between cells describe the growth of blood vessels at cellular and subcellular levels.
Collective cellular motion of epithelial cells can be described using simpler active vertex models, in which cells are polygons forming a Voronoi tessellation of the tissue. The dual Delaunay triangulation comprises cells centers that evolve according to dynamics including collective inertia and active forces. Numerical simulations qualitatively agree with experiments on wound healing assays, formation of fingers, and antagonistic migration assays of a precancerous cellular aggregate invading the space of a healthy tissue and displacing its cells. On longer length scales it is possible to derive coarse grained partial differential equations from the vertex models that describe fluid or elastic behavior of the cellular aggregates.
This talk is based on joint work with Manuel Carretero, Filippo Terragni (Universidad Carlos III de Madrid, Spain), Björn Birnir (University of California at Santa Barbara, USA), Ana Carpio (Universidad Complutense de Madrid, Spain), Carolina Trenado (Princeton University, USA), Gloria Triguero (UNED), Rocío Vega (Reganosa, Spain), and Falko Ziebert (Heidelberg University, Germany).