MITACS Math Biology Seminar 2006

Rolling is an important manifestation of biological cell adhesion, especially for the leukocyte cell in the immune process. It combines several phenomena such as the affinity, the junction and failure between specific adhesion molecules, and an active deformation of the cell during the motility. Several models were developed in a probabilistic or a deterministic context. The focus is here on the local mechanical description (2D) of the kinetics of adhesion of the contact interface of a single cell with a wall (e.g., the blood vein), in terms of the failure and creation of connections during the rolling. The failure and adhesion are considered as bieng modeled by stochastic fields. The local model focuses on the interfacial zone, as a preliminary step towards an integrated model including the cell membrane behavior. Hence, the net effect of the fluid flow is represented by a punctual force, coupled to the Van der Waals, electrostatic forces and the viscoelastic behavior of the interfacail bonds. Numerical simulations emphasize the rolling phenomenon and the kinetics of creation and rupture of the ligands~Vreceptors connections. Perspectives in terms of the coupling of the interface behavior with a stochastic finite element description of the cell membrane in a 3D context are mentioned.