Mechanical modeling of the rolling phenomenon at the cell scale

Rolling is an important manifestation of cell adhesion [Viallat, A., Akarian, M., Campillo, C., Faivre, M., Pepin-Dona, B., 2005. Dynamique de vésicules géantes et de globules rouges sous écoulement de cisaillement. In: 17e`me Congrès Français de Mécanique, Troyes], especially for the leukocyte cell in the immune process [Bell, G.I., Dembo, M., Bongrand, P., 1984. Cell adhesion: competition between non-specific repulsion and specific bonding. Biophys. J. 45, 1051–1064]. The purpose of this work is the mechanical description of the kinetic of adhesion of a single cell adhering to an extracellular wall, in terms of the failure and creation of connections during the rolling of a single adherent cell subjected to a fluid flow. A 2D model is developed in the present contribution, which describes the local behavior of the contact zone between the cell and the wall. The contact zone is assimilated to two rigid rectilinear beams linked by elastic springs, subjected to the fluid flow and to interaction forces, namely Van der Waals (attractive) and electrostatic (repulsive) forces.The first aspect being investigated concerns the mechanism of failure of the existing connections: the distribution of the failure limits of these fibers is described as a random gaussian field. Moreover, we use a spatial and temporal discretization, thereby assuming that the mass of the cell is concentrated in nodal points, which correspond to the junction points between the cell and the wall. Using the principle of virtual work and a failure criterion, the vibration-failure behavior of the contact interface is described, neglecting mechanical damping in a first step [Mefti, N., Haussy, B., Ganghoffer, J.F., 2005. Mechanical modeling of the rolling phenomenon at the cell scale. Euromech Colloquium 463, Gronnigen, Netherland].Accounting for the maturation of the fibbers properties results in a pseudo-periodical response due to the competition between the increase of the fibbers stiffness and the increase of the applied pulling effort. The creation of new connections on a part of the cell boundary located opposite to the plasma flow, is integrated into the modeled, and analyzed. A set of free adhesion molecules – ligands and receptors – is distributed on the wall and cell external surfaces. As the ligands are subjected to the Brownian motion of the fluid particles, the orientation and the amplitude of this movement are assume to be described by gaussian random processes. The effects of the chemical affinity are accounted for as molecular Van der Waals interactions.Numerical simulations emphasize the rolling phenomenon, the mechanism of which being the creation and the rupture of the bonds of the contact zone, which involve the rotation of the cell and the relaxation effects of the elastic properties of these connections.