Influence of the mechanical damping on the rolling of a single biological cell: A stochastic approach

Abstract
The rolling is an important kind of cell adhesion, especially in the case of the immune mechanism, due to the leukocyte action, which is strongly influenced by molecular affinity [1].
Our purpose, in this paper, is the presentation of a 2D model which describes the behaviour of the contact interface cell-wall during the rolling. The cell membrane and the wall are assimilated to two rectilinear elastic beams, linked by elastic springs in the case of undamped connections [2] or viscoelastic element in the case of a dissipative behavior. As a first step, the motion of the interface is analyzed, under the external actions of the dynamical fluid pressure, the Van der Waals (attractive forces) and electrostatic effects (repulsive). The second point corresponds to the combination of the vibration of the contact zone and the rupture of the existing connections under a pulling effort. The last step concerns the description of the kinetic of junction between the free ligands and receptors, which constitutes the new connections.
The numerical simulations show the rolling phenomenon, the influence of the mechanical damping on the behavior of the contact interface and the kinetics of junctions between the adhesion free molecules.