Local modeling of the rolling phenomenon in the cell adhesion kinetics: A probabilistic approach

Abstract

Cell adhesion plays an important role in biology: essentially with regard to immunizing defence and the transport of medicinal substances toward specific zones. The focus is here on the mechanical description of adhesion kinetics, in terms of the failure and creation of connections during the rolling phenomenon. Hence, we consider the case of a single cell, which is linked to a rigid substratum. A 2D model is established. We consider that the contact zone cell-wall is rectilinear and composed of vertical fibers and two horizontal rigid beams (complex cell membrane- fibers-vein wall). These connections are modeled by elastic springs having identical elastic properties (e.g stiffness), but different failure strengths. The cell is subjected to the flow of plasma, which can generate the rolling phenomenon; we accordingly consider two distinct zones, one associated with the failure of the old fibers and one with the creation of the new fibers (in the direction opposite to the flow). Several interactions are taken into account in this model: van der Waals (attractive) and electrostatic (repulsive) forces and the effects of fluid pressure, assimilated into a periodic point force applied to the interface zone. We also study the vibration induced failure in the contact zone without mechanical damping using the principle of virtual work and a failure criterion to establish the equation of motion and the time evolution of the failure (dynamical approach). Rupture of a fiber can occur if the stress applied to the fiber is above a certain limit. These limits are determinated with using a probabilistic approach by use of a spectral method to simulate a stochastic and Gaussian field. Modeling of the creation of new fibers is also achieved by the combination of a dynamical and probabilistic method and a kinematical criterion. On the basis of these elements, numerical simulations are developed, that elucidate the rupture and rolling phenomena.