A 1D model of leukocyte adhesion coupling bond dynamics with blood velocity.

Cell adhesion on the vascular wall is a highly coupled process where blood flow and adhesion dynamics are closely linked. Cell dynamics in the vicinity of the vascular wall is driven mechanically by the competition between the drag force of the blood flow and the force exerted by the bonds created between the cell and the wall. Bonds exert a friction force. Here, we propose a mathematical model of such a competitive system, namely leukocytes whose capacity to create bonds with the vascular wall and transmigratory ability are coupled by integrins and chemokines. The model predicts that this coupling gives rise to a dichotomic cell dynamic, whereby cells switch from sliding to firm arrest, through non linear effects. Cells can then transmigrate through the wall. These predicted dynamic regimes are compared to in-vitro trajectories of leukocytes. We expect that competition between friction and drag force in particle dynamics (such as shear stress-controlled nanoparticle capture) can lead to similar dichotomic mode.