A Model of Ligand-Receptor Adhesion for Microparticles and Ellipsoidal Cells

Blood platelets play a key role in hemostasis and thrombosis. In the present work, a mathematical model of adhesive interaction between a non-activated platelet and an adhesive substrate is proposed. The cell is represented as a solid non-deformable ellipsoid on the surface of which adhesion receptor proteins are evenly distributed. A plane uniformly coated with an adhesive ligand, collagen or von Willebrand factor, is considered an adhesive substrate. The platelet is attached to the plane by the formation of elastic ligand-receptor bonds. The motion of the platelet with constant velocity directed perpendicular to the surface and under the action of a constant force also directed perpendicular to the surface is considered. The influence of the platelet shape on the adhesion force is demonstrated. In the case of motion under a constant force, the threshold forces were obtained that determine two possible states: the separation of a platelet or its retention at the surface.