The biological concepts of adhesion rely on creating receptor-ligand (R-L) encounter complexes between the receptor patches located on the surface of the cell and ligands distributed on the functionalized surfaces. Existence of the encounter complex does not guarantee there is a physical link between receptor and ligand. It means that receptor and ligand are in close vicinity that allows for a possible creation of linked bond. During the time the encounter complex exists, R-L are either in the linked state (there is a physical bond) or they are unlinked (no bond). Depending on the state in the previous time slot, R-L can react to creation of a bond, or existing R-L bond can rupture. This event can be described by association and dissociation rates leading to probablilities of the creation and rupture of the bonds.

 

The described model of adhesion mechanism is based on bonds between the receptor site on a cell and the ligand site on a wall. Once the stiffness of such a bond is known, one can model this bond by putting a repulsive or attractive force at the corresponding mesh points. The computation of the adhesive forces acting on the end points of the bond is based on the harmonic spring.

 

We included this mechanism into PyOIF and we analyzed whether such model can recover mean velocities in a channel where cells adhere to the surface. We also showed that such model can recover the dependence of averaged velocities in the channel on the surface shear rate.

Bond formation, receptors are denoted by black points. (a) The distance of the cell to the surface is larger than the capture radius r0. No encounter complex has been formed and thus no bonds can be created. (b) Three boundary points B, C and D are within the capture radius. For these points, an encounter complex has been created. Stochastic bond creation resulted in two bonds C and D, and no bond for receptor B. Corresponding ligand positions at the wall are C′ and D′. (c) Stochasticity caused that there still has not been any bond formed for receptor B. Receptor C is now out of the capture radius, however, the bond CC′ has not reached the critical length for the rupture bond still exists. Receptor D is out of the capture radius. It had reached the critical bond length and the bond has ruptured. (d) The cell has moved away from the wall and all the bonds have ruptured. From Computational Blood Cell Mechanics.

 

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