FIGURE 1.

Depiction of two particles (i.e., cells, liposomes, or nanoparticles) bridged by tethered ligand/receptor bonds. The gap height, or surface separation, h(D,r), is a function of the spheres' tip-to-tip distance (D) and the position along the lateral axis (r). The surface curvature limits how many particles may bridge the two surfaces. The relevant interaction area is constrained by the tether extension, or contour length (L), and the corresponding radial distance (r_L). The area containing bound tethers is geometrically limited by the effective binding range of an individual tether (l_B) and the corresponding radial distance (r_B). Ligands tethered to extensible molecules, such as polymers in good solvents, will stochastically sample many distances (l) away from their tether's anchor, which can be much farther away than the tether's time-average or equilibrium extension (l_eq) (16,17). These larger extensions produce the bridging forces that we model in this article.