Self-Sustained Motion of a Train of Haptotactic Microcapsules

Using theory and simulation, we design a train of N microcapsules that undergoes self-sustained, directed motion along all adhesive surface in solution. The motion is initiated by the release of nanoparticles from a single signaling capsule at one end of the train. The released nanoparticles can bind to the underlying surface and thereby induce;in adhesion gradient on the substrate. Through the combined effects of the self-imposed adhesion gradient and hydrodynamic interactions, the N microcapsules autonomously move in single rite toward the region of greatest adhesion. At late times, this train reaches a steady-state velocity U, which decreases with train length as N-1/2. We calculate the maximum length for which the train maintains this cooperative, autonomous motion.