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 an 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 an 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 file 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.