Boundary conditions are important for pattern formation in active matter. However, it is still not well-understood how alterations in the boundary conditions (dynamic boundary conditions) impact pattern formation. To elucidate the effect of dynamic boundary conditions on the pattern formation by active matter, we investigate an in vitro gliding assay of microtubules on a deformable soft substrate. The dynamic boundary conditions were realized by applying mechanical stress through stretching and compression of the substrate during the gliding assay. A single cycle of stretch-and-compression (relaxation) of the substrate induces perpendicular alignment of microtubules relative to the stretch axis, whereas repeated cycles resulted in zigzag patterns of microtubules. Our model shows that the orientation angles of microtubules correspond to the direction to attain smooth movement without buckling, which is further amplified by the collective migration of the microtubules. Our results provide an insight into understanding the rich dynamics in self-organization arising in active matter subjected to time-dependent boundary conditions.
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