The directional collective migration along traveling signal waves is indispensable for the development in multicellular tissues. However, little is known about how the net motion occurs under wave-like activation while the forces are balanced. To reveal the law of migration with the traveling wave, we study collective migration by considering the signal-dependent coordination of contractile stress and adhesive friction to the substratum. We show that their interplay forms a non-reciprocal motion that enhances the backward motion against a signal wave. Moreover, the relaxation dynamics during this non-reciprocal motion realize a noise filter by which the migration velocity is optimized under a certain wave velocity. Our finding thus brings deep understanding of the rectified migration by a traveling signal wave, which may be involved in wound healing of epithelial tissues.
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