  Interaction between active materials and the boundaries of geometrical
confinement is key to many emergent phenomena in active systems. For living
active matter consisting of animal cells or motile bacteria, the confinement
boundary is often a deformable interface, and it has been unclear how
activity-induced interface dynamics might lead to morphogenesis and pattern
formation. Here we studied the evolution of bacterial active matter confined by
a deformable boundary. We discovered that an ordered morphological pattern
emerged at the interface characterized by periodically-spaced interfacial
protrusions; behind the interfacial protrusions, bacterial swimmers
self-organized into multicellular clusters displaying +1/2 nematic defects.
Subsequently, a hierarchical sequence of transitions from interfacial
protrusions to creeping branches allowed the bacterial active drop to rapidly
invade surrounding space with a striking self-similar branch pattern. We found
that this interface patterning is controlled by the local curvature of the
interface, a phenomenon we denote as collective curvature sensing. Using a
continuum active model, we revealed that the collective curvature sensing
arises from enhanced active stresses near high-curvature regions, with the
active length-scale setting the characteristic distance between the interfacial
protrusions. Our findings reveal a protrusion-to-branch transition as a novel
mode of active matter invasion and suggest a new strategy to engineer pattern
formation of active materials.
