  Epithelial morphogenesis, a signature problem of tissue biology and tissue
mechanics, continues to inspire biologists and physicists alike. Many
treatments focus on tissue fluidization, apical/basal ratio changes, or
mechanical instabilities. In contrast to these approaches, shape-programmable
materials, where the local lengths in the material change in a prescribed way,
offer an appealing analogy. In this analogy, certain in-plane collective cell
behaviors could also actively alter the local lengths in a tissue and therefore
provide the ingredients necessary for shape programming. In this Letter we
demonstrate that this is indeed the case for directed, active T1 rearrangements
of cells. We determine the required shape programming parameters associated to
tissue patches with both fixed numbers of rearrangements and patches at steady
state between directed T1 events and counterbalancing randomly oriented ones
using a simple free-boundary vertex model approach. Along the way we uncover a
surprising connection between tissues with active T1 events and the central
limit theorem, and through it, the physics of entropic springs.
