Stability of oriented deformation in developing biological tissues*

In polar and nematic active materials, the homogeneously deforming state exhibits a well-known instability. Meanwhile, during development of multicellular animals, tissues often undergo oriented deformation processes that are robust. How can such deformation be stable despite the known active matter instability? Here, we explore a scenario where the gradient of a scalar field defines active anisotropic stresses in the system. This is motivated by the existence of molecular concentration fields that can control biological tissue deformation during development (e.g. “morphogen gradients”). We find that the homogeneously deforming state is stable in the extensile case, but unstable in the contractile case. Intriguingly, while there are several examples for extensile tissues in nature, we could so far not identify any example for the contractile case. Hence, our results point to a potential new developmental principle in biology that is directly rooted in active matter physics.