Deforming polar active matter in a scalar field gradient

Active matter with local polar or nematic order is subject to the well-known Simha-Ramaswamy instability. It is so far unclear how, despite this instability, biological tissues can undergo robust active anisotropic deformation during animal morphogenesis. Here we ask under which conditions protein concentration gradients (e.g. morphogen gradients), which are known to control large-scale coordination among cells, can stabilize such deformations. To this end, we study a hydrodynamic model of an active polar material. To account for the effect of the protein gradient, the polar field is coupled to the boundary-provided gradient of a scalar field that also advects with material flows. Focusing on the large system size limit, we show in particular: (a) the system can be stable for an effectively extensile coupling between scalar field gradient and active stresses, i.e. gradient-extensile coupling, while it is always unstable for a gradient-contractile coupling. Intriguingly, there are many systems in the biological literature that are gradient-extensile, while we could not find any that are clearly gradient-contractile. (b) Stability is strongly affected by the way polarity magnitude is controlled. Taken together, our findings, if experimentally confirmed, suggest new developmental principles that are directly rooted in active matter physics.

Automated summary

By studying a hydrodynamic model of active polar material, it is found that protein concentration gradients can stabilize active anisotropic deformation, and stability is strongly affected by the coupling way between fluid pressure and protein concentration gradient as well as the control of polarity magnitude.