Deforming polar active matter in a scalar field gradient

Abstract

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 show that 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: (i) 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. (ii) 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.

Soft matter roadmap*

“…However, the orientationally ordered state in wet active matter is generally unstable, consistent with in-vitro experiments [506]. How oriented tissue deformation can be robust during morphogenesis despite this instability is still unclear [507]. More generally, much remains to be done to bridge between active material theories and the full complexity of living organisms.…”

Marangoni-like tissue flows enhance symmetry breaking of embryonic organoids

“…Fourth, while we have focused here on the recirculating flows in the aggregate, we did not include any mechanism creating aggregate elongation, which would necessitate both active driving forces and globally aligned orientational information [49]. Indeed, it has been shown for fish embryonic stem cell aggregates, that cell polarity proteins are present and play an important role for gastruloid elongation [50, 51].…”