Mechanochemical active nematics: how to design topology sensing enzymes

Active nematic fluids are an important class of materials whose dynamics are intrinsically chaotic. Towards developing bioinspired signaling pathways that shape these flows into desired configurations, we aim to design feedback loops that spatiotemporally modulate active stress in response to structural cues from the nematic. Here, we focus on the ``sensing'' part of that problem: the conversion of structural (Q-field) information into chemical fields. We show that a curvature-dependent reaction dipole is sufficient for creating a system that dynamically senses topology by producing a concentration field possessing local extrema coinciding with +/- 1/2 defects. We consider two possible physical origins of such dipoles that can inspire experiments: (i) curved molecules that preferentially bind to nematic regions matching their curvature and (ii) nematic molecules that polarize (become reaction dipoles) when deformed. We demonstrate the behavior of this system for stationary defects and in the presence of active hydrodynamic flows.