Mechanochemical Topological Defects in an Active Nematic

We propose a reaction-diffusion system that converts topological information of an active nematic into chemical signals. We show that a curvature-activated reaction dipole is sufficient for creating a system that dynamically senses topology by producing a concentration field possessing local extrema coinciding with $\pm\frac{1}{2}$ defects. The enabling term is analogous to polarization charge density seen in dielectric materials. We demonstrate the ability of this system to identify defects in both passive and active nematics. The model demonstrates that a relatively simple feedback scheme in the form of a PDE system is capable of producing chemical signals in response to inherently non-local structures in anisotropic media. We posit that such coarse-grained systems can help generate testable hypotheses for regulated processes in biological systems such as morphogenesis and motivate the creation of bioinspired materials that utilize dynamic coupling between nematic structure and biochemistry.