Active nematics on deformable surfaces

Morphogenesis in biological surfaces resulting from an interplay among nematic order, geometric properties, topological constraints and hydrodynamic interaction has been a subject of experimental investigation. From the computational standpoint, this interplay has been widely explored on rigid surfaces using coarse-grained or agent-based active nematic models. However, shape change in deformable surfaces resulting from this tight coupling has been explored in fewer studies. In this study, we propose an active gel model that accounts for shape changes in a deformable surface resulting from an interplay between the evolution of orientational order, Newtonian Rheology as well as active flows. We describe the numerical solution of the resulting Euler-Lagrange equations for biologically relevant case studies such as for shape changes in the manifold of contractile cytoskeleton network undergoing cell division and for shape changes in a monolayer of microtubules and kinesin enclosed in a lipid vesicle. The trends obtained from numerical studies are compared and verified against the experimental data.