Benchmarking the flow of epithelial cell monolayer with self-aligning deformable active membranes
Collective cell migration emerges from the interplay between motility, deformability and mechanical interactions, yet incorporating these ingredients into computationally efficient tissue models remains challenging. Here, we benchmark self-aligning deformable active membranes in a confined-flow geometry that mimics epithelial monolayer migration around a circular obstacle. In this model, cells are represented as deformable, adhesive membranes whose self-propulsion direction relaxes towards their velocity. By systematically varying the self-alignment timescale, cell-cell adhesion and inlet forcing, we characterize the resulting flows through collective alignment, relative density, neighbor rearrangements and spatial velocity fields. The model captures a broad spectrum of tissue behaviors, ranging from disordered, liquid-like flows to highly aligned, solid-like states. Compared with a related multiparticle model, self-aligning active membranes achieve stronger collective alignment, exhibit a more systematic density response and access states closer to both limits of the solid-liquid spectrum. We further show that increasing the target shape index promotes cell elongation and accelerates tissue flow, directly linking cell-scale deformability to tissue-scale transport. Finally, we compare simulated velocity profiles with experimental measurements from in vitro migrating MDCK epithelial cell monolayers and find qualitative agreement across multiple horizontal and vertical transects around the obstacle. These results establish self-aligning deformable active membranes as a versatile framework for connecting cell mechanics, shape adaptation and self-alignment to collective tissue migration in confined geometries.