Collective dynamics of coherent motile cells on curved surfaces

Cellular dynamic behaviors in organ morphogenesis and embryogenesis are affected by geometrical constraints. In this paper, we investigate how the surface topology and curvature of the underlying substrate tailor collective cell migration, which are crucial in many important aspects of development and disease. An active vertex model is developed to explore the collective dynamics of coherent cells crawling on curved surfaces. We show that cells can self-organize into rich dynamic patterns including local swirling, global rotation, spiral crawling, serpentine crawling, and directed migration, depending on the interplay between cell–cell interactions and geometric constraints. Increasing substrate curvature results in higher cell–cell bending energy and thus tends to suppress local swirling and enhance density fluctuations. Substrate topology is revealed to regulate both the collective migration modes and density fluctuations of cell populations. In addition, upon increasing noise intensity, a Kosterlitz–Thouless-like ordering transition can emerge on both undevelopable and developable surfaces. This study paves the way to investigate various in vivo morphogenetic processes that involve surface curvature and topology.