Internal geometries regulate the symmetry of defect configurations in cell populations confined to domains with a negative Euler characteristic

Abstract

Nematic order of confined cell populations plays an important role in determining cell alignment and stable configurations of topological defects, which are related to various biomechanical phenomena. Topological charges (or winding numbers) of topological defects strictly depend on the Euler characteristic of the confining domain, which has typically been non-negative in studies focused on domains without internal obstacles. However, biological tissues often surround two or more internal obstacles or holes, which inherently generate defects with negative charges. To understand the mechanical interaction between cellular tissue and obstacles, it is necessary to elucidate the geometrical effects of obstacles on cell alignment and defects with negative charges. Here, we investigate how cell populations achieve stable defect configurations of two -1/2 defects in a triply connected domain. First, we present experimental observations of C2C12 myoblasts confined by two circular obstacles of varying diameter, demonstrating that two $-1/2$ defects are the most frequent configuration when the obstacles are sufficiently large. Second, to theoretically validate these experimental observations, we perform systematic stability analyses of defect configurations using an explicit expression of cell alignment and numerical minimization of the Frank elastic energy. Our numerical calculations reveal that the most stable configuration shifts continuously from a horizontal, through off-axis, to a vertical configuration as the obstacle size increases. In addition, the experimentally observed defect positions agreed with these theoretical predictions to within 60 $μ$m. These findings suggest that obstacle sizes control the symmetry of cell alignment, providing insights into how geometric and topological constraints can generate complex force patterns during morphogenesis or organ movements.