Anisotropy profoundly alters stress fields within contractile cells and cell aggregates

Abstract

Many biological phenomena such as cell proliferation and death are correlated with stress fields within cells. Stress fields are quantified using computational methods which rely on fundamental assumptions about local mechanical properties. Most existing methods such as Monolayer Stress Microscopy assume isotropic properties, yet experimental observations strongly suggest anisotropy. We first model anisotropy in circular cells analytically using Eshelby's inclusion method. Our solution reveals that uniform anisotropy cannot exist in cells due to the occurrence of substantial stress concentration in the central region. A more realistic non-uniform anisotropy model is then introduced based on experimental observations and implemented numerically which interestingly clears out stress concentration. Stresses within the entire aggregate also drastically change compared to the isotropic case, resulting in better agreement with observed biomarkers. We provide a physics-based mechanism to explain the low alignment of stress fibers in the center of cells, which might explain certain biological phenomena e.g., existence of disrupted rounded cells, and higher apoptosis rate at the center of circular aggregates.

Keywords: Anisotropic contractility; Circular constrained cells; Mechanical stress; Stress-biomarker relations.