Sascha Hilgenfeldt, "Tissue modeling: Insight from continuum mechanics"

Thursday 30 Jul 2026, 14:00 → 15:00 Europe/Ljubljana

A/1-106 - Seminarska soba fizike (F5) (Jamova)

Two-dimensional vertex models have been used extensively to study and simulate the mechanical behavior of monolayer tissues, a simplified approach that allows for detailed study of structure and disorder in large systems. Morphological indicators from the structure are then taken as indicators for mechanical behavior and even biological fitness. The most common 2D vertex models use generic elasticity terms whose validity has not been closely scrutinized. Starting from experimental data from MDCK epithelial cells, we question (i) the appropriateness of a 2D model in the light of severe breaking of mechanical symmetry along the apical-basal axis, and (ii) the accuracy of the functional form of the standard modeling terms. To make progress in both cases, we describe cells as continuum materials and use the equations of continuum elasticity to derive correlations between elastic deformation energy and shape parameters. Representing the cortex of a three-dimensional cell as a cylindrical shell, we find that agreement with experimental data requires proper modeling of the 3D deformation, i.e., the non-uniformity along the apical-basal axis caused primarily by anisotropic actin contractility at the basal side. The relationship between elastic energy and perimeter is then found to be non-harmonic, even in the limit of vanishing actin content. Therefore, we construct a 2D model modeling cytoplasm and cortex as different materials, but uniform in the apical-basal direction. Here, we can analytically compute the deformation shape and energy for arbitrary outlines of the deformed cell. We find that the non-harmonic relationship between energy and perimeter persists, pointing towards a revised vertex model that retains the simplicity of the standard vertex model, but is informed by and consistent with continuum mechanics.