Linear viscoelastic properties of the vertex model for biological tissues

Biological tissues can repair themselves, respond to environmental changes and grow without compromising their integrity. Consequently, they exhibit complex viscoelastic rheological behavior where constituent cells actively tune their mechanical properties to change the overall response of the tissue, e.g., from solid-like to fluid-like. Mesoscopic mechanical properties of tissues are commonly modeled with the vertex model. While previous studies have predominantly focused on the rheological properties of the vertex model at long time scales, we systematically studied the full dynamic range by applying small oscillatory shear and bulk deformations in both solid-like and fluid-like phases. Furthermore, we considered systems with external (e.g., cell-substrate) and internal (e.g., cell-cell) dissipation mechanisms. We showed that the linear rheological response of the system can be described using the normal mode formalism, where each normal mode responds with a characteristic relaxation timescale. This semi-analytical method based on normal modes allows full characterization of the potentially complex linear rheological response of the system at all driving frequencies and identification of collective excitations. We show that internal and external dissipation mechanisms lead to qualitatively different rheological behaviors, which is particularly pronounced at high driving frequencies. Our findings, therefore, underscore the importance of microscopic dissipation mechanisms in understanding the rich rheological behavior of biological tissues.