An interpenetrating-network theory of the cytoskeletal networks in living cells

Abstract

Cells undergo dramatic deformations during many physiological and pathological processes such as division and migration, and their mechanical integrity is supported by cytoskeletal networks (i.e. intermediate filaments, F-actin, and microtubules). Recent observations of cytoplasmic microstructure indicate interpenetration among different cytoskeletal networks, and micromechanical experiments have shown evidence of complex characteristics in the mechanical response of the interpenetrating cytoskeletal networks of living cells including viscoelastic, nonlinear stiffening, microdamage, and healing characteristics (Hu et al., 2019). However, a theoretical framework describing such a response is missing, and thus it is not clear how different cytoskeletal components with distinct mechanical properties come together to build the overall complex mechanical features of the cytoskeletal networks. In this work, we address this gap by developing a finite-deformation continuum-mechanical theory with a multi-branch visco-hyperelastic constitutive relation coupled with phase-field damage and healing. The proposed interpenetrating-network model elucidates the coupling among interpenetrating cytoskeletal components, and the roles of finite elasticity, viscoelastic relaxation, damage, and healing in the experimentally-observed mechanical response of interpenetrating cytoskeletal networks in living eukaryotic cells.