Vertex models capturing subcellular scales in epithelial tissues
Fig 3
The effective relation between forces and cell shapes in the vertex model can be changed by introducing submodules featuring active regulation and mechanosensitive feedback describing activities at the subcellular scale.
(A) The mechanics in the reference vertex model [23] are governed by an energy function (a phenomenological Hamiltonian) that dictates a linear relation between forces and cell shape (observed e.g., in the ground states or a proliferation-free simulation). To be able to capture realistic tissue morphologies, vertex models are commonly extended to a full simulation framework with components refining the subcellular scales, resulting in effectively nonlinear relations between forces and cell geometry [65]. The subcellular activities include the activation and turnover of cytoskeleton machinery and adhesion proteins, the relaying of mechanical signals through mechanotransduction molecules, the modulation of mechanical forces by the spatiotemporal dynamics of signaling pathways, and the activation and deactivation of genetic programs instructing protein synthesis. (B) Examples of submodules that actively regulate quantities are strain-dependent remodeling of the target edge length, edge length-dependent active tension, or strain-dependent remodeling of the density of a biomolecule, e.g., myosin. In systems with mechanosensitive feedback, these remodeled quantities are usually interdependent and formulated as coupled differential equations.