Active tension network model suggests an exotic mechanical state realized in epithelial tissues

Abstract

Mechanical interactions play a crucial role in epithelial morphogenesis, yet understanding the complex mechanisms through which stress and deformation affect cell behavior remains an open problem. Here we formulate and analyze the Active Tension Network (ATN) model, which assumes that the mechanical balance of cells within a tissue is dominated by cortical tension and introduces tension-dependent active remodeling of the cortex. We find that ATNs exhibit unusual mechanical properties. Specifically, an ATN behaves as a fluid at short times, but at long times supports external tension like a solid. Furthermore, an ATN has an extensively degenerate equilibrium mechanical state associated with a discrete conformal - “isogonal” - deformation of cells. The ATN model predicts a constraint on equilibrium cell geometries, which we demonstrate to approximately hold in certain epithelial tissues. We further show that isogonal modes are observed in the fruit y embryo, accounting for the striking variability of apical areas of ventral cells and helping understand the early phase of gastrulation. Living matter realizes new and exotic mechanical states, the study of which helps to understand biological phenomena.

Differential growth triggers mechanical feedback that elevates Hippo signaling

“…In contrast with earlier vertex models (20), we allow for an adaptive cytoskeletal response, decreasing cortical tension proportionally with increasing pressure acting on a cell. The model of adaptive cytoskeletal response used here is consistent with the recently proposed "active tension network" theory (32), which postulated that the rate of myosin recruitment (or release) into the actin-myosin cortex and concomitant changes in cortical tension is modulated by changes in mechanical stress. Model simulations considering cell growth and resulting heterogeneity of pressure confirm that differential clone growth leads to higher cellular pressure, and lower cortical tension, within faster-growing cells (Fig.…”

Correlating cell shape and cellular stress in motile confluent tissues

“…These methods rely on advances in imaging techniques that provide a spatially resolved view of tissue development during morphogenesis, with visualization of the cell boundaries of two dimensional cell sheets [20][21][22][23][24]. Assuming mechanical equilibrium, one can then infer the tensions along cell edges and pressures within each cell from the cell configurations.…”

Using cell deformation and motion to predict forces and collective behavior in morphogenesis

“…The goal of one class of recent theoretical work is to infer cellular forces within epithelia based on images of flourescently labeled membranes [17, 34–40]. These methods attempt to infer tensions along cell-cell interfaces and pressures within cells by observing the angles at which cell-cell interfaces intersect.…”

“…A third assumption must be made to infer tensions, and and three different strategies have been proposed for doing so. First, one can make additional assumptions about the biological system, for instance that cell pressure differences do not play a large role [37, 40]. Second, additional measurements can be taken into account, for instance the curvature of cell-cell interfaces [39].…”