Vertex model instabilities for tissues subject to cellular activity or applied stresses

Continuum description of confluent tissues with spatial heterogeneous activity

A continuum description is built to characterize the stationary and transient deformations of confluent tissues subject to heterogeneous activities. By defining a coarse-grained texture matrix field to represent the shape and size of cells, we derive the coarse-grained stress tensor for the vertex model. Activity in the tissue takes the form of inhomogeneous apical contractions, which can be modeled as reductions of the vertex model reference areas or perimeters representing activity in the medial and perimeter regions of the cells, respectively. For medial activity, the extra stress is just an isotropic pressure, while for perimeter activity, it also has a deviatoric component, which is aligned with the texture matrix. The predictions of the continuum description are compared with the average spatiotemporal deformations obtained in simulations of the vertex model subject to localized apical contractions, showing an excellent agreement, even if the active patch is as small as one cell. The fluctuations around the average are more prominent when the activity is in the medial region due to the lack of negative active shape feedback, which, coupled with the confluent property, increases cellular shape and size variations.

Network model of active elastic shells swollen by hydrostatic pressure

Many organisms have an elastic skeleton that consists of a closed shell of epithelial cells that is filled with fluid, and can actively regulate both elastic forces in the shell and hydrostatic pressure inside it. In this work we introduce a simple network model of such pressure-stabilized active elastic shells in which cross-links are represented by material points connected by non-linear springs of some given equilibrium lengths and spring constants. We mimic active contractile forces in the system by changing the parameters of randomly chosen springs and use computer simulations to study the resulting local and global deformation dynamics of the network. We elucidate the statistical properties of these deformations by computing the corresponding distributions and correlation functions. We show that pressure-induced stretching of the network introduces coupling between its local and global behavior: while the network opposes the contraction of each excited spring and affects the amplitude and relaxation time of its deformation, random local excitations give rise to contraction of the network and to fluctuations of its surface area.

Geometrical characterization of active contraction pulses in epithelial cells using the two-dimensional vertex model

Several models have been proposed to describe the dynamics of epithelial tissues undergoing morphogenetic changes driven by apical constriction pulses, which differ in where the constriction is applied, either at the perimeter or in the medial regions. To help discriminate between these models, we analyse the impact of where constriction is applied on the final geometry of the active contracted cell, using the two-dimensional vertex model. We find that medial activity, characterized by a reduction in the reference area, generates anisotropic cell shapes, whereas isotropic cell shapes are produced when the reference perimeter is reduced. When plasticity is included, sufficiently slow processes of medial contractile activity, compared with the characteristic times of elasticity and plasticity, cells can achieve less elongated shapes. Similarly, for perimeter activity, the highest level of contraction is achieved. Finally, we apply the model to describe the apical contractile pulses observed within the epithelial enveloping cell layer during the pre-epiboly of the annual killifish Austrolebias nigripinnis. The analysis of the cell shape changes allowed a global fit of all parameters of the vertex model, with the pulses being quantitatively captured using perimeter activity and area plasticity.