The SLAM - Smart, Living, & Active Matter - initiative unites theory and experimental groups of the Leiden Institute of Physics. It currently gathers the groups of Luca Giomi, Louise Jawerth, Daniela Kraft, Martin van Hecke, Silke Henkes and Alexandre Morin.
Stress patterns in an epithelial cell sheet model
Epithelial cell dynamics drive global self-organisational processes, such as morphogenesis and wound healing. The actomyosin cortex as part of the cell cytoskeleton is responsible for active force generation, balancing the pressure exerted by the cell’s cytoplasm and forming tension network spanning the entire monolayer.
We approximate the cell sheet as two-dimensional, with cellular tensions and pressures compensating each other on a triangular force network, resembling the planar tiling used in Vertex Models. Using the quasistatic argument that viscous relaxation occurs at much shorter time scales than morphogenetic processes, we assume that each vertex of the network is in mechanical equilibrium. To investigate active stress fluctuations in this heterogeneous, discrete mechanical system, we adapt and apply a Monte Carlo algorithm from statistical granular theory. We generalise the wheel move, from the Force Network Ensemble (FNE), to irregular polygons, allowing us to calculate estimations of global statistical properties of our cell sheet. We systematically find states of self-stress where tensions are balanced by compressive apical forces. Tension chains along junctions are visible, whilst retaining truncated normal distributions for both junctional tension and apical pressures separately. Varying the anisotropy and geometric disorder in the network, we show that tension chain patterns are highly sensitive to these changes. By adapting the stress ensemble theory for granular matter, we formulate a microcanonical ensemble to calculate the the probability of a single force in the network model. Comparing the analytical probability distributions with the simulation plots, we find that our analytical distributions quantitively capture the increase in distribution width as the allowed range of apical forces is increased.
Authors: Charlotte Benney*, Silke Henkes** and Isaac Chenchiah*.
*University of Bristol, **Universiteit Leiden