Coherent Motion of Monolayer Sheets under Confinement and Its Pathological Implications
Fig 1
A schematic of cell center model depicting the arrangement of cells and the forces acting on them.
(a) A 2-D monolayer of epithelial cells, confined inside a circular geometry is considered with cells represented as points at their center. (b) Delaunay triangulation (blue) has been used to model cell—cell connectivity, which finds the nearest neighbors of each point and form the connectivity array accordingly. Because of the greater clarity it affords and better connection with the experimental geometry, Voronoi tessellation (topological dual of Delaunay triangulation) is used for visualization of cells. (c) When two originally connected cells move apart and form new neighbors, the connectivity of the system is updated using Delaunay triangulation. This connectivity update automatically takes T1 transitions into account. (d) Enlarged view of a representative cell i, along with its connection to neighboring cells. The position vector of this cell center is denoted by ri and position vector of its jth neighbor is denoted by rj. The blue arrow indicates the force, Fij acting between cells i and j. The total force acting on ith cell is the sum of the contributions from all the connecting neighbors. (e) The interaction between two adjacent cells is either compressive or tensile, depending upon the relative deformation of connecting spring with respect to its undeformed length, a0. Here compressive and tensile stiffness of each spring is represented by kc and kt, respectively. While kc mimics the bulk cell stiffness, kt mimics cell-cell cohesivity. It is assumed that if the deformation of any spring is greater than dmax, the cell-cell connection is broken and there is no force transfer between these two cells. (f) Force acting on each cell is resolved along anti-parallel (Fll) and perpendicular(F⊥) to the direction of the cell’s polarization(). Here v denotes the velocity vector on each particle. (g) Velocity profile in the direction of polarization as a function of Fll.