Exploring the effects of mechanical feedback on epithelial topology

Abstract

SUMMARYApical cell surfaces in metazoan epithelia, such as the wing disc of Drosophila, resemble polygons with different numbers of neighboring cells. The distribution of these polygon numbers has been shown to be conserved. Revealing the mechanisms that lead to this topology might yield insights into how the structural integrity of epithelial tissues is maintained. It has previously been proposed that cell division alone, or cell division in combination with cell rearrangements, is sufficient to explain the observed epithelial topology. Here, we extend this work by including an analysis of the clustering and the polygon distribution of mitotic cells. In addition, we study possible effects of cellular growth regulation by mechanical forces, as such regulation has been proposed to be involved in wing disc size regulation. We formulated several theoretical scenarios that differ with respect to whether cell rearrangements are allowed and whether cellular growth rates are dependent on mechanical stress. We then compared these scenarios with experimental data on the polygon distribution of the entire cell population, that of mitotic cells, as well as with data on mitotic clustering. Surprisingly, we observed considerably less clustering in our experiments than has been reported previously. Only scenarios that include mechanical-stress-dependent growth rates are in agreement with the experimental data. Interestingly, simulations of these scenarios showed a large decrease in rearrangements and elimination of cells. Thus, a possible growth regulation by mechanical force could have a function in releasing the mechanical stress that evolves when all cells have similar growth rates.

Emergence of collective modes and tri-dimensional structures from epithelial confinement

“…Several models based on non-uniform cell growth across growing islets have emphasized the role of free edges [41][42][43][44][45] , some of them resulting in out-of-plane modulations 41 . Our results do not exclude these mechanisms by which more cells get to be produced at peripheral regions.…”

Mechanisms and mechanics of cell competition in epithelia

“…Examples of the second approach are vertex models that consider cells as individual objects 82 . They are increasingly used to study cellular processes within epithelia, including cell motility, cell-cell adhesion, mitosis, delamination and apoptosis 77,84,88,89 . As currently implemented, these models share the key assumption that epithelial mechanics are dominated by forces acting within the plane of cellular junctions (adherens junctions).…”

“…Another limitation of most current vertex models is that they are restricted to two dimensions, although recent work suggests that three-dimensional modelling is possible 91 . Despite these simplifications, vertex models have successfully represented biologically relevant processes 77,84,88,89,92 . Nevertheless, there is a need for validation with experimental measurements of forces within tissues.…”

Impact of implementation choices on quantitative predictions of cell-based computational models

“…Vertex models have been used to study a variety of processes in epithelial tissues [3][4][5][6][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. These processes include growth of the Drosophila wing imaginal disc [3,4], migration of the visceral endoderm of mouse embryos [5], and tissue size control in the Drosophila embryonic epidermis [31].…”

“…The functional form for this total stored energy varies between applications, but is typically chosen to reflect the effect of the force-generating molecules which localise at or near the apical surface. This energy function is then used either to derive forces that feed into a deterministic equation of motion for each vertex, which must be integrated over time [4,24,28], or else minimised directly assuming the tissue to be in quasistatic mechanical equilibrium at all times [3,25]. A third approach is to apply Monte Carlo algorithms to find energy minima [39,40].…”