Modeling collective cell migration in geometric confinement.

Monolayer expansion has generated great interest as a model system to study collective cell migration. During such an expansion the culture front often develops 'fingers', which we have recently modeled using a proposed feedback between the curvature of the monolayer's leading edge and the outward motility of the edge cells. We show that this model is able to explain the puzzling observed increase of collective cellular migration speed of a monolayer expanding into thin stripes, as well as describe the behavior within different confining geometries that were recently observed in experiments. These comparisons give support to the model and emphasize the role played by the edge cells and the edge shape during collective cell motion.

Inter-trabecular angle: A parameter of trabecular bone architecture in the human proximal femur that reveals underlying topological motifs.

UNLABELLED: Trabecular bone is an intricate 3D network of struts and plates. Although the structure-function relations in trabecular bone have been studied since the time of Julius Wolff, controversy still exists regarding the architectural parameters responsible for its stability and resilience. We present a parameter that measures the angle between two connected trabeculae - the Inter-Trabecular Angle (ITA). We studied the ITA values derived from µCT scans of different regions of the proximal femora of 5 individuals of different age and sex. We show that the ITA angle distribution of nodes with 3 connecting trabeculae has a mean close to 120°, nodes with 4 connecting trabeculae has a mean close to 109° and nodes of higher connectivity have mean ITA values around 100°. This tendency to spread the ITAs around geometrically symmetrical motifs is highly conserved. The implication is that the ITAs are optimized such that the smallest amount of material spans the maximal 3D volume, and possibly by so doing trabecular bone might be better adapted to multidirectional loading. We also draw a parallel between trabecular bone and tensegrity structures - where lightweight, resilient and stable tetrahedron-based shapes contribute to strain redistribution amongst all the elements and to collective impact dampening. STATEMENT OF SIGNIFICANCE: The Inter-Trabecular Angle (ITA) is a new topological parameter of trabecular bone. The ITA characterizes the way trabeculae connect with each other at nodes, regardless of their thickness and shape. The mean ITA value of nodes with 3 trabeculae is close to 120°, of nodes with 4 trabeculae is just below 109°, and the mean ITA of nodes with 5 and more trabeculae is around 100°. Thus the connections of trabeculae trend towards adopting symmetrical shapes. This implies that trabeculae can maximally span 3D space using the minimal amount of material. We draw a parallel between this motif and the concept of tensegrity - an engineering premise to which many living creatures conform at multiple levels of organization.

Regulation of epithelial cell organization by tuning cell-substrate adhesion.

Collective migration of cells is of fundamental importance for a number of biological functions such as tissue development and regeneration, wound healing and cancer metastasis. The movement of cell groups consisting of multiple cells connected by cell-cell junctions depends on both extracellular and intercellular contacts. Epithelial cell assemblies are thus regulated by a cross-talk between cell-substrate and cell-cell interactions. Here, we investigated the onset of collective migration in groups of cells as they expand from a few cells into large colonies as a function of extracellular matrix (ECM) protein coating. By varying the amount of ECM presented to the cells, we observe that the mode of colony expansion, as well as their overall geometry, is strongly dependent on substrate adhesiveness. On high ECM protein coated surfaces, cells at the edges of the colonies are well spread exhibiting large outward-pointing protrusive activity, whereas cellular colonies display more circular and convex shapes on less adhesive surfaces. Actin structures at the edge of the colonies also show different organizations with the formation of lamellipodial structures on highly adhesive surfaces and a pluricellular actin cable on less adhesive ones. The analysis of traction forces and cell velocities within the cellular assemblies confirm these results. By increasing ECM protein density, cells exert higher traction forces together with a higher outward motility at the edges. Furthermore, tuning cell-cell adhesion of epithelial cells modified the mode of expansion of the colonies. Finally, we used a recently developed computational model to recapitulate the emergent experimental behaviors of expanding cell colonies and extract that the main effect of the different cell-substrate interactions is on the ability of edge cells to form outward lamellipodia-driven motility. Overall, our data suggest that switching behaviors of epithelial cell assemblies result in a tug-of-war between friction forces at the cell-substrate interface and cell-cell interactions.

Modeling the finger instability in an expanding cell monolayer.

Collective motion occurs in many biological processes, such as wound healing, tumor invasion and embryogenesis. Experiments of cell monolayer migration have revealed the spontaneous formation of finger-like instabilities, with leader cells at their tips. We present a particle-based model for collective cell migration, based on several elements that have been found experimentally to influence cellular movement. Inside the bulk we include velocity alignment interactions between neighboring cells. At the border contour of the layer we introduce the following additional forces: surface-elasticity restoring force, curvature-dependent positive feedback, and contractile acto-myosin cables. We find that the curvature-driven instability at the layer edge is necessary and sufficient for the formation of cellular fingers, which are in good agreement with experimental observations.