Density-Velocity Relation Is Scale-Dependent in Epithelial Monolayers

TL;DR

This study reveals that the relationship between cell density and velocity in epithelial monolayers depends on the spatial scale, with positive correlation at small scales and negative at large scales, due to competing active forces and mechanical confinement.

Contribution

It demonstrates the scale-dependent nature of density-velocity relations in epithelial monolayers and introduces a minimal model explaining the observed crossover.

Findings

Positive density-velocity correlation at small scales

Negative correlation at large scales

Identification of a characteristic length scale for pressure segregation

Abstract

The relationship between cell density and velocity is often assumed to be negative, reflecting crowding-induced suppression of movement. However, observations across systems reveal a more nuanced picture: while some emphasize contact inhibition of locomotion, others suggest that dense regions exhibit enhanced activity due to force generation and stress buildup. Here, using experimental measurements we show that density-velocity relations in epithelial monolayers are inherently scale dependent. By coarse-graining cell trajectories over multiple spatial windows, we find that cell velocity correlates positively with local density at small scales, but negatively at large scales. Employing traction force measurements, we find that this crossover coincides with the emergence of mechanical pressure segregation, defining a characteristic length scale beyond which crowding dominates. A minimal model incorporating activity-induced shape changes reproduces this crossover and identifies the competition between active force generation and mechanical confinement as the underlying mechanism. Our results reconcile conflicting views of density-regulated migration and highlight an emergent length scale as a key factor in interpreting collective cell dynamics.