Bistable front dynamics in a contractile medium: Travelling wave fronts and cortical advection define stable zones of RhoA signaling at epithelial adherens junctions

Mechanical coherence of cell layers is essential for epithelia to function as tissue barriers and to control active tissue dynamics during morphogenesis. RhoA signaling at adherens junctions plays a key role in this process by coupling cadherin-based cell-cell adhesion together with actomyosin contractility. Here we propose and analyze a mathematical model representing core interactions involved in the spatial localization of junctional RhoA signaling. We demonstrate how the interplay between biochemical signaling through positive feedback, combined with diffusion on the cell membrane and mechanical forces generated in the cortex, can determine the spatial distribution of RhoA signaling at cell-cell junctions. This dynamical mechanism relies on the balance between a propagating bistable signal that is opposed by an advective flow generated by an actomyosin stress gradient. Experimental observations on the behavior of the system when contractility is inhibited are in qualitative agreement with the predictions of the model.Author summary: Mathematical models play a key role in uncovering mechanisms responsible for the formation of patterns in cells and tissues. The well known Turing mechanism based on nonlinear reaction kinetics and differential diffusion explains the formation of static patterns, while positive feedback interactions can generate dynamical structures such as propagating fronts and excitable pulses. Recent studies have demonstrated the importance of mechanical forces that can lead to novel mechanisms of pattern formation such as clustering and oscillations in contractile systems. Here we investigate how contractile forces in mechanically active media can affect bistable front propagation. We found that contraction regulates the front speed or can fully suppress its propagation in space to create a static localized zone. The proposed model provides a new mechanism for cross-talk between mechanical activity of cells and biochemical signaling.