Mechanochemical patterning and wave propagation in multicellular tubes

Multicellular tubes are fundamental tissues for transporting and distributing liquids and gases in living organisms. Although the molecular, cellular and mechanical aspects in tube formation have been addressed experimentally, how these factors are coupled to control tube patterning and dynamics at the tissue level remains incompletely understood. Here, we propose a three-dimensional (3D) vertex model that incorporates a mechanochemical feedback loop correlating cell deformation and actomyosin signaling pathway to probe the morphodynamics of multicellular tubes. We show that diverse patterns, including ring, helix, double helix, and labyrinth, are generated in tubes through pitchfork bifurcation, where spatial fluctuations of both biochemical signaling and 3D cell deformation are remarkably involved. The mechanochemical feedback loop enables cell oscillations via Hopf bifurcation, which induces the mechanical and chemical patterns to propagate successively as either traveling or pulse waves while their spatial configurations are maintained, strikingly distinct from the classical Turing instability. Our simulations, together with stability analysis of a minimal model, uncover the essential role of mechanochemical principles in sculpting biological tubes.