Coarse-graining the vertex model and its response to shear Articles uri icon

publication date

  • October 2023


  • 044118


  • 108

International Standard Serial Number (ISSN)

  • 1539-3755

Electronic International Standard Serial Number (EISSN)

  • 1550-2376


  • Tissue dynamics and collective cell motion are crucial biological processes. Their biological machinery is mostly known, and simulation models such as the active vertex model (AVM) exist and yield reasonable agreement with experimental observations like tissue fluidization or fingering. However, a good and well-founded continuum description for tissues remains to be developed. In this work we derive a macroscopic description for a two-dimensional cell monolayer by coarse-graining the vertex model through the Poisson bracket approach. We obtain equations for cell density, velocity and the cellular shape tensor. We then study the homogeneous steady states, their stability (which coincides with thermodynamic stability), and especially their behavior under an externally applied shear. Our results contribute to elucidate the interplay between flow and cellular shape. The obtained macroscopic equations present a good starting point for adding cell motion, morphogenetic and other biologically relevant processes.


  • Mathematics
  • Physics


  • mecánica estadística; termodinámica irreversible; no equilibrio; células epiteliales; biomecánica; reología