Linear and nonlinear mechanical responses can be quite different in models for biological tissues

Preeti Sahu, Janice Kang, Gonca Erdemci-Tandogan, M. Lisa Manning

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The fluidity of biological tissues-whether cells can change neighbors and rearrange-is important for their function. In traditional materials, researchers have used linear response functions, such as the shear modulus, to accurately predict whether a material will behave as a fluid. Similarly, in disordered 2D vertex models for confluent biological tissues, the shear modulus becomes zero precisely when the cells can change neighbors and the tissue fluidizes, at a critical value of control parameter s0∗ = 3.81. However, the ordered ground states of 2D vertex models become linearly unstable at a lower value of control parameter (3.72), suggesting that there may be a decoupling between linear and nonlinear response. We demonstrate that the linear response does not correctly predict the nonlinear behavior in these systems: when the control parameter is between 3.72 and 3.81, cells cannot freely change neighbors even though the shear modulus is zero. These results highlight that the linear response of vertex models should not be expected to generically predict their rheology. We develop a simple geometric ansatz that correctly predicts the nonlinear response, which may serve as a framework for making nonlinear predictions in other vertex-like models.

Original languageEnglish (US)
Pages (from-to)1850-1856
Number of pages7
JournalSoft Matter
Issue number7
StatePublished - Feb 21 2020

ASJC Scopus subject areas

  • General Chemistry
  • Condensed Matter Physics


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