TY - JOUR

T1 - Linear and nonlinear mechanical responses can be quite different in models for biological tissues

AU - Sahu, Preeti

AU - Kang, Janice

AU - Erdemci-Tandogan, Gonca

AU - Manning, M. Lisa

PY - 2020/2/21

Y1 - 2020/2/21

N2 - 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.

AB - 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.

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U2 - 10.1039/c9sm01068h

DO - 10.1039/c9sm01068h

M3 - Article

C2 - 31984411

AN - SCOPUS:85080845784

VL - 16

SP - 1850

EP - 1856

JO - Soft Matter

JF - Soft Matter

SN - 1744-683X

IS - 7

ER -