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Parameter degeneracy in the vertex model for tissues.

Paulo C Godolphim1,2, Leonardo G Brunnet2, Rodrigo Soto1

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Summary
This summary is machine-generated.

The heterogeneous vertex model exhibits parameter degeneracy, making average target area and stiffness irrelevant. Methods are presented to resolve this degeneracy and ensure physical relevance of tissue model observables.

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Area of Science:

  • Quantitative Biology
  • Biophysics
  • Computational Biology

Background:

  • The vertex model is a key tool for simulating biological tissues.
  • Homogeneous vertex models show parameter degeneracy, where dynamics are independent of target area.
  • This degeneracy complicates the physical interpretation of model parameters.

Purpose of the Study:

  • To investigate parameter degeneracy in heterogeneous vertex models.
  • To identify the specific parameters rendered dynamically irrelevant in heterogeneous models.
  • To develop methods for resolving degeneracy and ensuring physical relevance of observables.

Main Methods:

  • Analysis of the heterogeneous vertex model with varying cell size and stiffness.
  • Identification of the average product of target areas and stiffness as a dynamically irrelevant quantity.
  • Development of symmetry transformations for cell target areas to fix gauge pressure.
  • Investigation of degeneracy under different boundary conditions and approximations.

Main Results:

  • Parameter degeneracy is present in heterogeneous vertex models.
  • The average product of target area and stiffness is dynamically irrelevant.
  • Degeneracy undermines the physical relevance of observables like cell shape index and pressure.
  • Methods to resolve degeneracy and set gauge pressure were successfully developed.
  • Degeneracy is removed by specific boundary conditions and partially by planar approximations.

Conclusions:

  • Parameter degeneracy in heterogeneous vertex models requires careful treatment.
  • The developed methods allow for physically relevant parameter estimation in tissue models.
  • The findings have implications for fitting vertex model parameters to experimental data.
  • The framework can be extended to assess degeneracy in other physical models.