Parameter degeneracy in the vertex model for tissues.

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.