Parameter degeneracy in the vertex model for tissues

TL;DR

This paper investigates parameter degeneracy in the vertex model for tissues, showing how it affects physical observables and proposing methods to resolve it, with implications for model fitting and broader physical models.

Contribution

It identifies and addresses parameter degeneracy in heterogeneous vertex models, offering methods to fix gauge pressure and improve physical relevance of simulations.

Findings

Degeneracy involves the product of target areas and stiffness.

Fixing this product fixes the global tissue pressure.

Boundary conditions can remove degeneracy.

Abstract

The vertex model with homogeneous cell properties is known to exhibit a parameter degeneracy in which the system's dynamics is independent of the target area. Here, we show, for the heterogeneous vertex model where cells differ in size and stiffness, that degeneracy is also present with the average product of target areas and stiffness becoming dynamically irrelevant. Fixing this quantity is equivalent to fixing the global internal tissue pressure. Unless properly treated, this degeneracy undermines the physical relevance of key observables' numerical values, such as cell target shape index, cell pressure, and cell stress tensor. We present methods to resolve the degeneracy and to correctly set the gauge pressure via symmetry transformations applied to the cells' target areas. We further demonstrate that the degeneracy is removed under certain boundary conditions and partially lifted when spherical tissues are modeled using a locally planar approximation, leading to numerical consequences when fitting model parameters to experimental data. The approach extends beyond vertex models and provides a framework for testing whether the parameter spaces of other physical models are free from degeneracy.