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This study explores 3D vertex models for multicellular systems, analyzing cell shape and configurations. Findings reveal how surface energy terms influence cell geometry in both 2D and 3D simulations.

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Area of Science:

  • Computational biology
  • Biophysics
  • Mathematical modeling

Background:

  • Vertex models simulate multicellular systems, impacting rheology and jamming transitions.
  • Existing 2D models are common, but 3D models are less explored due to complexity.
  • Energy functionals dictate cellular responses in these simulations.

Purpose of the Study:

  • Investigate single and two-cell configurations in 3D vertex models.
  • Analyze the impact of energy terms and model parameters on cell shape.
  • Compare 2D and 3D model behaviors, particularly with linear and quadratic surface energy terms.

Main Methods:

  • Analytical deduction of cell radius and contractility limits for linear and quadratic surface energy terms (2D and 3D).
  • Analysis of aspect ratio and relative radius evolution in symmetrical and asymmetrical two-cell systems.
  • Validation of analytical results using a 3D vertex model simulation.

Main Results:

  • Derived analytical solutions for single-cell radius and contractility limits in 2D and 3D.
  • Demonstrated that linear surface terms yield consistent aspect ratios in 2D and 3D.
  • Showcased distinct cell configurations for quadratic surface terms in 2D versus 3D.

Conclusions:

  • 3D vertex models offer insights into multicellular system geometry.
  • Surface energy terms significantly influence cell shape and system configurations.
  • Analytical and simulation results align with capillarity theory principles.