A two-dimensional vertex model for curvy cell-cell interfaces at the subcellular scale.

Area of Science:

• Cell biology
• Biophysics
• Computational modeling

Background:

• Tissue cross-sections typically show convex polygons, but non-convex shapes with curved interfaces exist.
• Existing 2D vertex models are largely limited to convex polygons, restricting their applicability.

Purpose of the Study:

• To develop a computational framework for modeling curvy cell-cell interfaces at the subcellular scale within vertex models.
• To extend vertex models to accommodate non-convex polygons and analyze their mechanical properties.

Main Methods:

• Introduced a framework using parametrized curves expanded in Fourier series to represent curvy cell-cell interfaces.
• Incorporated Fourier coefficients as additional degrees of freedom in vertex models.
• Analyzed the energetic favorability of local subcellular curvature versus larger-scale deformations.

Main Results:

• The extended model allows cells with the same shape index to exhibit diverse morphologies (e.g., elongated or globular with lobes).
• Local subcellular curvature or buckling can be energetically favorable over larger-scale deformations under anisotropic stress.
• Subcellular curvature emerges in response to surrounding cell swelling, mimicking experimental observations.

Conclusions:

• The new framework enables the study of non-convex cell shapes and curvy interfaces in tissue mechanics.
• This approach accounts for a broader range of multicellular responses to tissue environment constraints.
• Provides a more realistic computational tool for understanding tissue morphogenesis and mechanics.