Vertex dynamics simulations of viscosity-dependent deformation during tissue morphogenesis

Area of Science:

• Biophysics
• Developmental Biology
• Computational Biology

Background:

• Tissue morphogenesis relies on cell mechanical interactions, including active forces and viscoelastic responses.
• Dynamic tissue deformations are significantly influenced by spatially inhomogeneous viscous properties of tissue components.
• Existing vertex dynamics models often neglect tissue viscosities, limiting their application to quasi-static processes.

Purpose of the Study:

• To propose a novel vertex dynamics model that incorporates viscosity-dependent dynamic deformation processes in tissue morphogenesis.
• To enhance the model's accuracy by ensuring Galilean invariance and formulating friction forces based on relative velocities.
• To simulate and analyze epithelial growth dynamics under varying viscous conditions.

Main Methods:

• Developed a vertex dynamics model by incorporating local velocity fields into vertex movement equations, achieving Galilean invariance.
• Formulated friction forces as functions of relative velocities among vertices to represent viscous properties of tissue components.
• Conducted epithelial growth simulations, comparing the proposed model with conventional models under quasi-static and dynamic viscous conditions.

Main Results:

• The proposed model accurately reflects deformation timescales and shows linear elongation of epithelial vesicles with minimal stress, unlike conventional models exhibiting undulation and residual stress.
• Simulations with viscous extracellular materials demonstrated that epithelial vesicle morphology is highly sensitive to extracellular viscosity, confirming the model's ability to capture dynamic deformations.
• The model successfully simulated tubular shape formation driven by oriented cell divisions, highlighting the impact of extracellular viscosity.

Conclusions:

• The developed vertex dynamics model accurately simulates viscosity-dependent dynamic deformations crucial for tissue morphogenesis.
• The model's Galilean invariance and accurate representation of viscous forces enable realistic simulations of tissue development.
• This approach provides a valuable tool for investigating the role of viscous properties in various tissue engineering and developmental biology applications.