Viscoelastic approach to cell migration in epiboly.

Area of Science:

• Biophysics
• Developmental Biology
• Computational Biology

Background:

• Understanding tissue morphogenesis during early vertebrate development is crucial.
• The role of mechanical forces, specifically cell layer tension and velocity, in tissue propagation remains an active area of research.

Purpose of the Study:

• To develop a generalized viscoelastic model that couples cell layer velocities and tensions.
• To incorporate geometric corrections for spherical surfaces in the model.
• To analyze stress anisotropy and its influence on tissue propagation and mitotic spindle dynamics.

Main Methods:

• Construction of a viscoelastic model incorporating geometric corrections on a sphere.
• Derivation of leading-order equations for cell speeds and stresses.
• Development of an exact theoretical approach including inertial and advective terms for simulations.

Main Results:

• The model demonstrates increasing stress anisotropy in the cell layer as a function of the polar coordinate.
• This anisotropy is reinforced by the advancing cell front, which governs the mitotic spindle and contributes to tissue propagation.
• Simulations of the enveloping cell layer during epiboly, disperse, and reaggregation phases are enabled by the generalized model.

Conclusions:

• The developed viscoelastic model provides a general framework applicable to gastrulation in various vertebrates.
• The model's predictions for cell speeds and stresses align well with previous formulations.
• The inclusion of inertial and advective terms allows for comprehensive simulations of tissue development stages.