How a spherical cell sheet inverts itself: a mathematical and experimental approach

Xiaoyi Chen

BNU-HKBU United International College

Tuesday 26th September 2023

14:15:00

Aula Saleri

During its late stage of development, the Volvox embryo, which is a sphere made of a single layer of cells, turns itself inside out and forms complex folds along the way. We want to reveal the hidden mechanism behind it using the mathematical approach together with experimental data. We develop a new morphoelastic shell model, and derive algebraic-differential equations for the growth functions incorporating the experimental data into the coefficients. We assume a special scaling of the pressure, and construct asymptotic analytical solutions for the growth functions and the residual stress distribution of the cell sheet is also obtained. We find that the cell sheet uses two different growth rates to generate the folds: one that makes the fold shapes without causing tension in the shell, and another that produces tension to balance the pressure without changing the shapes. We also discover how the folds move along the cell sheet, which is like a race with two runners going in opposite directions. We study the residual stress and find out how it signals the coordination of the movement of the two folds. Contatto: pasquale.ciarletta@polimi.it This initiative is part of the "PhD Lectures" activity of the project "Departments of Excellence 2023-2027". This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.