Dynamics of a $Volvox$ Embryo Turning Itself Inside Out

TL;DR

This paper provides the first quantitative 3D visualization of Volvox embryo inversion and develops a mathematical model describing the elastic and fluid mechanics involved in this topological transformation.

Contribution

It introduces a novel 3D imaging approach and a theoretical framework for understanding the mechanics of Volvox embryo inversion.

Findings

First 3D visualization of inversion in vivo

Quantitative analysis of cell shape change dynamics

Mathematical model of elastic shell and fluid interactions

Abstract

Spherical embryos of the algal genus $Volvox$ must turn themselves inside out to complete their embryogenesis. This `inversion', which shares important features with morphological events such as gastrulation in animals, is perhaps the simplest example of a topological transition in developmental biology. Waves of cell shape changes are believed to play a major role in the process, but quantification of the dynamics and formulation of a mathematical description of the process have been lacking. Here, we use selective plane illumination microscopy on $V. globator$ to obtain the first quantitative three-dimensional visualizations of inversion $in~vivo$. A theory is formulated for inversion based on local variations of intrinsic curvature and stretching of an elastic shell, and for the mechanics of an elastic snap-through resisted by the surrounding fluid.