A mechanical bifurcation constrains the evolution of cell sheet folding in the family Volvocaceae

TL;DR

This study shows that mechanical bifurcations constrain the evolution of cell sheet inversion in Volvocaceae algae, explaining the absence of intermediate forms and highlighting how mechanical constraints influence morphogenetic evolution.

Contribution

The paper develops a continuum mechanical model linking cell shape changes to bifurcations, revealing how these bifurcations constrain evolutionary transitions in algae.

Findings

Mechanical bifurcation predicts inversion constraints in Pleodorina.

Parameters for Pleodorina fall within the bifurcation-allowed region.

More complex Volvox inversion strategies bypass this bifurcation.

Abstract

The processes of morphogenesis that give rise to the shapes of organs and organisms during development are often driven by mechanical instabilities. Can such mechanical bifurcations also drive or constrain the evolution of these processes in the first place? We discover an instance of these constraints in the green algae of the family Volvocaceae. During their development, their bowl-shaped embryonic cell sheet turns itself inside out. This inversion is driven by a simple wave of cell wedging in the genus Pleodorina (16-128 cells) and more complex programmes of cell shape changes in Volvox (~400-50000 cells). However, no species with intermediate cell numbers (256 cells) have been described. Here, we relate this gap to a mechanical bifurcation: Focusing on the inversion of Pleodorina californica (64 cells), we develop a continuum model, in which the cell shape changes driving inversion appear as changes of the intrinsic curvature of an elastic surface. A mechanical bifurcation in this model predicts that inversion is only possible in a subset of its parameter space. Strikingly, parameters estimated for P. californica fall into this possible subset, but those that we extrapolate to 256 or more cells using allometric observations and a model of cell cleavage in Volvocaceae do not. Our work thus suggests that the more complex inversion strategies of Volvox are an evolutionary necessity to obviate this bifurcation and indicates more broadly how mechanical bifurcations can drive the evolution of morphogenesis.