The noisy basis of morphogenesis: Mechanisms and mechanics of cell sheet folding inferred from developmental variability

Abstract

Variability is emerging as an integral part of development. It is therefore imperative to ask how to access the information contained in this variability. Yet most studies of development average their observations and, discarding the variability, seek to derive models, biological or physical, that explain these average observations. Here, we analyse this variability in a study of cell sheet folding in the green alga Volvox, whose spherical embryos turn themselves inside out in a process sharing invagination, expansion, involution, and peeling of a cell sheet with animal models of morphogenesis. We generalise our earlier, qualitative model of the initial stages of inversion by combining ideas from morphoelasticity and shell theory. Together with three-dimensional visualisations of inversion using light sheet microscopy, this yields a detailed, quantitative model of the entire inversion process. With this model, we show how the variability of inversion reveals that two separate, temporally uncoupled processes drive the initial invagination and subsequent expansion of the cell sheet. This implies a prototypical transition towards higher developmental complexity in the volvocine algae and provides proof of principle of analysing morphogenesis based on its variability.

Embryonic inversion inVolvox carteri: The flipping and peeling of elastic lips

“…1c) during type-B inversion in Volvox globator is mainly driven by contraction of parts of the cell sheet [17]. This contraction is regulated separately from the earlier invagination of the cell sheet, and therefore indicative of a transition towards higher developmental complexity within Volvocaceae [17]. The present result that type-A inversion does not rely on this additional deformation mode lends further support to this inference.…”

“…By contrast, we have previously shown that the peeling of the anterior hemisphere ( Fig. 1c) during type-B inversion in Volvox globator is mainly driven by contraction of parts of the cell sheet [17]. This contraction is regulated separately from the earlier invagination of the cell sheet, and therefore indicative of a transition towards higher developmental complexity within Volvocaceae [17].…”

“…The elastic model builds on the model we derived previously to describe type-B inversion in detail [17], although the present calculation is more intricate because axisymmetry is broken owing to the presence of the lips. We consider a spherical shell of radius R and uniform thickness h R ( Fig.…”

“…4 self-intersect; we expect the corresponding parts of the branches to be replaced with configurations of the shell where the rim of the lips is in contact with the uninverted part of the cell sheet. In these configurations, axisymmetry is necessarily broken in the uninverted part of the shell; we do not pursue this further, although we note that we have previously analyzed an analogous contact problem in the absence of lips [17]. These configurations will not in fact be important for the discussion that follows.…”

Systems Properties and Spatiotemporal Regulation of Cell Position Variability during Embryogenesis

“…Most studies in developmental biology have focused on deciphering molecular and cellular mechanisms that regulate the average behavior of developmental processes, with less attention paid to variability in these processes. However, more and more evidence shows that developmental processes exhibit considerable intrinsic vari-ability at the molecular and cellular levels, such as in gene expression (Burga et al, 2011;Raj et al, 2010), cell proliferation (Fang and Yuste, 2017), growth (Hong et al, 2016), differentiation, and morphogenesis (Haas et al, 2018). Systems-level analysis of the sources, properties, and implications of developmental variability will provide an important perspective to understand the establishment and maintenance of developmental reproducibility.…”