Dynamics of aVolvoxEmbryo Turning Itself Inside Out

Abstract

Deformations of cell sheets are ubiquitous in early animal development, often arising from a complex and poorly understood interplay of cell shape changes, division, and migration. Here, we explore perhaps the simplest example of cell sheet folding: the "inversion" process of the algal genus Volvox, during which spherical embryos turn themselves inside out through a process hypothesized to arise from cell shape changes alone. We use light sheet microscopy to obtain the first three-dimensional visualizations of inversion in vivo, and develop the first theory of this process, in which cell shape changes appear as local variations of intrinsic curvature, contraction and stretching of an elastic shell. Our results support a scenario in which these active processes function in a defined spatiotemporal manner to enable inversion.

Curvature-Induced Instabilities of Shells

“…Above a critical stimulus, we observe a snap-through in- Fig. 1 (d)), reminiscent of the abrupt concaveconvex shape changes employed by the Venus fly trap [9], and the embryonic inversion of Volvox [21]. Here, the critical curvature stimulus increases withθ.…”

“…This is a large value, corresponding to a radius of natural curvature equal to two-third's of the thickness (via residual swelling we are experimentally limited to values of |κh| < 1/4), yet it is comparable to natural curvatures observed during the eversion of the Volvox for which κh 2 [21]. In contrast to open shells, where the characteristic curvature for snapping and buckling is 1/R due to the existence of nearly isometric deformations, the characteristic curvature in closed shells becomes 1/h.…”

Batchelor Prize Lecture Fluid dynamics at the scale of the cell

“…Examples of systems in which this has begun to be explored include gastrulation in Drosophila (He et al 2014), where large-scale morphological transformations are driven by cell shape changes. Similar issues arise in the mechanics of embryonic inversion of Volvox Höhn et al 2015). Finally, moving beyond evolutionary transitions from singleto multicellular organisms we encounter the development of animals.…”

“…We used the same basic geometry as Vézy et al (2007), shown in figure 4(a), but introduced microspheres into the fluid within and external to the vesicle and used a multicomponent lipid membrane in a regime of two-phase coexistence: either involving small domains of a 'liquid disordered' (L d ) phase in a background of 'liquid ordered' (L o ) phase or solid-like 'gel' domains in a background of L d phase (figure 4b-d), made visible with fluorescent dyes. Tracking the microspheres and the domains under shear, it was possible, with confocal imaging, to map out stacks of two-dimensional slices of the flow field inside, outside and within these vesicles (Honerkamp-Smith et al 2013), as seen in figure 4(e,f ). Using the constraint of incompressibility of the fluid flow within the vesicle, the two-dimensional slices of the velocity field can be used to reconstruct the full three-dimensional flow within the vesicle, as shown in figure 5(a).…”

Non-model model organisms

“…As a developmental system Volvox has some appealing features, including organismal size and clarity that make it well suited to live-cell 3D imaging methods, including selective plane illumination microscopy (SPIM) [159]. The chlorophyll and other pigments that are in Volvox cells can interfere with live-cell fluorescence detection methods just as in plants, but more discriminating confocal microscopy technology and sensitive detection systems have helped to mitigate this issue [160].…”