Dynamics of a Volvox Embryo Turning Itself Inside Out

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.

Figure 1

Embryonic inversion in Volvox. (a) Adult V. globator spheroid containing multiple embryos. (b) Embryo undergoing type-A inversion (e.g., V. carteri). (c) Embryo undergoing type-B inversion (e.g., V. globator, V. aureus). (d) Light micrograph shows semi-thin section of V. globator embryo exhibiting different cell shapes. (e) Schematic representation of cells in region marked in (d). PC: paddle-shaped cells, two different views illustrate anisotropic shape; SC: spindle-shaped cells; red line: position of cytoplasmic bridges (CB). (f) 3D renderings of a single V. globator embryo in three successive stages of inversion. (g) Optical midsagittal cross sections of embryo in (f). (h) Traced cell sheet contours overlaid on sections in (g), with color-coded curvature $\kappa$. (i) Surfaces of revolution computed from averaged contours. Panels (d) and (e) modified from [13].

Figure 2

Dynamic characterization of inversion in V. globator. Red lines in (a)–(c) are data for one representative embryo, whose traced outlines are shown in (b). (a) Distance $e$ from posterior pole to bend region, normalized by its value $e_0$ at $t\approx -10\min$, decreases at a speed that increases abruptly midinversion. (b) Surface area $A$ of the embryo, normalized by its value $A_0$ at $t\approx -20\min$, peaks after $t=0$, and then decreases. Traced embryo shapes correspond to time points indicated by open circles on the red curve. (c) Most negative embryo curvature ${\kappa }^{*}$ in the bend region peaks concurrently with speed-up.

Figure 3

Elastic model. (a) Undeformed elastic spherical shell of radius $R$ and thickness $h$. (b) Deformed configuration of the shell. (c) Stretches $f_s,f_{\varphi }$ relate undeformed and deformed geometries. (d) Imposed intrinsic curvature ${\kappa }_s^0=-k<0$ in a region of width $\lambda$ just below the equator. Posterior contraction modifies the intrinsic properties (d,e,f) by introducing a posterior radius $r_{\mathrm{p}}<R$.

Figure 4

Results of elastic model and comparison with experiment. (a) In the absence of contraction, there is a purse-string effect. (b) Correct “mushroom” shapes are obtained once contraction is included, which allows (c) the inverted posterior to fit into the anterior hemisphere. (d) Decay of strains in both hemispheres away from bend region. (e) Asymmetry of meridional curvatures of contracted shapes corresponds to passive formation of second bend region. (f), (h) Outlines (gray) of 10 embryos in an early stage ($e/e_0=0.97\pm 0.07$) and a later stage ($e/e_0=0.49\pm 0.09$) of inversion, and averages (black). Bars indicate standard deviations. (g), (i) Computed shapes (green) lie within a standard deviation (gray areas) of average shapes.