Volume segregation programming in a nematode's early embryogenesis

Nematode species are well-known for their invariant cell lineage pattern during development. Combining knowledge about the fate specification induced by asymmetric division and the anti-correlation between cell cycle length and cell volume in Caenorhabditis elegans, we propose a minimal model to simulate lineage initiation by altering cell volume segregation ratio in each division, and quantify the derived pattern's performance in proliferation speed, fate diversity, and space robustness. The stereotypic pattern in C. elegans embryo is found to be one of the most optimal solutions taking minimum time to achieve the cell number before gastrulation, by programming asymmetric divisions as a strategy.

Figure 1

C. elegans embryogenesis up to 24-cell stage. (a) In vivo C. elegans embryo morphology illustrated with fluorescence on cell nucleus (GFP, i.e., Green Fluorescent Protein) and cell membrane (mCherry); scale bar, $10\mu \mathrm{m}$. (b) Lineage pattern with invariant division order and fate specification. Numbers under each division indicate the order of synchronized cleavages. (c) Cell volume segregation ratio; error bar, standard deviation. (d) Anticorrelation between cell cycle length and cell volume fitted with power-law curves; inset, data shown on the logarithmic scale.

Figure 2

A sequence of cell cleavage events during early embryogenesis whose timings are illustrated by solid circles along the time axis. Events that fall within a window of size ${\delta }_s$ form a cluster while neighboring clusters or isolated events need to be separated by a minimal time gap ${\delta }_a>{\delta }_s$ to ensure punctuated cell movement.

Figure 3

Lineage solutions at $N=24$ from random sampling. (a) Distribution of the 19 654 nonidentical solutions in $P\text{−}F$ space; lineage patterns with the lowest and highest fate diversity (Patterns No. 1 and Nos. 11–24), the lowest and highest proliferation speed (Patterns No. 10 and Nos. 3–8) are indicated with purple, green, blue, and red points, respectively; the C. elegans pattern is denoted by a red asterisk (Pattern No. 2). A complete list of the labeled lineage patterns can be found in the SM, Figs. S4 and S5. (b) The C. elegans pattern. (c) The fully symmetric solution (Pattern No. 1). (d) The fastest solution (Pattern No. 3). Orange triangles denote the asymmetric divisions with $\eta >{\eta }_c$.

Figure 4

Proliferation speed under asymmetric divisions. (a) Cell number against developmental time with a single asymmetric division of volume ratio ${\eta }_1$ at the root. (b) A path from the fully symmetric pattern to the C. elegans pattern through successive addition of asymmetric divisions (orange triangles); red lines indicate the time to reach 24 cells.

Figure 5

Division timings up to 24 cells with constant and lineage-specific $\beta$ values. (a) The cell volume segregation ratio of germline cells P0-P2 derived by simulations and measured in experiment. (b) The C. elegans patterns plotted with constant (gray) and lineage-specific (black) $\beta$, using the $\eta$ values shown in (a).