A mechanical model of early somite segmentation

Abstract

Somitogenesis is often described using the clock-and-wavefront (CW) model, which does not explain how molecular signaling rearranges the pre-somitic mesoderm (PSM) cells into somites. Our scanning electron microscopy analysis of chicken embryos reveals a caudally-progressing epithelialization front in the dorsal PSM that precedes somite formation. Signs of apical constriction and tissue segmentation appear in this layer 3-4 somite lengths caudal to the last-formed somite. We propose a mechanical instability model in which a steady increase of apical contractility leads to periodic failure of adhesion junctions within the dorsal PSM and positions the future inter-somite boundaries. This model produces spatially periodic segments whose size depends on the speed of the activation front of contraction (F), and the buildup rate of contractility (Λ). The Λ/F ratio determines whether this mechanism produces spatially and temporally regular or irregular segments, and whether segment size increases with the front speed.

Keywords: Developmental Biology; Mechanical Modeling; Poultry Embryology.

Graphical abstract

Figure 1

Early signs of pre-somitic epithelium segmentation (A) SEM images of para-sagittally sectioned chicken embryos show the epithelialization of dorsal PSM cells at least 3 somite lengths caudal (left) to the S1 somite. (B) Scale bar is 100 μm. Cells are colored according to their aspect ratio in (B). (C) Quantification of side-to-side distances of adjacent cell pairs near the dorsal surface. The black arrowheads in (B) mark cell pairs with increased apical-apical distances. (D) Location of the apical peaks for four different embryo, indicating the number of cell pairs in each segment. The red line is for the sample shown in A–C. (E) Inset showing the side-to-side distance quantification metric.

Figure 2

Proposed models of segment formation (A) Epithelialized cells, with defined apical (red) and basal (blue) sides form a rostral (right)-caudal (left) monolayer along the dorsal side of the PSM. (B) Mechanical instability model: a caudally-progressing front of myosin activation (orange arrows) initiates apical constriction of the cells in the monolayer eventually leading to the periodic segmentation of the tissue. (C) Cell condensation model: a caudally-progressing maturation front (orange arrows) initiates random cell-cell groupings that eventually organizes the tissue into regularly-sized clusters. (D) Seeded activation model: instead of a continuously progressing front, small groups of cells activate and rearrange neighboring cells into a segment.

Figure 3

Tension and segment-size distributions for fixed tissue sizes and simultaneous increase in contractility (A) Snapshots of 4 simulations of 10 cells with different levels of maximal apical contractility strength. The tissue becomes more constricted for larger values of λ_A. (White – ectodermal tissue; black – core PSM; cells domain colors as in Figures 2A–2D; vertical white lines – internal distance constraints between domains in a single cell (Equation 3); horizontal white lines – distance constraints between domains in neighboring cells (Equation 5)). (B) Plot of average apical tension (Equation 7) between cell pairs at the end of multiple simulations with different numbers of cells (from 4 to 24). In all simulations λ_A= 600. (C) Maximum cell-pair tension versus the number of cells in the tissue for different maximal values of λ_A. (D and E) Histogram of distribution of segment sizes (D) and normalized segment sizes (E) for different rates of simultaneous buildup of apical contractility. (F) Snapshot of a simulation with Λ = 0.05 showing a wide distribution of segment sizes.

Figure 4

Tissue segmentation from a caudally-propagating activation-front initiating apical constriction (A) Time series of a simulation showing the sequential segmentation of a tissue due to a linear increase of λ_A as cells progressively activate from rostral (right) to caudal (left). Colors as in Figure 2A and parameters from Table S2. Snapshots taken at the approximate moment separation occurs (17000, 21,000, 24,000, and 28,000 MCS). (B) Time evolution of cell-pair tensions in two consecutive segments. Colors code different cell-pairs, beginning with the rostral-most pair for each segment and ending with the caudal-most pair. When the links break the pairwise tension goes to 0. (C) The line of a given color corresponds to the arrowheads of the same color in (B). The colors denote: (red) time of formation of the rostral segment boundary; (blue) time of formation of the caudal segment boundary; and a time after caudal boundary formation when the forces in the segment have reached mechanical equilibrium (black).

Figure 5

Segmentation as a function of activation-front speed (A) Average segment size $⟨S⟩$ as a function of front speed F. For slower speeds, segments are of roughly constant size. For faster speeds segment size increases as a power of the speed. (B) Average segmentation time $⟨\tau ⟩$ decreases as a power law with F^{−0.80±0.008}. (A and B) Each line shows a similar behavior for different base values of the buildup rate of apical contractility (Λ).

Figure 6

Λ/F defines the boundaries between segmentation regimes (A and B) Rescaled version of Figure 5A and S3B, showing average segment size $⟨S⟩$ as a function of (A) activation-front speed over buildup rate, and (B) its inverse. Vertical dashed line at Λ/F = 22 indicates the transition threshold between near-constant-size and scaling-size segments. (C) Parameter space diagram showing regions where the combination of the parameters Λ and F leads to nearlyconstant segment sizes (green), nearly constant segment sizes with flattened cells (gray), scaling segment sizes (blue), or irregularly-sized segments (orange). Black dashed line shows transition from stable to splitting segments. The point marked X indicates the reference simulation parameters (see Table S2).

Figure 7

Segment size variation (A) Typical simulation showing a wide range of segment sizes for a simulation with parameters in the irregular regime (orange) of the parameter space in Figure 6C (F = 0.03, Λ = 0.013). (B–D) Histogram of segment sizes for combinations of Λ and F in the nearly constant-size regime (B), scaling regime (C), and irregular regime (D), of the parameter space for 5 replicas each. (E) Coefficient of variation as a function of front speed F for different buildup rates of apical contractility, Λ. (F) Coefficient of variation as a function of Λ for different front speeds F. (E and F) Dashed red lines at ${\sigma }_s/⟨S⟩=0.2$ indicate the threshold defining irregular segment sizes in Figure 6C.

Figure 8

Splitting of Large Segments (A) Simulation snapshots showing the splitting of a large segment for Λ = 0.013, F = 0.005 (times, from top to bottom: 47,000, 49,000, 52,000, 54,000, and 56,500 MCS). (B) Evolution of the tension profile for the splitting segment shown in (A). (C) Plot of final versus initial segment sizes. Data points below the diagonal dashed line indicate splitting. (D) Splitting frequency as a function of front speed F.

Figure 9

Influence of breaking tension and cell aspect ratio on segmentation (A) Average segment size $⟨S⟩$ as a function of the breaking tension (Γ_Break). Blue lines are initial segment sizes, red lines are segments sizes after splitting. (B) Average number of splits per segment as a function of the breaking tension (Γ_Break). (C) Average segment size $⟨S⟩$ (blue) and average segmentation time $⟨\tau ⟩$ (red) as functions of cell aspect ratio AR. (D) Frequency of segment splitting (red) as a function of cell aspect ratio AR. Dashed lines show reference simulation values for breaking tension (Γ_Break=-7500) and aspect ratio (AR=2).