A Multi-cell, Multi-scale Model of Vertebrate Segmentation and Somite Formation
(A) In silico somite formation for different segmentation clock periods. From top to bottom, Tclock = 67.5 min, 90 min (reference), 135 min, 180 min. (B) In silico somite formation for different PSM growth rates. From top to bottom, growth rate = 1.08 µm/min, 1.63 µm/min (reference), 2.04 µm/min, 2.72 µm/min. In (A) and (B), well-formed smaller somites (top of each panel) require decreased cell motility (for PSM cells, λsurf = 20 and Dcell = 0.945 µm2/min in (A); λsurf = 25 in (B)); larger somites form for reference motility parameters. In each case, we adjust the ML dimension to produce roughly circular somites. Segmentation and somite separation, however, succeed both for smaller and larger ML widths (data not shown). (C) In silico somite formation for different values of cell motility parameter λsurf. From top to bottom, low cell motility (λsurf = 25, Dcell = 0.86 µm2/min), reference motility (λsurf = 15, Dcell = 1.08 µm2/min), high motility (λsurf = 5, Dcell = 1.76 µm2/min). For low motility, somites round up slowly and there is little somite shape variation compared to reference simulations. For high motility, excessive mixing of cell types across presumptive somite borders leads to fused somites. (D) In silico somitogenesis with a uniform Wnt3a concentration. When [Wnt3a] is uniform throughout the PSM, traveling Lfng stripes do not form, but segmentation is normal, demonstrating that traveling stripes of high protein concentration are not necessary for somitogenesis in our model. (E) In silico somitogenesis for shorter-than-normal determination-differentiation delay (90 min); from top to bottom, t = 450 min, 750 min, 1050 min. (F) In-silico somitogenesis for longer-than-normal determination-differentiation delay (720 min); from top to bottom, t = 750 min, 1050 min, 1350 min, 1860 min. (G) In silico somitogenesis for long determination-differentiation delay (720 min) and less pronounced cell adhesion changes at determination. Modified contact energies: Jpre_EphA4,pre_EphA4 = −22; Jpre_ephrinB2,pre_ephrinB2 = −22; Jpre_Core,pre_Core = −25; Jpre_EphA4,EphA4 = −22; Jpre_ephrinB2,ephrinB2 = −22. Increased mixing of determined cell types is corrected by cell sorting after differentiation. (H–K) In silico somitogenesis for delayed adhesion changes after determination with and without a period of intermediate adhesion before differentiation. (H) 180-min determination-differentiation delay and no intermediate adhesion. (I) 360-min determination-differentiation delay with a 180-min period of intermediate adhesion after 180 min of unchanged adhesion. (J) 225-min determination-differentiation delay and no intermediate adhesion. (K) 360-min determination-differentiation delay with a 135-min period of intermediate adhesion after 225 min of unchanged adhesion. For a determination-differentiation delay of 180 min or greater and no period of intermediate adhesion, the excessive mixing of determined cell types across their original borders leads to fused somites and a greater-than-normal occurrence of stranded Core cells in the intersomitic gaps (H, J). A period of intermediate adhesion after such a period of cell mixing partially corrects resulting defects (I, K). With and without a period of intermediate adhesion, defect severity increases with increasing periods of cell mixing. All panels: anterior to the left, scale bars 40 µm, cell-type colors same as Figure 5, parameters have reference values (Figure 7) unless otherwise noted. For greater detail and resolution, see Supporting Figures S5, S6, S7, S8, S9, S10, S11.