Fig. 2.

Intrinsic NP curvature and midline tapering can promote tube folding. (A) Schematic representation of model I. $w_{\text{NP}}$, NP width; $h_{\text{NP}}$, NP apicobasal height; $h_{\text{HP}}$, MHP (midline) height; $w_{\text{HP}}$, hinge point domain width; d, domain distance to center; ${\kappa }_{\text{int}}$, intrinsic tissue curvature; ${\kappa }_{\text{mid}}$, intrinsic tissue curvature at the hinge point midline; ${\kappa }_{\text{max}}$, theoretical maximum tissue curvature. (B) Model I simulations rendered between t = 0 ($w_{\text{NP}}=500$ µm) and t = 1 ($w_{\text{NP}}=1000$ µm). The area underneath the tissue horizontal midline is fixed at 0. (C) Mouse live-imaging of early NT closure at E8.5. R, rostral; C, caudal; magenta, cell membrane; white, nucleus. Cyan lines in dorsal view images indicate rostrocaudal position (somite 4.5) of transverse view. (Scale bars: 200 µm [dorsal view] and 100 µm [transverse view].) (D) Human transverse sections of early NT closure at SS4 to SS13, rostrocaudal position somite 4. Images were derived with permission from refs. 35 and 36 under a Creative Commons Attribution license. (Scale bars: 100 µm.) (E) Measured NP apicobasal height ($h_{\text{NP}}$) during NT folding progression along the rostrocaudal axis in developing mouse embryos. (F) Measured NP apicobasal height ($h_{\text{NP}}$) along the rostrocaudal axis in human embryos (SS4, SS6, SS7, and SS13). (G) Measured NP midline thickness ratio ($h_{\text{NP}}/h_{\text{HP}}$) during NT folding progression along the rostrocaudal axis in developing mouse embryos. (H) Measured NP midline thickness ratio ($h_{\text{NP}}/h_{\text{HP}}$) along the rostrocaudal axis in human embryos (SS4, SS6, SS7, and SS13). Lines in E–H represent linear least-squares fit; C1 indicates closure 1 rostrocaudal position. In E and G, error bars indicate SEM, $N=1\text{–}3$ (SI Appendix, Table S1). In F and H, open circles indicate that NP is in the process of folding; closed circles indicate that NP is closed. (I–K) NP folding simulations (t = 1) with midline tapering thickness ratio versus tapering domain width (I), intrinsic midline curvature strength versus intrinsic curvature domain width (J), and intrinsic dorsolateral curvature (${\kappa }_{\text{mid}}={\kappa }_{\text{max}}/2$) distance to center versus intrinsic curvature domain width (K). In I, simulation renderings were flipped along the y axis to point downward. Color scale represents the percentage of intermediate simulation steps in which the neural ectoderm is sufficiently symmetrical along the x axis and the neuroepithelium midline is buckled; i.e., the sum of the x coordinates of the elements on the left and right half of the neural ectoderm differ by less than 10%, and the middle element has $\left|y\right|>h_{\text{NP}}$.