Current theories about the forces that drive neurulation shape changes are evaluated using computer simulations. Custom, three-dimensional, finite element-based computer software is used. The software draws on current engineering concepts and makes it possible to construct a ‘virtual’ embryo with any user-specified mechanical properties. To test a specific hypothesis about the forces that drive neurulation, the whole virtual embryo or any selected part of it is ascribed with the force generators specified in the hypothesis. The shape changes that are produced by these forces are then observed and compared with experimental data. The simulations demonstrate that, when uniform, isotropic circumferential microfilament bundle (CMB) constriction and cephalocaudal (axial) elongation act together on a circular virtual neural plate, it becomes keyhole shaped. When these forces act on a spherical (amphibian) embryo, dorsal surface flattening occurs. Simulations of transverse sections further show that CMB constriction, acting with or without axial elongation, can produce numerous salient transverse features of neurulation. These features include the sequential formation of distinct neural ridges, narrowing and thickening of the neural plate, skewing just medial to the ridges, ‘hinge’ formation and neural tube closure. No region-specific ‘programs’ or non-mechanical cell-cell communications are used. The increase in complexity results entirely from mechanical interactions. The transverse simulations show how changes to the driving forces would affect the patterns of shape change produced. Hypotheses regarding force generation by microtubules, intercellular adhesions and forces extrinsic to the neural plate are also evaluated. The simulations show that these force-generating mechanisms do not, by themselves, produce shape changes that are consistent with normal development. The simulations support the concept of cooperation of forces and suggest that neurulation is robust because redundant force generating mechanisms exist.
Geometric auxetics
