Blastula wall invagination examined on the basis of shape behavior of vesicular objects with laminar envelopes.

A complete description of the blastula shape transformations which occur in the process of gastrulation involves the mechanics of the blastula wall. It is inferred that the mechanical properties of this wall can, to a first approximation, be described in terms of elastic deformational modes which are equivalent to those of simple vesicular systems such as phospholipid vesicles and red blood cells. For membranes composed of an arbitrary number of aligned, laterally unconnected thin layers, these are area expansivity and local and non-local bending. Stable shapes of vesicular objects with laminar envelopes are defined as shapes which correspond to the minimum of the system elastic energy. The shape behavior of these objects is briefly reported. The criterion for the stability of the spherical shape of a vesicular object is derived. In particular we analyze the shape transition from a sphere to an invaginated gastrula. Conditions are demonstrated under which this shape transition can occur through a series of continuous shape transformations. A possible example of such a shape transformation is given. The blastula wall of the sea urchin is modeled as a closed laminar membranous system with three layers, the monocellular epithelial sheet and the extracellular apical lamina and hyaline layers. Experimentally measured elastic constants of some of these layers are shown to be in accord with the restrictions on their values imposed by the requirement for continuous shape transformations.