Growth pressure can drive early chick lens geometries

Over a number of morphological stages during chick lens morphogenesis, a flat plate of cuboidal ectodermal cells infolds to form a deep cup of tall, pyramidal lenticular cells. This invagination process is accompanied by asynchronous cellular multiplication over a basal region constrained by an adhesive extracellular matrix. A lens placode is formed as the cells crowd into columnar "palisades." A lens cup forms as the cells pyramidalize owing to basal nuclear movements. Invagination ends when the opening into the lens cup is closed to form a lens vesicle. In this paper, equations are developed that provide a quantitative, mathematical formulation of an earlier theory that explains this invagination as a growth driven process. The equations take into account the lens cell cycle, the extracellular matrix, and nuclear migratory behaviors. Based on the equations, geometries simulating the morphological stages and the cell cycle phases are generated for the 1st day of lens development. The mathematical formulation of lens invagination helps demonstrate how growth pressure alone can be the primary driving force for tissue folding. In this view, recruitment occurs before the shape changes; and cell-autonomous mechanisms of invagination, involving the cytoskeleton or differential adhesion alone, offer inadequate explanations of these changes.