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 acco
mpanied by asynchronous cellular multiplication over a basal region co
nstrained by an adhesive extracellular matrix. A lens placode is forme
d 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 vesic
le. In this paper, equations are developed that provide a quantitative
, mathematical formulation of an earlier theory that explains this inv
agination as a growth driven process. The equations take into account
the lens cell cycle, the extracellular matrix, and nuclear migratory b
ehaviors. Based on the equations, geometries simulating the morphologi
cal stages and the cell cycle phases are generated for the lst day of
lens development. The mathematical formulation of lens invagination he
lps demonstrate how growth pressure alone can be the primary driving f
orce for tissue folding. In this view, recruitment occurs before the s
hape changes; and cell-autonomous mechanisms of invagination, involvin
g the cytoskeleton or differential adhesion alone, offer inadequate ex
planations of these changes. (C) 1993 Wiley-Liss, Inc.