A key morphogenetic event in dicotyledonous embryo development is the transition from the globular stage to the heart stage which involves the apical differentiation of two cotyledons, the basal differentiation of the radicle, and the formation of the hypocotyl axis. This developmental transition in a dicotyledonous embryo is explained through the combined effect of substrate and hormones on growth rate and cellular differentiation. It is proposed that limitations in the transport of substrate act as a signal determining the onset of axial vascularization of the embryo. Overall morphological changes result from the mechanical stress fields generated by the growth pattern of the embryo. Cotyledonary growth is consequential to differences in growth rates between the central core and the periphery of the embryo. A continuum mathematical model for embryo morphogenesis is formulated and includes conservation equations for substrate and hormone, a low-Reynolds force balance and a biomass balance relating the velocity field to the spatial growth rate distribution. By using a linear viscoelastic constitutive equation for the mechanical stress tensor in the force balance, modified Stokes equations are obtained in two limiting cases. A simplified and qualitative analysis supports the selection of hormone synthesis and nutrient consumption models.
Bibliographical noteFunding Information:
This study was supported in part by the National Science Foundation through grants to WSH (ECE-85-52670) and TJC-(DCB-89-17378) and by a grant from the Minnesota Supercomputer Institute. HV acknowledges helpful discussions with Manuel Garcia, Juan M. de Santos and Jeff J. Derby on modeling issues.
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