Few mechanistic ideas from the pre-molecular era of biology have had as enduring an impact as the morphogen concept. In the classical view, cells in developing embryos obtain positional information by measuring morphogen concentrations and comparing them with fixed concentration thresholds; as a result, graded morphogen distributions map into discrete spatial arrangements of gene expression. Recent studies on Hedgehog and other morphogens suggest that establishing patterns of gene expression may be less a function of absolute morphogen concentrations, than of the dynamics of signal transduction, gene expression, and gradient formation. The data point away from any universal model of morphogen interpretation and suggest that organisms use multiple mechanisms for reading out developmental signals in order to accomplish specific patterning goals.

In developing tissues, cell polarization and proliferation are regulated by morphogens and signaling pathways. Cells throughout the Drosophila wing primordium typically show subcellular localization of the unconventional myosin Dachs on the distal side of cells (nearest the center of the disc). Dachs localization depends on the spatial distribution of bonds between the protocadherins Fat (Ft) and Dachsous (Ds), which form heterodimers between adjacent cells; and the Golgi kinase Four-jointed (Fj), which affects the binding affinities of Ft and Ds. The Fj concentration forms a linear gradient while the Ds concentration is roughly uniform throughout most of the wing pouch with a steep transition region that propagates from the center to the edge of the pouch during the third larval instar. Although the Fj gradient is an important cue for polarization, it is unclear how the polarization is affected by cell division and the expanding Ds transition region, both of which can alter the distribution of Ft-Ds heterodimers around the cell periphery. We have developed a computational model to address these questions. In our model, the binding affinity of Ft and Ds depends on phosphorylation by Fj. We assume that the asymmetry of the Ft-Ds bond distribution around the cell periphery defines the polarization, with greater asymmetry promoting cell proliferation. Our model predicts that this asymmetry is greatest in the radially-expanding transition region that leaves polarized cells in its wake. These cells naturally retain their bond distribution asymmetry after division by rapidly replenishing Ft-Ds bonds at new cell-cell interfaces. Thus we predict that the distal localization of Dachs in cells throughout the pouch requires the movement of the Ds transition region and the simple presence, rather than any specific spatial pattern, of Fj.