UC Irvine

The spatial patterns of cell proliferation and polarization in developing organisms depend on, yet differ from, the profiles of related signaling molecules. A classic case is the fruit fly wing primordium, a developing tissue whose cells demonstrate a consistent polarization despite depending on proteins with fairly uniform concentration profiles. Although the profiles of the Fat (Ft) pathway components Four-jointed (Fj) and Dachsous (Ds) are typically viewed as smoothly graded with uniform slope stretching across the wing pouch, this is not the case. Rather, the protocadherin Ds is expressed at high levels outside the wing pouch and low, roughly uniform levels within it, with a steep transition region at the border of the wing pouch. The Golgi kinase Fj has a complementary profile with uniformly high expression levels within the pouch, low levels in the periphery of the wing disc, and a steep concentration gradient in the transition region. However, the Fj and Ds profiles are not static; Ds-expressing cells are gradually recruited into the Fj-expressing wing pouch. We present a computational model that incorporates these profiles and their dynamics. Ft and Ds are protocadherins that form heterodimers between adjacent cells with a binding affinity that depends on Fj. In our model the asymmetry of the Ft-Ds bond distribution around the periphery of a cell defines the polarization. This asymmetry is greatest in the transition region. The transition region expands radially outwards with time, leaving in its wake polarized cells that retain their asymmetric bond distributions and direction of polarization, even after cell division. Similarly, the cells of the pouch proliferate roughly uniformly despite nonuniform profiles of proteins involved in growth signaling, such as Decapentaplegic (Dpp) and Wingless (Wg). In our model, cells grow and proliferate in response to the asymmetry of their Ft-Ds bond distributions as well as to the local morphogen (Dpp and Wg) concentration which increases with time. Since the morphogen profile decays exponentially with radial distance, Dpp and Ft-Ds-Fj signaling

form counterbalancing gradients that result in fairly uniform cell proliferation. The overall result is a pattern of cell polarization and proliferation that is consistent with experimental observations.