Mathematical Modeling of Sub-Cellular Asymmetry of Fat-Dachsous Heterodimer for Generation of Planar Cell Polarity

Abstract

Planar Cell Polarity (PCP) is an evolutionarily conserved characteristic of animal tissues marked by coordinated polarization of cells or structures in the plane of a tissue. In insect wing epithelium, for instance, PCP is characterized by en masse orientation of hairs orthogonal to its apical-basal axis and pointing along the proximal-distal axis of the organ. Directional cue for PCP has been proposed to be generated by complex sets of interactions amongst three proteins - Fat (Ft), Dachsous (Ds) and Four-jointed (Fj). Ft and Ds are two atypical cadherins, which are phosphorylated by Fj, a Golgi kinase. Ft and Ds from adjacent cells bind heterophilically via their tandem cadherin repeats, and their binding affinities are regulated by Fj. Further, in the wing epithelium, sub-cellular levels of Ft-Ds heterodimers are seen to be elevated at the distal edges of individual cells, prefiguring their PCP. Mechanisms generating this sub-cellular asymmetry of Ft-Ds heterodimer in proximal and distal edges of cells, however, have not been resolved yet. Using a mathematical modeling approach, here we provide a framework for generation of this sub-cellular asymmetry of Ft-Ds heterodimer. First, we explain how the known interactions within Ft-Ds-Fj system translate into sub-cellular asymmetry of Ft-Ds heterodimer. Second, we show that this asymmetric localization of Ft-Ds heterodimer is lost when tissue-level gradient of Fj is flattened, or when phosphorylation of Ft by Fj is abolished, but not when tissue-level gradient of Ds is flattened or when phosphorylation of Ds is abrogated. Finally, we show that distal enrichment of Ds also amplifies Ft-Ds asymmetry. These observations reveal that gradient of Fj expression, phosphorylation of Ft by Fj and sub-cellular distal accumulation of Ds are three critical elements required for generating sub-cellular asymmetry of Ft-Ds heterodimer. Our model integrates the known experimental data and presents testable predictions for future studies.

Jagged mediates differences in normal and tumor angiogenesis by affecting tip-stalk fate decision

“…Loss of this brake, as seen in aggressive tumors such as basal-like breast cancer (32)(33)(34), can enable tumors to attain sustained angiogenesis (35), which is a hallmark of cancer (44). Overall, our results about Fringe are also consistent with experimental and theoretical observations that Fringe promotes lateral inhibition patterns (19,45) and are reminiscent of how asymmetric modifications of transmembrane ligand-receptor pairs can govern tissue-level pattern formation (46).…”

Integrating planar polarity and tissue mechanics in computational models of epithelial morphogenesis

“…Elsewhere, further molecular detail was included in a system of coupled ordinary differential equations describing interactions, again forming the predominant complex (Ft P binding Ds U ), in a one-dimensional row of cells [41]. However, for the majority of this study, the authors did not consider the orientation of those complexes at individual junctions, but only the asymmetry of total complexes across each cell, thus questions related to Ft and Ds polarity were not addressed.…”

Planar cell polarity of the kidney

“…Ft is expressed evenly throughout the wing. The Fj gradient is proposed to result in the graded phosphorylation and activation of Ft across the tissue [14,18,19]. Although this model is supported in some tissues, in others, there does not appear to be a gradient in the expression of any of these molecules and in cases where proposed gradients have been perturbed or even abolished, they do not seem to affect PCP.…”