Mathematical Modeling of Planar Cell Polarity to Understand Domineering Nonautonomy

Abstract

Planar cell polarity (PCP) signaling generates subcellular asymmetry along an axis orthogonal to the epithelial apical-basal axis. Through a poorly understood mechanism, cell clones that have mutations in some PCP signaling components, including some, but not all, alleles of the receptor frizzled, cause polarity disruptions of neighboring wild-type cells, a phenomenon referred to as domineering nonautonomy. Here, a contact-dependent signaling hypothesis, derived from experimental results, is shown by reaction-diffusion, partial differential equation modeling and simulation to fully reproduce PCP phenotypes, including domineering nonautonomy, in the Drosophila wing. The sufficiency of this model and the experimental validation of model predictions reveal how specific protein-protein interactions produce autonomy or domineering nonautonomy.

Modelling and Analysis of Planar Cell Polarity

“…Since there is to date no specific experimental evidence supporting a particular form for the polarity cues generated by the first tier of the PCP mechanism, a weak initial polarity in each cell and an initial gradient are both potentially reasonable forms of initial cues. In contrast to the existing models by Le Garrec et al [8] and Amonlirdviman et al [2], the models that we study here are not based on detailed assumptions about interactions of specific PCP core proteins. Rather, they encode a more general picture of possible mechanisms driving the second tier of the PCP mechanism.…”

“…Two models for PCP, focusing on the wing of the fruit fly, have been developed by Amonlirdviman et al ( [2], [12]) and Le Garrec et al [8] (applied to the Drosophila eye in [7]). Both models centre around the idea of amplification of polarity via asymmetric complex formation of the core proteins.…”

Planar cell polarity genes, Celsr1-3, in neural development

“…Initially, a longrange signal establishes the direction of polarity, and the factors involved form the "upstream group" of PCP signaling that is enriched at the proximal side. This asymmetric subcellular localization is mediated by a feedback loop between the two complexes, which propagates molecular polarity from cell to cell [12] . Flamingo is symmetrically localized on the distal and proximal sides, possibly stabilizing both complexes through homophilic interactions and promoting adhesion between neighboring cell surfaces (Fig.…”

Far from solved: A perspective on what we know about early mechanisms of left–right asymmetry

“…PCP also enables orientation of cell polarity within the large-scale axes of a host; for example, when grafts of embryonic skin were transplanted into adults, the skin cells realigned their planar hair polarity to match that of the hosts (Devenport and Fuchs, 2008). PCP is an attractive mechanism for LR asymmetry because it can impose the initial orientation of cells or small groups of blastomeres to entire cell fields (Amonlirdviman et al, 2005), as was originally proposed in the ''LR Coordinator'' model (Hyatt and Yost, 1998). A similar mechanism was recently proposed to explain the instructive influence by means of which primary organizers (existing during the initial cytoskeletal rearrangements) can impose correct asymmetry upon secondary organizers induced later in development (which can otherwise correctly pattern all of their axes except the LR; Vandenberg and Levin, 2010).…”