Emergence of planar cell polarity from the interplay of local interactions and global gradients.

Planar cell polarity (PCP) - tissue-scale alignment of the direction of asymmetric localization of proteins at the cell-cell interface - is essential for embryonic development and physiological functions. Abnormalities in PCP can result in developmental imperfections, including neural tube closure defects and misaligned hair follicles. Decoding the mechanisms responsible for PCP establishment and maintenance remains a fundamental open question. While the roles of various molecules - broadly classified into 'global' and 'local' modules - have been well-studied, their necessity and sufficiency in explaining PCP and connecting their perturbations to experimentally observed patterns have not been examined. Here, we develop a minimal model that captures the proposed features of PCP establishment - a global tissue-level gradient and local asymmetric distribution of protein complexes. The proposed model suggests that while polarity can emerge without a gradient, the gradient not only acts as a global cue but also increases the robustness of PCP against stochastic perturbations. We also recapitulated and quantified the experimentally observed features of swirling patterns and domineering non-autonomy, using only three free model parameters - rate of protein binding to membrane, the concentration of PCP proteins, and the gradient steepness. We explain how self-stabilizing asymmetric protein localizations in the presence of tissue-level gradient can lead to robust PCP patterns and reveal minimal design principles for a polarized system.