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 cell-cell interface - is essential for embryonic development and physiological functions. Abnormalities in PCP can lead to neural tube closure defects and misaligned hair follicles. Decoding the mechanism 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 has not been examined. Here, we develop a minimal model that captures the proposed features of these modules - a global tissue-level gradient and local asymmetric distribution of protein complexes. Our model suggests that while polarity can emerge without a gradient, the gradient can provide the direction of polarity and maintain PCP robustly in presence of stochastic perturbations. We also recapitulated swirling patterns seen experimentally and features of domineering non-autonomy, using only three free model parameters - protein binding rate, concentration of proteins forming heterodimer across cell boundaries and gradient steepness. We explain how self-stabilizing asymmetric localizations in presence of tissue-level gradient can lead to robust PCP patterns and reveal minimal design principles for a polarized system.