Planar Cell Polarity in Disordered Tissues: A Model for Robust Long-range Correlations

Planar cell polarity (PCP) is a highly conserved long-range signaling mechanism that regulates cellular processes in epithelial tissues, including cellular-rearrangements. Long-range PCP is usually already established in a highly disordered tissue, guiding the process of oriented reorganization of cells towards more ordered lattices. Given the detrimental effects of quenched disorder on long-range correlation in condensed matter systems, we ask how PCP survives the static geometrical disorder. In this study, we propose a reaction-diffusion mechanism with nonlocal interactions and show that such a mechanism facilitates the emergence and stability of long-range order of polarization in highly disordered systems. Furthermore, the global orientation of polarization is influenced by a variety of external cues. Elongation is regarded as one symmetry- breaking cue that fixes the orientation of PCP; perpendicular to the elongation axis. We show in this study, how nonlocal interactions can stabilize the distribution of proteins on longer junctions; hence perpendicular polarization, when reaction- diffusion is the dominant mechanism of PCP dynamics.