Asymmetric driving forces and spatial heterogeneity enhance metachronal order in ciliary carpets

Ciliary carpets drive biological flows through the coordination of thousands of multiciliated cells, each containing hundreds of cilia. Despite progress in analyzing cilia coordination in certain models, general quantitative theories that can resolve both the multi-scale cilia coordination and flow patterns remain lacking. Combining numerics and theory based on the phased oscillator model of individual cilia, we systematically demonstrate how multi-scale disorder affects the long-term synchronization dynamics and resulting flow patterns in ciliary carpets. In particular, we show how individual cilium activity that leads to worse synchrony under uniformly covered tissues can surprisingly accelerate the formation of global metachronal order and outperform their counterparts when cilia coverage is reduced and tissue-level patchiness is introduced. Our findings are consistent with recent suggestion that spatial heterogeneity in cilia organization and tissue architecture enhance particle clearance, and go beyond these results to simultaneously probe the effect of spatial heterogeneity on cilia coordination and cilia-induced flows.