  Motile cilia are slender, hair-like cellular appendages that spontaneously
oscillate under the action of internal molecular motors and are typically found
in dense arrays. These active filaments coordinate their beating to generate
metachronal waves that drive long-range fluid transport and locomotion. Until
now, our understanding of their collective behavior largely comes from the
study of minimal models that coarse-grain the relevant biophysics and the
hydrodynamics of slender structures. Here we build on a detailed biophysical
model to elucidate the emergence of metachronal waves on millimeter scales from
nanometer scale motor activity inside individual cilia. Our study of a 1D
lattice of cilia in the presence of hydrodynamic and steric interactions
reveals how metachronal waves are formed and maintained. We find that in
homogeneous beds of cilia these interactions lead to multiple attracting
states, all of which are characterized by an integer charge that is conserved.
This even allows us to design initial conditions that lead to predictable
emergent states. Finally, and very importantly, we show that in nonuniform
ciliary tissues, boundaries and inhomogeneities provide a robust route to
metachronal waves.
