A multiscale biophysical model delivers quantized metachronous waves in a lattice of beating cilia

abstract

Motile cilia are slender, hair-like cell 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 create metachronous waves that power fluid transport and long-distance locomotion. So far, our understanding of their collective behavior relies largely on the study of minimal models, which coarsen the relevant biophysics and hydrodynamics of slender structures. Here, we build on a detailed biophysical model to elucidate the emergence of millimeter-scale metachronous waves from nanometer-scale motor activity within single cilia. Our study of a one-dimensional ciliary lattice in the presence of hydrodynamic and steric interactions reveals how metachronous waves are formed and sustained. We find that these interactions result in multiple states of attraction in homogeneous cilia beds, all characterized by a conserved integer charge. This even allows us to design initial conditions that lead to predictable emerging states. Finally, and very importantly, we show that boundaries and inhomogeneities in patchy ciliary tissue provide a robust route to metachronous waves.