Synchronized oscillations, metachronal waves, and jammed clusters in sterically interacting active filament arrays

Autonomous active, elastic filaments that interact with each other to achieve cooperation and synchrony underlie many critical functions in biology. A striking example is ciliary arrays in the mammalian respiratory tract; here individual filaments communicate through direct interactions and through the surrounding fluid to generate metachronal traveling waves crucial for mucociliary clearance. The mechanisms underlying this collective response and the essential ingredients for stable synchronization remain a mystery. In this article, we describe Brownian dynamics simulations of multi-filament arrays, demonstrating that short-range steric inter-filament interactions and surface-roughness are sufficient to generate a rich variety of collective spatiotemporal oscillatory, traveling and static patterns. Starting from results for the collective dynamics of two- and three-filament systems, we identify parameter ranges in which inter-filament interactions lead to synchronized oscillations. We then study how these results generalize to large one-dimensional arrays of many interacting filaments. The phase space characterizing the multi-filament array dynamics and deformations exhibits rich behaviors, including oscillations and traveling metachronal waves, depending on the interplay between geometric spacing between filaments, activity, and elasticity of the filaments. Interestingly, the existence of metachronal waves is nonmonotonic with respect to the inter-filament spacing. We also find that the degree of filament surface roughness significantly affects the dynamics -- roughness on scales comparable to the filament thickness generates a locking-mechanism that transforms traveling wave patterns into statically stuck and jammed configurations. Our simulations suggest that short-ranged steric inter-filament interactions are sufficient and perhaps even critical for the development, stability and regulation of collective patterns.