Locally synchronized ciliary domains and tissue-scale cilia alignment underlie global metachronal wave patterns

Motile cilia are hair-like cell extensions present in multiple organs of the body. How cilia coordinate their regular beat in multiciliated epithelia to efficiently displace fluids remains elusive. Here, we propose the zebrafish nose as an accessible model system to study ciliary dynamics, due to its conserved properties with other ciliated tissues and its high availability for non-invasive imaging. We reveal that cilia are locally synchronized, and that the size of local synchronization domains increases with the viscosity of the surrounding medium. Despite this merely local synchronization, we observe global patterns of traveling metachronal waves across the multiciliated epithelium. Intriguingly, these global wave direction patterns are conserved across individual fish, but different for left and right nose, revealing a chiral asymmetry of metachronal coordination. In conclusion, we show that local synchronization together with tissue-scale cilia alignment shape global wave patterns in multiciliated epithelia.

Longitudinal to transverse metachronal wave transitions in an in-vitro model of ciliated bronchial epithelium

Myriads of cilia beat on ciliated epithelia, which are ubiquitous in life. When ciliary beats are synchronized, metachronal waves emerge, whose direction of propagation depends on the living system in an unexplained way. We show on a reconstructed human bronchial epithelium in-vitro that the direction of propagation is determined by the ability of mucus to be transported at the epithelial surface. Numerical simulations show that longitudinal waves maximise the transport of mucus while transverse waves, observed when the mucus is rigid and still, minimize the energy dissipated by the cilia.

Conditions for metachronal coordination in arrays of model cilia

On surfaces with many motile cilia, beats of the individual cilia coordinate to form metachronal waves. We present a theoretical framework that connects the dynamics of an individual cilium to the collective dynamics of a ciliary carpet via systematic coarse graining. We uncover the criteria that control the selection of frequency and wave vector of stable metachronal waves of the cilia and examine how they depend on the geometric and dynamical characteristics of a single cilium, as well as the geometric properties of the array. We perform agent-based numerical simulations of arrays of cilia with hydrodynamic interactions and find quantitative agreement with the predictions of the analytical framework. Our work sheds light on the question of how the collective properties of beating cilia can be determined using information about the individual units and, as such, exemplifies a bottom-up study of a rich active matter system.

A Quantitative Interspecies Comparison of The Respiratory Mucociliary Clearance Mechanism

Background: Collectively coordinated ciliary activity constantly propels the airway surface liquid, which lines the luminal surface of the vertebrate respiratory system, in cranial direction – constituting mucociliary clearance, the primary defence mechanism of our airways. Our contemporary understanding on how the quantitative characteristics of the metachronal wave field determines the resulting mucociliary transport is still limited, which is partly due to the sparse availability of quantitative observational data. Methods: We employed high-speed video reflection contrast microscopy to simultaneously image and quantitatively characterize the metachronal wave field as well as the mucociliary transport in excised bovine, porcine, ovine, lapine, turkey and ostrich samples of the luminal tracheal wall. Advanced image processing techniques were used to determine the ciliary beating frequency (CBF), the velocity and the wavelength of the metachronal wave as well as the mucociliary transport velocity. Results: The mucociliary transport direction was found to strongly correlate with the mean wave propagation direction in all six species. The CBF yielded similar values (10−15 Hz) for all six species. Birds were found to exhibit considerably higher transport speeds (130−260 μm/s) than mammals (20−80 μm/s). While the average transport direction significantly deviates from the tracheal long axis (TLA) in mammals, no significant deviation from the TLA was found in birds. In comparison to mammals, longer metachronal wavelengths were found in birds. Finally, the metachronal waves were found to propagate at about 4−8 times the speed of mucociliary transport in mammals, whereas the metachronal waves propagate at about the speed of mucociliary transport in birds. Conclusions: The tracheal mucociliary clearance mechanism is based on a symplectic metachronsim in all examined species. The mucociliary transport in birds is fast and roughly follows the TLA, whereas the transport is slower and proceeds along a left-handed spiral in mammals. The longer wavelengths and the lower ratio between the metachronal wave speed and the mucociliary transport speed provide further evidence that the mucociliary clearance mechanism operates differently in birds than in mammals.

Significance of Slippage and Electric Field in Mucociliary Transport of Biomagnetic Fluid

Shear stress at the cilia wall is considered as an imperative factor that affects the efficiency of cilia beatings as it describes the momentum transfer between the fluid and the cilia. We consider a visco-inelastic Prandtl fluid in a ciliated channel under electro-osmotic pumping and the slippage effect at cilia surface. Cilia beating is responsible for the stimulation of the flow in the channel. Evenly distributed cilia tend to move in a coordinated rhythm to mobilize propulsive metachronal waves along the channel surface by achieving elliptic trajectory movements in the flow direction. After using lubrication approximations, the governing equations are solved by the perturbation method. The pressure rise per metachronal wavelength is obtained by numerically integrating the expression. The effects of the physical parameters of interest on various flow quantities, such as velocity, pressure gradient, pressure rise, stream function, and shear stress at the ciliated wall, are discussed through graphs. The analysis reveals that the axial velocity is enhanced by escalating the Helmholtz–Smoluchowski velocity and the electro-osmosis effects near the elastic wall. The shear stress at the ciliated boundary elevates with an increase in the cilia length and the eccentricity of the cilia structure.

Metachronal waves in magnetic micro-robotic paddles for artificial cilia

Biological cilia generate fluid movement within viscosity-dominated environments using beating motions that break time-reversal symmetry. This creates a metachronal wave, which enhances flow efficiency. Artificially mimicking this behaviour could improve microfluidic point-of-care devices, since viscosity-dominated fluid dynamics impede fluid flow and mixing of reagents, limiting potential for multiplexing diagnostic tests. However, current biomimicry schemes require either variation in the hydrodynamic response across a cilia array or a complex magnetic anisotropy configuration to synchronise the actuation sequence with the driving field. Here, we show that simple modifications to the structural design introduce phase differences between individual actuators, leading to the spontaneous formation of metachronal waves. This generates flow speeds of up to 16 μm/s as far as 675 μm above the actuator plane. By introducing metachronal waves through lithographic structuring, large scale manufacture becomes feasible. Additionally, by demonstrating that metachronal waves emerge from non-uniformity in internal structural mechanics, we offer fresh insight into the mechanics of cilia coordination.

Metachronal patterns in artificial cilia for low Reynolds number fluid propulsion

Cilia are hair-like organelles, present in arrays that collectively beat to generate flow. Given their small size and consequent low Reynolds numbers, asymmetric motions are necessary to create a net flow. Here, we developed an array of six soft robotic cilia, which are individually addressable, to both mimic nature’s symmetry-breaking mechanisms and control asymmetries to study their influence on fluid propulsion. Our experimental tests are corroborated with fluid dynamics simulations, where we find a good agreement between both and show how the kymographs of the flow are related to the phase shift of the metachronal waves. Compared to synchronous beating, we report a 50% increase of net flow speed when cilia move in an antiplectic wave with phase shift of −π/3 and a decrease for symplectic waves. Furthermore, we observe the formation of traveling vortices in the direction of the wave when metachrony is applied.