Evaluating efficiency and robustness in cilia design

Metachrony drives effective mucociliary transport via a calcium-dependent mechanism

The mucociliary transport apparatus is critical for maintaining lung health via the coordinated movement of cilia to clear mucus and particulates. A metachronal wave propagates across the epithelium when cilia on adjacent multiciliated cells beat slightly out of phase along the proximal-distal axis of the airways in alignment with anatomically directed mucociliary clearance. We hypothesized that metachrony optimizes mucociliary transport (MCT) and that disruptions of calcium signaling would abolish metachrony and decrease MCT. We imaged bronchi from human explants and ferret tracheae using micro-optical coherence tomography (µOCT) to evaluate airway surface liquid depth (ASL), periciliary liquid depth (PCL), cilia beat frequency (CBF), MCT, and metachrony in situ. We developed statistical models that included covariates of MCT. Ferret tracheae were treated with BAPTA-AM (chelator of intracellular Ca2+), lanthanum chloride (nonpermeable Ca2+ channel competitive antagonist), and repaglinide (inhibitor of calaxin) to test calcium dependence of metachrony. We demonstrated that metachrony contributes to mucociliary transport of human and ferret airways. MCT was augmented in regions of metachrony compared with nonmetachronous regions by 48.1%, P = 0.0009 or 47.5%, P < 0.0020 in humans and ferrets, respectively. PCL and metachrony were independent contributors to MCT rate in humans; ASL, CBF, and metachrony contribute to ferret MCT rates. Metachrony can be disrupted by interference with calcium signaling including intracellular, mechanosensitive channels, and calaxin. Our results support that the presence of metachrony augments MCT in a calcium-dependent mechanism.NEW & NOTEWORTHY We developed a novel imaging-based analysis to detect coordination of ciliary motion and optimal coordination, a process called metachrony. We found that metachrony is key to the optimization of ciliary-mediated mucus transport in both ferret and human tracheal tissue. This process appears to be regulated through calcium-dependent mechanisms. This study demonstrates the capacity to measure a key feature of ciliary coordination that may be important in genetic and acquired disorders of ciliary function.

Flow Physics Explains Morphological Diversity of Ciliated Organs

Organs that pump fluids by the coordinated beat of motile cilia through the lumen are integral to animal physiology. Such organs include the human airways, brain ventricles, and reproductive tracts. Although cilia organization and duct morphology vary drastically in the animal kingdom, ducts are typically classified as either carpet or flame designs. The reason behind this dichotomy and how duct design relates to fluid pumping remain unclear. Here, we demonstrate that two structural parameters -- lumen diameter and cilia-to-lumen ratio -- organize the observed duct diversity into a continuous spectrum that connects carpets to flames across all animal phyla. Using a unified fluid model, we show that carpet and flame designs maximize flow rate and pressure generation, respectively. We propose that convergence of ciliated organ designs follows functional constraints rather than phylogenetic distance, along with universal design rules for ciliary pumps.

An operative framework to model mucus clearance in silico by coupling cilia motion with the liquid environment

Mucociliary clearance is the first defense mechanism of the respiratory tract against inhaled particles. This mechanism is based on the collective beating motion of cilia at the surface of epithelial cells. Impaired clearance, either caused by malfunctioning or absent cilia, or mucus defects, is a symptom of many respiratory diseases. Here, by exploiting the lattice Boltzmann particle dynamics technique, we develop a model to simulate the dynamics of multiciliated cells in a two-layer fluid. First, we tuned our model to reproduce the characteristic length- and time-scales of the cilia beating. We then check for the emergence of the metachronal wave as a consequence of hydrodynamic mediated correlations between beating cilia. Finally, we tune the viscosity of the top fluid layer to simulate the mucus flow upon cilia beating, and evaluate the pushing efficiency of a carpet of cilia. With this work, we build a realistic framework that can be used to explore several important physiological aspects of mucociliary clearance.

Metachronal Coordination of Multiple Appendages for Swimming and Pumping

As a strategy for creating fluid flow, metachronal motion is widespread across sizes and species, including a broad array of morphologies, length scales, and coordination patterns. Because of this great diversity, it has not generally been viewed holistically: the study of metachrony for swimming and pumping has historically been taxonomically siloed, in spite of many commonalities between seemingly disparate organisms. The goal of the present symposium was to bring together individuals from different backgrounds, all of whom have made substantial individual contributions to our understanding of the fluid dynamics of metachronal motion. Because these problems share a common physical-mathematical basis, intentionally connecting this community is likely to yield future collaborations and significant scientific discovery. Here, we briefly introduce the concept of metachronal motion, present the benefits of creating a research network based on the common aspects of metachrony across biological systems, and outline the contributions to the symposium.

Instability-driven oscillations of elastic microfilaments

Cilia and flagella are highly conserved slender organelles that exhibit a variety of rhythmic beating patterns from non-planar cone-like motions to planar wave-like deformations. Although their internal structure, composed of a microtubule-based axoneme driven by dynein motors, is known, the mechanism responsible for these beating patterns remains elusive. Existing theories suggest that the dynein activity is dynamically regulated, via a geometric feedback from the cilium's mechanical deformation to the dynein force. An alternative, open-loop mechanism based on a 'flutter' instability was recently proven to lead to planar oscillations of elastic filaments under follower forces. Here, we show that an elastic filament in viscous fluid, clamped at one end and acted on by an external distribution of compressive axial forces, exhibits a Hopf bifurcation that leads to non-planar spinning of the buckled filament at a locked curvature. We also show the existence of a second bifurcation, at larger force values, that induces a transition from non-planar spinning to planar wave-like oscillations. We elucidate the nature of these instabilities using a combination of nonlinear numerical analysis, linear stability theory and low-order bead-spring models. Our results show that, away from the transition thresholds, these beating patterns are robust to perturbations in the distribution of axial forces and in the filament configuration. These findings support the theory that an open-loop, instability-driven mechanism could explain both the sustained oscillations and the wide variety of periodic beating patterns observed in cilia and flagella.

Magnetically-actuated artificial cilium: a simple theoretical model

We propose a theoretical model for a magnetically-actuated artificial cilium in a fluid environment and investigate its dynamical behaviour, using both analytical calculations and numerical simulations. The cilium consists of a spherical soft magnet, a spherical hard magnet, and an elastic spring that connects the two magnetic components. Under a rotating magnetic field, the cilium exhibits a transition from phase-locking at low frequencies to phase-slipping at higher frequencies. We study the dynamics of the magnetic cilium in the vicinity of a wall by incorporating its hydrodynamic influence, and examine the efficiency of the actuated cilium in pumping viscous fluids. This cilium model can be helpful in a variety of applications such as transport and mixing of viscous solutions at small scales and fabricating microswimmers.

Mixing and pumping by pairs of helices in a viscous fluid

Here, we study the fluid dynamics of a pair of rigid helices rotating at a constant velocity, tethered at their bases, in a viscous fluid. Our computations use a regularized Stokeslet framework, both with and without a bounding plane, so we are able to discern precisely what flow features are unaccounted for in studies that ignore the surface from which the helices emanate. We examine how the spacing and phase difference between identical rotating helices affects their pumping ability, axial thrust, and power requirements. We also find that optimal mixing of the fluid around two helices is achieved when they rotate in opposite phase, and that the mixing is enhanced as the distance between the helices decreases.

Assessing the Collective Dynamics of Motile Cilia in Cultures of Human Airway Cells by Multiscale DDM

The technique of differential dynamic microscopy is extended here, showing that it can provide a powerful and objective method of video analysis for optical microscopy videos of in vitro samples of live human bronchial epithelial ciliated cells. These cells are multiciliated, with motile cilia that play key physiological roles. It is shown that the ciliary beat frequency can be recovered to match conventional analysis, but in a fully automated fashion. Furthermore, it is shown that the properties of spatial and temporal coherence of cilia beat can be recovered and distinguished, and that if a collective traveling wave (the metachronal wave) is present, this has a distinct signature and its wavelength and direction can be measured.

Passive swimming in viscous oscillatory flows

Fluid-based locomotion at low Reynolds number is subject to the constraints of Purcell's scallop theorem: reciprocal shape kinematics identical under a time-reversal symmetry cannot cause locomotion. In particular, a single degree-of-freedom scallop undergoing opening and closing motions cannot swim. Most strategies for symmetry breaking and locomotion rely on direct control of the swimmer's shape kinematics. Less is known about indirect control via actuation of the fluid medium. To address how such indirect actuation strategies can lead to locomotion, we analyze a Λ-shaped model system analogous to Purcell's scallop but able to deform passively in oscillatory flows. Neutrally buoyant scallops undergo no net locomotion. We show that dense, elastic scallops can exhibit passive locomotion in zero-mean oscillatory flows. We examine the efficiency of swimming parallel to the background flow and analyze the stability of these motions. We observe transitions from stable to unstable swimming, including ordered transitions from fluttering to chaoticlike motions and tumbling. Our results demonstrate that flow oscillations can be used to passively actuate and control the motion of microswimmers, which may be relevant to applications such as surgical robots and cell sorting and manipulation in microfluidic devices.