Longitudinal to Transverse Metachronal Wave Transitions in an In Vitro Model of Ciliated Bronchial Epithelium

Hydrodynamic synchronization of elastic cilia: How surface effects determine the characteristics of metachronal waves

Cilia are hairlike microactuators whose cyclic motion is specialized to propel extracellular fluids at low Reynolds numbers. Clusters of these organelles can form synchronized beating patterns, called metachronal waves, which presumably arise from hydrodynamic interactions. We model hydrodynamically interacting cilia by microspheres elastically bound to circular orbits, whose inclinations with respect to a no-slip wall model the ciliary power and recovery stroke, resulting in an anisotropy of the viscous flow. We derive a coupled phase-oscillator description by reducing the microsphere dynamics to the slow timescale of synchronization and determine analytical metachronal wave solutions and their stability in a periodic chain setting. In this framework, a simple intuition for the hydrodynamic coupling between phase oscillators is established by relating the geometry of flow near the surface of a cell or tissue to the directionality of the hydrodynamic coupling functions. This intuition naturally explains the properties of the linear stability of metachronal waves. The flow near the surface stabilizes metachronal waves with long wavelengths propagating in the direction of the power stroke and, moreover, metachronal waves with short wavelengths propagating perpendicularly to the power stroke. Performing simulations of phase-oscillator chains with periodic boundary conditions, we indeed find that both wave types emerge with a variety of linearly stable wave numbers. In open chains of phase oscillators, the dynamics of metachronal waves is fundamentally different. Here the elasticity of the model cilia controls the wave direction and selects a particular wave number: At large elasticity, waves traveling in the direction of the power stroke are stable, whereas at smaller elasticity waves in the opposite direction are stable. For intermediate elasticity both wave directions coexist. In this regime, waves propagating towards both ends of the chain form, but only one wave direction prevails, depending on the elasticity and initial conditions.

Metachronal Motion of Biological and Artificial Cilia

Cilia are slender, hair-like cell protrusions that are present ubiquitously in the natural world. They perform essential functions, such as generating fluid flow, propulsion, and feeding, in organisms ranging from protozoa to the human body. The coordinated beating of cilia, which results in wavelike motions known as metachrony, has fascinated researchers for decades for its role in functions such as flow generation and mucus transport. Inspired by nature, researchers have explored diverse materials for the fabrication of artificial cilia and developed several methods to mimic the metachronal motion observed in their biological counterparts. In this review, we will introduce the different types of metachronal motion generated by both biological and artificial cilia, the latter including pneumatically, photonically, electrically, and magnetically driven artificial cilia. Furthermore, we review the possible applications of metachronal motion by artificial cilia, focusing on flow generation, transport of mucus, particles, and droplets, and microrobotic locomotion. The overall aim of this review is to offer a comprehensive overview of the metachronal motions exhibited by diverse artificial cilia and the corresponding practical implementations. Additionally, we identify the potential future directions within this field. These insights present an exciting opportunity for further advancements in this domain.

Mechanisms and functions of multiciliary coordination

Ciliated organisms are present in virtually every branch of the eukaryotic tree of life. In diverse systems, cilia operate in a coordinated manner to drive fluid flows, or even propel entire organisms. How do groups of motile cilia coordinate their activity within a cell or across a tissue to fulfil essential functions of life? In this review, we highlight the latest developments in our understanding of the mechanisms and functions of multiciliary coordination in diverse systems. We explore new and emerging trends in bioimaging, analytical, and computational methods, which together with their application in new model systems, have conspired to deliver important insights into one of the most fundamental questions in cellular dynamics.

Gastropod Slime-Based Gel as an Adjustable Synthetic Model for Human Airway Mucus

Airway mucus works as a protective barrier in the human body, as it entraps pathogens that will be later cleared from the airways by ciliary transport or by coughing, thus featuring the rheological properties of a highly stretchable gel. Nonetheless, the study of these physical barrier as well as transport properties remains limited due to the restricted and invasive access to lungs and bronchi to retrieve mucus and to the poor repeatability inherent to native mucus samples. To overcome these limits, we report on a biobased synthetic mucus prepared from snail slime and multibranched thiol cross-linker, which are able to establish disulfide bonds, in analogy with the disulfide bonding of mucins, and therefore build viscoelastoplastic hydrogels. The gel macroscopic properties are tuned by modifying the cross-linker and slime concentrations and can quantitatively match those of native sputum from donors with cystic fibrosis (CF) or non-cystic fibrosis bronchiectasis (NCFB) both in the small- and large-deformation regimes. Heterogeneous regimes were locally found in the mucus model by passive microrheology, in which both diffusive and non-diffusive motion are present, similar to what is observed in sputa. The biobased synthetic approach proposed in the present study thus allows to produce, with commercially available components, a promising model to native respiratory mucus regarding both mechanical and, to a lesser extent, physicochemical aspects.

Nanoparticle Diffusion in Respiratory Mucus Influenced by Mucociliary Clearance: A Review of Mathematical Modeling

Background: Inhalation and deposition of particles in human airways have attracted considerable attention due to importance of particulate pollutants, transmission of infectious diseases, and therapeutic delivery of drugs at targeted areas. We summarize current state-of-the art research in particle deposition on airway surface liquid (ASL) influenced by mucociliary clearance (MCC) by identifying areas that need further investigation. Methodology: We aim to review focus on governing and constitutive equations describing MCC geometry followed by description of mathematical modeling of ciliary forces, mucus rheology properties, and numerical approaches to solve modified time-dependent Navier-Stokes equations. We also review mathematical modeling of particle deposition in ASL influenced by MCC, particle transport in ASL in terms of Eulerian and Lagrangian approaches, and discuss the corresponding mass transport issues in this layer. Whenever required, numerical predictions are contrasted with the pertinent experimental data. Results: Results indicate that mean mucus and periciliary liquid velocities are strongly influenced by mucus rheological characteristics as well as ciliary abnormalities. However, most of the currently available literature on mucus fiber spacing, ciliary beat frequency, and particle surface chemistry is based on particle deposition on ASL by considering a fixed value of ASL velocity. The effects of real ASL flow regimes on particle deposition in this layer are limited. In addition, no other study is available on modeling nonhomogeneous and viscoelastic characteristics of mucus layer on ASL drug delivery. Conclusion: Simplification of assumptions on governing equations of drug delivery in ASL influenced by MCC leads to imposing some limitations on numerical results.