Emergence of metachronal waves in cilia arrays Elgeti, Jens; Gompper, Gerhard
Proceedings of the National Academy of Sciences - PNAS,
03/2013, Letnik:
110, Številka:
12
Journal Article
Recenzirano
Odprti dostop
Propulsion by cilia is a fascinating and universal mechanism in biological organisms to generate fluid motion on the cellular level. Cilia are hair-like organelles, which are found in many different ...tissues and many uni- and multicellular organisms. Assembled in large fields, cilia beat neither randomly nor completely synchronously—instead they display a striking self-organization in the form of metachronal waves (MCWs). It was speculated early on that hydrodynamic interactions provide the physical mechanism for the synchronization of cilia motion. Theory and simulations of physical model systems, ranging from arrays of highly simplified actuated particles to a few cilia or cilia chains, support this hypothesis. The main questions are how the individual cilia interact with the flow field generated by their neighbors and synchronize their beats for the metachronal wave to emerge and how the properties of the metachronal wave are determined by the geometrical arrangement of the cilia, like cilia spacing and beat direction. Here, we address these issues by large-scale computer simulations of a mesoscopic model of 2D cilia arrays in a 3D fluid medium. We show that hydrodynamic interactions are indeed sufficient to explain the self-organization of MCWs and study beat patterns, stability, energy expenditure, and transport properties. We find that the MCW can increase propulsion velocity more than 3-fold and efficiency almost 10-fold—compared with cilia all beating in phase. This can be a vital advantage for ciliated organisms and may be interesting to guide biological experiments as well as the design of efficient microfluidic devices and artificial microswimmers.
Although collective cell motion plays an important role, for example during wound healing, embryogenesis, or cancer progression, the fundamental rules governing this motion are still not well ...understood, in particular at high cell density. We study here the motion of human bronchial epithelial cells within a monolayer, over long times. We observe that, as the monolayer ages, the cells slow down monotonously, while the velocity correlation length first increases as the cells slow down but eventually decreases at the slowest motions. By comparing experiments, analytic model, and detailed particle-based simulations, we shed light on this biological amorphous solidification process, demonstrating that the observed dynamics can be explained as a consequence of the combined maturation and strengthening of cell–cell and cell–substrate adhesions. Surprisingly, the increase of cell surface density due to proliferation is only secondary in this process. This analysis is confirmed with two other cell types. The very general relations between the mean cell velocity and velocity correlation lengths, which apply for aggregates of self-propelled particles, as well as motile cells, can possibly be used to discriminate between various parameter changes in vivo, from noninvasive microscopy data.
Sperm cells swim through the fluid by a periodic wave-like beating of their flagellum. At low Reynolds numbers and in confinement, the directed motion of sperm and other microswimmers is strongly ...influenced by steric and hydrodynamic wall interactions. We model sperm motility in mesoscale hydrodynamics simulations by imposing a planar traveling bending wave along the flagellum. Sperm are simulated swimming in curved, straight, shallow and zigzag-shaped microchannels. Changes in the sidewall modulations and the imposed beat pattern allow the identification of a strong dependence of the surface attraction on the beat-shape envelope of the sperm cell. For swimming in zigzag microchannels, the deflection-angle distribution at sharp corners is calculated and found to be in good agreement with recent microfluidic experiments. The simulations reveal a strong dependence of the deflection angle on the orientation of the beat plane with respect to the channel sidewall, and thus deepen the understanding of sperm navigation under strong confinement. Detachment of sperm, while swimming along curved walls, is dominated by the change of beat-plane orientation. Therefore, either the emergence of a nonplanar component of the flagellar beat with increasing wavelength or the strong confinement in shallow channels drastically increases wall attraction. Our simulation results reveal a consistent picture of passive sperm guidance that is dominated by the steric interactions of the beat pattern with the nearby surfaces.
The dynamics and motion of multi-ciliated microswimmers with a spherical body and a small number
N
(with
5
<
N
<
60
) of cilia with length comparable to the body radius, is investigated by mesoscale ...hydrodynamics simulations. A metachronal wave is imposed for the cilia beat, for which the wave vector has both a longitudinal and a latitudinal component. The dynamics and motion is characterized by the swimming velocity, its variation over the beat cycle, the spinning velocity around the main body axis, as well as the parameters of the helical trajectory. Our simulation results show that the microswimmer motion strongly depends on the latitudinal wave number and the longitudinal phase lag. The microswimmers are found to swim smoothly and usually spin around their own axis. Chirality of the metachronal beat pattern generically generates helical trajectories. In most cases, the helices are thin and stretched, i.e., the helix radius is about an order of magnitude smaller than the pitch. The rotational diffusion of the microswimmer is significantly smaller than the passive rotational diffusion of the body alone, which indicates that the extended cilia contribute strongly to the hydrodynamic radius. The swimming velocity is found to increase with the cilia number
N
with a slightly sublinear power law, consistent with the behavior expected from the dependence of the transport velocity of planar cilia arrays on the cilia separation.
Graphic abstract
Recent experiments have shown that spreading epithelial sheets exhibit a long-range coordination of motility forces that leads to a buildup of tension in the tissue, which may enhance cell division ...and the speed of wound healing. Furthermore, the edges of these epithelial sheets commonly show finger-like protrusions whereas the bulk often displays spontaneous swirls of motile cells. To explain these experimental observations, we propose a simple flocking-type mechanism, in which cells tend to align their motility forces with their velocity. Implementing this idea in a mechanical tissue simulation, the proposed model gives rise to efficient spreading and can explain the experimentally observed long-range alignment of motility forces in highly disordered patterns, as well as the buildup of tensile stress throughout the tissue. Our model also qualitatively reproduces the dependence of swirl size and swirl velocity on cell density reported in experiments and exhibits an undulation instability at the edge of the spreading tissue commonly observed in vivo. Finally, we study the dependence of colony spreading speed on important physical and biological parameters and derive simple scaling relations that show that coordination of motility forces leads to an improvement of the wound healing process for realistic tissue parameters.
In recent years, the combination of synthetic micro‐ and nanomaterials with spermatozoa as functional components has led to the development of tubular and helical spermbots – microrobotic devices ...with potential applications in the biomedical and nanotechnological field. Here, the initial advances in this field are discussed and the use of spermatozoa as functional parts in microdevices elaborated. Besides the potential uses of these hybrid robotic microswimmers, the obstacles along the way are discussed, with suggestions for solutions of the encountered challenges also given.
The initial advances in using spermatozoa as functional components in robotic microdevices are summarized giving an overview of the state‐of‐the‐art combinations of single‐spermatozoa‐carrying robotic components, as well as of their potential applications and current challenges.
During the formation of tissues, cells organize collectively by cell division and apoptosis. The multicellular dynamics of such systems is influenced by mechanical conditions and can give rise to ...cell rearrangements and movements. We develop a continuum description of tissue dynamics, which describes the stress distribution and the cell flow field on large scales. In the absence of division and apoptosis, we consider the tissue to behave as an elastic solid. Cell division and apoptosis introduce stress sources that, in general, are anisotropic. By combining cell number balance with dynamic equations for the stress source, we show that the tissue effectively behaves as a viscoelastic fluid with a relaxation time set by the rates of division and apoptosis. If the system is confined in a fixed volume, it reaches a homeostatic state in which division and apoptosis balance. In this state, cells undergo a diffusive random motion driven by the stochasticity of division and apoptosis. We calculate the expression for the effective diffusion coefficient as a function of the tissue parameters and compare our results concerning both diffusion and viscosity to simulations of multicellular systems using dissipative particle dynamics.
PDF
