Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia

Cells carrying cilia on their surface show many striking features: alignment of cilia in an array, two-phase asymmetric beating for each cilium, and existence of metachronal coordination with a constant phase difference between two adjacent cilia. We give simple theoretical arguments based on hydrodynamic coupling and an internal mechanism of the cilium derived from the behavior of a collection of molecular motors to account qualitatively for these cooperative features. Hydrodynamic interactions can lead to the alignment of an array of cilia. We study the effect of a transverse external flow and obtain a two-phase asymmetrical beating, faster along the flow and slower against the flow, proceeding around an average curved position. We show that an aligned array of cilia is able to spontaneously break the left-right symmetry and to create a global average flow. Metachronal coordination arises as a consequence of the internal mechanism of the cilia and their hydrodynamic couplings, with a wavelength comparable to that found in experiments. It allows the cilia to start beating at a lower adenosine-triphosphate threshold and at a higher frequency than for a single cilium. It also leads to a rather stationary flow, which might be its major advantage.     

Ciliary motion modeling, and dynamic multicilia interactions

This paper presents a rigorous and accurate modeling tool for ciliary motion. The hydrodynamics analysis, originally suggested by Lighthill (1975), has been modified to remove computational problems. This approach is incorporated into a moment-balance model of ciliary motion in place of the previously used hydrodynamic analyses, known as Resistive Force Theory. The method is also developed to include the effect of a plane surface at the base of the cilium, and the effect of the flow fields produced by neighboring cilia. These extensions were not possible with previous work using the Resistive Force Theory hydrodynamics. Performing reliable simulations of a single cilium as well as modeling multicilia interactions is now possible. The result is a general method which could now be used for detailed modeling of the mechanisms for generating ciliary beat patterns and patterns of metachronal interactions in arrays of cilia. A computer animation technique was designed and applied to display the results.     

Computation of the internal forces in cilia: application to ciliary motion, the effects of viscosity, and cilia interactions.

This paper presents a simple and reasonable method for generating a phenomenological model of the internal mechanism of cilia. The model uses a relatively small number of parameters whose values can be obtained by fitting to ciliary beat shapes. Here, we use beat patterns observed in Paramecium. The forces that generate these beats are computed and fit to a simple functional form called the "engine." This engine is incorporated into a recently developed hydrodynamic model that accounts for interactions between neighboring cilia and between the cilia and the surface from which they emerge. The model results are compared to data on ciliary beat patterns of Paramecium obtained under conditions where the beats are two-dimensional. Many essential features of the motion, including several properties that are not built in explicitly, are shown to be captured. In particular, the model displays a realistic change in beat pattern and frequency in response to increased viscosity and to the presence of neighboring cilia in configurations such as rows of cilia and two-dimensional arrays of cilia. We found that when two adjacent model cilia start beating at different phases they become synchronized within several beat periods, as observed in experiments where two flagella are brought into close proximity. Furthermore, examination of various multiciliary configurations shows that an approximately antiplectic wave pattern evolves autonomously. This modeling evidence supports earlier conjectures that metachronism may occur, at least partially, as a self-organized phenomenon due to hydrodynamic interactions between neighboring cilia.     

Nodal cilia dynamics and the specification of the left/right axis in early vertebrate embryo development

Nodal cilia dynamics is a key factor for left/right axis determination in mouse embryos through the induction of a leftward fluid flow. So far it has not been clearly established how such dynamics is able to induce the asymmetric leftward flow within the node. Herein we propose that an asymmetric two-phase nonplanar beating cilia dynamics that involves the bending of the ciliar axoneme is responsible for the leftward fluid flow. We support our proposal with a host of hydrodynamic arguments, in silico experiments and in vivo video microscopy data in wild-type embryos and inv mutants. Our phenomenological modeling approach underscores how the asymmetry and speed of the flow depends on different relevant parameters. In addition, we discuss how the combination of internal and external mechanisms might cause the two-phase beating cilia dynamics.     

Actin and microtubules drive differential aspects of planar cell polarity in multiciliated cells

Planar cell polarization represents the ability of cells to orient within the plane of a tissue orthogonal to the apical basal axis. The proper polarized function of multiciliated cells requires the coordination of cilia spacing and cilia polarity as well as the timing of cilia beating during metachronal synchrony. The planar cell polarity pathway and hydrodynamic forces have been shown to instruct cilia polarity. In this paper, we show how intracellular effectors interpret polarity to organize cellular morphology in accordance with asymmetric cellular function. We observe that both cellular actin and microtubule networks undergo drastic reorganization, providing differential roles during the polarized organization of cilia. Using computational angular correlation analysis of cilia orientation, we report a graded cellular organization downstream of cell polarity cues. Actin dynamics are required for proper cilia spacing, global coordination of cilia polarity, and coordination of metachronic cilia beating, whereas cytoplasmic microtubule dynamics are required for local coordination of polarity between neighboring cilia.     

Ciliary activity under normal conditions and under viscous load

Ciliary metachronism and motility were examined optically in muco-ciliary tissue cultures from three different systems: a) frog's palate epithelium, b) frog's oesophagus, and c) human nasal polyps. In addition, lateral cilia of Mytilus edulis (water transporting cilia) were examined. It was revealed that the degree of synchronization between muco-ciliary systems is lower than that of water transporting cilia. There are no significant differences between different muco-ciliary systems, within the accuracy of our measurement although relatively large statistical ensembles were used. In addition the wavelength and wave direction of the metachronal wave was examined. All four systems exhibit similar wavelength. The metachronal parameters of muco-ciliary systems exhibit fluctuations (as was demonstrated by the degree of synchronization), however, the magnitude and repetitivity of these fluctuations, is dependent on the loading of the ciliary system. We have loaded the system by increasing the viscosity of the medium. Under viscous load the frequency of the beating decreased. The metachronal wavelength became longer and the metachronal coordination type more orthoplectic.     

An Outer Arm Dynein Conformational Switch Is Required for Metachronal Synchrony of Motile Cilia in Planaria

Motile cilia mediate the flow of mucus and other fluids across the surface of specialized epithelia in metazoans. Efficient clearance of peri-ciliary fluids depends on the precise coordination of ciliary beating to produce metachronal waves. The role of individual dynein motors and the mechanical feedback mechanisms required for this process are not well understood. Here we used the ciliated epithelium of the planarian Schmidtea mediterranea to dissect the role of outer arm dynein motors in the metachronal synchrony of motile cilia. We demonstrate that animals that completely lack outer dynein arms display a significant decline in beat frequency and an inability of cilia to coordinate their oscillations and form metachronal waves. Furthermore, lack of a key mechanosensitive regulatory component (LC1) yields a similar phenotype even though outer arms still assemble in the axoneme. The lack of metachrony was not due simply to a decrease in ciliary beat frequency, as reducing this parameter by altering medium viscosity did not affect ciliary coordination. In addition, we did not observe a significant temporal variability in the beat cycle of impaired cilia. We propose that this conformational switch provides a mechanical feedback system within outer arm dynein that is necessary to entrain metachronal synchrony.     

STUDIES ON CILIA : The Fixation of the Metachronal Wave

Upon excision into spring water, the lateral cilia of the gill of the freshwater mussel Elliptio complanatus (Solander) stop beating, but 0.04 M potassium ion can activate the gill so that these cilia again beat with metachronal rhythm. One per cent osmium tetroxide quickly pipetted onto a fully activated gill fixes the lateral cilia in a pattern that preserves the form and arrangement of the metachronal wave, and permits the cilia to be studied with the electron microscope in all stages of their beat cycle. Changes are seen in the fixed active preparation that are not present in the inactive control, i.e., in the packing of the cilia, the position of the axis of the ciliary cross-section, and the diameter of the ring of peripheral filaments. Analysis of these parameters may lead to new correlations between ciliary fine structure and function.     

On metachronism in ciliary systems: a model describing the dependence of the metachronal wave properties on the intrinsic ciliary parameters

A mathematical model is proposed to explain the dependence of the direction and the length of the metachronal wave on parameters that characterize the ciliary beat, the dimensions of the cilia, and the geometry of their arrangement on the ciliated surface. The metachronal wave is decomposed into two mutually perpendicular components, which are chosen in such a way that the direction of one of them is in the direction of the effective stroke. The magnitudes of the two components are determined by using the concept of the time of delay between adjacent cilia. The properties of the metachronal wave are then calculated as a function of the ciliary parameters. The results obtained with the present model predict that the direction of the wave propagation is strongly dependent on the type of metachronism in the direction of the effective stoke and the polarization in time and in space of the ciliary beat. The metachronal wavelength is found to depend on four parameters: the ciliary length, the angle of the arc projected on the cell surface by the ciliary tip during the recovery stroke, the degree of asymmetry of ciliary beat, and the portion of the cycle occupied by the pause. The metachronal wavelength is also found to be only weakly dependent on the ciliary frequency. At this stage there exists relatively little experimental information with which to characterize fully the metachronal properties of ciliary systems. Even when only partial information exists, the model allows prediction, to within a certain range, of the direction of the wave propagation. It also suggests a possible mechanism for the influence of changes in environmental conditions on wave direction and wavelength. In several cases in which full information does exist, good agreement between the experimental findings and the predictions of the model is found. According to this model it will be worthwhile to invest more effort in measuring the time and space polarization of ciliary beating and times of delay between cilia.     

Direct measurement of the velocity of the metachronal wave in beating cilia

Recently a computerized electro-optical method was developed which enables one to simultaneously measure the frequency and the wavelength of the metachronal waves in beating cilia. The method is based on measurement of scattered light from two areas at a given distance apart. The distance between measured areas can be varied from zero to hundreds of microns. The relative ease of the measurement and data analysis of this method enable one to create large statistical ensembles in order to obtain reliable averages. In this work we show that in addition to the previously mentioned parameters this system can measure directly the velocity of the metachronal wave. It was found that the average velocity in the tissue culture from frog's palate epithelium at room temperature is approximately 270 micron/sec, about twice the average particle velocity at the frog's palate.     

A numerical study of muco-ciliary transport under the condition of diseased cilia

Structural and functional disorders of pulmonary cilia may result from genetic disorders and acquired insults. A two-dimensional numerical model based on the immersed boundary method coupled with the projection method is used to study the flow physics of muco-ciliary transport of the human respiratory tract under various abnormalities of cilia. The effects of the cilia beat pattern (CBP), ciliary length, immotile cilia, beating amplitude and uncoordinated beating of cilia are investigated. As expected, the mucus velocity decreases as the beating amplitude reduces. The windscreen wiper motion and rigid planar motion, which are two abnormal CBPs owing to genetic disorders, greatly reduce or almost stop the mucus transport. If the ciliary length varies from its standard length, the mucus velocity would decrease. The mucus velocity decreases rather linearly if the number of uniformly distributed immotile cilia increases. The numerical results show that the mucus velocity would be further reduced marginally when the uniformly distributed immotile cilia are rearranged as a cluster of immotile cilia. Furthermore, if half of the cilia are immotile and uniformly distributed and motile cilia beat at reduced amplitude, the incoordination between the active motile cilia would not significantly affect the mucus velocity.     

THE METACHRONAL WAVE OF LATERAL CILIA OF MYTILUS EDULIS

The form of beat of cilia and the structure of the metachronal wave on the lateral gill epithelium of Mytulus edulis have been studied on living material by interference-contrast microscopy and stroboscopic illumination, and compared with the same features in rapid-fixed preparations studied by light microscopy and with the scanning electron microscope. The most striking finding is that the beat of the cilia is not planar, as previously assumed, but involves a sideways movement in the recovery stroke Previous reports on nonplanar ciliary beating from protozoan examples describe a planar effective stroke and a counterclockwise rotation in the recovery stroke; in this molluscan example there is a clockwise rotation in the recovery stroke The lateral inclination of the cilia in the recovery stroke is in the same direction as the propagation of the waves, and the orientation of cilia in the recovery stroke is thought to determine whether the waves move to the left or right of the direction of the effective stroke     

Oral Regeneration in the Ciliate Stentor coeruleus: A Scanning and Transmission Electron Optical Study

SYNOPSIS. Elaboration of ciliated feeding organelles in the protozoon Stentor coeruleus was reinvestigated for the first time by scanning electron microscopy which gives the most realistic 3-dimensional images. Parallel transmission EM studies of synchronized regenerating stentors gave further ultrastructural details of stomatogenesis, while also confirming the expectation that in the structure of its kineties this now classical experimental object does not differ from other species of Stentor previously studied. Within 2 hr after the stimulus to regeneration, several generations of new kinetosomes for the oral primordium are produced, first in association with kinetosomes of kineties at the restricted primordium site. These kinetosomes rapidly sprout membranellar cilia as well as subpellicular microtubules but are still randomly oriented (anarchic field). The forming membranellar band increases from its center-line to both sides while it grows in length. Young cilia are blunt-ended. Recession of the early anlage occurs without rupture of the pellicle; soon apparent is the clear border stripe of unknown function along the right side of the membranellar band. Instantaneous fixation of beating cilia in early primordia revealed random beating, with coordination and presumably membranellar organization not yet attained. In late anlagen there are 2 types of metachronal rhythm: transversely from cilium to cilium across any given membranelle, as well as the easily observable serial beating of membranelles along the entire band. A single file of cilia leads the subsequent cytostomal invagination. The posterior end of the membranellar band then follows to line the cytopharynx.     

Coordinated Flagellar and Ciliary Beating in the Protozoon Tritrichomonas foetus1

ABSTRACT. Tritrichomonas foetus is a flagellated protozoon found in urogenital tract of cattle. Its free movement in liquid medium is powered by the coordinated movement of three flagella projecting towards the anterior region of the cell, and one recurrent flagellum that forms a junction with the cell body and ends as a free projection in the posterior region of the cell. We have used video microscopy and digital image processing to analyze the relationships between the movements of these flagella. The anterior flagella beat in a ciliary type pattern displaying effective and recovery strokes, while the recurrent flagellum beats in a typical flagellar wave form. One of the three anterior flagella has a distinctive pattern of beating. It beats straight in its forward direction as opposed to the ample beats performed by the others. Frequency measurements obtained from cells swimming in a viscous medium shows that the beating frequency of the recurrent flagelium is approximate twice the frequency for the three anterior flagella. We also observed that the costa and the axostyle do not show any active motion. On the contrary, they form a cytoskeletal base for the anchoring and orientation of the flagella.     

Flow in tubules due to ciliary activity

A simplified model for cilia-induced flows in tubules is presented. Each cilium is a long slender body which is constrained to move similar to its beat. An array of cilia is defined and coordinated in such a way as to represent the metachronal wave. The velocity field is represented by a distribution of viscous fluid singularities (Stokes flow) along the centerline of each slender body. The total mean velocity field due to all the cilia is obtained. It is found that backflow (reflux) can occur near the walls for cilia exhibiting antiplectic metachronism. Maximum flow rates are obtained for cilia whose length is 0.3 to 0.6 the radius of the tube.     

How Does Cilium Length Affect Beating?

The effects of cilium length on the dynamics of cilia motion were investigated by high-speed video microscopy of uniciliated mutants of the swimming alga, Chlamydomonas reinhardtii. Cells with short cilia were obtained by deciliating cells via pH shock and allowing cilia to reassemble for limited times. The frequency of cilia beating was estimated from the motion of the cell body and of the cilium. Key features of the ciliary waveform were quantified from polynomial curves fitted to the cilium in each image frame. Most notably, periodic beating did not emerge until the cilium reached a critical length between 2 and 4 μm. Surprisingly, in cells that exhibited periodic beating, the frequency of beating was similar for all lengths with only a slight decrease in frequency as length increased from 4 μm to the normal length of 10–12 μm. The waveform average curvature (rad/μm) was also conserved as the cilium grew. The mechanical metrics of ciliary propulsion (force, torque, and power) all increased in proportion to length. The mechanical efficiency of beating appeared to be maximal at the normal wild-type length of 10–12 μm. These quantitative features of ciliary behavior illuminate the biophysics of cilia motion and, in future studies, may help distinguish competing hypotheses of the underlying mechanism of oscillation.     

Evidence for Two Extremes of Ciliary Motor Response in a Single Swimming Microorganism

Because arrays of motile cilia drive fluids for a range of processes, the versatile mechano-chemical mechanism coordinating them has been under scrutiny. The protist Paramecium presents opportunities to compare how groups of cilia perform two distinct functions, swimming propulsion and nutrient uptake. We present how the body cilia responsible for propulsion and the oral-groove cilia responsible for nutrient uptake respond to changes in their mechanical environment accomplished by varying the fluid viscosity over a factor of 7. Analysis with a phenomenological model of trajectories of swimmers made neutrally buoyant with magnetic forces combined with high-speed imaging of ciliary beating reveal that the body cilia exert a nearly constant propulsive force primarily by reducing their beat frequency as viscosity increases. By contrast, the oral-groove cilia beat at a nearly constant frequency. The existence of two extremes of motor response in a unicellular organism prompts unique investigations of factors controlling ciliary beating.     

Inductive interactions and embryonic equivalence groups in a basal metazoan, the ctenophore Mnemiopsis leidyi

Ctenophores undergo locomotion via the metachronal beating of eight longitudinally arrayed rows of comb plate cilia. These cilia are normally derived from two embryonic lineages, which include both daughters of the four e1 micromeres (e11 and e12) and a single daughter of the four m1 micromeres (the m12 micromeres). Although the e1 lineage is established autonomously, the m1 lineage requires an inductive interaction from the e1 lineage to contribute to comb plate formation. Successive removal of the e1 progeny at later stages of development indicates that this interaction takes place after the 32-cell stage and likely proceeds over a prolonged period of development. Normally, the e1, cell lies in closest proximity to the m12 cell that generates comb plate cilia; however, either of the e1 daughters (e11 or e12) is capable of emitting the signal required for m1 descendants to form comb plates. Previous cell lineage analyses indicate that the two e1 daughters generate the same suite of cell fates. On the other hand, the m1 daughters (m11 and m12) normally give rise to different cell fates. Reciprocal m1 daughter deletions show that in the absence of one daughter, the other cell can generate all the cell types normally formed by the missing cell. Together, these findings demonstrate that the two m1 daughters (m11 and m12) represent an embryonic equivalence group or field and that differences in the fates of the two m1 daughters are normally controlled by cell-cell interactions. These combined properties of ctenophore development, including the utilization of deterministic cleavage divisions, inductive interactions, and the establishment of embryonic fields or equivalence groups, are remarkably similar to those present in the development of various bilaterian metazoans.     

Evidence for Two Extremes of Ciliary Motor Response in a Single Swimming Microorganism

Because arrays of motile cilia drive fluids for a range of processes, the versatile mechano-chemical mechanism coordinating them has been under scrutiny. The protist Paramecium presents opportunities to compare how groups of cilia perform two distinct functions, swimming propulsion and nutrient uptake. We present how the body cilia responsible for propulsion and the oral-groove cilia responsible for nutrient uptake respond to changes in their mechanical environment accomplished by varying the fluid viscosity over a factor of 7. Analysis with a phenomenological model of trajectories of swimmers made neutrally buoyant with magnetic forces combined with high-speed imaging of ciliary beating reveal that the body cilia exert a nearly constant propulsive force primarily by reducing their beat frequency as viscosity increases. By contrast, the oral-groove cilia beat at a nearly constant frequency. The existence of two extremes of motor response in a unicellular organism prompts unique investigations of factors controlling ciliary beating.