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Flow physics guides morphology of ciliated organs

Nature Physics (2024)Cite this article

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Abstract

Organs that pump luminal fluids by the coordinated beat of motile cilia 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 carpet or flame designs. The reason behind the appearance of these two different designs and how they relate 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 carpets and flames represent trade-offs between flow rate and pressure generation. We propose that the convergence of ciliated organ designs follows functional constraints rather than phylogenetic distance and offer guiding design principles for synthetic ciliary pumps.

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Fig. 1: Comparison of ciliated ducts with ciliary flame and ciliary carpet designs in B. mcnutti.
Fig. 2: The morphospace of ciliated ducts in nature.
Fig. 3: Brinkman–Stokes model maps ciliated duct morphology to fluid pumping.
Fig. 4: Optimal ciliated duct designs.

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All source code used to generate the simulated data and figures is available in the manuscript or the Supplementary Information.

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Acknowledgements

This work was funded by the National Science Foundation (RAISE Grant No. IOS-2034043 to E.K., CBET Grant No. 2100209 to E.K. and Inspire Grant No. MCB1608744 to E.K. and M.M.-N.), the National Institutes of Health (R01 Grant No. HL153622 to E.K. and J.C.N.), the European Research Council (Starting Grant No. 950219 to J.C.N.), the National Institutes of Health (Grant Nos. R37 AI50661, COBRE P20 GM125508, OD11024 and GM135254 to M.M.-N.) and the David & Lucile Packard Foundation (K.K.). Acquisition of the Leica TCS SP8 X confocal microscope was supported by the National Science Foundation (DBI Grant No. 1828262 to M.M.-N.). E.K. is grateful to M. J. Shelley and D. Stein for useful conversations on this study.

Author information

Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA, USA

    Feng Ling, Janna C. Nawroth & Eva Kanso

  2. Helmholtz Pioneer Campus and Institute for Biological and Medical Imaging Member of the German Lung Research Center (DZL CPC-M), Helmholtz Zentrum München, Deutsches Forschungszentrum für Gesundheit und Umwelt (GmbH), Neuherberg, Germany

    Feng Ling & Janna C. Nawroth

  3. Kewalo Marine Laboratory, University of Hawaii at Manoa, Honolulu, HI, USA

    Tara Essock-Burns & Margaret McFall-Ngai

  4. Pacific Biosciences Research Center, University of Hawaii at Manoa, Honolulu, HI, USA

    Margaret McFall-Ngai

  5. Biology and Environmental Research Division, Carnegie Institute, Stanford, CA, USA

    Margaret McFall-Ngai

  6. Monterey Bay Aquarium Research Institute, Moss Landing, CA, USA

    Kakani Katija

  7. Chair of Biological Imaging at the Central Institute for Translational Cancer Research (TranslaTUM), School of Medicine and Health, Technical University of Munich, Munich, Germany

    Janna C. Nawroth

  8. Department of Physics and Astronomy, University of Southern California, Los Angeles, CA, USA

    Eva Kanso

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Contributions

E.K. supervised the project. E.K. and J.C.N designed the study. K.K. and M.M.-N. provided access to animals and imaging facilities. F.L., J.C.N. and E.K. performed the research and analysed the data. All authors discussed the results. F.L., J.C.N. and E.K. wrote the paper, and all authors revised and approved it.

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Correspondence to Janna C. Nawroth or Eva Kanso.

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Extended data

Extended Data Fig. 1 Ciliary flame of the giant larvacean draws ambient seawater through a lattice of non-motile cilia and pumps it into the blood sinus.

A, The ciliated funnel (CF) in the giant larvacean B.stygius branches off the mouth cavity (M). B, Phase-contrast cross-section of entire ciliated funnel shows protective lattice of non-motile cilia in the funnel entry (opening to mouth cavity), ciliary flame, and connection to blood sinus with putative hemocytes (small arrows). The direction of the cilia-driven flow is inwards (large arrow), consistent with a multi-stage filtration system73. C, Cross-sectional confocal image of the ciliated funnel in B.stygius including the funnel entry and the ciliary flame. D, Close-up on the ciliary flame, showing an actin mesh (magenta) encasing the large ciliary flame (cyan) which is composed of multiple, tightly packed ciliary flame cells and connects to the blood sinus. E, Close-up on the lattice of non-motile cilia that project into the funnel entry. The morphology shown in A-E was confirmed in a minimum of 3 animals.

Extended Data Fig. 2 Ciliary beat coordination in metachronal and traveling waves.

A, Ciliary carpets generate long-range or short-range metachronal waves of ciliary beat. Left, larvacean esophagus; right, engineered human airway epithelium. White arrows (left) and white dashed lines (right) indicate crests of metachronal waves. Black arrows indicate wave traveling direction. L, metachronal wave length. B, Ciliary flames generate long-range or short-range metachronal waves of ciliary beat. Left, time lapse of wave traveling along flame of larvacean ciliary funnel; right, time lapse of wave traveling along flame of planarian (flatworm) protonephridium. L, traveling wave length. The data shown in A-B was collected from one sample per species each.

Extended Data Fig. 3 Methods to measure duct lumen diameter and cilia-to-lumen ratio.

In carpet-style ciliated ducts h/H was determined as the ratio of the ciliary layer height h and the duct lumen diameter H. Since ciliary carpets are assumed to line both ‘floor’ and ‘ceiling’ of the ciliated duct, ciliary length corresponds to 1/2 h. In flame-style ciliated ducts the cilia are aligned longitudinally to the duct and hence cilia density rather than length determines the cilia-to-lumen ratio. h/H was therefore determined as the square root of the ratio of the cross-sectional area of the cilia to the cross-sectional area of the duct lumen.

Extended Data Fig. 4 Examples of duct lumen diameter and cilia-to-lumen ratio measurements.

A, Example analyses of carpet designs with low cilia-to-lumen ratio h/H and high cilia-to-lumen ratio h/H values (own data). B, Example analyses of flame designs with low h/H and high h/H values. The left TEM image was adapted from81 to highlight areas with sparse ciliation, under Creative Commons CC BY license. The right TEM image was adapted from41, with permission from John Wiley and Sons.

Extended Data Fig. 5 Carpet and flame-type ciliated ducts in Urochordates and Mollusks analyzed in this study.

A, The ciliated pharnyx in larvaceans, here B. stygius (Urochordata), is characterized by a ciliary carpet and a low cilia-to-lumen ratio h/H. B, The ciliated funnel in larvaceans, here Mesochordaeus erythrocephalus (Urochordata), is a flame design. C, The ciliated conduit of the light organ in the Hawaian Bobtail Squid Euprymna scolopes (Mollusca) features a carpet design in the duct and antechamber regions and a flame-like design in the bottleneck region, as seen in the close-up immunofluorescent (left subpanels) and transmission electrode images (right subpanels) of D, the ciliated duct and E, the bottleneck region. The data shown in A-B are taken in one animal each; data shown in C-E were validated in at least 3 animals as part of a published study33.

Extended Data Fig. 6 Indexed plot of cilia-to-lumen ratio h/H as a function of lumen diameter H.

For all ciliated ducts surveyed, we plot their index numbers listed in Supplementary Table 1 at their corresponding cilia-to-lumen ratio h/H and lumen diameter H coordinates shown in Fig. 2a. These numbers can be used to trace their animal species and associated source information from Supplementary Table 1. Color of the numbers indicate their corresponding animal phylum.

Supplementary information

Supplementary Information

Supplementary discussion, Tables 1 and 2, Algorithm 1 and Figs. 1–3.

Reporting Summary

Supplementary Video 1

In vivo beat kinematics and flow generation of the ciliated carpet of the oesophagus in the giant larvacean. Video is slowed down ×2 from its original speed.

Supplementary Video 2

In vivo beat kinematics of ciliary flame in the ciliated funnel of the giant larvacean. Note that video is slowed down ×16 from its original speed so that the flow moves very slowly.

Supplementary Video 3

In vivo beat kinematics and flow generation of the ciliary flame in the giant larvacean. Video is slowed down ×8 from its original speed.

Supplementary Code

MATLAB code used to generate all simulated data and figures in this manuscript.

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Ling, F., Essock-Burns, T., McFall-Ngai, M. et al. Flow physics guides morphology of ciliated organs. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02591-0

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