Universal elastic mechanism for stinger design

Abstract

Living organisms use stingers that vary in length L over eight orders of magnitude, from a few tens of nanometres to several metres, across a wide array of biological taxa. Despite the extreme variation in size, their structures are strikingly similar. However, the mechanism responsible for this remarkable morphological convergence remains unknown. Using basic physical arguments and biomimetic experiments, we reveal an optimal design strategy that links their length, base diameter d0, Young’s modulus E and friction force per unit area μp0. This principle can be framed simply as \({d}_{0} \approx {(\mu {p}_{0}/E)}^{1/3}L\). Existing data from measurements on viruses, algae, marine invertebrates, terrestrial invertebrates, plants, terrestrial vertebrates, marine vertebrates—as well as man-made objects such as nails, needles and weapons—are consistent with our predictions. Our results highlight the evolutionary adaptation of mechanical traits to the constraints imposed by friction, elastic stability and cost.

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Fig. 1: Stinger morphology.
Fig. 2: Buckling experiments.
Fig. 3: Stinger design principle.
Fig. 4: Universal elastic mechanism for stinger design.

Data availability

Source data are available in Supplementary Table 1. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. 1.

    van Tol, H. M., Irwin, A. J. & Finkel, Z. V. Macroevolutionary trends in silicoflagellate skeletal morphology: the costs and benefits of silicification. Paleobiology 38, 391–402 (2012).

    Article  Google Scholar 

  2. 2.

    Mershon, J. P., Becker, M. & Bickford, C. P. Linkage between trichome morphology and leaf optical properties in New Zealand alpine Pachycladon (Brassicaceae). New Zealand J. Botany 53, 175–182 (2015).

    Article  Google Scholar 

  3. 3.

    Emlen, D. J. The evolution of animal weapons. Annu. Rev. Ecol. Evol. Syst. 39, 387–413 (2008).

    Article  Google Scholar 

  4. 4.

    Kodric-Brown, A., Sibly, R. M. & Brown, J. H. The allometry of ornaments and weapons. Proc. Natl Acad. Sci. USA 103, 8733–8738 (2006).

    ADS  Article  Google Scholar 

  5. 5.

    Gould, S. J. Allometry and size in ontogeny and phylogeny. Biol. Rev. 41, 587–638 (1966).

    Article  Google Scholar 

  6. 6.

    Weigend, M., Mustafa, A. & Ensikat, H.-J. Calcium phosphate in plant trichomes: the overlooked biomineral. Planta 247, 277–285 (2018).

    Article  Google Scholar 

  7. 7.

    Farmer, E. E. Leaf Defence (Oxford Univ. Press, 2014).

  8. 8.

    Bartual, S. G. et al. Structure of the bacteriophage T4 long tail fiber receptor-binding tip. Proc. Natl Acad. Sci. USA 107, 20287–20292 (2010).

    ADS  Article  Google Scholar 

  9. 9.

    Uriz, M.-J., Turon, X., Becerro, M. A. & Agell, G. Siliceous spicules and skeleton frameworks in sponges: origin, diversity, ultrastructural patterns and biological functions. Microsc. Res. Tech. 62, 279–299 (2003).

    Article  Google Scholar 

  10. 10.

    Silverman, H. & Dunbar, M. Aggressive tusk use by the narwhal (Monodon monoceros L.). Nature 284, 57–58 (1980).

    ADS  Article  Google Scholar 

  11. 11.

    Wells, T. Nail chronology: the use of technologically derived features. Hist. Archaeol. 32, 78–99 (1998).

    Article  Google Scholar 

  12. 12.

    Gill, H. S. & Prausnitz, M. R. Does needle size matter? J. Diabetes Sci. Technol. 1, 725–729 (2007).

    Article  Google Scholar 

  13. 13.

    Markle, M. M. III The Macedonian sarissa, spear and related armor. Am. J. Archaeol. 81, 323–339 (1977).

    Article  Google Scholar 

  14. 14.

    DeVries, K. & Smith, R. D. Medieval Weapons: An Illustrated History of their Impact (ABC-CLIO, 2007).

  15. 15.

    Williams, A., Edge, D., Capwell, T. & Tschegg, S. A technical note on the armour and equipment for jousting. Gladius 32, 139–184 (2012).

    Article  Google Scholar 

  16. 16.

    Walters, D. Fortress Plant: How to Survive when Everything Wants to Eat You (Oxford Univ. Press, 2017).

  17. 17.

    Heemstra, P. C. & Heemstra, E. Coastal Fishes of Southern Africa (NISC, 2004).

  18. 18.

    Hu, B., Margolin, W., Molineux, I. J. & Liu, J. Structural remodeling of bacteriophage T4 and host membranes during infection initiation. Proc. Natl Acad. Sci. USA 112, E4919–E4928 (2015).

    ADS  Article  Google Scholar 

  19. 19.

    McMahon, T. A. & Bonner, J. T. On Size and Life (Scientific American Library, 1983).

  20. 20.

    Timoshenko, S. P. & Gere, J. M. Theory of Elastic Stability (McGraw-Hill, 1988).

  21. 21.

    Keller, J. B. The shape of the strongest column. Arch. Rational Mech. Anal. 5, 275–285 (1960).

    ADS  MathSciNet  Article  Google Scholar 

  22. 22.

    Monn, M. A. & Kesari, H. A new structure–property connection in the skeletal elements of the marine sponge Tethya aurantia that guards against buckling instability. Sci. Rep. 7, 39547 (2017).

    ADS  Article  Google Scholar 

  23. 23.

    Keller, J. B. & Niordson, F. I. The tallest column. J. Math. Mech. 16, 433–446 (1966).

    MathSciNet  MATH  Google Scholar 

  24. 24.

    Wei, Z., Mandre, S. & Mahadevan, L. The branch with the furthest reach. Europhys. Lett. 97, 14005 (2012).

    ADS  Article  Google Scholar 

  25. 25.

    von Karman, T. & Biot, M. A. Mathematical Methods in Engineering (McGraw Hill, 1940).

  26. 26.

    Johnston, I., McCluskey, D., Tan, C. & Tracey, M. Mechanical characterization of bulk Sylgard 184 for microfluidics and microengineering. J. Micromech. Microeng. 24, 035017 (2014).

    ADS  Article  Google Scholar 

  27. 27.

    Brzinski, T. A. III, Mayor, P. & Durian, D. J. Depth-dependent resistance of granular media to vertical penetration. Phys. Rev. Lett. 111, 168002 (2013).

    ADS  Article  Google Scholar 

  28. 28.

    Roesthuis, R. J., Van Veen, Y. R., Jahya, A. & Misra, S. Mechanics of needle-tissue interaction. In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2557–2563 (IEEE, 2011).

  29. 29.

    Davis, S. P., Landis, B. J., Adams, Z. H., Allen, M. G. & Prausnitz, M. R. Insertion of microneedles into skin: measurement and prediction of insertion force and needle fracture force. J. Biomech. 37, 1155–1163 (2004).

    Article  Google Scholar 

  30. 30.

    Ling, J. et al. Insertion and pull behavior of worker honeybee stinger. J. Bionic Eng. 13, 303–311 (2016).

    Article  Google Scholar 

  31. 31.

    van Gerwen, D. J., Dankelman, J. & van den Dobbelsteen, J. J. Needle-tissue interaction forces—a survey of experimental data. Med. Eng. Phys. 34, 665–680 (2012).

    Article  Google Scholar 

  32. 32.

    Kim, W. & Bush, J. W. Natural drinking strategies. J. Fluid Mech. 705, 7–25 (2012).

    ADS  Article  Google Scholar 

  33. 33.

    Montel, F. et al. Stress clamp experiments on multicellular tumor spheroids. Phys. Rev. Lett. 107, 188102 (2011).

    ADS  Article  Google Scholar 

  34. 34.

    Broders-Bondon, F., Ho-Bouldoires, T. H. N., Fernandez-Sanchez, M.-E. & Farge, E. Mechanotransduction in tumor progression: the dark side of the force. J. Cell Biol. 217, 1571–1587 (2018).

    Article  Google Scholar 

  35. 35.

    Pailler-Mattei, C., Bec, S. & Zahouani, H. In vivo measurements of the elastic mechanical properties of human skin by indentation tests. Med. Eng. Phys. 30, 599–606 (2008).

    Article  Google Scholar 

  36. 36.

    Jewel, R., Panaitescu, A. & Kudrolli, A. Micromechanics of intruder motion in wet granular medium. Phys. Rev. Fluids 3, 084303 (2018).

    ADS  Article  Google Scholar 

  37. 37.

    Quicke, D., Fitton, M., Tunstead, J., Ingram, S. & Gaitens, P. Ovipositor structure and relationships within the Hymenoptera, with special reference to the Ichneumonoidea. J. Nat. Hist. 28, 635–682 (1994).

    Article  Google Scholar 

  38. 38.

    Gibson, L. J. The hierarchical structure and mechanics of plant materials. J. R. Soc. Interface 9, 2749–2766 (2012).

    Article  Google Scholar 

  39. 39.

    McCartney, K., Witkowski, J. & Harwood, D. M. Early evolution of the silicoflagellates during the cretaceous. Marine Micropaleontol. 77, 83–100 (2010).

    ADS  Article  Google Scholar 

  40. 40.

    Kellenberger, E., Stauffer, E., Häner, M., Lustig, A. & Karamata, D. Mechanism of the long tail-fiber deployment of bacteriophages T-even and its role in adsorption, infection and sedimentation. Biophys. Chem. 59, 41–59 (1996).

    Article  Google Scholar 

  41. 41.

    Præstmark Juul, K. A. et al. Influence of hypodermic needle dimensions on subcutaneous injection delivery—a pig study of injection deposition evaluated by CT scanning, histology and backflow. Skin Res. Technol. 18, 447–455 (2012).

    Article  Google Scholar 

  42. 42.

    Zhu, J. et al. Gelatin methacryloyl microneedle patches for minimally invasive extraction of skin interstitial fluid. Small 16, 1905910 (2020).

    Article  Google Scholar 

  43. 43.

    Backholm, M. & Bäumchen, O. Micropipette force sensors for in vivo force measurements on single cells and multicellular microorganisms. Nat. Protoc. 14, 594–615 (2019).

    Article  Google Scholar 

  44. 44.

    Hooke, R. Micrographia, or Some Physiological Descriptions of Minute Bodies Made by Magnifying Glasses, with Observations and Inquiries Thereupon (Royal Society, 1665).

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Acknowledgements

This work was supported by two research grants (17587 and 13166) from Villum Fonden.

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Affiliations

Authors

Contributions

K.H.J. designed the research. A.H.C. and K.H.J. derived the model. K.S.H., K.P. and J.K. performed experiments. K.H.J., K.P. and J.K. collected and analysed data. K.H.J. wrote the manuscript with support from K.P. and J.K.

Corresponding author

Correspondence to Kaare H. Jensen.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Douglas Holmes, Hamed Rajabi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Fig. 1, Table 1 and refs. 1–55.

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Jensen, K.H., Knoblauch, J., Christensen, A.H. et al. Universal elastic mechanism for stinger design. Nat. Phys. (2020). https://doi.org/10.1038/s41567-020-0930-9

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