Metachronal swimming

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A metachronal swimming or metachronal rowing is the swimming technique used by animals with multiple pairs of swimming legs. In this technique, appendages are sequentially stroked in a back-to-front wave moving along the animal’s body.[1] In literature, while metachronal rhythm or metachronal wave usually refer to the movement of cilia;[2] metachronal coordination,[3] metachronal beating,[4] metachronal swimming or metachronal rowing[5] usually refer to the leg movement of arthropods, such as mantis shrimp, copepods, antarctic krill etc. though all of them refer to the similar locomotion pattern.

Metachronous indicates something not functioning or occurring synchronously, or occurring or starting at different times.[6] This word is derived from Greek meta- μετά- meaning, occurring later than or in succession to : after, and -chronous -Χρόνος meaning, of (such) a time or period.[7][8]

Swimming legs should coordinate to avoid interference among appendage pairs. To accomplish this challenge, almost all free-swimming crustaceans adapted to some version of metachronism.[5]

Significance[edit]

Ecologically and economically important crustaceans such as copepods, krill, shrimp, crayfish, and lobsters[9][10][11][12] use metachronal swimming for locomotion. Using this technique, animals propel significant portion of earth's aquatic biomass. As an example, the biomass of a sole metachronally swimming species, the Antarctic krill Euphausia superba, is more than the total adult human biomass.[13][14] Moreover, this technique is important from biomechanics point of view because it has been adapted to perform extreme swimming actions. The highest animal acceleration of 200 m/s^2, for example, belongs to the escape jump of the copepod Calanus finmarchicus.[9] On the other hand, Antarctic krill uses metachronal swimming to efficiently migrate distances up to 10 km per day.[15]

It is believed that, during power stroke appendages are subject to drag which creates forward thrust, during the recovery stroke appendages are folded towards body to reduce the drag.[16] Furthermore, back-to-front swimming pattern is thought to be more efficient than front-to-back or synchronous pattern.[17]

Examples from nature[edit]

Cilia in metazoa[edit]

Knight-Jones[18] defines the types of metachronism in ciliary beat of metazoa depending on the relative direction of wave to the effective beat. If the effective beat is in the same direction as metachronal wave, then it is called as symplectic metachronal wave. If opposite, the wave is called antiplectic. There are cases where the wave is directed to the right or to the left of the effective beat. In these cases the metachronal wave is called dexioplectic if effective beat is to the right of the wave, and laeoplectic if effective beat is to the left of the wave.

Mantis shrimp[edit]

Mantis shrimp have 5 pairs of pleopods which they use to swim. Kinematics of their swimming reveals metachronal pattern. Study by Campos et al.[3] shows that the power stroke of the mantis shrimp (Odontodactylus Havanensis) is metachronal, creating back-to-front wave motion. While power stroke is completed metachronally, recovery stroke occurs nearly synchronous. The same rowing pattern was observed by another study.[19] Stein et al. also report the metachronal rowing in mantis shrimp in their study[20]

Copepods[edit]

Metachronism in copepods was observed by numerous studies.[21][22][23][4] Copepods show metachronal beating pattern while foraging and escape movements.[4] In this study by van Duren and Videler, it was observed that during foraging, copepods metachronally beat their first three mouth appendages (antennae, mandibular palps and maxillules) creating backward motion of water. During escape, their mouth appendages stop moving and swimming legs beat in a very fast metachronal rhythm, accelerating a jet of water backwards.

Slow-motion video by Jiang and Kiorboe[24] reveals the metachronal beating of legs of cyclopoid copepod Oithona davisae during jumping. In this video, last pair of legs initiate the power stroke followed by the adjacent pair. Power stroke ends with the first pair. While power stroke is metachronal, recovery stroke is near synchronous.  

Antarctic krill[edit]

Antarctic krill swim in a metachronal fashion.[5][25][26][27] They have several swimming modes which include hovering, fast-forward swimming and upside-down swimming. All these swimming modes have common metachronal pattern although their kinematics differ. Hovering (HOV), which is defined as the swimming mode corresponding to the body angles of 25-50° and normalized speeds less than half of a body length per second, is performed at lower pleopod amplitudes and lower beat frequencies as compared to fast-forward swimming (FFW). FFW is defined as the swimming mode corresponding to speeds higher than 2 body lengths per second without restriction to body angles. Typical swimming speeds in this study was found as 0.25, 4 and 1.6 body lengths per second, and typical beat frequencies were found as 3, 6.2 and 3.8 Hz for hovering, fast-forward swimming and upside-down swimming, respectively. The average animal size was about 4 cm[5]

Metachronal rowing seems to be efficient propulsive aid for Antarctic krill to travel long distances. Study done by Alben et al.[28] show that metachronal rhythm produce larger average propulsion velocity compared to more synchronous stroke rhythms. It has also been shown that krill produce lift to balance the force acting on them as a result of negative buoyancy, allowing them to swim forward while maintaining their position in the water column [29]

Bio-inspired robotics[edit]

Metachronal swimmers have inspired solutions for underwater locomotion in the intermediate Reynolds number regime due to their high maneuverability. Model organisms used to inspired designs include krill, ctenophores (comb jelly), and copepods.[29][30][31] Bio-inspired robots can be used to find design solutions for underwater locomotion, as well as give greater insight into their model organism. Robotic models allow for parameter variations that live organisms don't, which gives us the opportunity to explore solutions outside of nature imposed boundaries. A shrimp-inspired metachronal robot can be used to study and understand the flexural asymmetry of shrimp pleopods, and their influence on efficiency and propulsion.

See also[edit]

References[edit]

  1. ^ Knight-Jones E.W. and A. Macfadyen, 1959. The metachronism of limb and body movements in annelids and arthropods. Proc. XVth Int. Cong. Zool. pp. 969-971.
  2. ^ Niedermayer, Thomas; Eckhardt, Bruno; Lenz, Peter (September 2008). "Synchronization, phase locking, and metachronal wave formation in ciliary chains". Chaos: An Interdisciplinary Journal of Nonlinear Science. 18 (3): 037128. doi:10.1063/1.2956984. ISSN 1054-1500. PMID 19045502.
  3. ^ a b Campos, Eric Octavio; Caldwell, Roy L.; Vilhena, Daril (2012-01-01). "Pleopod Rowing Is Used to Achieve High Forward Swimming Speeds During the Escape Response of Odontodactylus havanensis (Stomatopoda)". Journal of Crustacean Biology. 32 (2): 171–179. doi:10.1163/193724011x615596. ISSN 0278-0372.
  4. ^ a b c van Duren, L. A. (2003-01-15). "Escape from viscosity: the kinematics and hydrodynamics of copepod foraging and escape swimming". Journal of Experimental Biology. 206 (2): 269–279. doi:10.1242/jeb.00079. ISSN 0022-0949. PMID 12477897.
  5. ^ a b c d Murphy, D. W.; Webster, D. R.; Kawaguchi, S.; King, R.; Yen, J. (2011-07-28). "Metachronal swimming in Antarctic krill: gait kinematics and system design". Marine Biology. 158 (11): 2541–2554. doi:10.1007/s00227-011-1755-y. ISSN 0025-3162.
  6. ^ "Medical Definition of METACHRONOUS". www.merriam-webster.com. Retrieved 2019-02-27.
  7. ^ "Definition of META". www.merriam-webster.com. Retrieved 2019-02-27.
  8. ^ "Definition of -CHRONOUS". www.merriam-webster.com. Retrieved 2019-02-27.
  9. ^ a b Lenz, P.H.; Hower, A.E.; Hartline, D.K. (August 2004). "Force production during pereiopod power strokes in Calanus finmarchicus". Journal of Marine Systems. 49 (1–4): 133–144. doi:10.1016/j.jmarsys.2003.05.006. ISSN 0924-7963.
  10. ^ Kils U.,1981. Swimming behaviour, swimming performance, and energy balance of Antarctic krill, Euphausia superba. BIOMASS Sci Ser 3: 1-122.
  11. ^ Stamhuis, E. J.; Videler, J. J. (1998a). "Burrow ventilation in the tube-dwelling shrimp (Callianassa subterranea (Decapoda: Thalassinidea). I. Morphology and motion of the pleopods, uropods and telson" (PDF). J. Exp. Biol. 201 (Pt 14): 2151–2158. doi:10.1242/jeb.201.14.2151. PMID 9639589.
  12. ^ Lim, J. L.; DeMont, M. E. (2009-08-14). "Kinematics, hydrodynamics and force production of pleopods suggest jet-assisted walking in the American lobster (Homarus americanus)". Journal of Experimental Biology. 212 (17): 2731–2745. doi:10.1242/jeb.026922. ISSN 0022-0949. PMID 19684205.
  13. ^ Atkinson, A.; Siegel, V.; Pakhomov, E.A.; Jessopp, M.J.; Loeb, V. (May 2009). "A re-appraisal of the total biomass and annual production of Antarctic krill". Deep Sea Research Part I: Oceanographic Research Papers. 56 (5): 727–740. doi:10.1016/j.dsr.2008.12.007. ISSN 0967-0637.
  14. ^ Walpole, Sarah Catherine; Prieto-Merino, David; Edwards, Phil; Cleland, John; Stevens, Gretchen; Roberts, Ian (2012-06-18). "The weight of nations: an estimation of adult human biomass". BMC Public Health. 12 (1): 439. doi:10.1186/1471-2458-12-439. ISSN 1471-2458. PMC 3408371. PMID 22709383.
  15. ^ Kanda, K.; Takagi, K.; Seki, Y. (1982). "Movement of the larger swarms of Antarctic krill Euphausia superba population off Enderby Land during 1976-1977 season". J. Of Tokyo U. Of Fisheries. 68: 25–42.
  16. ^ Hessler, Robert R. (1985). "Swimming in Crustacea". Transactions of the Royal Society of Edinburgh: Earth Sciences. 76 (2–3): 115–122. doi:10.1017/s0263593300010385. ISSN 0263-5933.
  17. ^ Sleigh M.A. and D. I. Barlow, 1980. Metachronism and control of locomotion in animals with many propulsive structures. In: Elder HY, Trueman ER (ed) Aspects of Animal Movement, Cambridge University Press, Cambridge, pp 49-70.
  18. ^ Knight-Jones, E. W. (1954). "Relations between metachronism and the direction of ciliary beat in Metazoa". Journal of Cell Science. 3 (32): 503–521. doi:10.1242/jcs.s3-95.32.503.
  19. ^ Garayev, K., & Murphy, D. (2018). Metachronal Rowing by a Peacock Mantis Shrimp. Bulletin of the American Physical Society.
  20. ^ Stein, Wolfgang; Städele, Carola; Smarandache-Wellmann, Carmen R. (2015-12-01), "Perspective— Evolutionary Aspects of Motor Control and Coordination: The Central Pattern Generators in the Crustacean Stomatogastric and Swimmeret Systems", Structure and Evolution of Invertebrate Nervous Systems, Oxford University Press, pp. 583–596, doi:10.1093/acprof:oso/9780199682201.003.0046, ISBN 9780199682201
  21. ^ Storch, O (1929). "Die Schwimmbewegung der Copepoden, aufgrund von Mikro-Zeitlupenaufnahmen analysiert". Verh Dtsch Zool Ges (Zool Anz Suppl). 4: 118–129.
  22. ^ Strickler, J. Rudi (1975), "Swimming of Planktonic Cyclops Species (Copepoda, Crustacea): Pattern, Movements and Their Control", Swimming and Flying in Nature, Springer US, pp. 599–613, doi:10.1007/978-1-4757-1326-8_9, ISBN 9781475713282
  23. ^ Svetlichnyy, L. S. (1987). "Speed, force and energy expenditure in the movement of copepods". Oceanology. 27 (4): 497–502.
  24. ^ Jiang, H.; Kiorboe, T. (2011-01-05). "The fluid dynamics of swimming by jumping in copepods". Journal of the Royal Society Interface. 8 (61): 1090–1103. doi:10.1098/rsif.2010.0481. ISSN 1742-5689. PMC 3119873. PMID 21208972.
  25. ^ Boyd, Carl M.; Heyraud, Mireille; Boyd, Charles N. (1984-10-01). "Feeding of the Antarctic Krill Euphausia Superba". Journal of Crustacean Biology. 4 (5): 123–141. doi:10.1163/1937240x84x00543. ISSN 0278-0372.
  26. ^ Kils, U. (1981). Swimming behavior, swimming performance and energy balance of Antarctic krill Euphausia superba. BIOMASS Sci. Ser. , 3 , 1-121.
  27. ^ Swadling, K. M.; Ritz, D. A.; Nicol, S.; Osborn, J. E.; Gurney, L. J. (2005-01-08). "Respiration rate and cost of swimming for Antarctic krill, Euphausia superba, in large groups in the laboratory" (PDF). Marine Biology. 146 (6): 1169–1175. doi:10.1007/s00227-004-1519-z. ISSN 0025-3162.
  28. ^ Alben, S.; Spears, K.; Garth, S.; Murphy, D.; Yen, J. (2010-04-22). "Coordination of multiple appendages in drag-based swimming". Journal of the Royal Society Interface. 7 (52): 1545–1557. doi:10.1098/rsif.2010.0171. ISSN 1742-5689. PMC 2988259. PMID 20413558.
  29. ^ a b Oliveira Santos, Sara; Tack, Nils; Su, Yunxing; Cuenca-Jimenez, Francisco; Morales-Lopez, Oscar; Gomez-Valdez, P. Antonio; Wilhelmus, Monica M. (June 13, 2023). "Pleobot: a modular robotic solution for metachronal swimming". Scientific Reports. 13 (1). arXiv:2303.00805. doi:10.1038/s41598-023-36185-2.
  30. ^ Ford, Mitchell P; Santhanakrishnan, Arvind (2021-09-27). "On the role of phase lag in multi-appendage metachronal swimming of euphausiids". Bioinspiration & Biomimetics. 16 (6): 066007. doi:10.1088/1748-3190/abc930. ISSN 1748-3182.
  31. ^ He, Zhiguo; Yang, Yang; Jiao, Pengcheng; Wang, Haipeng; Lin, Guanzheng; Pähtz, Thomas (April 2023). "Copebot: Underwater Soft Robot with Copepod-Like Locomotion". Soft Robotics. 10 (2): 314–325. arXiv:2302.08217. doi:10.1089/soro.2021.0158. ISSN 2169-5172.
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