Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T20:20:51.518Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydrodynamic interaction of two deformable torque swimmers

Published online by Cambridge University Press:  29 April 2020

Hitomu Matsui ,
Toshihiro Omori Open the ORCID record for Toshihiro Omori [Opens in a new window]  and
Takuji Ishikawa Open the ORCID record for Takuji Ishikawa [Opens in a new window]
Hitomu Matsui
Affiliation:
Department of Finemechanics, Tohoku University, 6-6-01, Aoba, Aoba-ku, Sendai980-8579, Japan
Toshihiro Omori
Affiliation:
Department of Finemechanics, Tohoku University, 6-6-01, Aoba, Aoba-ku, Sendai980-8579, Japan
Takuji Ishikawa*
Affiliation:
Department of Finemechanics, Tohoku University, 6-6-01, Aoba, Aoba-ku, Sendai980-8579, Japan Department of Biomedical Engineering, Tohoku University, 6-6-01, Aoba, Aoba-ku, Sendai980-8579, Japan
*
† Email address for correspondence: ishikawa@bfsl.mech.tohoku.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

When two swimming cells collide, some ciliates show biological reactions such as avoidance and escape on sensing mechanical agitation through membrane ion channels. However, there is still no clear understanding of the mechanosensing mechanism, despite it being proposed more than 50 years ago. Moreover, it is largely unknown how the deformability of cells affects hydrodynamic interactions between microswimmers. In this study, we investigate hydrodynamic interactions between two deformable microswimmers and quantify the membrane tension during the interaction. A ciliate was modelled as a capsule with a hyperelastic membrane, and thrust generated by the cilia was modelled as torque distributed above the cell body. The model we use is the simplest we could think of that can swim, deform and exert membrane tension, such that hydrodynamic interactions can be analysed non-trivially. The results showed that softer swimmers induced smaller membrane tension during the interaction, and tended to have smaller scattering angles after the interaction. In the case of chasing interactions, swimmers attracted each other, which was not observed in non-deformable velocity squirmer models. Finally, we discuss the biological implications of these results, comparing them to those of our former experiments using Paramecium. This study is useful for understanding the effect of swimmer deformability in hydrodynamic interactions, and provides a theoretical basis for investigating a mechanical picture of the biological reactions of ciliates.

JFM classification

Biological Fluid Dynamics: Swimming/flying Biological Fluid Dynamics: Capsule/cell dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 894 , 10 July 2020 , A9
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Avron, J. E., Gat, O. & Kenneth, O. 2004 Optimal swimming at low Reynolds numbers. Phys. Rev. Lett. 93, 186001.CrossRefGoogle ScholarPubMed
Blake, J. R. 1971 A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46, 199–208.CrossRefGoogle Scholar
Campillo, C., Fisch, C., Jerber, J., Desforges, B., Dupuis-Williams, P., Nassoy, P. & Sykes, C. 2012 Mechanics of membrane-cytoskeleton attachment in Paramecium. New J. Phys. 14, 125016.Google Scholar
Eckert, R. 1972 Bioelectric control of ciliary activity. Science 176, 473–481.CrossRefGoogle ScholarPubMed
Farutin, A., Rafai, S., Dysthe, D. K., Duperray, A., Peyla, P. & Misbah, C. 2013 Amoeboid swimming: a generic self-propulsion of cells in fluids by means of membrane deformations. Phys. Rev. Lett. 111, 228102.CrossRefGoogle ScholarPubMed
Foissner, W., Chao, A. & Katz, L. A. 2008 Diversity and geographic distribution of ciliates (Protista: Ciliophora). Biodivers. Conserv. 17, 345–363.CrossRefGoogle Scholar
Freund, J. B. 2007 Leukocyte margination in a model microvessel. Phys. Fluids 19, 023301.CrossRefGoogle Scholar
Fujiu, K., Nakayama, Y., Iida, H., Sokabe, M. & Yoshimura, K. 2011 Mechanoreception in motile flagella of Chlamydomonas. Nat. Cell Biol. 13, 630–633.CrossRefGoogle ScholarPubMed
Gao, T. & Li, Z. 2017 Self-driven droplet powered by active nematics. Phys. Rev. Lett. 119, 108002.CrossRefGoogle ScholarPubMed
Helfrich, W. 1973 Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 28, 693–703.CrossRefGoogle ScholarPubMed
Hochmuth, R. M. 2000 Micropipette aspiration of living cells. J. Biomech. 33, 15–22.CrossRefGoogle ScholarPubMed
Ishikawa, T. 2009 Suspension biomechanics of swimming microbes. J. R. Soc. Interface 6, 815–834.CrossRefGoogle ScholarPubMed
Ishikawa, T. & Hota, M. 2006 Interaction of two swimming Paramecia. J. Expl Biol. 209, 4452–4463.CrossRefGoogle ScholarPubMed
Ishikawa, T. & Kikuchi, K. 2018 Biomechanics of Tetrahymena escaping from a dead end. Proc. R. Soc. Lond. B 285, 20172368.CrossRefGoogle ScholarPubMed
Ishikawa, T., Simmonds, M. P. & Pedley, T. J. 2006 Hydrodynamic interaction of two swimming model micro-organisms. J. Fluid Mech. 568, 119–160.CrossRefGoogle Scholar
Ishikawa, T., Tanaka, T., Imai, Y., Omori, T. & Matsunaga, D. 2016 Deformation of a micro torque swimmer. Proc. R. Soc. Lond. A 472, 20150604.CrossRefGoogle ScholarPubMed
Kung, C. 2005 A possible unifying principle for mechanosensation. Nature 436, 647–654.CrossRefGoogle ScholarPubMed
Kung, C., Chang, S. Y., Satow, Y., van Houten, J. & Hansma, H. 1975 Genetic dissection of behavior in Paramecium. Science 188, 898–904.Google ScholarPubMed
Lac, E., Morel, A. & Barthes-Biesel, D. 2007 Hydrodynamic interaction between two identical capsules in simple shear flow. J. Fluid Mech. 573, 149–169.CrossRefGoogle Scholar
Lighthill, M. J. 1952 On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun. Pure Appl. Math. 5, 109–118.CrossRefGoogle Scholar
Löber, J., Ziebert, F. & Aranson, I. S. 2015 Collisions of deformable cells lead to collective migration. Sci. Rep. 5, 9172.Google ScholarPubMed
Maeda, M. 1985 Roles of ciliated protozoa in the aquatic ecosystem. Bull. Soc. Sea Water Sci., Japan 39, 175–181.Google Scholar
Martinac, B., Saimi, Y. & Kung, C. 2008 Ion channels in microbes. Phys. Rev. 88, 1449–1490.Google ScholarPubMed
Matsuo, M. Y., Tanimoto, H. & Sano, M. 2013 Large fluctuation and levy movement of an active deformable particle. Europhys. Lett. 102, 40012.CrossRefGoogle Scholar
Morita, T., Omori, T. & Ishikawa, T. 2018a Passive swimming of a microcapsule in vertical fluid oscillation. Phys. Rev. E 98, 023108.Google Scholar
Morita, T., Omori, T. & Ishikawa, T. 2018b Biaxial fluid oscillations can propel a micro-capsule swimmer in an arbitrary direction. Phys. Rev. E 98, 063102.Google Scholar
Naitoh, Y. & Eckert, R. 1969 Ionic mechanisms controlling behavioral responses of Paramecium to mechanical stimulation. Science 164, 963–965.CrossRefGoogle ScholarPubMed
Naitoh, Y. & Sugino, K. 1984 Ciliary movement and its control in Paramecium. J. Protozool. 31, 31–40.CrossRefGoogle Scholar
Newbold, C. J., Fuente, G., Belanche, A., Ramos-Morales, E. & McEwan, N. R. 2015 The role of ciliate protozoa in the rumen. Front. Microbiol. 6, 1313.CrossRefGoogle ScholarPubMed
Ohta, T. 2017 Dynamics of deformable active particles. J. Phys. Soc. Japan 86, 072001.CrossRefGoogle Scholar
Ohta, T. & Ohkuma, T. 2009 Deformable self-propelled particles. Phys. Rev. Lett. 102, 154101.CrossRefGoogle ScholarPubMed
Onimaru, H., Ohki, K., Nozawa, Y. & Naitoh, Y. 1980 Electrical properties of Tetrahymena, a suitable tool for studies on membrane excitation. Proc. Japan Acad. B 56, 538–543.CrossRefGoogle Scholar
Ou-Yang, Z. & Helfrich, W. 1989 Bending energy of vesicle membranes: general expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders. Phys. Rev. A 39, 5280–5288.Google Scholar
Pak, O. S., Young, Y.-N., Marple, G. R., Veerapaneni, S. & Stone, H. A. 2015 Gating of a mechanosensitive channel due to cellular flows. Proc. Natl Acad. Sci. USA 112, 9822–9827.CrossRefGoogle ScholarPubMed
Perozo, E., Cortes, D. M., Sompornpisut, P., Kloda, A. & Martinac, B. 2002 Open channel structure of MscL and the gating mechanism of mechanosensitive channels. Nature 418, 942–948.CrossRefGoogle ScholarPubMed
Plattner, H. 2017 Signalling in ciliates: long- and short-range signals and molecular determinants for cellular dynamics. Biol. Rev. 92, 60–107.CrossRefGoogle ScholarPubMed
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.CrossRefGoogle Scholar
Pozrikidis, C. 2010 Computational Hydrodynamics of Capsules and Biological Cells. CRC Press.CrossRefGoogle Scholar
Prescott, D. M. 1994 The DNA of ciliated protozoa. Microbiol. Rev. 58, 233–267.CrossRefGoogle ScholarPubMed
Reuter, A. T., Stuermer, C. A. O. & Plattner, H. 2013 Identification, localization, and functional implications of the microdomain-forming stomatin family in the ciliated protozoan Paramecium tetraurelia. Eukaryotic Cell 12, 529–544.CrossRefGoogle ScholarPubMed
Skalak, R., TozereN, A., Zarda, R. P. & Chien, S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13, 245–264.CrossRefGoogle ScholarPubMed
Sukharev, S. I., Blount, P., Martinac, B. & Kung, C. 1997 Mechanosensitive channels of Escherichia coli: the MscL gene, protein, and activities. Annu. Rev. Physiol. 59, 633–657.CrossRefGoogle ScholarPubMed
Tarama, M. 2017 Dynamics of deformable active particles under external flow field. J. Phys. Soc. Japan 86, 101011.CrossRefGoogle Scholar
Walter, J., Salsac, A.-V. & Barthes-Biesel, D. 2011 Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shape. J. Fluid Mech. 676, 318–347.CrossRefGoogle Scholar
Walter, J., Salsac, A.-V., Barthes-Biesel, D. & Tallec, P. L. 2010 Coupling of finite element and boundary integral methods for a capsule in a Stokes flow. Intl J. Numer. Meth. Engng 83, 829–850.Google Scholar
Whitfield, C. A. & Hawkins, R. J. 2016 Instabilities, motion and deformation of active fluid droplets. New J. Phys. 18, 123016.Google Scholar
Wu, H., Farutin, A., Hu, W.-F., Thiébaud, M., Rafaï, S., Peyla, P., Lai, M.-C. & Misbah, C. 2016 Amoeboid swimming in a channel. Soft Matt. 12, 7470–7484.CrossRefGoogle ScholarPubMed
Wu, H., Thiébaud, M., Hu, W.-F., Farutin, A., Rafaï, S., Lai, M.-C., Peyla, P. & Misbah, C. 2015 Amoeboid motion in confined geometry. Phys. Rev. E 92, 050701(R).Google ScholarPubMed