Skip to main content
SpringerLink
Log in

A hydrodynamic-stochastic model of chemotactic ciliated microorganisms

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract.

Biological systems like ciliated microorganisms are capable of responding to the external chemical gradients, a process known as chemotaxis. In this process, the internal signaling network of the microorganism is triggered due to binding of the chemoattractant molecules with the receptors on the surface of the body. This can alter the activity at the surface of the microorganism. We study the chemotaxis of ciliated microorganisms using the chiral squirmer model, a spherical body with a surface slip velocity. In the presence of a chemical gradient, the coefficients of the slip velocity get modified resulting in a change in the path followed by the body. We observe that the strength of the gradient is not the only parameter which controls the dynamics of the body but also the adaptation time plays a very significant role in the success of chemotaxis. The trajectory of the body is smooth if we ignore the discreteness in the ligand-receptor binding which is stochastic in nature. In the presence of the latter, the path is not only irregular but the whole dynamics of the body changes. We calculate the mean first passage time, by varying the strength of the chemical gradient and the adaptation time, to determine the success rate of chemotaxis.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B.M. Friedrich, F. Jülicher, Proc. Natl. Acad. Sci. U.S.A. 104, 13256 (2007)

    Article  ADS  Google Scholar 

  2. J.A. Hadwiger, S. Lee, R.A. Firtel, Proc. Natl. Acad. Sci. U.S.A. 91, 10566 (1994)

    Article  ADS  Google Scholar 

  3. T. Shaw, P. Martin, J. Cell Sci. 122, 3209 (2009)

    Article  Google Scholar 

  4. P. Martin, S.M. Parkhurst, Development 131, 3021 (2004)

    Article  Google Scholar 

  5. X. Wang, SIAM J. Math. Anal. 31, 535 (2000)

    Article  MathSciNet  Google Scholar 

  6. P.K. Ghosh, Y. Li, F. Marchesoni, F. Nori, Phys. Rev. E 92, 012114 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  7. I. Lagzi, Cent. Eur. J. Med. 8, 377 (2013)

    Google Scholar 

  8. A. Sahari, D. Headen, B. Behkam, Biomed. Microdevices 14, 999 (2012)

    Article  Google Scholar 

  9. B. Dai, J. Wang, Z. Xiong, W. Dai, C.C. Li, S.P. Feng, J. Tang, Nat. Nanotechnol. 11, 1087 (2016)

    Article  ADS  Google Scholar 

  10. T. Bickel, G. Zecua, Alois Würger, Phys. Rev. E 89, 050303 (2014)

    Article  ADS  Google Scholar 

  11. S.H. Larsen, R. Macnab, D.E. Koshland, Nature 249, 74 (1974)

    Article  ADS  Google Scholar 

  12. T. Nebl, P.R. Fisher, J. Cell Sci. 110, 2845 (1997)

    Google Scholar 

  13. H.S. Jennings, Behaviour of The Lower Organisms (Columbia University Press, 1906) p. 41

  14. A.N. Sarvestani, A. Shamloo, M.T. Ahmadian, Cell Biochem. Biophys. 74, 241 (2016)

    Article  Google Scholar 

  15. I. Nakatani, J. Fac. Sci, Hokkaido Univ., Ser. VI Zool. 17, 401 (1970)

    Google Scholar 

  16. J.V. Houten, J. Comp. Physiol. 127, 167 (1978)

    Article  Google Scholar 

  17. M. Almagor, A. Ron, J. Bar-Tana, Cell Motil. 1, 261 (1981)

    Article  Google Scholar 

  18. W. Korohoda, J. Golda, J. Sroka, A. Wojnarowicz, P. Jochym, Z. Madeja, Cytoskeleton 38, 38 (1997)

    Article  Google Scholar 

  19. S. Dev, S. Chatterjee, Phys. Rev. E 91, 042714 (2015)

    Article  ADS  Google Scholar 

  20. S. Samanta, R. Layek, S. Kar, M.K. Raj, S. Mukhopadhyay, S. Chakraborty, Phys. Rev. E 96, 032409 (2017)

    Article  ADS  Google Scholar 

  21. B.M. Friedrich, F. Jülicher, Phys. Rev. Lett. 103, 068102 (2009)

    Article  ADS  Google Scholar 

  22. Y.H. Hussain, J.S. Guasto, R.K. Zimmer, R. Stocker, J.A. Riffell, J. Exp. Biol. 219, 1458 (2016)

    Article  Google Scholar 

  23. Z. Lu, S. Wang, Z. Sun, R. Niu, J. Wang, Arch. Toxicol. 88, 533 (2014)

    Article  Google Scholar 

  24. M. Yoshida, K. Yoshida, Mol. Hum. Reprod. 17, 457 (2011)

    Article  Google Scholar 

  25. J.F. Jikeli, L. Alvarez, B.M. Friedrich, L.G. Wilson, R. Pascal, R. Colin, M. Pichlo, A. Rennhack, C. Brenker, U.B. Kaupp, Nat. Commun. 6, 7985 (2015)

    Article  ADS  Google Scholar 

  26. M. Pichlo, S.B. Plümke, I. Weyand, R. Seifert, W. Bönigk, T. Strünker, N.D. Kashikar, N. Godwin, A. Müller, H.G. Körschen, U. Collienne, P. Pelzer, Q. Van, J. Enderlein, C. Klemm, E. Krause, C. Trötschel, A. Poetsch, E. Kremmer, U.B. Kaupp, J. Cell Biol. 206, 541 (2014)

    Article  Google Scholar 

  27. A. Darszon, T. Nishigaki, C. Beltran, C.L. Treviño, Physiol. Rev. 91, 1305 (2011)

    Article  Google Scholar 

  28. L. Alvarez, B.M. Friedrich, G. Gompper, U.B. Kaupp, Trends Cell Biol. 24, 198 (2014)

    Article  Google Scholar 

  29. A. Perez-Miravete, Behaviour of Micro-Organisms (Plenum Press, 1973)

  30. G.A. Antipa, K. Martin, M.T. Rintz, J. Protozool. 30, 55 (1983)

    Article  Google Scholar 

  31. M.J. Doughty, Comp. Biochem. Physiol. C 63, 183 (1979)

    Article  Google Scholar 

  32. K. Oami, J. Comp. Physiol. A 179, 345 (1996)

    Article  Google Scholar 

  33. A.S. Shah, Y.B. Shahar, T.O. Moninger, J.N. Kline, M.J. Welsh, Science 325, 1131 (2009)

    Article  ADS  Google Scholar 

  34. R.R. Preston, P.N.R. Usherwood, J. Comp. Physiol. B 158, 345 (1988)

    Article  Google Scholar 

  35. J. Elgeti, G. Gompper, Proc. Natl. Acad. Sci. U.S.A. 110, 4470 (2013)

    Article  ADS  Google Scholar 

  36. C. Battle, C.M. Ott, D.T. Burnette, J.L. Schwartz, C.F. Schmidt, Proc. Natl. Acad. Sci. U.S.A. 112, 1410 (2015)

    Article  ADS  Google Scholar 

  37. M.J. Lighthill, Commun. Pure Appl. Math. 5, 109 (1952)

    Article  Google Scholar 

  38. J.R. Blake, J. Fluid. Mech. 46, 199 (1971)

    Article  ADS  Google Scholar 

  39. S. Michelin, E. Lauga, Bull. Math. Biol. 72, 973 (2010)

    Article  MathSciNet  Google Scholar 

  40. E. Lauga, T.R. Powers, Rep. Prog. Phys. 72, 096601 (2009)

    Article  ADS  Google Scholar 

  41. T. Ishikawa, M.P. Simonds, T.J. Pedley, J. Fluid. Mech. 568, 119 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  42. H.C. Crenshaw, Biophys. J. 56, 1029 (1989)

    Article  ADS  Google Scholar 

  43. T. Fenchel, P.R. Jonsson, Mar. Ecol. Prog. Ser. 48, 1 (1988)

    Article  ADS  Google Scholar 

  44. S. Jana, S.H. Um, S. Jung, Phys. Fluids 24, 041901 (2012)

    Article  ADS  Google Scholar 

  45. P.S. Burada, F. Jülicher, private communication

  46. O.S. Pak, E. Lauga, J. Eng. Math. 88, 1 (2014)

    Article  Google Scholar 

  47. E.M. Purcell, Am. J. Phys. 45, 3 (1977)

    Article  ADS  Google Scholar 

  48. G.K. Batchelor, J. Fluid Mech. 74, 1 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  49. J. Happel, H. Brenner Low Reynolds Number Hydrodynamics (Springer, 1983)

  50. H.A. Stone, A.D.T. Samuel, Phys. Rev. Lett. 77, 4102 (1996)

    Article  ADS  Google Scholar 

  51. I.A. Suwan, M.G. Daraghmeh, A.M. Ziqan, Appl. Math. Sci. 7, 7143 (2013)

    MathSciNet  Google Scholar 

  52. R. Wittkowski, H. Löwen, Phys. Rev. E 85, 021406 (2012)

    Article  ADS  Google Scholar 

  53. V. Sourjik, N.S. Wingreen, Curr. Opin. Cell Biol. 24, 262 (2012)

    Article  Google Scholar 

  54. V. Sourjik, Trends Microbiol. 12, 569 (2004)

    Article  Google Scholar 

  55. R.A. Bradshaw, E.A. Dennis, Handbook of Cell Signaling (Academic Press, 2009)

  56. M.F. Goy, M.S. Springer, J. Adler, Proc. Natl. Acad. Sci. U.S.A. 74, 4964 (1977)

    Article  ADS  Google Scholar 

  57. M. Bohmer, Q. Van, I. Wayand, V. Hagen, M. Beyermann, M. Matsumoto, M. Hoshi, E. Hilderbrand, U.B. Kaupp, EMBO J. 24, 2741 (2005)

    Article  Google Scholar 

  58. N.D. Kashikar, L. Alvarez, R. Seifert, I. Gregor, O. Jackle, M. Beyermann, E. Krause, U.B. Kaupp, J. Cell Biol. 198, 1075 (2012)

    Article  Google Scholar 

  59. N. Barkai, S. Leibler, Nature 387, 913 (1997)

    Article  ADS  Google Scholar 

  60. N. Vladimirov, L. Lovdok, D. Lebiedz, V. Sourjik, PLOS Comput. Biol. 4, e1000242 (2008)

    Article  ADS  Google Scholar 

  61. V. Sourjik, N.S. Wing, Curr. Opin. Cell Biol. 24, 262 (2012)

    Article  Google Scholar 

  62. H.C. Berg, Random Walks in Biology (Princeton University Press, 1983)

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur, India

    Ruma Maity & P. S. Burada

  2. Center for Theoretical Studies, Indian Institute of Technology Kharagpur, Kharagpur, India

    P. S. Burada

Authors
  1. Ruma Maity
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. S. Burada
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. S. Burada.

Additional information

Publisher’s Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maity, R., Burada, P.S. A hydrodynamic-stochastic model of chemotactic ciliated microorganisms. Eur. Phys. J. E 42, 20 (2019). https://doi.org/10.1140/epje/i2019-11780-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2019-11780-4

Keywords

Search

Navigation