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Biomechanics of bacterial gliding motion with Oldroyd-4 constant slime

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Abstract

Microscale gliders are regularly affected by the local surrounding environment, such as liquid rheology and physical (nearby) boundaries. This article focuses on the numerical simulations of bacterial speed over a non-Newtonian slime and its power expenditure. The flow rate generated by the swimmer, slime speed, shear stress and level curves are also points of interest. To fulfill the purpose, Oldroyd-4 constant model is assumed over a rigid boundary. A complex undulating sheet is approximated as a bacterial surface. Since a slime (present below the undulating sheet) is a non-Newtonian fluid, a modeling approach of peristaltic flow problem is adopted, and dynamic equilibrium conditions are implemented for steady motion. Implicit finite difference method (FDM) is employed to calculate the numerical solution of reduced boundary value problem. To compute the flow rate and cell speed, Broyden’s root finding algorithm is integrated with FDM. These computed values are further utilized to perceive the behavior of work done, shear stress at the surface of bacteria, velocity of slime and streamlines.

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References

  1. R.P. Burchard, Gliding motility and taxes. In Myxobacteria. Springer, New York (1984). pp. 139–161

  2. R.W. Castenholz, Motility and taxes. Biol. Cyanobacteria 19, 413–440 (1982)

    Google Scholar 

  3. R.P. Burchard, Gliding motility of prokaryotes: ultrastructure, physiology, and genetics. Annu. Rev. Microbiol. 35(1), 497–529 (1981)

    Article  Google Scholar 

  4. J.L. Pate, Gliding motility in procaryotic cells. Can. J. Microbiol. 34(4), 459–465 (1988)

    Article  Google Scholar 

  5. R.P. Burchard, The effect of surfactants on the motility and adhesion of gliding bacteria. Arch. Microbiol. 146(2), 147–150 (1986)

    Article  Google Scholar 

  6. J.W.F. Costerton, R.G.E. Murray, C.F. Robinow, Observations on the motility and the structure of Vitreoscilla. Can. J. Microbiol. 7(3), 329–339 (1961)

    Article  Google Scholar 

  7. L.N. Halfen, R.W. Castenholz, Gliding in a blue–green alga: a possible mechanism. Nature 225(5238), 1163–1165 (1970)

    Article  ADS  Google Scholar 

  8. L.N. Halfen, Gliding motility of oscillatoria: ultrastructure and chemical characterization of the fibrillar layer 1, 2. J. Phycol. 9(3), 248–253 (1973)

    Google Scholar 

  9. B. Nan, D.R. Zusman, Uncovering the mystery of gliding motility in the myxobacteria. Annu. Rev. Genet. 45, 21–39 (2011)

    Article  Google Scholar 

  10. B. Chan, N.J. Balmforth, A.E. Hosoi, Building a better snail: Lubrication and adhesive locomotion. Phys. Fluids 17(11), 113101 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. B. Nan, D.R. Zusman, Novel mechanisms power bacterial gliding motility. Mol. Microbiol. 101(2), 186–193 (2016)

    Article  Google Scholar 

  12. J. Tchoufag, P. Ghosh, C.B. Pogue, B. Nan, K.K. Mandadapu, Mechanisms for bacterial gliding motility on soft substrates. Proc. NAS USA 116(50), 25087–25096 (2019)

    Article  ADS  Google Scholar 

  13. R.W. O’Brien, The gliding motion of a bacterium: Flexibacter strain BH3. ANZIAM J. 23(1), 2–16 (1981)

    MathSciNet  MATH  Google Scholar 

  14. A.M. Siddiqui, R.P. Burchard, W.H. Schwarz, An undulating surface model for the motility of bacteria gliding on a layer of non-Newtonian slime. Int. J. Non-Linear Mech. 36(5), 743–761 (2001)

    Article  MATH  Google Scholar 

  15. Y. Wang, T. Hayat, A.M. Siddiqui, Gliding motion of bacteria on power-law slime. Math. Methods Appl. Sci. 28(3), 329–347 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. T. Hayat, Y. Wang, A.M. Siddiqui, S. Asghar, A mathematical model for the study of gliding motion of bacteria on a layer of non-Newtonian slime. Math. Methods Appl. Sci. 27(12), 1447–1468 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. N. Ali, Z. Asghar, O.A. Bég, M. Sajid, Bacterial gliding fluid dynamics on a layer of non-Newtonian slime: perturbation and numerical study. J. Theor. Biol. 397, 22–32 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Z. Asghar, N. Ali, M. Sajid, Interaction of gliding motion of bacteria with rheological properties of the slime. Math. Biosci. 290, 31–40 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  19. S. Bariş, Steady flow of an Oldroyd 4-constant fluid in a corner region formed by two planes. Turk. J. Eng. Environ. Sci. 25(6), 587–594 (2001)

    Google Scholar 

  20. N. Ali, Y. Wang, T. Hayat, M. Oberlack, Long wavelength approximation to peristaltic motion of an Oldroyd 4-constant fluid in a planar channel. Biorheology 45(5), 611–628 (2008)

    Article  Google Scholar 

  21. H.M. Atif, N. Ali, M.A. Javed, M. Sajid, A numerical analysis of calendering of Oldroyd 4-constant fluid. J. Polym. Eng. 38(10), 1007–1016 (2018)

    Article  Google Scholar 

  22. H. Shahzad, X. Wang, M. Mughees, M. Sajid, N. Ali, A mathematical analysis for the blade coating process of Oldroyd 4-constant fluid. J. Polym. Eng. 39(9), 852–860 (2019)

    Article  Google Scholar 

  23. A. Abbasi, W. Farooq, N. Ali, I. Ahmad, Simultaneous effects of Brownian motion, thermophoresis and curvature on peristaltic flow of an Oldroyd 4-constant fluid. J. Nanofluids 8(4), 736–745 (2019)

    Article  Google Scholar 

  24. P. Shivapooja, Q. Wang, B. Orihuela, D. Rittschof, G.P. López, X. Zhao, Bioinspired surfaces with dynamic topography for active control of biofouling. Adv. Mater. 25(10), 1430–1434 (2013)

    Article  Google Scholar 

  25. G.D. Maso, A. DeSimone, M. Morandotti, An existence and uniqueness result for the motion of self-propelled microswimmers. SIAM J. Math. Anal. 43(3), 1345–1368 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  26. J.S. Guasto, R. Rusconi, R. Stocker, Fluid mechanics of planktonic microorganisms. Annu. Rev. Fluid Mech. 44, 373–400 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. K. Ishimoto, E. Lauga, The N-flagella problem: elastohydrodynamic motility transition of multi-flagellated bacteria. Proc. R. Soc. A 475(2225), 20180690 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. E.E. Riley, E. Lauga, Small-amplitude swimmers can self-propel faster in viscoelastic fluids. J. Theor. Biol. 382, 345–355 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. E. Lauga, Propulsion in a viscoelastic fluid. Phys. Fluids 19(8), 083104 (2007)

    Article  ADS  MATH  Google Scholar 

  30. H.C. Fu, C.W. Wolgemuth, T.R. Powers, Swimming speeds of filaments in nonlinearly viscoelastic fluids. Phys. Fluids 21(3), 033102 (2009)

    Article  ADS  MATH  Google Scholar 

  31. H.C. Fu, T.R. Powers, C.W. Wolgemuth, Theory of swimming filaments in viscoelastic media. Phys. Rev. Lett. 99(25), 258101 (2007)

    Article  ADS  Google Scholar 

  32. Z. Asghar, N. Ali, O. Anwar Bég, T. Javed, Rheological effects of micropolar slime on the gliding motility of bacteria with slip boundary condition. Results Phys. 9, 682–691 (2018)

    Article  ADS  Google Scholar 

  33. Z. Asghar, N. Ali, a mathematical model of the locomotion of bacteria near an inclined solid substrate: effects of different waveforms and rheological properties of couple stress slime. Can. J. Phys. 97, 537–547 (2019)

    Article  ADS  Google Scholar 

  34. N. Ali, Z. Asghar, M. Sajid, F. Abbas, A hybrid numerical study of bacteria gliding on a shear rate-dependent slime. Physica A Stat. Mech. Appl. 535, 122435 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  35. R.A. Shah, Z. Asghar, N. Ali, Mathematical modeling related to bacterial gliding mechanism at low Reynolds number with Ellis Slime. Eur. Phys. J. Plus 137(5), 1–12 (2022)

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank Prince Sultan University for its support through the TAS research lab.

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Authors and Affiliations

  1. Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia

    Zeeshan Asghar & Wasfi Shatanawi

  2. NUTECH, School of Applied Sciences and Humanities, National University of Technology, Islamabad, 44000, Pakistan

    Zeeshan Asghar & Sajid Hussain

  3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Wasfi Shatanawi

  4. Department of Mathematics, Faculty of Science, The Hashemite University, PO Box 330127, Zarqa, 13133, Jordan

    Wasfi Shatanawi

Authors
  1. Zeeshan Asghar
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  2. Wasfi Shatanawi
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Correspondence to Zeeshan Asghar or Wasfi Shatanawi.

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Asghar, Z., Shatanawi, W. & Hussain, S. Biomechanics of bacterial gliding motion with Oldroyd-4 constant slime. Eur. Phys. J. Spec. Top. 232, 915–925 (2023). https://doi.org/10.1140/epjs/s11734-022-00723-2

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