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Journal for Biophysical Chemistry

Continuum model of mechanical interactions between biological cells and artificial nanostructures

Abstract

The controlled insertion of artificial nanostructures into biological cells has been utilized for patch clamping, targeted drug delivery, cell lysing, and cell mechanics measurements. In this work, an elastic continuum model is implemented to treat the deformation of spherical cells in solution due to their interaction with cylindrical probes. At small deformations, the force varies nonlinearly with indentation due to global deformation of the cell shape. However, at large indentations, the force varies linearly with indentation due to more localized deformations. These trends are consistent with experimental measurements under comparable conditions and can be used to develop design rules for optimizing probe-cell interactions.

References

  1. 1

    N. Hilal, W. Bowen, L. Alkhatib, and O. Ogunbiyi, Chem. Eng. Res. Des. 84, 282 (2006).

    Article  CAS  Google Scholar 

  2. 2

    F. Gaboriaud and Y. F. Dufrene, Colloids Surf., B 54, 10 (2007).

    Article  CAS  Google Scholar 

  3. 3

    Y. F. Dufrêne, Nat. Rev. Microbiol. 6, 674 (2008).

    Article  Google Scholar 

  4. 4

    P. Sun, F. O. Laforge, T. P. Abeyweera, S. A. Rotenberg, J. Carpino, and M. V. Mirkin, Proc. Natl. Acad. Sci. U.S.A. 105, 443 (2008).

    Article  CAS  Google Scholar 

  5. 5

    I. Kleps, M. Miu, F. Craciunoiu, and M. Simion, Proceedings of the 32nd International Conference on Micro- and Nano-Engineering [Microelectron. Eng.] 84, 1744 (2007)].

  6. 6

    W. Kim, J. K. Ng, M. E. Kunitake, B. R. Conklin, and P. Yang, J. Am. Chem. Soc. 129, 7228 (2007).

    Article  CAS  Google Scholar 

  7. 7

    Y. Qiao, J. Chen, X. Guo, D. Cantrell, R. Ruoff, and J. Troy, Nanotechnology 16, 1598 (2005).

    Article  CAS  Google Scholar 

  8. 8

    X. Chen, A. Kis, A. Zettl, and C. R. Bertozzi, Proc. Natl. Acad. Sci. U.S.A. 104, 8218 (2007).

    Article  CAS  Google Scholar 

  9. 9

    A. K. Shalek et al., Proc. Natl. Acad. Sci. U.S.A. 107, 1870 (2010).

    Article  CAS  Google Scholar 

  10. 10

    S. D. Conner and S. L. Schmid, Nature (London) 422, 37 (2003).

    Article  CAS  Google Scholar 

  11. 11

    M. E. Davis, Z. G. Chen, and D. M. Shin, Nat. Rev. Drug Discovery 7, 771 (2008).

    Article  CAS  Google Scholar 

  12. 12

    W. Jiang, B. Y. S. Kim, J. T. Rutka, and W. C. W. Chan, Nat. Nanotechnol. 3, 145 (2008).

    Article  CAS  Google Scholar 

  13. 13

    B. D. Chithrani, A. A. Ghazani, and W. C. W. Chan, Nano Lett. 6, 662 (2006).

    Article  CAS  Google Scholar 

  14. 14

    J. A. Champion and S. Mitragotri, Proc. Natl. Acad. Sci. U.S.A. 103, 4930 (2006).

    Article  CAS  Google Scholar 

  15. 15

    S. Mitragotri and J. Lahann, Nature Mater. 8, 15 (2009).

    Article  CAS  Google Scholar 

  16. 16

    R. G. Thakar, M. G. Chown, A. Patel, L. Peng, S. Kumar, and T. A. Desai, Small 4, 1416 (2008).

    Article  CAS  Google Scholar 

  17. 17

    M. M. Stevens and J. H. George, Science 310, 1135 (2005).

    Article  CAS  Google Scholar 

  18. 18

    T. Brown, J. Biomech. 33, 3 (2000).

    Article  CAS  Google Scholar 

  19. 19

    G. W. Schmidschonbein, K. L. Sung, H. Tozeren, R. Skalak, and S. Chien, Biophys. J. 36, 243 (1981).

    Article  CAS  Google Scholar 

  20. 20

    D. P. Theret, M. J. Levesque, M. Sato, R. M. Nerem, and L. T. Wheeler, J. Biomech. Eng. 110, 190 (1998).

    Article  Google Scholar 

  21. 21

    E. Evans and A. Yeung, Biophys. J. 56, 151 (1989).

    Article  CAS  Google Scholar 

  22. 22

    D. Needham and R. M. Hochmuth, J. Biomech. Eng. 112, 269 (1990).

    Article  CAS  Google Scholar 

  23. 23

    C. Dong, R. Skalak, and K. L. Sung, Biorheology 28, 557 (1991).

    CAS  Google Scholar 

  24. 24

    B. D. Hoffman and J. C. Crocker, Annu. Rev. Biomed. Eng. 11, 259 (2009).

    Article  CAS  Google Scholar 

  25. 25

    B. D. Almquist and N. A. Melosh, Proc. Natl. Acad. Sci. U.S.A. 107, 5815 (2010).

    Article  CAS  Google Scholar 

  26. 26

    S. Sen, S. Subramanian, and D. E. Discher, Biophys. J. 89, 3203 (2005).

    Article  CAS  Google Scholar 

  27. 27

    V. Gordon, C. Xi, J. Hutchinson, A. Bausch, M. Marquez, and D. Weitz, J. Am. Chem. Soc. 126, 14117 (2004).

    Article  CAS  Google Scholar 

  28. 28

    B. Daily, E. L. Elson, and G. I. Zahalak, Biophys. J. 45, 671 (1984).

    Article  CAS  Google Scholar 

  29. 29

    E. A. Evans and R. Skalak, CRC Crit. Rev. Bioeng. 3, 181 (1979).

    CAS  Google Scholar 

  30. 30

    R. Aris, Vectors, Tensors, and the Basic Equations of Fluid Mechanics (Prentice-Hall, Englewood Cliffs, NJ, 1962).

    Google Scholar 

  31. 31

    D. H. Boal, Mechanics of the Cell (Cambridge University Press, Cambridge, UK, 2002).

    Google Scholar 

  32. 32

    E. A. Evans, Biophys. J. 30, 265 (1980).

    Article  CAS  Google Scholar 

  33. 33

    E. Evans and W. Rawicz, Phys. Rev. Lett. 64, 2094 (1990).

    Article  CAS  Google Scholar 

  34. 34

    B. M. Discher, Y. Y. Won, D. S. Ege, J. C. Lee, F. S. Bates, D. E. Discher, and D. A. Hammer, Science 284, 1143 (1999).

    Article  CAS  Google Scholar 

  35. 35

    Y. Zhou and R. M. Raphael, Biophys. J. 89, 1789 (2005).

    Article  CAS  Google Scholar 

  36. 36

    S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, Engineering Societies Monographs, 2nd ed. (McGraw-Hill, New York, 1959).

    Google Scholar 

  37. 37

    A. Hategan, R. Law, S. Kahn, and D. E. Discher, Biophys. J. 85, 2746 (2003).

    Article  CAS  Google Scholar 

  38. 38

    E. A. Evans and R. Skalak, Mechanics and Thermodynamics of Biomembranes (CRC, Boca Raton, FL, 1980).

    Google Scholar 

  39. 39

    D. Di Carlo, K.-H. Jeong, and L. P. Lee, Lab Chip 3, 287 (2003).

    Article  Google Scholar 

  40. 40

    E. A. Evans, R. Waugh, and L. Melnik, Biophys. J. 16, 585 (1976).

    Article  CAS  Google Scholar 

  41. 41

    M. G. Schrlau, N. J. Dun, and H. H. Bau, ACS Nano 3, 563 (2009).

    Article  CAS  Google Scholar 

  42. 42

    I. U. Vakarelski, S. C. Brown, K. Higashitani, and B. M. Moudgil, Langmuir 23, 10893 (2007).

    Article  CAS  Google Scholar 

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Verma, P., Wong, I.Y. & Melosh, N.A. Continuum model of mechanical interactions between biological cells and artificial nanostructures. Biointerphases 5, 37–44 (2010). https://doi.org/10.1116/1.3431960

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