Skip to main content
Log in

Development of three-dimensional haptotaxis model for single crawling cell

  • Original Research
  • Published:
BioChip Journal Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

This paper proposes a three-dimensional diffuse interface dynamic model with multiple mechanisms and confirms the high possibility of adequate predictions. In particular, we consider the nucleus that exhibits three-dimensional motion in the crawling cell, which enables a more realistic representation of haptotactic migration. A diffuse interface model that incorporates the haptotaxis mechanism and interface energies is employed. The semi-implicit Fourier spectral scheme is adopted for efficient evaluation of the simulation model. The simulation results confirm the reliability of the developed model.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Adler, J. A method for measuring chemotaxis and use of the method to determine optimum conditions for chemotaxis by Escherichia coli. J. Gen. Microbiol. 74, 77–91 (1973).

    CAS  Google Scholar 

  2. Zigmond, S.H. Ability of polymorphonuclear leukocytes to orient in gradients of chemotactic factors. J. Cell Biol. 75, 606–616 (1977).

    Article  CAS  Google Scholar 

  3. Robert, D.N., Paul, G.Q. & Richard, L.S. Chemotaxis under agarose: A new and simple method for measuring chemotaxis and spontaneous migration of human polymorphonuclear leukocytes and monocytes. J. Immunol. 115, 1650–1656 (1975).

    Google Scholar 

  4. Lauffenburger, D.A., Rothman, C. & Zigmond, S.H. Measurement of leukocyte motility and chemotaxis parameters with a linear under-agarose migration assay. J. Cell Biol. 131, 940–947 (1983).

    CAS  Google Scholar 

  5. Tranquillo, R.T., Zigmond, S.H. & Lauffernburger, D.A. Measurement of the chemotaxis coefficient for human-neutrophils in the under-agarose migration assay. Cell Motil. Cytoskel. 11, 1–15 (1988).

    Article  CAS  Google Scholar 

  6. Berg, H. How to track bacteria. Rev. Sci. Instrum. 42, 868–871 (1971).

    Article  CAS  Google Scholar 

  7. Diao, J.P. A three-channel microfluidic device for generating static linear gradients and its application to the quantitative analysis of bacterial chemotaxis. Lab. Chip 6, 381–388 (2006).

    Article  CAS  Google Scholar 

  8. Rot, A. Neutrophil attractant activation protein-1 (interleukin-8) induces invitro neutrophil migration by haptotactic mechanism. Eur. J. Immunol. 23, 303–306 (1993).

    Article  CAS  Google Scholar 

  9. Webb, L.M.C. et al. Binding to heparan-sulfate or heparin enhances neutrophil responses to interleukin-8. Proc. Natl. Acad. Sci. USA 90, 7158–7162 (1993).

    Article  CAS  Google Scholar 

  10. Webster, R.O., Zanolari, B. & Henson, P.M. Neutrophil chemotaxis in response to surface-bound C5A. Exp. Cell Res. 129, 55–62 (1980).

    Article  CAS  Google Scholar 

  11. Wilkinson, P.C. & Allan, R.B. Chemotaxis of leucocytes towards substratum-bound protein attractants. Exp. Cell Res. 117, 403–412 (1978).

    Article  CAS  Google Scholar 

  12. Keller, E.F. Model for chemotaxis. J. Theor. Biol. 30, 225–234 (1971).

    Article  CAS  Google Scholar 

  13. Murray, J.D. Mathematical Biology. Springer-Verlag, New York (1993).

    Book  Google Scholar 

  14. Tracqui, P. From passive diffusion to active cellular migration in mathematical models of tumour invasion. Acta Biotheor. 43, 443–464 (1995).

    Article  CAS  Google Scholar 

  15. Lu, W. & Kim, D. Thin-film structures induced by electrostatic field and substrate kinetic constraint. Appl. Phys. Lett. 88, 153116 (2006).

    Article  CAS  Google Scholar 

  16. Kim, D. Computational analysis of the interfacial effect on electromigration in flip chip solder joints. Microelectron. Eng. 86, 2132–2137 (2009).

    Article  CAS  Google Scholar 

  17. Kim, D. & Lu, W. Self-organized nanostructures in multi-phase epilayers. Nanotech. 15, 667–674 (2004).

    Article  CAS  Google Scholar 

  18. Kim, D. & Lu, W. Creep flow, diffusion, and electromigration in small scale interconnects. J. Mech. Phys. Solids 54, 2554–2568 (2006).

    Article  CAS  Google Scholar 

  19. Kim, D. & Lu, W. Three-dimensional model of electrostatically induced pattern formation in thin polymer films. Phys. Rev. B. 73, 035206 (2006).

    Article  CAS  Google Scholar 

  20. Lu, W. & Kim, D. Patterning nanoscale structures by surface chemistry. Nano Lett. 4, 313–316 (2004).

    Article  CAS  Google Scholar 

  21. Lu, W. & Kim, D. Engineering nanophase self-assembly with elastic field. Acta Mater. 53, 3689–3694 (2005).

    Article  CAS  Google Scholar 

  22. Song, J.H. & Kim, D. Three-dimensional chemotaxis model for a single bacterium. J. Comput. Theor. Nanos. 6, 1687–1693 (2009).

    Article  CAS  Google Scholar 

  23. Ganiko, L. et al. Neutrophil haptotaxis induced by the lectin KM+. Glycoconjugate J. 15, 527–530 (1998).

    Article  CAS  Google Scholar 

  24. Smith, J.T., Elkin, J.T. & Reichert, W.M. Directed cell migration on fibronectin gradients: Effect of gradient slope. Exp. Cell Res. 312, 2424–2432 (2006).

    Article  CAS  Google Scholar 

  25. Zhang, L., Song, J. & Kim, D. A study on cancer-cell invasion based on multi-physics analysis technology. BioChip J. 4, 161–165 (2010).

    Article  CAS  Google Scholar 

  26. Cahn, J.W. Free energy of a nonuniform system.1. Interfacial free energy. J. Chem. Phys. 28, 258–267 (1958).

    Article  CAS  Google Scholar 

  27. Alber, M. et al. Multiscale dynamics of biological cells with chemotactic interactions: From a discrete stochastic model to a continuous description. Phys. Rev. E. 73, 051901 (2006).

    Article  CAS  Google Scholar 

  28. Cahn, J.W. Free energy of a nonuniform system. 1. Interfacial free energy. J. Chem. Phys. 28, 258–267 (1958).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dongchoul Kim.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Song, J., Kim, D. Development of three-dimensional haptotaxis model for single crawling cell. BioChip J 4, 184–188 (2010). https://doi.org/10.1007/s13206-010-4304-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13206-010-4304-8

Keywords

Navigation