Development of Three-dimensional Chemotaxis Model for a Single Crawling Cell, Considering the Interaction between the Cell and Substrate

세포와 흡착면간의 영향을 고려한 흡착형 세포의 3 차원 동적 해석 모델 개발

  • Received : 2010.12.13
  • Accepted : 2011.09.30
  • Published : 2011.11.01


The interaction between the cell and the substrate is the most prominent feature affecting the migration of a crawling cell. This paper proposes a three-dimensional dynamic model using the diffuse interface description that reveals the effects of the interaction between a single crawling cell and the substrate during chemotactic migration. To illustrate the effects of interaction between the cell and the substrate, we consider the interfacial energy between the coexistent materials. Multiple mechanisms including the interface energy, chemotaxis effect, and diffusion, are addressed by employing a diffuse interface model.


Chemotaxis;Crawling Cell;Interface Energy;Diffuse Interface Model


  1. Berg, H. C. and Brown, D. A., 1972, "Chemotaxis in Escherichia coli Analysed by Three-Dimensional Tracking," Nature, Vol. 239, No. 5374, pp. 500-504.
  2. Nelson, R. D., Quie, P. G. and Simmons, R. L., 1975, "Chemotaxis Under Agarose: A New and Simple Method for Measuring Chemotaxis and Spontaneous Migration of Human Polymorphonuclear Leukocytes and Monocytes," J. Immunol., Vol. 115, pp. 1650-1656.
  3. Adler, J., 1969, "Chemoreceptors in Bacteria," Science, Vol. 166, No. 3913, pp. 1588-1597.
  4. Zigmond, S. H., 1977, "Ability of Polymorphonuclear Leukocytes to Orient in Gradients of Chemotactic Factors," J. Cell Biol., Vol. 75, No. 2, pp. 606-616.
  5. Jeon, N. L. et al., 2002, "Neutrophil Chemotaxis in Linear and Complex Gradients of Interleukin-8 Formed in a Microfabricated Device," Nat. Biotechnol., Vol. 20, No. 8, pp. 826-830.
  6. Adler, J., 1973, "A Method for Measuring Chemotaxis and Use of the Method to Determine Optimum Conditions for Chemotaxis by Escherichia Coli," J. Gen. Microbiol., Vol. 74, No. 1, pp. 77-91.
  7. Ford, R. M. et al., 1991, "Measurement of Bacterial Random Motility and Chemotaxis Coefficients .1. Stopped-Flow Diffusion Chamber Assay," Biotechnol. Bioeng., Vol. 37, No. 7, pp. 647-660.
  8. Lewus, P. and Ford, R. M., 2001, "Quantification of Random Motility and Chemotaxis Bacterial Transport Coefficients Using Individual-Cell and Population- Scale Assays," Biotechnol. Bioeng., Vol. 75, No. 3, pp. 292-304.
  9. Berg, H., 1971, "How to Track Bacteria," Review of Scientific Instruments, Vol. 42, No. 6, pp. 868.
  10. Diao, J. P., 2006, "A Three-Channel Microfluidic Device for Generating Static Linear Gradients and Its Application to the Quantitative Analysis of Bacterial Chemotaxis," Lab. Chip, Vol. 6, No. 3, pp. 381-388.
  11. Frevert, C. W. et al., 2006, "Measurement of Cell Migration in Response to an Evolving Radial Chemokine Gradient Triggered by a Microvalve," Lab Chip., Vol. 6, No. 7, pp. 849-856.
  12. Tharp, W. G. et al., 2006, "Neutrophil Chemorepulsion in Defined Interleukin-8 Gradients in Vitro and in Vivo," J. Leukocyte Biol., Vol. 79, No. 3, pp. 539-554.
  13. Weiner, O. D. et al., 1999, "Spatial Control of Actin Polymerization During Neutrophil Chemotaxis," Nat. Cell Biol., Vol. 1, No. 2, pp. 75-81.
  14. Zhou, Y. et al., 2004, "Biomaterial Surface- Dependent Neutrophil Mobility," J. Biomed. Mater. Res. A, Vol. 69A, No. 4, pp. 611-620.
  15. Balaban, N. Q. et al., 2001, "Force and Focal Adhesion Assembly: A Close Relationship Studied Using Elastic Micropatterned Substrates," Nature Cell Biology, Vol. 3, No. 5, pp. 466-472.
  16. Keller, E. F., 1971, "Model for Chemotaxis," J. Theor. Biol. , Vol. 30, No. 2, pp. 225-234.
  17. Ford, R. M. and Lauffenburger, D. A., 1991, "Analysis of Chemotactic Bacterial Distributions in Population Migration Assays Using a Mathematical- Model Applicable to Steep or Shallow Attractant Gradients," B. Math. Biol., Vol. 53, No. 5, pp. 721-749.
  18. Lapidus, R. I. and Schiller, R., 1976, "Model for the Chemotactic Response of a Bacterial Population," Biophys. J., Vol. 16, No. 7, pp. 779-789.
  19. Painter, K. J. and Sherratt, J. A., 2003, "Modelling the Movement of Interacting Cell Populations," J. Theor. Biol., Vol. 225, No. 3, pp. 327-339.
  20. Rivero, M. A., 1989, "Transport Models for Chemotactic Cell-Populations Based on Individual Cell Behavior," Chem. Eng. Sci., Vol. 44, No. 12, pp. 2881-2897.
  21. Jabbarzadeh, E. and Abrams, C. F., 2005, "Chemotaxis and Random Motility in Unsteady Chemoattractant Fields: a Computational Study," J. Theor. Biol., Vol. 235, No. 2, pp. 221-232.
  22. Stokes, C. L., Lauffenburger, D. A. and Williams, S. K., 1991, "Migration of Individual Microvessel Endothelial-Cells - Stochastic-Model and Parameter Measurement," J. Cell Sci., Vol. 99, pp. 419-430.
  23. Song, J. and Kim, D., 2010, "Three-Dimensional Chemotaxis Model for a Crawling Neutrophil," Physical Review E, Vol. 82, No. 5, pp. 051902.
  24. Linan, Z., Song, J. and Kim, D., 2010, "A Study on Cancer-Cell Invasion Based on Multi-Physics Analysis Technology," Biochip Journal, Vol. 4, No. 2,
  25. Song, J. and Kim, D., 2010, "Development of Three-Dimensional Haptotaxis Model for Single Crawling Cell," Biochip Journal, Vol. 4, No. 3, pp. 184-188.
  26. Song, J. H. and Kim, D., 2009, "Three-Dimensional Chemotaxis Model for a Single Bacterium," J. Comput. Theor. Nanos., Vol. 6, No. 7, pp. 1687-1693.
  27. Kim, D. and Lu, W., 2004, "Self-Organized Nanostructures in Multi-Phase Epilayers," Nanotechnology, Vol. 15, No. 5, pp. 667-674.
  28. Kim, D. and Lu, W., 2006, "Creep Flow, Diffusion, and Electromigration in Small Scale Interconnects," J. Mech. Phys. Solids, Vol. 54, No. 12, pp. 2554-2568.
  29. Kim, D. and Lu, W., 2006, "Three-Dimensional Model of Electrostatically Induced Pattern Formation in Thin Polymer Films," Phys. Rev. B, Vol. 73, No. 3, pp. 035206.
  30. Lu, W. and Kim, D., 2005, "Engineering Nanophase Self-Assembly with Elastic Field," Acta Mater., Vol. 53, No. 13, pp. 3689-3694.
  31. Lu, W. and Kim, D., 2004, "Patterning Nanoscale Structures by Surface Chemistry," Nano Lett., Vol. 4, No. 2, pp. 313-316.
  32. Karma, A. and Rappel, W. J., 1998, "Quantitative Phase-Field Modeling of Dendritic Growth in Two and Three Dimensions," Phys. Rev. E, Vol. 57, No. 4, pp. 4323-4349.
  33. Alber, M. et al., 2006, "Multiscale Dynamics of Biological Cells with Chemotactic Interactions: From a Discrete Stochastic Model to a Continuous Description," Phys. Rev. E, Vol. 73, No. 5, pp. 051901.
  34. Cahn, J. W., 1958, "Free Energy of a Nonuniform System .1. Interfacial Free Energy," J. Chem. Phys., Vol. 28, No. 2, pp. 258-267.