A self-consistent cell flux expression for simultaneous chemotaxis and contact guidance in tissues

Journal of Mathematical Biology

Volumn 41, Issue 4, 2000, Pages 315-330

  Wagle, Mihir A ^a   Tranquillo, Robert T ^a  

^a University of Minnesota   (United States)

Author keywords

Cell migration; Chemotaxis; Contact guidance; Diffusion approximation; Fokker Planck equation; Mathematical model

Indexed keywords

ANIMAL; ANISOTROPY; ARTICLE; BIOLOGICAL MODEL; CELL ADHESION; CELL MOTION; CHEMOTAXIS; MATHEMATICS; PHYSIOLOGY; STATISTICS; WOUND HEALING;

ANIMALS; ANISOTROPY; CELL ADHESION; CELL MOVEMENT; CHEMOTAXIS; MATHEMATICS; MODELS, BIOLOGICAL; STOCHASTIC PROCESSES; WOUND HEALING;

EID: 0034304709     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850000040     Document Type: Article

References (18)

1. Wolfgang Alt.: Correlation analysis of two-dimensional locomotion paths. In W. Alt and G. Hoffman, editors, Biological Motion, volume 89 of Lecture Notes in Biomathematics, pages 254-68, Springer-Verlag (1989)
2. Barocas, V.H., Girton, T.S., Tranquillo, R.T.: Engineered alignment in media equivalents - magnetic prealignment and mandrel compaction. J. Biomech. Engg., 120(5), 660-666 (1998)
3. Barocas, V.H., Tranquillo, R.T.: An anisotropic biphasic theory of tissue-equivalent mechanics: the interplay among cell traction, fibrillar network deformation, alignment and cell contact guidance. Journal of Biomechanical Engineering, 119(2), 137-45 (1997)
4. Dickinson, R.B., Guido, S., Tranquillo, R.T.: Biased cell migration of fibroblasts exhibiting contact guidance in oriented collagen gels. Ann. Biomed. Engg., 22, 342-356 (1994)
5. Dickinson, R.B.: A model for cell migration by contact guidance. In W. Alt, A. Deutsch, and G. Dunn, editors, Dynamics of Cell and Tissue Motion, Birkhäuser-Verlag, Basel (1997)
6. Dickinson, R.B., Tranquillo, R.T.: Transport equations and indices for random and biased cell migration based on single cell properties. SIAM Journal of Applied Math, 55(5), 1429-54 (1995)
7. Girton, T.S., Barocas, V.H., Tranquillo, R.T.: Reorganization and alignment of collagen fibrils and tissue cells in confined compression of a tissue equivalent. 1999. In preparation.
8. Guido, S., Tranquillo, R.T.: A methodology for the systematic and quantitative study of cell contact guidance in oriented collagen gels: correlation of fibroblast orientation and gel birefringence. J. Cell Sci., 105, 317-331 (1993)
9. Knapp, D.M., Helou, E.F., Tranquillo, R.T.: A fibrin or collagen gel assay for tissue cell chemotaxis: Assessment of fibroblast chemotaxis to GRGDSP. Experimental Cell Research, 247, 543-553 (1999)
10. Oster, G. F., Murray, J. D., Harris, A. K.: Mechanical aspects of mesenchymal morphogenesis. Journal of Embryology & Experimental Morphology, 78, 83-125 (1983)
11. Oster, G.F., Murray, J.D., Maini, P.K.: A model for chondrogenetic condensations in the developing limb: the role of extracellular matrix and cell tractions. Journal of Embryology & Experimental Morphology, 89, 93-112 (1985)
12. Perelson, A.S., Maini, P.K., Murray, J.D., Hyman, J.M., Oster, G.F.: Nonlinear pattern selection in a mechanical model for morphogenesis. J. Math. Biology, 24(5), 525-541 (1986)
13. Sherratt, J. A., Chemotaxis and chemokinesis in eukaryotic cells: the keller-segel equations as an approximation to a detailed model. Bulletin of Mathematical Biology, 56(1), 129-46 (1994)
14. Tranquillo, R.T., Barocas, V.H.: A continuum model for the role of fibroblast contact guidance in wound contraction. In W. Alt, A. Deutsch, and G. Dunn, editors, Dynamics of Cell and Tissue Motion, pages 159-164, Birkhäuser-Verlag, Basel, (1997)
15. Tranquillo, R.T., Murray, J.D.: Continuum model of fibroblast-driven wound contraction: inflammation-mediation. J. Theor. Biol., 158, 135-172 (1992)
16. Wagle, M.A., Knapp, D.M., Tranquillo., R.T.: Reversing fibroblast locomotion in tissue-equivalents. 1999. In preparation.
17. Weiss, P.: Erzwingung elementarer strukturverschiedenheiten am in vitro wachsenden gewebe. Wilhelm Roux Arch., 116, 438-554 (1929)
18. Wilkinson, P. C., Lackie, J. M.: The influence of contact guidance on chemotaxis of human neutrophil leukocytes. Experimental Cell Research, 145(2), 255-64 (1983)