A model for the kinetics of homotypic cellular aggregation under static conditions

Biophysical Journal

Volumn 72, Issue 1, 1997, Pages 51-64

  Neelamegham, Sriram ^a,b   Munn, Lance L ^a,c   Zygourakis, Kyriacos ^a  

^a Rice University   (United States)

^b BAYLOR COLLEGE OF MEDICINE   (United States)

^c HARVARD MEDICAL SCHOOL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CELL ADHESION; CELL AGGREGATION; CELL MIGRATION; MATHEMATICAL MODEL; MICROSCOPY; VIDEORECORDING;

EID: 0031019846     PISSN: 00063495     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0006-3495(97)78646-6     Document Type: Article

References (43)

1. Adam, G., and M. Delbrück. 1968. Reduction of dimensionality in biological diffusion processes. In Structural Chemistry and Molecular Biology. A. Rich and N. Davidson, editors. W. H. Freeman and Company, San Francisco. 198-215.
2. Alt, W. 1980. Biased random walk models for chemotaxis and related diffusion approximations. J. Math. Biol. 9:147-177.
3. Bednarczyk, J. L., and B. W. McIntyre. 1990. A monoclonal antibody to VLA-4 α-chain (CDw49d) induces homotypic lymphocyte aggregation. J. Immunol. 144:777-784.
4. Bell, G. I. 1978. Models for the specific adhesion of cells to cells. Science. 200:618-627.
5. Bell, G. I. 1979. A theoretical model for adhesion between cells mediated by multivalent ligands. Cell Biophys. 1:133-147.
6. Bird, R. B., W. E. Steward, and E. N. Lightfoot. 1960. Transport Phenomenon. John Wiley and Sons, New York.
7. Botet, R., and R. Jullien. 1984. Size distribution of clusters in irreversible kinetic aggregation. J. Phys. A. Math. Gen. 17:2517-2530.
8. Bretscher, M. S. 1984. Endocytosis: relation to capping and cell locomotion. Science. 224:681-686.
9. Bretscher, M. S. 1987. How animal cells move. Sci. Am. 257:72-76, 89-90.
10. Campanero, M. R., R. Pulido, M. A. Ursa, M. Rodríguez-Moya, M. O. de Landázuri, and F. Sánchez-Madrid. 1990. An alternative leukocyte homotypic adhesion mechanism, LFA-1/ICAM-1 -independent, triggered through the human VLA-4 integrin. J. Cell Biol. 110:2157-2165.
11. Carslaw, H. S., and J. C. Jaeger. 1959. Conduction of Heat in Solids. Oxford University Press, London.
12. Chandrasekhar, S. 1943. Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15:2-89.
13. Clayberger, C., A. M. Krensky, B. W. McIntyre, T. D. Koller, P. Parham, F. Brodsky, D. J. Linn, and E. L. Evans. 1987. Identification and characterization of two novel lymphocyte function-associated antigens, L24 and L25. J. Immunol. 138:1510-1514.
14. DiMilla, P. A., K. Barbee, and D. A. Lauffenburger. 1991. Mathematical model for the effects of adhesion and mechanics on cell migration speed. Biophys. J. 60:15-37.
15. Dolgosheina, E. B., A. Y. Karulin, and A. V. Bobylev. 1992. A kinetic model of the agglutination process. Math. Biosci. 109:1-10.
16. Doob, J. L. 1942. The Brownian movement and stochastic equations. Ann. Math. 43:351-369.
17. Dunn, G. A., and A. F. Brown. 1987. A unified approach to analysing cell motility. In Cell Behaviour: Shape, Adhesion and Motility. J. E. Heaysman, C. A. Middleton, and F. M. Watt, editors. The Company of Biologists Limited, Cambridge. 81-102.
18. Evans, C. W., and J. Proctor. 1978. A collision analysis of lymphoid cell aggregation. J. Cell Sci. 33:17-36.
19. Farrell, B. E., R. P. Daniele, and D. A. Lauffenburger. 1990. Quantitative relationship between single-cell and cell-population model parameters for chemosensory migration response of alveolar macrophages to C5a. Cell Motil. Cytoskel. 16:279-293.
20. Fehlberg, E. 1970. Klassische Runge-Kutta-formeln vieter und niedregerer ordnung mit schrittweitenkontrolle und ihre anwendung auf warmeleitungsprobleme. Computing. 6:61-71.
21. Freshney, R. I. 1987. Culture of Animal Cells: A Manual of Basic Technique. Wiley-Liss, New York.
22. Grinnell, F. 1986. Focal adhesion sites and the removal of substratumbound fibronectin. J. Cell Biol. 103:2697-2706.
23. Hammer, D. A., and D. A. Lauffenburger. 1987. Dynamic model for receptor-mediated cell adhesion to surfaces. Biophys. J. 52:475-487.
24. Huang, P. Y., and J. D. Hellums. 1993. Aggregation and disaggregation kinetics of human blood platelets. Part I. development and validation of a population balance method. Biophys. J. 65:334-343.
25. Lauffenburger, D. 1989. A simple model for the effects of receptor-mediated cell-substratum adhesion on cell migration. Chem. Eng. Sci. 44:1903-1914.
26. Munn, L. L., M. W. Glacken, B. W. McIntyre, and K. Zygourakis. 1993. Analysis of lymphocyte aggregation using digital image analysis. J. Immunol. Methods. 166:11-25.
27. 1 integrin. Ph.D. thesis, Rice University.
28. 1 integrin. J. Leukocyte Biol. 59:872-882.
29. Neelamegham, S., and K. Zygourakis. 1997. A quantitative assay for intercellular aggregation. Ann. Biomed. Eng. In press.
30. Nguyen, P. D., and E. A. O'Rear. 1990. Temporary aggregate size distribution from simulation of platelet aggregation and disaggregation. Ann. Biomed. Eng. 18:427-444.
31. Oster, G. F. 1984. On the crawling of cells. J. Embryol. Exp. Morphol. 83:329-364.
32. Overbeek, J. T. G. 1952. Kinetics of flocculation. In Colloid Science. H. R. Kruyt, editor. Elsevier Publishing Company, Amsterdam. 278-301.
33. Rothlein, R., and T. A. Springer. 1986. The requirement for lymphocyte function-associated antigen 1 in homotypic leukocyte adhesion stimulated by phorbol ester. J. Exp. Med. 163:1132-1148.
34. Samsel, R. W., and A. S. Perelson. 1982. Kinetics of rouleaux formation. I. A mass action approach with geometric features. Biophys. J. 37: 493-514.
35. Samsel, R. W., and A. S. Perelson. 1984. Kinetics of rouleaux formation. II. Reversible reactions. Biophys. J. 45:805-824.
36. Segal, D. M., and D. A. Stephany. 1984. The mechanism of intercellular aggregation: the kinetics of the Fcγ receptor-mediated aggregation of P388D1 cells with antibody-coated lymphocytes at 4°C. J. Immunol. 132:1924-1930.
37. Shampine, L. F., H. A. Watts, and S. M. Davenport. 1976. Solving non-stiff ordinary differential equations: the state of the art. SIAM Rev. 18: 376-441.
38. Smoluchowski, M. V. 1917. Versuch einer mathematischen theorie der koagulationskinetik kolloider lösungen. Z. Phys. Chem. 92:129-168.
39. Springer, T. A. 1995. Traffic signals on endothelium for lymphocyte recirculation and leukocyte emigration. Annu. Rev. Physiol. 57: 827-872.
40. Stokes, C. L., D. A. Lauffenburger, and S. K. Williams. 1991. Migration of individual microvessel endothelial cells: stochastic model and parameter measurement. J. Cell Sci. 99:419-430.
41. Sutherland, D. N., and I. Goodarx-nia. 1971. Floe simulation: the effect of collision sequence. Chem. Eng. Sci. 26:2071-2085.
42. van de Wiel-van Kemenade, E., Y. van Kooyk, A. J. de Boer, R. J. F. Huijbens, P. Weder, W. van de Kasteele, C. J. M. Melief, and C. G. Figdor. 1992. Adhesion of T and B lymphocytes to extracellular matrix and endothelial cells can be regulated through the β subunit of VLA. J. Cell Biol. 117:461-470.
43. Zeichner, G. R., and W. R. Schowalter. 1979. Effects of hydrodynamic and colloidal forces on the coagulation of dispersions. J. Colloid Interface Sci. 71:237-253.