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Mechanical models for cell movement – locomotion, translocation, migration

Part of: Physiological, cellular and medical topics Limit theorems Markov processes

Published online by Cambridge University Press:  14 July 2016

Joseph C. Watkins
Joseph C. Watkins*
Affiliation:
University of Arizona
*
∗Postal address: Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA. e-mail: jwatkins@math.arizona.edu
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Abstract

This paper provides a detailed stochastic analysis of leucocyte cell movement based on the dynamics of a rigid body. The cell's behavior is studied in two relevant anisotropic environments displaying adhesion mediated movement (haptotaxis) and stimulus mediated movement (chemotaxis). This behavior is modeled by diffusion processes on three successively longer time scales, termed locomotion, translocation, and migration.

Keywords

CELL MOVEMENTCHEMOTAXISHAPTOTAXISLOCOMOTIONTRANSLOCATIONMIGRATIONDIFFUSION PROCESSESADIABATIC AVERAGING

MSC classification

Primary: 60F05: Central limit and other weak theorems 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 92C10: Biomechanics
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 4 , December 1997 , pp. 827 - 846
Copyright
Copyright © Applied Probability Trust 1997 

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References

Buck, C. A. and Horwitz, A. F. (1987) Integrin, a transmembrane glycoprotein complex mediating cell-substratum adhesion. J. Cell Sci. Suppl. 8, 231–250.Google Scholar
Delgrosso, G. and Marchetti, F. (1983) Limit theorems in stochastic biochemical modeling. Math. Biosci. 66, 157–165.Google Scholar
Devreotes, P. and Zigmond, S. (1988) Chemotaxis in eucaryotic cells. Ann. Rev. Cell Biol. 93, 649–686.Google Scholar
Dickenson, R. B. and Tranquillo, R. T. (1993) A stochastic model for cell random motility and haptotaxis based on adhesion receptor fluctuations. J. Math. Biol. 31, 563–600.Google Scholar
Dickenson, R. B. and Tranquillo, R. T. (1995) Transport equations and indices for random and biased cell migration based on single cell properties. SIAM J. Appl. Math. 55, 1419.Google Scholar
Ethier, S. N. and Kurtz, T. G. (1986) Markov Processes: Characterization and Convergence. Wiley, New York.CrossRefGoogle Scholar
Heubach, S. P. and Watkins, J. C. (1995) A stochastic model for the motion of a white blood cell. Adv. Appl. Prob. 27, 443–475.Google Scholar
Lackie, J. M. (1986) Cell Movement and Cell Behavior. Allen and Unwin, London.CrossRefGoogle Scholar
Theriot, J. A. and Mitchison, T. J. (1991) Actin microfilament dynamics in locomoting cells. Nature 352, 126–131.CrossRefGoogle ScholarPubMed
Tranquillo, R. T. (1990) Theories and models of gradient perception. In Biology of the Chemotactic Response. ed. Armitage, J. P. and Lackie, J. M. Cambridge University Press, Cambridge.Google Scholar