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Cell migration in multicell spheroids: Swimming against the tide

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Abstract

Multicell spheroids, small spherical clusters of cancer cells, have become an importantin vitro model for studying tumour development given the diffusion limited geometry associated with many solid tumour growths. Spheroids expand until they reach a dormant state where they exhibit a grossly static three-layered structure. However, at a cellular level, the spheroid is demonstrably dynamic with constituent cells migrating from the outer well-nourished region of the spheroid toward the necrotic central core. The mechanism that drives the migrating cells in the spheroid is not well understood. In this paper we demonstrate that recent experiments on internationalization can be adequately described by implicating pressure gradients caused by differential cell proliferation and cell death as the primary mechanism. Although chemotaxis plays a role in cell movement, we argue that it acts against the passive movement caused by pressure differences.

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Literature

  • Acker, H., J. Carlsson, R. Durand and R. M. Sutherland (Eds). 1984.Spheroids in Cancer Research. Berlin: Springer-Verlag.

    Google Scholar 

  • Adam, J. A. and S. A. Maggelakis. 1990. Diffusion regulated growth characteristics of a spherical prevascular carcinoma.Bull. math. Biol. 52, 549–582.

    MATH  Google Scholar 

  • Algire, G. M. and H. W. Chalkley. 1945. Vascular reactions of normal and malignant tissuein vivo.J. Nat. Cancer. 6, 73–85.

    Google Scholar 

  • Alt, W. and D. A. Lauffenburger. 1985. Transient behavior of a chemotaxis system modelling certain types of tissue inflammation.J. math. Biol. 24, 691–722.

    MathSciNet  Google Scholar 

  • Balding, D. and D. L. S. McElwain. 1985. A mathematical model of tumour-induced capillary growth.J. theor. Biol. 114, 53–73.

    Article  Google Scholar 

  • Deakin, A. S. 1975. Model for the growth of a solidin vitro tumor.Growth 39, 159–165.

    Google Scholar 

  • Dew, P. M. and J. Walsh. 1981. A set of library routines for solving parabolic equations in one space variable.A.C.M. Trans. Math. Software 7, 295–314.

    Article  MATH  Google Scholar 

  • Dorie, M. J., R. F. Kallman, D. F. Rapacchietta, D. van Antwerp and Y. R. Huang. 1982. Migration and internalization of cells and polystyrene microspheres in tumour cell spheroids.Exp. Cell Res. 141, 201–209.

    Article  Google Scholar 

  • Dorie, M. J., R. F. Kallman and M. A. Coyne. 1986. Effect of Cytochalasin B, Nocodazole and irradiation on migration and internalization of cells and microspheres in tumour cell spheroids.Exp. Cell Res. 166, 370–378.

    Article  Google Scholar 

  • Folkman, J. 1984. Tumour angiogenesis.Adv. Cancer Res. 43, 175–203.

    Article  Google Scholar 

  • Goldacre, R. J. and B. Sylven. 1962. On the access of blood-borne dyes to various tumour regions.Br. J. Cancer. 16, 306–322.

    Google Scholar 

  • Greenspan, H. P. 1972. Models for the growth of a solid tumor by diffusion.Stud. Appl. Math. 52, 317–340.

    Google Scholar 

  • Greenspan, H. P. 1976. On the growth and stability of cell cultures and solid tumours.J. theor. Biol. 56, 229–242.

    Article  MathSciNet  Google Scholar 

  • Hirst, D. G. and J. Denekamp. 1979. Tumour cell proliferation in relation to the vasculature.Cell Tissue Kinet. 12, 31–42.

    Google Scholar 

  • Jones, B. and R. S. Camplejohn. 1983. Strathmokinetic measurement of tumour cell proliferation in relation to vascular proximity.Cell Tissue Kinet. 16, 351–355.

    Google Scholar 

  • Keller, E. F. and L. A. Segel. 1971. Model for chemotaxis.J. theor. Biol. 30, 225–234.

    Article  Google Scholar 

  • Lauffenburger, D. A. and C. R. Kennedy. 1983. Localized bacterial infection in a distributed model for tissue inflammation.J. math. Biol. 16, 141–163.

    Article  MATH  Google Scholar 

  • Maggelakis, S. A. and J. A. Adam. 1990. Mathematical model of prevascular growth of a spherical carcinoma.Mathl. Comput. Modelling. 13, 23–38.

    Article  MATH  Google Scholar 

  • McElwain, D. L. S. and P. J. Ponzo. 1977. A model for the growth of a solid tumour with nonuniform oxygen consumption.Math. Biosci. 35, 267–279.

    Article  MATH  Google Scholar 

  • McElwain, D. L. S. and L. E. Morris. 1978. Apoptosis as a volume loss mechanism in mathematical models of solid tumour growth.Math. Biosci. 39, 147–157.

    Article  Google Scholar 

  • McElwain, D. L. S., R. Calcott and L. E. Morris. 1979. A model of vascular compression in solid tumours.J. theor. Biol. 78, 405–415.

    Article  Google Scholar 

  • Moore, J. V., H. A. Hopkins and W. B. Looney. 1984. Tumour-cord parameters in two rat hepatomas that differ in their radiobiological oxygenation status.Radiat. Envir. Biophys. 23, 213–222.

    Article  Google Scholar 

  • Moore, J. V., P. S. Haselton and C. M. Buckley. 1985. Tumour cords in 52 human bronchial and cervical squamous cell carcinomas: Inferences for their cellular kinetics and radiobiology.Br. J. Cancer. 51, 407–413.

    Google Scholar 

  • Murray, J. D. 1989.Mathematical Biology. Berlin: Springer-Verlag.

    MATH  Google Scholar 

  • Myerscough, M. R., P. K. Maini, J. D. Murray and K. H. Winters. 1990. Two dimensional pattern formation in a chemotactic system. InDynamics of Complex Interconnected Biological Systems, T. L. Vincent, A. I. Mees and L. S. Jennings (Eds), pp. 65–83. Boston: Birkhauser.

    Google Scholar 

  • Sincovec, R. F. and N. K. Madsen. 1975. Software for non-linear partial differential equations.A.C.M. Trans. math. Software. 1, 233–260.

    Google Scholar 

  • Strauli, P. and L. Weiss. 1977. Cell locomotion and tumour penetration.Eur. J. Cancer. 15, 1–12.

    Google Scholar 

  • Suh, O. and L. Weiss. 1984. The development of a technique for the morphometric analysis of invasion in cancer.J. theor. Biol. 107, 547–561.

    Google Scholar 

  • Sutherland, R. M. 1988. Cell and environment interactions in tumor microregions: the multicell spheroid model.Science 240, 177–184.

    Google Scholar 

  • Tannock, I. F. 1968. The relation between cell proliferation and the vascular system in a transplanted mouse mammary tumour.Br. J. Cancer 22, 258–273.

    Google Scholar 

  • Thomlinson, R. H. and L. H. Gray. 1955. The histological structure of some human lung cancers and the possible implications for radiotherapy.Br. J. Cancer. 9, 539–549.

    Google Scholar 

  • Wette, R., I. N. Katz and E. Y. Rodin. 1974. Stochastic processes for solid tumour kinetics II. Diffusion-regulated growth.Math. Biosci. 21, 311–338.

    Article  MATH  Google Scholar 

  • Young, J. S., C. E. Lumsden and A. L. Stalker. 1950. The significance of the “tissue pressure” of normal testicular and neoplastic (Brown-Pearce carcinoma) tissue in the rabbit.J. path. Bact. 62, 313–333.

    Article  Google Scholar 

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McElwain, D.L.S., Pettet, G.J. Cell migration in multicell spheroids: Swimming against the tide. Bltn Mathcal Biology 55, 655–674 (1993). https://doi.org/10.1007/BF02460655

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  • DOI: https://doi.org/10.1007/BF02460655

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