Abstract
In an earlier work a model of the autocrine and paracrine pathways of tumor growth control was developed (Michelson and Leith. 1991. Autocrine and paracrine growth factors in tumor growth.Bull. math. Biol. 53, 639–656). The target population, a generic tumor, was modeled as a single, homogeneous population using the standard Verhulst equation of logistic growth. Mitogenic signals were represented by modifications to the Malthusian growth parameter and adaptational signals were represented by modifications to the carrying capacity. Three growth scenarios were described: (1) normal tissue wound healing, (2) unperturbed tumor growth, and (3) tumor growth in a radiation damaged environment, a phenomenon termed the Tumor Bed Effect (TBE).
In this paper, we extend those results to include a “triad” of growth factor controls (autocrine, paracrine and endocrine) and heterogeneity of the target population. The heterogeneous factors in the model represent either intrinsic, epigenetic or environmental differences in both normally differentiating tissues and tumors.
Three types of growth are modeled: (1) normal tissue differentiation or wound healing, assuming no communication between differentiated and undifferentiated cell compartments; (2) normal wound healing with feedback inhibition, due to signalling from the differentiated compartment; and (3) the development of hypoxia in a spherical tumor. The signal processing within the triad is discussed for each model and biologically reasonable constraints are defined for limits on growth control.
Similar content being viewed by others
Literature
Adam, J. A. and S. A. Maggelakis. 1990. Diffusion related growth characteristics of a spherical prevascular carcinoma.Bull. math. Biol. 52, 549–582.
Freyer J. P. and R. M. Sutherland. 1983. Determination of diffusion constants for metabolites in multicell tumor spheroids. InOxygen Transport to Tissue IV, pp. 463–475 New York: Plenum Press.
Freyer, J. P., E. Tustanoff, A. J. Franko and R. M. Sutherland. 1984.In situ oxygen consumption rates of cells in V-79 multicellular tumor spheroids during growth.J. Cell Physiol. 118, 53–61.
Goustin, A. S., E. B. Loef, G. D. Shipley and H. L. Moses. 1986. Growth factors and cancer.Cancer Res. 46, 1015–1029.
Howe P. H., C. C. Bascom, M. R. Cunningham and E. B. Loef. 1989. Regulation of transforming growth factor-beta action by multiple transducing pathways: evidence for both G protein-dependent and-independent signalling.Cancer Res. 49, 6024–6031.
Inui, T., A. Tsubara and S. Morii. 1989. Incidence of precancerous foci of mammary glands and growth rate of transplantable mammary cancers in sialoadenectomized mice.JNCI,81, 1660–1663.
Jansson, B. and L. Revesz. 1975. Analysis of the growth of tumor cell populations.Math. Biosci. 19, 131–154.
Karey, K. P. and D. A. Sirbasku. 1988. Differential responsiveness of human breast cancer cell lines MCF-7 and T47D to growth factors and 17-beta estradiol.Cancer Res. 48, 4083–4092.
Keski-Oja, J., A. E. Postlethwaite and H. L. Moses. 1988. Transforming growth factors in the regulation of malignant cell growth and invasion.Cancer Invest. 6, 705–724.
King, I. and A. C. Sartorelli. 1989. Epidermal growth factor receptor gene expression, protein kinase activator, and terminal differentiation of human malignant epidermal cells.Cancer Res. 49, 5677–5681.
Loef, E. B., J. A. Proper, A. S. Goustin, G. D. Shipley, P. E. DiCorleto and H. L. Moses. 1986. Induction of c-sis mRNA and activity similar to platelet-derived growth factor by transforming growth factor beta: a propposed model for indirect mitogenesis involving autocrine activity.PNAS 83, 2453–2457.
Michelson, S. and J. T. Leith. 1991. Autocrine and paracrine growth factors in tumor growth.Bull. math. Biol. 53, 639–656.
Michelson, S., B. E. Miller, A. S. Glicksman and J. T. Leith. 1987. Tumor microecology and competitive interactions.J. theor. Biol. 128, 233–246.
Osborne, C. K., K. Hobbs and G. M. Clark. 1985. Effect of estrogens and antiestrogens on growth of human breast cancer cells in athymic nude mice.Cancer Res. 45, 584–590.
Roberts, A. B., M. A. Anzano, L. M. Wakefield, N. S. Roche, D. F. Stern and M. B. Sporn. 1985. Type beta transforming growth factor: a bifunctional regulator of cellular growth.PNAS 82, 119–123.
Sonnenchein, N. C. and A. M. Soto. 1989. Symposium on the control of cell proliferation and cancer.Cancer Res. 49, 6161.
Sporn, M. B. and A. B. Roberts. 1985. Autocrine growth factors and cancer.Nature 313, 745–747.
Sporn, M. B. and G. J. Todaro. 1980. Autocrine secretion and malignant transformation of cells.New Engl. J. Med.,303, 878–880.
Sutherland, R. M. 1988. Cell and environment interactions in tumor microregions: the multicell spheroid model.Science 240, 177–184.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Michelson, S., Leith, J.T. Growth factors and growth control of heterogeneous cell populations. Bltn Mathcal Biology 55, 993–1011 (1993). https://doi.org/10.1007/BF02460696
Issue Date:
DOI: https://doi.org/10.1007/BF02460696