2011, 8(2): 371-383. doi: 10.3934/mbe.2011.8.371

Tumor cells proliferation and migration under the influence of their microenvironment

1. 

Department of Mathematics, Ohio State University, Columbus, OH 43210, United States

2. 

Department of Mathematics & Statistics, University of Michigan, Dearborn, MI 48128

Received  February 2010 Revised  October 2010 Published  April 2011

It is well known that tumor microenvironment affects tumor growth and metastasis: Tumor cells may proliferate at different rates and migrate in different patterns depending on the microenvironment in which they are embedded. There is a huge literature that deals with mathematical models of tumor growth and proliferation, in both the avascular and vascular phases. In particular, a review of the literature of avascular tumor growth (up to 2006) can be found in Lolas [8] (G. Lolas, Lecture Notes in Mathematics, Springer Berlin / Heidelberg, 1872, 77 (2006)). In this article we report on some of our recent work. We consider two aspects, proliferation and of migration, and describe mathematical models based on in vitro experiments. Simulations of the models are in agreement with experimental results. The models can be used to generate hypotheses regarding the development of drugs which will confine tumor growth.
Citation: Avner Friedman, Yangjin Kim. Tumor cells proliferation and migration under the influence of their microenvironment. Mathematical Biosciences & Engineering, 2011, 8 (2) : 371-383. doi: 10.3934/mbe.2011.8.371
References:
[1]

K. Asano, C. D. Duntsch, Q. Zhou, J. D. Weimar, D. Bordelon, J. H. Robertson and T. Pourmotabbed, Correlation of n-cadherin expression in high grade gliomas with tissue invasion,, J Neurooncol, 70 (2004), 3. doi: 10.1023/B:NEON.0000040811.14908.f2.

[2]

S. Aznavoorian, M. L. Stracke, H. Krutzsch, E. Schiffmann and L. A. Liotta, Signal transduction for chemotaxis and haptotaxis by matrix molecules in tumor cells,, J Cell Biol, 110 (1990), 1427. doi: 10.1083/jcb.110.4.1427.

[3]

N. A. Bhowmick, E. G. Neilson and H. L. Moses, Stromal fibroblasts in cancer initiation and progression,, Nature, 432 (2004), 332. doi: 10.1038/nature03096.

[4]

E. Khain and L. M. Sander, Dynamics and pattern formation in invasive tumor growth,, Phys. Rev. Lett., 96 (2006). doi: 10.1103/PhysRevLett.96.188103.

[5]

Y. Kim and A. Friedman, Interaction of tumor with its microenvironment: A mathematical model,, Bull. Math. Biol., 72 (2010), 1029. doi: 10.1007/s11538-009-9481-z.

[6]

Y. Kim, J. Wallace, F. Li, M. Ostrowski and A. Friedman, Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: A mathematical model and experiments,, J. Math. Biol., 61 (2010), 401. doi: 10.1007/s00285-009-0307-2.

[7]

Y. Kim, S. Lawler, M. O. Nowicki, E. A Chiocca and A. Friedman, A mathematical model of brain tumor : Pattern formation of glioma cells outside the tumor spheroid core,, Journal of Theoretical Biology, 260 (2009), 359. doi: 10.1016/j.jtbi.2009.06.025.

[8]

G. Lolas, Mathematical modelling of proteolysis and cancer cell invasion of tissue,, in, (2006), 77.

[9]

M. M. Mueller and N. E. Fusenig, Friends or foes - bipolar effects of the tumour stroma in cancer,, Nat Rev Cancer, 4 (2004), 839. doi: 10.1038/nrc1477.

[10]

A. J. Perumpanani and H. M. Byrne, Extracellular matrix concentration exerts selection pressure on invasive cells,, Eur. J. Cancer, 35 (1999), 1274. doi: 10.1016/S0959-8049(99)00125-2.

[11]

M. Samoszuk, J. Tan and G. Chorn, Clonogenic growth of human breast cancer cells co-cultured in direct contact with serum-activated fibroblasts,, Breast Cancer Res, 7 (2005). doi: 10.1186/bcr995.

[12]

L. M. Sander and T. S. Deisboeck, Growth patterns of microscopic brain tumors,, Phys. Rev. E, 66 (2002). doi: 10.1103/PhysRevE.66.051901.

[13]

J. A. Sherratt and J. D. Murray, Models of epidermal wound healing,, Proc. R. Soc. Lond., B241 (1990), 29. doi: 10.1098/rspb.1990.0061.

[14]

A. M. Stein, T. Demuth, D. Mobley, M. Berens and L. M. Sander, A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment,, Biophys. J., 92 (2007), 356. doi: 10.1529/biophysj.106.093468.

[15]

K. R. Swanson, E. C. Alvord and J. D. Murray, A quantitative model for differential motility of gliomas in grey and white matter,, Cell Prolif., 33 (2000), 317. doi: 10.1046/j.1365-2184.2000.00177.x.

[16]

K. R. Swanson, E. C. Alvord and J. D. Murray, Virtual resection of gliomas: Effect of extent of resection on recurrence,, Math. Comp. Modelling, 37 (2003), 1177. doi: 10.1016/S0895-7177(03)00129-8.

[17]

M. Yashiro, K. Ikeda, M. Tendo, T. Ishikawa and K. Hirakawa, Effect of organ-specific fibroblasts on proliferation and differentiation of breast cancer cells,, Breast Cancer Res Treat, 90 (2005), 307. doi: 10.1007/s10549-004-5364-z.

[18]

K. Yuan, R. K. Singh, G. Rezonzew and G. P. Siegal, Cell motility in cancer invasion and metastasis,, in, (2006), 25.

show all references

References:
[1]

K. Asano, C. D. Duntsch, Q. Zhou, J. D. Weimar, D. Bordelon, J. H. Robertson and T. Pourmotabbed, Correlation of n-cadherin expression in high grade gliomas with tissue invasion,, J Neurooncol, 70 (2004), 3. doi: 10.1023/B:NEON.0000040811.14908.f2.

[2]

S. Aznavoorian, M. L. Stracke, H. Krutzsch, E. Schiffmann and L. A. Liotta, Signal transduction for chemotaxis and haptotaxis by matrix molecules in tumor cells,, J Cell Biol, 110 (1990), 1427. doi: 10.1083/jcb.110.4.1427.

[3]

N. A. Bhowmick, E. G. Neilson and H. L. Moses, Stromal fibroblasts in cancer initiation and progression,, Nature, 432 (2004), 332. doi: 10.1038/nature03096.

[4]

E. Khain and L. M. Sander, Dynamics and pattern formation in invasive tumor growth,, Phys. Rev. Lett., 96 (2006). doi: 10.1103/PhysRevLett.96.188103.

[5]

Y. Kim and A. Friedman, Interaction of tumor with its microenvironment: A mathematical model,, Bull. Math. Biol., 72 (2010), 1029. doi: 10.1007/s11538-009-9481-z.

[6]

Y. Kim, J. Wallace, F. Li, M. Ostrowski and A. Friedman, Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: A mathematical model and experiments,, J. Math. Biol., 61 (2010), 401. doi: 10.1007/s00285-009-0307-2.

[7]

Y. Kim, S. Lawler, M. O. Nowicki, E. A Chiocca and A. Friedman, A mathematical model of brain tumor : Pattern formation of glioma cells outside the tumor spheroid core,, Journal of Theoretical Biology, 260 (2009), 359. doi: 10.1016/j.jtbi.2009.06.025.

[8]

G. Lolas, Mathematical modelling of proteolysis and cancer cell invasion of tissue,, in, (2006), 77.

[9]

M. M. Mueller and N. E. Fusenig, Friends or foes - bipolar effects of the tumour stroma in cancer,, Nat Rev Cancer, 4 (2004), 839. doi: 10.1038/nrc1477.

[10]

A. J. Perumpanani and H. M. Byrne, Extracellular matrix concentration exerts selection pressure on invasive cells,, Eur. J. Cancer, 35 (1999), 1274. doi: 10.1016/S0959-8049(99)00125-2.

[11]

M. Samoszuk, J. Tan and G. Chorn, Clonogenic growth of human breast cancer cells co-cultured in direct contact with serum-activated fibroblasts,, Breast Cancer Res, 7 (2005). doi: 10.1186/bcr995.

[12]

L. M. Sander and T. S. Deisboeck, Growth patterns of microscopic brain tumors,, Phys. Rev. E, 66 (2002). doi: 10.1103/PhysRevE.66.051901.

[13]

J. A. Sherratt and J. D. Murray, Models of epidermal wound healing,, Proc. R. Soc. Lond., B241 (1990), 29. doi: 10.1098/rspb.1990.0061.

[14]

A. M. Stein, T. Demuth, D. Mobley, M. Berens and L. M. Sander, A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment,, Biophys. J., 92 (2007), 356. doi: 10.1529/biophysj.106.093468.

[15]

K. R. Swanson, E. C. Alvord and J. D. Murray, A quantitative model for differential motility of gliomas in grey and white matter,, Cell Prolif., 33 (2000), 317. doi: 10.1046/j.1365-2184.2000.00177.x.

[16]

K. R. Swanson, E. C. Alvord and J. D. Murray, Virtual resection of gliomas: Effect of extent of resection on recurrence,, Math. Comp. Modelling, 37 (2003), 1177. doi: 10.1016/S0895-7177(03)00129-8.

[17]

M. Yashiro, K. Ikeda, M. Tendo, T. Ishikawa and K. Hirakawa, Effect of organ-specific fibroblasts on proliferation and differentiation of breast cancer cells,, Breast Cancer Res Treat, 90 (2005), 307. doi: 10.1007/s10549-004-5364-z.

[18]

K. Yuan, R. K. Singh, G. Rezonzew and G. P. Siegal, Cell motility in cancer invasion and metastasis,, in, (2006), 25.

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