Population dynamics of cancer cells with cell state conversions

References

[1] Reya, T., Morrison, S. J., Clarke, M. F. and Weissman, I. L. (2001) Stem cells, cancer, and cancer stem cells. Nature, 414, 105–111

[2] Jordan, C. T., Guzman, M. L. and Noble, M. (2006) Cancer stem cells. N. Engl. J. Med., 355, 1253–1261

[3] Nguyen, L. V., Vanner, R., Dirks, P. and Eaves, C. J. (2012) Cancer stem cells: an evolving concept. Nat. Rev. Cancer, 12, 133–143

[4] Dalerba, P., Cho, R. W. and Clarke, M. F. (2007) Cancer stem cells: models and concepts. Annu. Rev. Med., 58, 267–284

[5] Hermann, P. C., Huber, S. L., Herrler, T., Aicher, A., Ellwart, J. W., Guba, M., Bruns, C. J. and Heeschen, C. (2007) Distinct populations of cancer stem cells determine tumor growth and metastatic activity in human pancreatic cancer. Cell Stem Cell, 1, 313–323

[6] Rosen, J. M. and Jordan, C. T. (2009) The increasing complexity of the cancer stem cell paradigm. Science, 324, 1670–1673.

[7] Alison, M. R., Lim, S. M. L. and Nicholson, L. J. (2011) Cancer stem cells: problems for therapy? J. Pathol., 223, 147–161

[8] Chaffer, C. L., Brueckmann, I., Scheel, C., Kaestli, A. J., Wiggins, P. A., Rodrigues, L. O., Brooks, M., Reinhardt, F., Su, Y., Polyak, K., (2011) Normal and neoplastic nonstem cells can spontaneously convert to a stem-like state. Proc. Natl. Acad. Sci. U.S.A., 108, 7950–7955

[9] Meyer, M. J., Fleming, J. M., Ali, M. A., Pesesky, M. W., Ginsburg, E. and Vonderhaar, B. K. (2009) Dynamic regulation of CD24 and the invasive, CD44posCD24neg phenotype in breast cancer cell lines. Breast Cancer Res., 11, R82

[10] Gupta, P. B., Fillmore, C. M., Jiang, G., Shapira, S. D., Tao, K., Kuperwasser, C. and Lander, E. S. (2011) Stochastic state transitions give rise to phenotypic equilibrium in populations of cancer cells. Cell, 146, 633–644

[11] Scaffidi, P. and Misteli, T. (2011) In vitro generation of human cells with cancer stem cell properties. Nat. Cell Biol., 13, 1051–1061

[12] Iliopoulos, D., Hirsch, H. A., Wang, G. and Struhl, K. (2011) Inducible formation of breast cancer stem cells and their dynamic equilibrium with non-stem cancer cells via IL6 secretion. Proc. Natl. Acad. Sci. U.S.A., 108, 1397–1402

[13] Yang, G., Quan, Y., Wang, W., Fu, Q., Wu, J., Mei, T., Li, J., Tang, Y., Luo, C., Ouyang, Q., (2012) Dynamic equilibrium between cancer stem cells and non-stem cancer cells in human SW620 and MCF-7 cancer cell populations. Br. J. Cancer, 106, 1512–1519

[14] Zapperi, S. and La Porta, C. A. M. (2012) Do cancer cells undergo phenotypic switching? The case for imperfect cancer stem cell markers. Sci. Rep., 2, 441

[15] Nordling, C. O. (1953) A new theory on the cancer-inducing mechanism. Br. J. Cancer, 7, 68–72.

[16] Armitage, P. and Doll, R. (1954) The age distribution of cancer and a multi-stage theory of carcinogenesis. Br. J. Cancer, 8, 1–12

[17] Fisher, J. C. (1958) Multiple-mutation theory of carcinogenesis. Nature, 181, 651–652

[18] Ganguly, R. and Puri, I. K. (2006) Mathematical model for the cancer stem cell hypothesis. Cell Prolif., 39, 3–14

[19] Enderling, H., Chaplain,M. A. J., Anderson, A. R. A. and Vaidya, J. S. (2007) A mathematical model of breast cancer development, local treatment and recurrence. J. Theor. Biol., 246, 245–259

[20] Michor, F. (2008) Mathematical models of cancer stem cells. J. Clin. Oncol., 26, 2854–2861

[21] La Porta, C. A. M., Zapperi, S. and Sethna, J. P. (2012) Senescent cells in growing tumors: population dynamics and cancer stem cells. PLoS Comput. Biol., 8, e1002316

[22] Johnston, M. D., Edwards, C. M., Bodmer, W. F., Maini, P. K. and Chapman, S. J. (2007) Mathematical modeling of cell population dynamics in the colonic crypt and in colorectal cancer. Proc. Natl. Acad. Sci. U.S.A., 104, 4008–4013

[23] Boman, B. M., Wicha, M. S., Fields, J. Z. and Runquist, O. A. (2007) Symmetric division of cancer stem cells—a key mechanism in tumor growth that should be targeted in future therapeutic approaches. Clin. Pharmacol. Ther., 81, 893–898

[24] Dingli, D., Traulsen, A. and Michor, F. (2007) (A)symmetric stem cell replication and cancer. PLoS Comput. Biol., 3, e53

[25] Dingli, D., Traulsen, A. and Pacheco, J. M. (2007) Compartmental architecture and dynamics of hematopoiesis. PLoS ONE, 2, e345

[26] Antal, T. and Krapivsky, P. L. (2011) Exact solution of a two-type branching process: models of tumor progression. J. Stat. Mech., P08018.

[27] Sottoriva, A., Vermeulen, L. and Tavaré S. (2011) Modeling evolutionary dynamics of epigenetic mutations in hierarchically organized tumors. PLoS Comput. Biol., 7, e1001132

[28] Werner, B., Dingli, D., Lenaerts, T., Pacheco, J. M. and Traulsen, A. (2011) Dynamics of mutant cells in hierarchical organized tissues. PLoS Comput. Biol., 7, e1002290

[29] Molina-Peña, R. and Álvarez, M. M. (2012) A simple mathematical model based on the cancer stem cell hypothesis suggests kinetic commonalities in solid tumor growth. PLoS ONE, 7, e26233

[30] Holz, M. and Fahr, A. (2001) Compartment modeling. Adv. Drug Deliv. Rev., 48, 249–264

[31] Tao, Y., Ruan, J., Yeh, S. H., Lu, X., Wang, Y., Zhai, W., Cai, J., Ling, S., Gong, Q., Chong, Z., (2011) Rapid growth of a hepatocellular carcinoma and the driving mutations revealed by cell-population genetic analysis of whole-genome data. Proc. Natl. Acad. Sci. U.S.A., 108, 12042–12047

[32] Cai, L., Friedman, N. and Xie, X. S. (2006) Stochastic protein expression in individual cells at the single molecule level. Nature, 440, 358–362

[33] Fillmore, C. M. and Kuperwasser, C. (2008) Human breast cancer cell lines contain stem-like cells that self-renew, give rise to phenotypically diverse progeny and survive chemotherapy. Breast Cancer Res., 10, R25

[34] Cowan, C. A., Klimanskaya, I., McMahon, J., Atienza, J., Witmyer, J., Zucker, J. P., Wang, S., Morton, C. C., McMahon, A. P., Powers, D., (2004) Derivation of embryonic stem-cell lines from human blastocysts. N. Engl. J. Med., 350, 1353–1356

[35] Marusyk, A., Almendro, V. and Polyak, K. (2012) Intra-tumour heterogeneity: a looking glass for cancer? Nat. Rev. Cancer, 12, 323–334

[36] Axelrod, R., Axelrod, D. E. and Pienta, K. J. (2006) Evolution of cooperation among tumor cells. Proc. Natl. Acad. Sci. U.S.A., 103, 13474–13479

[37] Ao, P., Galas, D., Hood, L. and Zhu, X. (2008) Cancer as robust intrinsic state of endogenous molecular-cellular network shaped by evolution. Med. Hypotheses, 70, 678–684

[38] Chen, L., Liu, R., Liu, Z. P., Li, M. and Aihara, K. (2012) Detecting early-warning signals for sudden deterioration of complex diseases by dynamical network biomarkers. Sci. Rep., 2, 342

[39] Zhang, X. J., Qian, H. and Qian, M. (2012) Stochastic theory of nonequilibrium steady states and its applications. part I. Phys. Rep., 510, 1–86.

[40] Ge, H., Qian, M. and Qian, H. (2012) Stochastic theory of nonequilibrium steady states. part II: Applications in chemical biophysics. Phys. Rep., 510, 87–118.

[41] Ao, P. (2008) Emerging of stochastic dynamical equalities and steady state thermodynamics from Darwinian dynamics. Commun. Theor. Phys., 49, 1073–1090

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg