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

ACKNOWLEDGEMENTS

We thank Dr. Gen Yang for helpful discussions, and thank Drs. Ping Ao, Jiandong Huang, Wei Huang, Chen Jia, Hong Qian, Monica C. Sleumer, Weikang Wang and Zhongjun Zhou for constructive comments. This work is supported by NBRPC grant (No. 2012CB316503), CPSF grant (No. 2012M510402), NSFC grant (Nos. 91010016, 31061160497) and NIH grant (No. ES017166).

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg