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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 606250, 5 pages
Effect of Delay on Selection Dynamics in Long-Term Sphere Culture of Cancer Stem Cells
1Breast Disease Center, Southwest Hospital, Third Military Medical University, Chongqing 400038, China
2Chongqing Academy of Science & Technology, Chongqing 401123, China
3Department of Applied Mathematics and Physics, Air Force Engineering University, Xi'an 710051, China
4School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, China
Received 26 January 2013; Accepted 15 February 2013
Academic Editor: Yonghui Xia
Copyright © 2013 Peng Tang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- T. Reya, S. J. Morrison, M. F. Clarke, and I. L. Weissman, “Stem cells, cancer, and cancer stem cells,” Nature, vol. 414, no. 6859, pp. 105–111, 2001.
- J. Marx, “Mutant stem cells may seed cancer,” Science, vol. 301, no. 5638, pp. 1308–1310, 2003.
- M. Al-Hajj and M. F. Clarke, “Self-renewal and solid tumor stem cells,” Oncogene, vol. 23, no. 43, pp. 7274–7282, 2004.
- B. K. Abraham, P. Fritz, M. McClellan, P. Hauptvogel, M. Athelogou, and H. Brauch, “Prevalence of CD44+/CD24-/low cells in breast cancer may not be associated with clinical outcome but may favor distant metastasis,” Clinical Cancer Research, vol. 11, no. 3, pp. 1154–1159, 2005.
- M. Balic, H. Lin, L. Young et al., “Most early disseminated cancer cells detected in bone marrow of breast cancer patients have a putative breast cancer stem cell phenotype,” Clinical Cancer Research, vol. 12, no. 19, pp. 5615–5621, 2006.
- M. S. Wicha, “Cancer stem cells and metastasis: lethal seeds,” Clinical Cancer Research, vol. 12, no. 19, pp. 5606–5607, 2006.
- S. Huang, “Non-genetic heterogeneity of cells in development: more than just noise,” Development, vol. 136, no. 23, pp. 3853–3862, 2009.
- T. Quinn and Z. Sinkala, “Dynamics of prostate cancer stem cells with diffusion and organism response,” BioSystems, vol. 96, no. 1, pp. 69–79, 2009.
- S. J. Altschuler and L. F. Wu, “Cellular heterogeneity: do differences make a difference?” Cell, vol. 141, no. 4, pp. 559–563, 2010.
- S. Huang, “Tumor progression: chance and necessity in Darwinian and Lamarckian somatic (mutationless) evolution,” Progress in Biophysics and Molecular Biology, vol. 110, no. 1, pp. 69–86, 2012.
- P. Cammareri, Y. Lombardo, M. G. Francipane, S. Bonventre, M. Todaro, and G. Stassi, “Isolation and culture of colon Cancer stem cells,” Methods in Cell Biology, vol. 86, pp. 311–324, 2008.
- Y. Zhong, K. Guan, S. Guo et al., “Spheres derived from the human SK-RC-42 renal cell carcinoma cell line are enriched in cancer stem cells,” Cancer Letters, vol. 299, no. 2, pp. 150–160, 2010.
- T. Peng, M. Qinghua, T. Zhenning, W. Kaifa, and J. Jun, “Long-term sphere culture cannot maintain a high ratio of Cancer stem cells: a mathematical model and experiment,” PLoS ONE, vol. 6, no. 11, Article ID e25518, 2011.
- P. B. Gupta, C. M. Fillmore, G. Jiang et al., “Stochastic state transitions give rise to phenotypic equilibrium in populations of cancer cells,” Cell, vol. 146, no. 4, pp. 633–644, 2011.
- Y. Yuan and J. Bélair, “Stability and Hopf bifurcation analysis for functional differential equation with distributed delay,” SIAM Journal on Applied Dynamical Systems, vol. 10, no. 2, pp. 551–581, 2011.
- M. A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life, The Belknap Press of Harvard University Press, Cambridge, Mass, USA, 2006.
- K. Wang, N. Zhang, and D. Niu, “Periodic oscillations in a spatially explicit model with delay effect for vegetation dynamics in freshwater marshes,” Journal of Biological Systems, vol. 19, no. 2, pp. 131–147, 2011.
- J. Hale, Theory of Functional Differential Equations, Springer, New York, NY, USA, 1977.
- Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, Mass, USA, 1993.
- H. I. Freedman, J. W.-H. So, and P. Waltman, “Coexistence in a model of competition in the chemostat incorporating discrete delays,” SIAM Journal on Applied Mathematics, vol. 49, no. 3, pp. 859–870, 1989.
- T. Zhao, “Global periodic solutions for a differential delay system modeling a microbial population in the chemostat,” Journal of Mathematical Analysis and Applications, vol. 193, no. 1, pp. 329–352, 1995.