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Effect of delay on selection dynamics in long-term sphere culture of cancer stem cells. (English) Zbl 1264.34164

Summary: To quantitatively study the effect of delay on selection dynamics in long-term sphere culture of cancer stem cells (CSCs), a selection dynamic model with time delay is proposed. Theoretical results show that the ubiquitous time delay in cell proliferation may be one of the important factors to induce fluctuation, and numerical simulations indicate that the proposed selection dynamical model with time delay can provide a better fitting effect for the experiment of a long-term sphere culture of CSCs. Thus, it is valuable to consider the delay effect in the future study on the dynamics of nongenetic heterogeneity of clonal cell populations.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
92C17 Cell movement (chemotaxis, etc.)
92C15 Developmental biology, pattern formation
37N25 Dynamical systems in biology
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[1] 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. · doi:10.1038/35102167
[2] J. Marx, “Mutant stem cells may seed cancer,” Science, vol. 301, no. 5638, pp. 1308-1310, 2003. · doi:10.1126/science.301.5638.1308
[3] M. Al-Hajj and M. F. Clarke, “Self-renewal and solid tumor stem cells,” Oncogene, vol. 23, no. 43, pp. 7274-7282, 2004. · doi:10.1038/sj.onc.1207947
[4] 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.
[5] 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. · doi:10.1158/1078-0432.CCR-06-0169
[6] M. S. Wicha, “Cancer stem cells and metastasis: lethal seeds,” Clinical Cancer Research, vol. 12, no. 19, pp. 5606-5607, 2006. · doi:10.1158/1078-0432.CCR-06-1537
[7] S. Huang, “Non-genetic heterogeneity of cells in development: more than just noise,” Development, vol. 136, no. 23, pp. 3853-3862, 2009. · doi:10.1242/dev.035139
[8] 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. · doi:10.1016/j.biosystems.2008.11.010
[9] S. J. Altschuler and L. F. Wu, “Cellular heterogeneity: do differences make a difference?” Cell, vol. 141, no. 4, pp. 559-563, 2010. · doi:10.1016/j.cell.2010.04.033
[10] 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.
[11] 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. · doi:10.1016/S0091-679X(08)00014-9
[12] 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. · doi:10.1016/j.canlet.2010.08.013
[13] 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.
[14] 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.
[15] 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. · Zbl 1226.34069 · doi:10.1137/100794493
[16] M. A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life, The Belknap Press of Harvard University Press, Cambridge, Mass, USA, 2006. · Zbl 1115.92047
[17] 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. · Zbl 1228.92080 · doi:10.1142/S0218339011003932
[18] J. Hale, Theory of Functional Differential Equations, Springer, New York, NY, USA, 1977. · Zbl 0352.34001
[19] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, Mass, USA, 1993. · Zbl 0777.34002
[20] 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. · Zbl 0676.92013 · doi:10.1137/0149050
[21] 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. · Zbl 0833.34069 · doi:10.1006/jmaa.1995.1239
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