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Recasting the Cancer Stem Cell Hypothesis: Unification Using a Continuum Model of Microenvironmental Forces

  • Mathematical Models of Stem Cell Behavior (M Kohandel, Section Editor)
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Abstract

Purpose of review

Here, we identify shortcomings of standard compartment-based mathematical models of cancer stem-cells, and propose a continuous formalism which includes the tumor microenvironment.

Recent findings

Stem-cell models of tumor growth have provided explanations for various phenomena in oncology including, metastasis, drug- and radio-resistance, and functional heterogeneity in the face of genetic homogeneity. While some of the newer models allow for plasticity, or de-differentiation, there is no consensus on the mechanisms driving this. Recent experimental evidence suggests that tumor microenvironment factors like hypoxia, acidosis, and nutrient deprivation have causative roles.

Summary

To settle the dissonance between the mounting experimental evidence surrounding the effects of the microenvironment on tumor stemness, we propose a continuous mathematical model where we model microenvironmental perturbations like forces, which then shape the distribution of stemness within the tumor. We propose methods by which to systematically measure and characterize these forces, and show results of a simple experiment which support our claims.

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References

Papers of particular interest, published recently, have been highlighted as: • Of importance •• Of major importance

  1. Fialkow P, Gartler S, Yoshida A. Clonal origin of chronic myelocytic leukemia in man. Proc Natl Acad Sci USA 1967;58 :1468–71.

    Article  CAS  PubMed  Google Scholar 

  2. Bonnet D, Dick J. Human acute myeloid leukemia is organized as a hierarchy that originates from a primitive hematopoietic cell. Nat Med 1997;3:730–7.

    Article  CAS  PubMed  Google Scholar 

  3. Schepers A, et al. Lineage tracing reveals Lgr5+ stem cell activity in mouse intestinal adenomas. Science 2012; 337:730–5. https://doi.org/10.1126/science.1224676.

    Article  CAS  PubMed  Google Scholar 

  4. Singh S, Hawkins C, Clarke I, Squire J. Identification of human brain tumour initiating cells. Nature 2004;432:396–401.

    Article  CAS  Google Scholar 

  5. Al-Hajj M, Wicha M, Benito-Hernandez A, Morrison S, Clarke M. Prospective identification of tumorigenic breast cancer cells. Proc Natl Acad Sci USA 2003;100:3983–8. https://doi.org/10.1073/pnas.0530291100.

    Article  CAS  PubMed  Google Scholar 

  6. Luo Y, et al. Aldh1a isozymes are markers of human melanoma stem cells and potential therapeutic targets. Stem Cells 2012;30:2100–13. https://doi.org/10.1002/stem.1193.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Sottoriva A, Verhoeff J, Borovski T, McWeeney S. Cancer stem cell tumor model reveals invasive morphology and increased phenotypical heterogeneity. Cancer Res 2010;70:46–56.

    Article  CAS  PubMed  Google Scholar 

  8. Magee J, Piskounova E, Morrison S. Cancer stem cells: impact, heterogeneity, and uncertainty. Cancer Cell 2012;21:283–296.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  9. Dean M, Fojo T, Bates S. Tumour stem cells and drug resistance. Nat Rev Cancer 2005;5:275–84. https://doi.org/10.1016/10.1038/nrc1590.

    Article  CAS  PubMed  Google Scholar 

  10. Chen J, et al. A restricted cell population propagates glioblastoma growth after chemotherapy. Nature 2012; 488:522–526. https://doi.org/10.1038/nature11287.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Werner B, et al. The cancer stem cell fraction in hierarchically organized tumors can be estimated using mathematical modeling and patient-specific treatment trajectories. Cancer Res. 2016;76:1705–1713. In this paper, Werner et al. use a standard, compartment-based ordinary differential equations model to show how the dynamics of a leukemia under therapy can be used to identify the relative fraction of cancer stem cells. This highlights the utility of the standard models in leukemia, and the clinical data analyzed show how heterogeneous the parameters of a given patient’s underlying system can be.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Bao S, et al. Glioma stem cells promote radioresistance by preferential activation of the dna damage response. Nature 2006;444:756–60. https://doi.org/10.1038/nature05236.

    Article  CAS  PubMed  Google Scholar 

  13. Diehn M, et al. Association of reactive oxygen species levels and radioresistance in cancer stem cells. Nature 2009;458:780–783.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Dhawan A, Kohandel M, Hill R, Sivaloganathan S. Tumour control probability in cancer stem cells hypothesis. PLOS ONE 2014;9:e96093.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  15. Dingli D, Michor F. Successful therapy must eradicate cancer stem cells. Stem Cells 2006;24:2603–10. https://doi.org/10.1634/stemcells.2006-0136.

    Article  CAS  PubMed  Google Scholar 

  16. Pang R, et al. A subpopulation of CD26+ cancer stem cells with metastatic capacity in human colorectal cancer. Cell Stem Cell 2010;6:603–15. https://doi.org/10.1016/j.stem.2010.04.001.

    Article  CAS  PubMed  Google Scholar 

  17. Gupta P, Chaffer C, Weinberg R. Cancer stem cells: mirage or reality? Nat Med 2009;15:1010–2. https://doi.org/10.1038/nm0909-1010.

    Article  CAS  PubMed  Google Scholar 

  18. Shaw F, et al. A detailed mammosphere assay protocol for the quantification of breast stem cell activity. J Mammary Gland Biol Neoplasia 2012;17:111–117.

    Article  PubMed  Google Scholar 

  19. Park S, et al. Heterogeneity for stem cell-related markers according to tumor subtype and histologic stage in breast cancer. Clin Cancer Res 2010;16:876–87. https://doi.org/10.1158/1078-0432.CCR-09-1532.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Gupta P, et al. Stochastic state transitions give rise to phenotypic equilibrium in populations of cancer cells. Cell 2011;146:633–644.

    Article  CAS  PubMed  Google Scholar 

  21. Shipitsin M, Polyak K. The cancer stem cell hypothesis: in search of definitions, markers, and relevance. Lab Investig 2008;88:459–463.

    Article  CAS  PubMed  Google Scholar 

  22. Leder K, Holland E, Michor F. 2010. The therapeutic implications of plasticity of the cancer stem cell phenotype. PLOS ONE.

  23. Vermeulen L, de Sousa e Melo F, Richel D, Medema J. The developing cancer stem-cell model: clinical challenges and opportunities. Lancet Oncol 2012;13:e83–e89.

    Article  PubMed  Google Scholar 

  24. Chaffer C, et al. Normal and neoplastic nonstem cells can spontaneously convert to a stem-like state. Proc Natl Acad Sci USA 2011;108:7950–5. https://doi.org/10.1073/pnas.1102454108.

    Article  PubMed  Google Scholar 

  25. Lagadec C, Vlashi E, Della Donna L, Dekmezian C, Pajonk F. Radiation-induced reprogramming of breast cancer cells. Stem Cells 2012;30:833–44. https://doi.org/10.1002/stem.1058.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  26. Conley S, et al. Antiangiogenic agents increase breast cancer stem cells via the generation of tumor hypoxia. Proc Natl Acad Sci USA 2012;109:2784–9. https://doi.org/10.1073/pnas.1018866109.

    Article  PubMed  Google Scholar 

  27. Dhawan A, et al. 2016. Mathematical modelling of phenotypic plasticity and conversion to a stem-cell state under hypoxia. Sci Rep 6.

  28. Michor F. Mathematical models of cancer stem cells. J Clin Oncol 2008;26:2854–61. https://doi.org/10.1200/JCO.2007.15.2421.

    Article  PubMed  Google Scholar 

  29. Hoffman M, et al. 2008. Noise-driven stem cell and progenitor population dynamics. PLOS ONE 3.

  30. Doumic M, Marciniak-Czochra A, Perthame B, Zubelli J. A structured population model of cell differentiation. SIAM J Appl Math 2011;71:1918–1940.

    Article  Google Scholar 

  31. Hjelmeland A, et al. Acidic stress promotes a glioma stem cell phenotype. Cell Death Differ 2011;18:829–40. https://doi.org/10.1038/cdd.2010.150.

    Article  CAS  PubMed  Google Scholar 

  32. Vermeulen L, et al. Wnt activity defines colon cancer stem cells and is regulated by the microenvironment. Nat Cell Biol 2010;12:468–76. https://doi.org/10.1038/ncb2048.

    Article  CAS  PubMed  Google Scholar 

  33. Liu S, et al. Breast cancer stem cells are regulated by mesenchymal stem cells through cytokine networks. Cancer Res 2011 ;71:614–24. https://doi.org/10.1158/0008-5472.CAN-10-0538.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Tamura K, et al. Accumulation of CD133-positive glioma cells after high-dose irradiation by Gamma Knife surgery plus external beam radiation. J Neurosurg 2010;113:310–318.

    Article  PubMed  Google Scholar 

  35. Hu X, et al. Induction of cancer cell stemness by chemotherapy. Cell Cycle 2012; 11: 2691–8. https://doi.org/10.4161/cc.21021.

    Article  CAS  PubMed  Google Scholar 

  36. Doetsch F, Petreanu L, Caille I, Garcia-Verdugo J, Alvarez-Buylla A. EGF converts transit-amplifying neurogenic precursors in the adult brain into multipotent stem cells. Neuron 2002;36:1021–1034.

    Article  CAS  PubMed  Google Scholar 

  37. Seidel S, et al. A hypoxic niche regulates glioblastoma stem cells through hypoxia inducible factor 2 alpha. Brain 2010;133:983–95. https://doi.org/10.1093/brain/awq042.

    Article  PubMed  Google Scholar 

  38. Enderling H, et al. 2009. Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics. Cancer research :0008–5472.

  39. Lander AD, Gokoffski KK, Wan FY, Nie Q, Calof AL. Cell lineages and the logic of proliferative control. PLoS biology 2009;7:e1000015.

    Article  CAS  PubMed Central  Google Scholar 

  40. Rodriguez-Brenes IA, Komarova NL, Wodarz D. Evolutionary dynamics of feedback escape and the development of stem-cell–driven cancers. Proc Natl Acad Sci 2011;108:18983–18988.

    Article  PubMed  Google Scholar 

  41. Werner B, Lutz D, Brümmendorf TH, Traulsen A, Balabanov S. Dynamics of resistance development to imatinib under increasing selection pressure: a combination of mathematical models and in vitro data. PLoS One 2011;6:e28955.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  42. Nazari F, Pearson AT, Nör JE, Jackson TL. A mathematical model for il-6-mediated, stem cell driven tumor growth and targeted treatment. PLoS Comput Biol 2018;14:e1005920.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  43. Werner B, et al. Reconstructing the in vivo dynamics of hematopoietic stem cells from telomere length distributions. Elife 2015;4:e08687.

    Article  PubMed  PubMed Central  Google Scholar 

  44. Morton C, Hlatky L, Hahnfeldt P, Enderling H. Non-stem cancer cell kinetics modulate solid tumor progression. Theor Biol Med Model 2011;8:48. https://doi.org/10.1186/1742-4682-8-48.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Scott J, Hjelmeland A, Chinnaiyan P, Anderson A, Basanta D. Microenvironmental variables must influence intrinsic phenotypic parameters of cancer stem cells to affect tumourigenicity. PLoS Comput Biol 2014;10 (e1003433). Scott et al. show, using a stochastic agent-based model of a tumor which grows obeying the standard hierarchy, that the parameters of the model must be affected by the microenvironment to affect tumorigenicity. This result further highlights the need for heterogeneity across cells within a solid tumor to reflect clinical reality.

  46. Christensen K, Schrøder H, Kristensen B. Cd133+ niches and single cells in glioblastoma have different phenotypes. J Neurooncol 2011;104:129–43. https://doi.org/10.1007/s11060-010-0488-y.

    Article  CAS  PubMed  Google Scholar 

  47. Hambardzumyan D, Cheng Y-K, Haeno H, Holland E, Michor F. The probable cell of origin of NF1- and PDGF-driven glioblastomas. PLOS ONE 2011;6:e24454.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  48. Haeno H, Levine R, Gilliland D, Michor F. A progenitor cell origin of myeloid malignancies. Proc Natl Acad Sci USA 2009;106:16616–16621.

    Article  PubMed  Google Scholar 

  49. Liu C, et al. Mosaic analysis with double markers reveals tumor cell of origin in glioma. Cell 2011;146:209–221.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Filatova A, et al. Acidosis acts through HSP90 in a PHD/VHL-independent manner to promote HIF function and stem cell maintenance in glioma. Cancer Res 2016;76:5845–5856.

    Article  CAS  PubMed  Google Scholar 

  51. Soeda A, et al. Hypoxia promotes expansion of the CD133-positive glioma stem cells through activation of HIF-1α. Oncogene 2009;28:3949–3959.

    Article  CAS  PubMed  Google Scholar 

  52. Griguer C, et al. Cd133 is a marker of bioenergetic stress in human glioma. PLOS ONE 2008;3:e3655.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  53. Filatova A, Acker T, Garvalov B. The cancer stem cell niche(s): the crosstalk between glioma stem cells and their microenvironment. Biochim Biophys Acta 2013;1830:2496–2508.

    Article  CAS  PubMed  Google Scholar 

  54. Kolenda J, et al. Effects of hypoxia on expression of a panel of stem cell and chemoresistance markers in glioblastoma-derived spheroids. J Neurooncol 2011;103:43–58.

    Article  CAS  PubMed  Google Scholar 

  55. Anderson A, Rejniak K, Gerlee P, Quaranta V. Microenvironment driven invasion: a multiscale multimodel investigation. J Math Biol 2009;58:579–624.

    Article  PubMed  Google Scholar 

  56. Gangemi R, et al. Sox2 silencing in glioblastoma tumor-initiating cells causes stop of proliferation and loss of tumorigenicity. Stem Cells 2009;27:40–48.

    Article  CAS  PubMed  Google Scholar 

  57. Weaver V, et al. Reversion of the malignant phenotype of human breast cells in three-dimensional culture and in vivo by integrin blocking antibodies. J Cell Biol 1997;137:231–45.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  58. Codling E, Plank M, Benhamou S. Random walk models in biology. J R Soc Interface 2008;5:813–34. https://doi.org/10.1098/rsif.2008.0014.

    Article  PubMed  PubMed Central  Google Scholar 

  59. Roeder I, Lorenz R. Asymmetry of stem cell fate and the potential impact of the niche: observations, simulations, and interpretations. Stem Cell Rev 2006;2:171–80. https://doi.org/10.1016/10.1007/s12015-006-0045-4.

    Article  PubMed  Google Scholar 

  60. Sprouffske K, et al. An evolutionary explanation for the presence of cancer nonstem cells in neoplasms. Evol Appl 2013;6:92–101.

    Article  PubMed  Google Scholar 

  61. Calabrese C, et al. A perivascular niche for brain tumor stem cells. Cancer Cell 2007;11:69–82. https://doi.org/10.1016/j.ccr.2006.11.020.

    Article  CAS  PubMed  Google Scholar 

  62. Boccaccio C, Comoglio P. Invasive growth: a met-driven genetic programme for cancer and stem cells. Nat Rev Cancer 2006;6:637–645.

    Article  CAS  PubMed  Google Scholar 

  63. Hitomi M, et al. Differential connexin function enhances self-renewal in glioblastoma. Cell Rep 2015;11: 1031–1042.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  64. Hitomi M, Stacey D. Cyclin d1 production in cycling cells depends on ras in a cell-cycle-specific manner. Curr Biol 1999;9:1075–S2.

    Article  CAS  PubMed  Google Scholar 

  65. Hitomi M, Stacey D. The checkpoint kinase atm protects against stress-induced elevation of cyclin d1 and potential cell death in neurons. Cytometry Part A 2010;77:524–533.

    Article  Google Scholar 

  66. Hall P, Lathia J, Caldwell M, et al. Laminin enhances the growth of human neural stem cells in defined culture media. BMC Neurosci 2008;9:71.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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Author information

Authors and Affiliations

  1. Departments of Translational Hematology and Oncology Research and Radiation Oncology, Cleveland Clinic, Cleveland, OH, 4163, USA

    Jacob G. Scott, Andrew Dhawan & Masahiro Hitomi

  2. Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, UK

    Jacob G. Scott & Philip K. Maini

  3. Department of Oncology, University of Oxford, Oxford, UK

    Andrew Dhawan

  4. Department of Cell, Developmental and Integrative Biology, University of Alabama, Birmingham, AL, 35487, USA

    Anita Hjelmeland

  5. Department of Cellular and Molecular Medicine, Lerner Research Institute, Cleveland Clinic, Cleveland, OH, USA

    Justin Lathia, Anastasia Chumakova & Masahiro Hitomi

  6. School of Mathematics and Statistics, University of Sheffield, Sheffield, UK

    Alexander G. Fletcher

  7. Bateson Centre, University of Sheffield, Sheffield, UK

    Alexander G. Fletcher

  8. Department of Integrated Mathematical Oncology, Moffitt Cancer Center and Research Institute, Tampa, FL, USA

    Alexander R. A. Anderson

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  1. Jacob G. Scott
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  2. Andrew Dhawan
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  3. Anita Hjelmeland
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  9. Alexander R. A. Anderson
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Correspondence to Alexander R. A. Anderson.

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Scott, J.G., Dhawan, A., Hjelmeland, A. et al. Recasting the Cancer Stem Cell Hypothesis: Unification Using a Continuum Model of Microenvironmental Forces. Curr Stem Cell Rep 5, 22–30 (2019). https://doi.org/10.1007/s40778-019-0153-0

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