Cancer stem cells: small subpopulation or evolving fraction?

Central to the debate about cancer stem cells in solid tumors is the proportion of cells that can initiate, propagate, and re-initiate tumors. An initially assumed minor subpopulation is confronted with recent data suggesting as many as 30% of primary tumor cells have stem cell characteristics. This review discusses quantitative modeling studies that augment our understanding of stem and non-stem cancer cell interactions during tumor progression and the resulting fraction of cancer stem cells. A discussion of how these findings can be carefully evaluated in novel, integrated interdisciplinary studies is offered.

[1]  Edward Kai-Hua Chow,et al.  Mechanisms of chemoresistance in cancer stem cells , 2013, Clinical and Translational Medicine.

[2]  J. Dick,et al.  Human acute myeloid leukemia is organized as a hierarchy that originates from a primitive hematopoietic cell , 1997, Nature Medicine.

[3]  J. Visvader,et al.  Cancer stem cells: current status and evolving complexities. , 2012, Cell stem cell.

[4]  Mario Moisés Álvarez,et al.  A Simple Mathematical Model Based on the Cancer Stem Cell Hypothesis Suggests Kinetic Commonalities in Solid Tumor Growth , 2012, PloS one.

[5]  L. Hlatky,et al.  Acute and fractionated irradiation differentially modulate glioma stem cell division kinetics. , 2013, Cancer research.

[6]  R. Weinberg,et al.  Cancer stem cells: mirage or reality? , 2009, Nature Medicine.

[7]  S. McWeeney,et al.  Cancer stem cell tumor model reveals invasive morphology and increased phenotypical heterogeneity. , 2010, Cancer research.

[8]  Philip Hahnfeldt,et al.  A Multicompartment Mathematical Model of Cancer Stem Cell-Driven Tumor Growth Dynamics , 2014, Bulletin of mathematical biology.

[9]  R. McLendon,et al.  Distribution of CD133 reveals glioma stem cells self-renew through symmetric and asymmetric cell divisions , 2011, Cell Death and Disease.

[10]  P. Sloot,et al.  Exploring cancer stem cell niche directed tumor growth , 2010, Cell cycle.

[11]  K. Rudolph,et al.  Telomeres and telomerase in cancer stem cells. , 2006, European journal of cancer.

[12]  J. Visvader,et al.  Cancer stem cells in solid tumours: accumulating evidence and unresolved questions , 2008, Nature Reviews Cancer.

[13]  C. Greider,et al.  Telomerase and cancer stem cells. , 2005, Cold Spring Harbor symposia on quantitative biology.

[14]  J S Spratt,et al.  Decelerating growth and human breast cancer , 1993, Cancer.

[15]  Simon Tavaré,et al.  Modeling Evolutionary Dynamics of Epigenetic Mutations in Hierarchically Organized Tumors , 2011, PLoS Comput. Biol..

[16]  T. Sharpee,et al.  Mathematical approaches to modeling development and reprogramming , 2014, Proceedings of the National Academy of Sciences.

[17]  Q. Nie,et al.  Nonlinear Growth Kinetics of Breast Cancer Stem Cells: Implications for Cancer Stem Cell Targeted Therapy , 2013, Scientific Reports.

[18]  G. Landberg,et al.  Wnt Pathway Activity in Breast Cancer Sub-Types and Stem-Like Cells , 2013, PloS one.

[19]  R T Prehn,et al.  The inhibition of tumor growth by tumor mass. , 1991, Cancer research.

[20]  C. Maley,et al.  Preneoplastic lesion growth driven by the death of adjacent normal stem cells , 2008, Proceedings of the National Academy of Sciences.

[21]  E. Castellón,et al.  Functional characteristics of cancer stem cells and their role in drug resistance of prostate cancer , 2014, International journal of oncology.

[22]  H. Enderling.  Cancer stem cells and tumor dormancy. , 2013, Advances in experimental medicine and biology.

[23]  J. Folkman,et al.  SELF-REGULATION OF GROWTH IN THREE DIMENSIONS , 1973, The Journal of experimental medicine.

[24]  C. Heeschen,et al.  Distinct populations of cancer stem cells determine tumor growth and metastatic activity in human pancreatic cancer. , 2007, Cell stem cell.

[25]  G. Koren,et al.  Hypoxia Enhances Tumor Stemness by Increasing the Invasive and Tumorigenic Side Population Fraction , 2008, Stem cells.

[26]  Jian Yang,et al.  A 3D multiscale model of cancer stem cell in tumor development , 2013, BMC Systems Biology.

[27]  Arne Traulsen,et al.  (A)Symmetric Stem Cell Replication and Cancer , 2007, PLoS Comput. Biol..

[28]  L. Ricci-Vitiani,et al.  Identification and expansion of human colon-cancer-initiating cells , 2007, Nature.

[29]  R. Bhatia,et al.  Stem Cell Quiescence , 2011, Clinical Cancer Research.

[30]  Leonard I. Zon,et al.  Intrinsic and extrinsic control of haematopoietic stem-cell self-renewal , 2008, Nature.

[31]  Loic Deleyrolle,et al.  The Cancer Stem Cell Hypothesis: Failures and Pitfalls , 2011, Neurosurgery.

[32]  S. Yamanaka,et al.  Induction of Pluripotent Stem Cells from Mouse Embryonic and Adult Fibroblast Cultures by Defined Factors , 2006, Cell.

[33]  Kevin Burrage,et al.  Determination of Somatic and Cancer Stem Cell Self-Renewing Symmetric Division Rate Using Sphere Assays , 2011, PloS one.

[34]  W. Bodmer,et al.  Failure of programmed cell death and differentiation as causes of tumors: some simple mathematical models. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Philip K Maini,et al.  On the proportion of cancer stem cells in a tumour. , 2010, Journal of theoretical biology.

[36]  L. Postovit,et al.  Microenvironmental regulation of cancer stem cell phenotypes. , 2012, Current stem cell research & therapy.

[37]  J. Gordon,et al.  The intestinal stem cell niche: There grows the neighborhood , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[38]  Yuri Kogan,et al.  Strategies for cancer stem cell elimination: insights from mathematical modeling. , 2012, Journal of theoretical biology.

[39]  Mauro Ferrari,et al.  Multiparameter computational modeling of tumor invasion. , 2009, Cancer research.

[40]  N. Maitland,et al.  Prospective identification of tumorigenic prostate cancer stem cells. , 2005, Cancer research.

[41]  J. Dick,et al.  A human colon cancer cell capable of initiating tumour growth in immunodeficient mice , 2007, Nature.

[42]  J. Till,et al.  Cytological Demonstration of the Clonal Nature of Spleen Colonies Derived from Transplanted Mouse Marrow Cells , 1963, Nature.

[43]  M. Kohandel,et al.  Quantitative approaches to cancer stem cells and epithelial-mesenchymal transition. , 2012, Seminars in cancer biology.

[44]  Larry Norton,et al.  Is cancer a disease of self-seeding? , 2006, Nature Medicine.

[45]  Martin A. Nowak,et al.  Dynamics of chronic myeloid leukaemia , 2005, Nature.

[46]  R. Jain,et al.  Solid stress generated by spheroid growth estimated using a linear poroelasticity model. , 2003, Microvascular research.

[47]  Haiyang Huang,et al.  Identification of the haematopoietic stem cell niche and control of the niche size , 2003, Nature.

[48]  Ignacio A. Rodriguez-Brenes,et al.  Evolutionary dynamics of feedback escape and the development of stem-cell–driven cancers , 2011, Proceedings of the National Academy of Sciences.

[49]  Jane E. Visvader,et al.  Cells of origin in cancer , 2011, Nature.

[50]  A. Gazdar,et al.  Demonstration of the stem cell nature of clonogenic tumor cells from lung cancer patients. , 1982, Stem cells.

[51]  Sylvain V Costes,et al.  Irradiation of Juvenile, but not Adult, Mammary Gland Increases Stem Cell Self‐Renewal and Estrogen Receptor Negative Tumors , 2014, Stem cells.

[52]  C. Waddington.  The strategy of the genes , 1957 .

[53]  Lei Wang,et al.  Bistable switches control memory and plasticity in cellular differentiation , 2009, Proceedings of the National Academy of Sciences.

[54]  Andrew E. Sloan,et al.  Brain Tumor Initiating Cells Adapt to Restricted Nutrition through Preferential Glucose Uptake , 2013, Nature Neuroscience.

[55]  R. Ganguly,et al.  Mathematical model for the cancer stem cell hypothesis , 2006, Cell proliferation.

[56]  R. Poulsom,et al.  Adult stem cell plasticity , 2002, The Journal of pathology.

[57]  S. Fuchs,et al.  The Neural Crest: Understanding Stem Cell Function in Development and Disease , 2007, Neurodegenerative Diseases.

[58]  A. Prokop,et al.  Modeling the Cancer Stem Cell Hypothesis , 2010 .

[59]  Irving L Weissman,et al.  Plasticity of Adult Stem Cells , 2004, Cell.

[60]  Aleksandar Dakic,et al.  Tumor Growth Need Not Be Driven by Rare Cancer Stem Cells , 2007, Science.

[61]  Larry Norton,et al.  Cancer stem cells, self-seeding, and decremented exponential growth: theoretical and clinical implications. , 2008, Breast disease.

[62]  E. Blackburn,et al.  A tandemly repeated sequence at the termini of the extrachromosomal ribosomal RNA genes in Tetrahymena. , 1978, Journal of molecular biology.

[63]  Christopher J. Jones,et al.  Telomere erosion triggers growth arrest but not cell death in human cancer cells retaining wild-type p53: implications for antitelomerase therapy , 2004, Oncogene.

[64]  Carol W. Greider,et al.  Identification of a specific telomere terminal transferase activity in tetrahymena extracts , 1985, Cell.

[65]  Zheng Sun,et al.  Stochastic modeling of stem-cell dynamics with control. , 2012, Mathematical biosciences.

[66]  R. Stupp,et al.  Targeting brain-tumor stem cells , 2007, Nature Biotechnology.

[67]  Hans Clevers,et al.  Crypt stem cells as the cells-of-origin of intestinal cancer , 2009, Nature.

[68]  Franziska Michor,et al.  Successful Therapy Must Eradicate Cancer Stem Cells , 2006, Stem cells.

[69]  Franziska Michor,et al.  Mathematical models of cancer stem cells. , 2008, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[70]  S. Morrison,et al.  Heterogeneity in Cancer: Cancer Stem Cells versus Clonal Evolution , 2009, Cell.

[71]  Wenjun Guo,et al.  The Epithelial-Mesenchymal Transition Generates Cells with Properties of Stem Cells , 2008, Cell.

[72]  Min-Jung Kim,et al.  Importance of PKCδ signaling in fractionated-radiation-induced expansion of glioma-initiating cells and resistance to cancer treatment , 2011, Journal of Cell Science.

[73]  Trachette L. Jackson,et al.  Pathways to tumorigenesis--modeling mutation acquisition in stem cells and their progeny. , 2008, Neoplasia.

[74]  Nick Jagiella,et al.  Estimating Dose Painting Effects in Radiotherapy: A Mathematical Model , 2014, PloS one.

[75]  H. Othmer,et al.  Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology , 1997 .

[76]  S. Morrison,et al.  Prospective identification of tumorigenic breast cancer cells , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[77]  Benjamin Gompertz,et al.  XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. F. R. S. &c , 1825, Philosophical Transactions of the Royal Society of London.

[78]  P Hahnfeldt,et al.  Migration rules: tumours are conglomerates of self-metastases , 2009, British Journal of Cancer.

[79]  R. Henkelman,et al.  Identification of human brain tumour initiating cells , 2004, Nature.

[80]  W. McBride,et al.  Radiation Resistance of Cancer Stem Cells: The 4 R's of Radiobiology Revisited , 2010, Stem cells.

[81]  D. Wodarz.  Effect of stem cell turnover rates on protection against cancer and aging. , 2007, Journal of theoretical biology.

[82]  Cynthia Hawkins,et al.  Identification of a cancer stem cell in human brain tumors. , 2003, Cancer research.

[83]  Michael Dean,et al.  Tumour stem cells and drug resistance , 2005, Nature Reviews Cancer.

[84]  Mark W. Dewhirst,et al.  Glioma stem cells promote radioresistance by preferential activation of the DNA damage response , 2006, Nature.

[85]  M. Chaplain,et al.  Mathematical modeling of tumor growth and treatment. , 2014, Current pharmaceutical design.

[86]  Michael Cross,et al.  Lineage Specification of Hematopoietic Stem Cells: Mathematical Modeling and Biological Implications , 2007, Stem cells.

[87]  A. Anderson,et al.  A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion , 2005 .

[88]  David Basanta,et al.  Microenvironmental Variables Must Influence Intrinsic Phenotypic Parameters of Cancer Stem Cells to Affect Tumourigenicity , 2013, bioRxiv.

[89]  B. Ross,et al.  Mathematical Modeling of PDGF-Driven Glioblastoma Reveals Optimized Radiation Dosing Schedules , 2014, Cell.

[90]  M. Chaplain,et al.  Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics. , 2009, Cancer research.

[91]  G. Dontu,et al.  Stem cells in mammary development and carcinogenesis , 2007, Stem Cell Reviews.

[92]  J. Campisi,et al.  Cellular senescence, cancer and aging: the telomere connection , 2001, Experimental Gerontology.

[93]  P. Hahnfeldt,et al.  Cancer Stem Cells: A Minor Cancer Subpopulation that Redefines Global Cancer Features , 2013, Front. Oncol..

[94]  P. Hahnfeldt,et al.  A Proposed Quantitative Index for Assessing the Potential Contribution of Reprogramming to Cancer Stem Cell Kinetics , 2014, Stem cells international.

[95]  J. Freyer,et al.  Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply. , 1986, Cancer research.

[96]  R. McLendon,et al.  Acidic stress promotes a glioma stem cell phenotype , 2011, Cell Death and Differentiation.

[97]  S. Morrison,et al.  Efficient tumor formation by single human melanoma cells , 2008, Nature.

[98]  Arthur D Lander.  The 'stem cell' concept: is it holding us back? , 2009, Journal of biology.

[99]  P. Hahnfeldt.  The host support niche as a control point for tumor dormancy: implications for tumor development and beyond. , 2013, Advances in experimental medicine and biology.

[100]  P. Maini,et al.  Mathematical modeling of cell population dynamics in the colonic crypt and in colorectal cancer , 2007, Proceedings of the National Academy of Sciences.

[101]  R. Levine,et al.  A progenitor cell origin of myeloid malignancies , 2009, Proceedings of the National Academy of Sciences.

[102]  Hans Clevers,et al.  Paneth cells constitute the niche for Lgr5 stem cells in intestinal crypts , 2011, Nature.

[103]  M. Curtis,et al.  Locating and labeling neural stem cells in the brain , 2011, Journal of cellular physiology.

[104]  Philip Hahnfeldt,et al.  Non-stem cancer cell kinetics modulate solid tumor progression , 2011, Theoretical Biology and Medical Modelling.

[105]  Larry Norton,et al.  Conceptual and practical implications of breast tissue geometry: toward a more effective, less toxic therapy. , 2005, The oncologist.

[106]  Yuval Ginosar,et al.  The universal properties of stem cells as pinpointed by a simple discrete model , 2002, Journal of mathematical biology.

[107]  J. Lowengrub,et al.  Multispecies model of cell lineages and feedback control in solid tumors. , 2012, Journal of theoretical biology.

[108]  M. Rudnicki,et al.  Niche regulation of muscle satellite cell self-renewal and differentiation. , 2008, Cell stem cell.

[109]  Ollivier Hyrien,et al.  A comprehensive stochastic model of irradiated cell populations in culture. , 2006, Journal of theoretical biology.

[110]  J. Shay,et al.  Role of telomeres and telomerase in cancer. , 2011, Seminars in cancer biology.

[111]  Philip Hahnfeldt,et al.  The Tumor Growth Paradox and Immune System-Mediated Selection for Cancer Stem Cells , 2013, Bulletin of mathematical biology.

[112]  Yuri Kogan,et al.  Dickkopf1 Regulates Fate Decision and Drives Breast Cancer Stem Cells to Differentiation: An Experimentally Supported Mathematical Model , 2011, PloS one.

[113]  A. Brú,et al.  The universal dynamics of tumor growth. , 2003, Biophysical journal.

[114]  E. Holland,et al.  The Probable Cell of Origin of NF1- and PDGF-Driven Glioblastomas , 2011, PloS one.

[115]  Trachette L. Jackson,et al.  A Mathematical Model of Cancer Stem Cell Driven Tumor Initiation: Implications of Niche Size and Loss of Homeostatic Regulatory Mechanisms , 2013, PloS one.

[116]  Max S Wicha,et al.  Cancer stem cells: an old idea--a paradigm shift. , 2006, Cancer research.

[117]  Benjamin D. Simons,et al.  Defining the mode of tumour growth by clonal analysis , 2012, Nature.

[118]  S. Kern,et al.  The fuzzy math of solid tumor stem cells: a perspective. , 2007, Cancer research.

[119]  T. Yang,et al.  Cancer stem cells: constantly evolving and functionally heterogeneous therapeutic targets. , 2014, Cancer research.

[120]  F. Pajonk,et al.  Characterization of the stem cell niche and its importance in radiobiological response. , 2013, Seminars in radiation oncology.

[121]  Philip Hahnfeldt,et al.  Simple ODE models of tumor growth and anti-angiogenic or radiation treatment , 2001 .

[122]  Z. Agur,et al.  The growth law of primary breast cancer as inferred from mammography screening trials data. , 1998, British Journal of Cancer.

[123]  L. Vermeulen,et al.  Regulation of stem cell self-renewal and differentiation by Wnt and Notch are conserved throughout the adenoma-carcinoma sequence in the colon , 2013, Molecular Cancer.

[124]  William E. Boyce.  Case studies in mathematical modeling , 1981 .

[125]  U. Rapp,et al.  Oncogene-induced plasticity and cancer stem cells , 2008, Cell cycle.

[126]  J. Jun,et al.  Long-Term Sphere Culture Cannot Maintain a High Ratio of Cancer Stem Cells: A Mathematical Model and Experiment , 2011, PloS one.

[127]  B. Boman,et al.  Computer modeling implicates stem cell overproduction in colon cancer initiation. , 2001, Cancer research.

[128]  S. Morrison,et al.  Tumorigenic cells are common in mouse MPNSTs but their frequency depends upon tumor genotype and assay conditions. , 2012, Cancer cell.

[129]  A M Olovnikov,et al.  A theory of marginotomy. The incomplete copying of template margin in enzymic synthesis of polynucleotides and biological significance of the phenomenon. , 1973, Journal of theoretical biology.

[130]  R. Barker,et al.  Stem cells and neurological disease , 2003, Journal of neurology, neurosurgery, and psychiatry.

[131]  M. Barcellos-Hoff.  It Takes a Tissue to Make a Tumor: Epigenetics, Cancer and the Microenvironment , 2001, Journal of Mammary Gland Biology and Neoplasia.

[132]  K. Musunuru,et al.  Stem cell models of cardiac development and disease. , 2010, Annual review of cell and developmental biology.

[133]  Anna K. Marciniak-Czochra,et al.  Characterization of stem cells using mathematical models of multistage cell lineages , 2011, Math. Comput. Model..

[134]  K. Makino,et al.  New Treatment Strategies to Eradicate Cancer Stem Cells and Niches in Glioblastoma , 2013, Neurologia medico-chirurgica.

[135]  J. Laterra,et al.  Cancer stem cells: distinct entities or dynamically regulated phenotypes? , 2012, Cancer research.

[136]  B. Neel,et al.  Phenotypic heterogeneity and instability of human ovarian tumor-initiating cells , 2011, Proceedings of the National Academy of Sciences.