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https://doi.org/10.1073/pnas.1416287112
74. Yuan Y (2016) Spatial heterogeneity in the
tumor microenvironment. Cold Spring Harb
Perspect Med 6:a026583. https://doi.org/
10.1101/cshperspect.a026583
75. Liu S, Cong Y, Wang D et al (2014) Breast
cancer stem cells transition between epithelial
and mesenchymal states reflective of their normal counterparts. Stem Cell Rep 2:78–91.
https://doi.org/10.1016/j.stemcr.2013.11.
009
76. Bocci F, Gearhart-Serna L, Boareto M et al
(2019) Toward understanding cancer stem
cell heterogeneity in the tumor microenvironment. Proc Natl Acad Sci 116:148–157.
https://doi.org/10.1073/pnas.1815345116
77. Nassar D, Blanpain C (2016) Cancer stem
cells: basic concepts and therapeutic implications. Annu Rev Pathol Mech Dis 11:47–76.
https://doi.org/10.1146/annurev-pathol012615-044438
78. Mani SA, Guo W, Liao M-J et al (2008) The
epithelial-mesenchymal transition generates
cells with properties of stem cells. Cell
133:704–715.
https://doi.org/10.1016/j.
cell.2008.03.027
79. Morel A-P, Lie `vre M, Thomas C et al (2008)
Generation of breast cancer stem cells through
epithelial-mesenchymal transition. PLoS One
3:e2888. https://doi.org/10.1371/journal.
pone.0002888
80. Iliopoulos D, Hirsch HA, Wang G, 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 108:1397–1402. https://doi.
org/10.1073/pnas.1018898108
81. Yang G, Quan Y, Wang W et al (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. https://doi.
org/10.1038/bjc.2012.126
82. Wang W, Quan Y, Fu Q et al (2014) Dynamics
between cancer cell subpopulations reveals a
model coordinating with both hierarchical
and stochastic concepts. PLoS One 9:e84654.
https://doi.org/10.1371/journal.pone.
0084654
83. Gupta PB, Fillmore CM, Jiang G et al (2011)
Stochastic state transitions give rise to phenotypic equilibrium in populations of cancer cells.
Cell 146:633–644. https://doi.org/10.1016/
j.cell.2011.07.026
84. Qiu C, Ma Y, Wang J et al (2010) Lin28mediated post-transcriptional regulation of
Oct4 expression in human embryonic stem
cells. Nucleic Acids Res 38:1240–1248.
https://doi.org/10.1093/nar/gkp1071
85. Niwa H, Miyazaki J, Smith AG (2000) Quantitative expression of Oct-3/4 defines differentiation, dedifferentiation or self-renewal of ES
cells. Nat Genet 24:372–376. https://doi.
org/10.1038/74199
86. Karwacki-Neisius V, Go ¨ke J, Osorno R et al
(2013) Reduced Oct4 expression directs a
robust pluripotent state with distinct signaling
activity and increased enhancer occupancy by
Oct4 and Nanog. Cell Stem Cell 12:531–545.
https://doi.org/10.1016/j.stem.2013.04.
023
87. Shu J, Wu C, Wu Y et al (2013) Induction of
pluripotency in mouse somatic cells with lineage specifiers. Cell 153:963–975. https://doi.
org/10.1016/j.cell.2013.05.001
88. Theunissen TW, van Oosten AL, CasteloBranco G et al (2011) Nanog overcomes reprogramming barriers and induces pluripotency in
minimal conditions. Curr Biol 21:65–71.
https://doi.org/10.1016/j.cub.2010.11.074
89. Jolly MK, Jia D, Boareto M et al (2015) Coupling the modules of EMT and stemness: a
tunable “stemness window” model. Oncotarget 6:25161–25174. https://doi.org/10.
18632/oncotarget.4629
Mathematical Modelling of EMT
413