# American Institute of Mathematical Sciences

September  2016, 21(7): 2275-2291. doi: 10.3934/dcdsb.2016047

## Controlling stochasticity in epithelial-mesenchymal transition through multiple intermediate cellular states

 1 Department of Mathematics, Univ. of California Irvine, Irvine, CA 92697-3875, United States, United States 2 Department of mathematics, University of California, CA, 92697-3875

Received  February 2016 Revised  May 2016 Published  August 2016

Epithelial-mesenchymal transition (EMT) is an instance of cellular plasticity that plays critical roles in development, regeneration and cancer progression. Recent studies indicate that the transition between epithelial and mesenchymal states is a multi-step and reversible process in which several intermediate phenotypes might coexist. These intermediate states correspond to various forms of stem-like cells in the EMT system, but the function of the multi-step transition or the multiple stem cell phenotypes is unclear. Here, we use mathematical models to show that multiple intermediate phenotypes in the EMT system help to attenuate the overall fluctuations of the cell population in terms of phenotypic compositions, thereby stabilizing a heterogeneous cell population in the EMT spectrum. We found that the ability of the system to attenuate noise on the intermediate states depends on the number of intermediate states, indicating the stem-cell population is more stable when it has more sub-states. Our study reveals a novel advantage of multiple intermediate EMT phenotypes in terms of systems design, and it sheds light on the general design principle of heterogeneous stem cell population.
Citation: Catherine Ha Ta, Qing Nie, Tian Hong. Controlling stochasticity in epithelial-mesenchymal transition through multiple intermediate cellular states. Discrete and Continuous Dynamical Systems - B, 2016, 21 (7) : 2275-2291. doi: 10.3934/dcdsb.2016047
##### References:
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Wang and C. C. Liu, et al., Noise attenuation in the ON and OFF states of biological switches, ACS Synth Biol, 2 (2013), 587-593. doi: 10.1021/sb400044g. [7] S. Di Talia, J. M. Skotheim and J. M. Bean, et al., The effects of molecular noise and size control on variability in the budding yeast cell cycle, Nature, 448 (2007), 947-951. doi: 10.1038/nature06072. [8] S. Gaudet, S. L. Spencer and W. W. Chen, et al., Exploring the contextual sensitivity of factors that determine cell-to-cell variability in receptor-mediated apoptosis, PLoS Comput Biol, 8 (2012), e1002482. doi: 10.1371/journal.pcbi.1002482. [9] A. Grosse-Wilde, A. Fouquier d'Herouel and E. McIntosh, et al., Stemness of the hybrid epithelial/mesenchymal state in breast cancer and its association with poor survival, PLoS One, 10 (2015), e0126522. doi: 10.1371/journal.pone.0126522. [10] Y. Hart, Y. E. Antebi and A. E. Mayo, et al., Design principles of cell circuits with paradoxical components, Proc Natl Acad Sci U S A, 109 (2012), 8346-8351. doi: 10.1073/pnas.1117475109. [11] K. Hayashi, S. de Sousa Lopes and F. Tang, et al., Dynamic equilibrium and heterogeneity of mouse pluripotent stem cells with distinct functional and epigenetic states, Cell Stem Cell, 3 (2008), 391-401. doi: 10.1016/j.stem.2008.07.027. [12] T. Hong, K. Watanabe and C. Ta, et al., An ovol2-zeb1 mutual inhibitory circuit governs bidirectional and multi-step transition between epithelial and mesenchymal states, PLoS Comput Biol, 11 (2015), e1004569. doi: 10.1371/journal.pcbi.1004569. [13] T. Hong, C. Oguz and J. J. Tyson, A mathematical framework for understanding four-dimensional heterogeneous differentiation of CD4+ T cells, Bulletin of Mathematical Biology, 77 (2015), 1046-1064. doi: 10.1007/s11538-015-0076-6. [14] R. Y. Huang, M. K. Wong and T. Z. Tan, et al., An EMT spectrum defines an anoikis-resistant and spheroidogenic intermediate mesenchymal state that is sensitive to e-cadherin restoration by a src-kinase inhibitor, saracatinib (AZD0530), Cell Death Dis, 4 (2013), e915. doi: 10.1038/cddis.2013.442. [15] M. K. Jolly, D. Jia and M. Boareto, et al., Coupling the modules of EMT and stemness: A tunable 'stemness window' model, Oncotarget, 6 (2015), 25161-25174. doi: 10.18632/oncotarget.4629. [16] R. Kalluri and R. A. Weinberg, The basics of epithelial-mesenchymal transition, The Journal of Clinical Investigation, 119 (2009), 1420-1428. [17] J. Keizer, Statistical Thermodynamics of Nonequilibrium Processes, Springer-Verlag, 1987. doi: 10.1007/978-1-4612-1054-2. [18] R. Kubo, The fluctuation-dissipation theorem, Reports on Progress in Physics, 29 (1966), 255-284. doi: 10.1088/0034-4885/29/1/306. [19] D. A. Lawson, N. R. Bhakta and K. Kessenbrock, et al., Single-cell analysis reveals a stem-cell program in human metastatic breast cancer cells, Nature, 526 (2015), 131-135. doi: 10.1038/nature15260. [20] J. Lei, S. A. Levin and Q. Nie, Mathematical model of adult stem cell regeneration with cross-talk between genetic and epigenetic regulation, Proc Natl Acad Sci U S A, 111 (2014), E880-E887. doi: 10.1073/pnas.1324267111. [21] W. A. Lim, C. M. Lee and C. Tang, Design principles of regulatory networks: Searching for the molecular algorithms of the cell, Mol Cell, 49 (2013), 202-212. doi: 10.1016/j.molcel.2012.12.020. [22] X. Liu, S. Johnson and S. Liu, et al., Nonlinear Growth Kinetics of Breast Cancer Stem Cells: Implications for Cancer Stem Cell Targeted Therapy, Sci Rep, 2013. [23] W. C. Lo, C. S. Chou and K. K. Gokoffski, et al., Feedback regulation in multistage cell lineages, Math Biosci Eng, 6 (2009), 59-82. doi: 10.3934/mbe.2009.6.59. [24] M. Lu, M. K. Jolly and H. Levine, et al., MicroRNA-based regulation of epithelial-hybrid-mesenchymal fate determination, Proc Natl Acad Sci U S A, 110 (2013), 18144-18149. doi: 10.1073/pnas.1318192110. [25] S. A. Mani, W. Guo and M. J. Liao, et al., The epithelial-mesenchymal transition generates cells with properties of stem cells, Cell, 133 (2008), 704-715. doi: 10.1016/j.cell.2008.03.027. [26] K. V. Price, R. M. Storn and J. A. Lampinen, Differential Evolution: A Practical Approach to Global Optimization, Springer, Berlin, 2005. [27] Y. Shen, C. Shi and W. Wei, et al., The heterogeneity and dynamic equilibrium of rat embryonic stem cells, Cell Res, 21 (2011), 1143-1147. doi: 10.1038/cr.2011.98. [28] M. S. Sosa, P. Bragado and J. A. Aguirre-Ghiso, Mechanisms of disseminated cancer cell dormancy: An awakening field, Nat Rev Cancer, 14 (2014), 611-622. doi: 10.1038/nrc3793. [29] W. L. Tam and R. A. Weinberg, The epigenetics of epithelial-mesenchymal plasticity in cancer, Nature Medicine, 19 (2013), 1438-1449. doi: 10.1038/nm.3336. [30] X. J. Tian, H. Zhang and J. Xing, Coupled reversible and irreversible bistable switches underlying TGF-$\beta$-induced epithelial to mesenchymal transition, Biophysical journal, 105 (2013), 1079-1089. [31] J. J. Tyson and B. Novak, Functional motifs in biochemical reaction networks, Annu Rev Phys Chem, 61 (2010), 219-240. doi: 10.1146/annurev.physchem.012809.103457. [32] N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, $3^{rd}$ edition, Elsevier, Amsterdam, 2007. [33] L. Wang, J. Xin and Q. Nie, A critical quantity for noise attenuation in feedback systems, PLoS Comput Biol, 6 (2010), e1000764, 17 pp. doi: 10.1371/journal.pcbi.1000764. [34] W. Weston, J. Zayas and R. Perez, et al., Dynamic equilibrium of heterogeneous and interconvertible multipotent hematopoietic cell subsets, Sci Rep, 4 (2014), 5199. doi: 10.1038/srep05199. [35] X. Ye, W. L. Tam and T. Shibue, et al., Distinct EMT programs control normal mammary stem cells and tumour-initiating cells, Nature, 525 (2015), 256-260. doi: 10.1038/nature14897. [36] J. Zhang, X. J. Tian and H. Zhang, et al., TGF-$\beta$-induced Epithelial-To-Mesenchymal Transition Proceeds Through Stepwise Activation of Multiple Feedback Loops, Science Signaling, 2014. [37] L. Zheng, M. Chen and Q. Nie, External noise control in inherently stochastic biological systems, J Math Phys, 53 (2012), 115616, 13 pp. doi: 10.1063/1.4762825. [38] , Differential Evolution (DE) for Continuous Function Optimization (an algorithm by Kenneth Price and Rainer Storn),, Accessed in May 2016. Available from: , (2016).

show all references

##### References:
 [1] J. Baulida and A. Garcia de Herreros, Snail1-driven plasticity of epithelial and mesenchymal cells sustains cancer malignancy, Biochim Biophys Acta, 1856 (2015), 55-61. doi: 10.1016/j.bbcan.2015.05.005. [2] T. Brabletz, A. Jung and S. Reu, et al., Variable beta-catenin expression in colorectal cancers indicates tumor progression driven by the tumor environment, Proc Natl Acad Sci U S A, 98 (2001), 10356-10361. [3] A. Q. Cai, K. Radtke and A. Linville, et al., Cellular retinoic acid-binding proteins are essential for hindbrain patterning and signal robustness in zebrafish, Development, 139 (2012), 2150-2155. doi: 10.1242/dev.077065. [4] H. H. Chang, M. Hemberg and M. Barahona, et al., Transcriptome-wide noise controls lineage choice in mammalian progenitor cells, Nature, 453 (2008), 544-547. doi: 10.1038/nature06965. [5] J. Chen, Q. Han and D. Pei, EMT and MET as paradigms for cell fate switching, J Mol Cell Biol, 4 (2012), 66-69. doi: 10.1093/jmcb/mjr045. [6] M. Chen, L. Wang and C. C. Liu, et al., Noise attenuation in the ON and OFF states of biological switches, ACS Synth Biol, 2 (2013), 587-593. doi: 10.1021/sb400044g. [7] S. Di Talia, J. M. Skotheim and J. M. Bean, et al., The effects of molecular noise and size control on variability in the budding yeast cell cycle, Nature, 448 (2007), 947-951. doi: 10.1038/nature06072. [8] S. Gaudet, S. L. Spencer and W. W. Chen, et al., Exploring the contextual sensitivity of factors that determine cell-to-cell variability in receptor-mediated apoptosis, PLoS Comput Biol, 8 (2012), e1002482. doi: 10.1371/journal.pcbi.1002482. [9] A. Grosse-Wilde, A. Fouquier d'Herouel and E. McIntosh, et al., Stemness of the hybrid epithelial/mesenchymal state in breast cancer and its association with poor survival, PLoS One, 10 (2015), e0126522. doi: 10.1371/journal.pone.0126522. [10] Y. Hart, Y. E. Antebi and A. E. Mayo, et al., Design principles of cell circuits with paradoxical components, Proc Natl Acad Sci U S A, 109 (2012), 8346-8351. doi: 10.1073/pnas.1117475109. [11] K. Hayashi, S. de Sousa Lopes and F. Tang, et al., Dynamic equilibrium and heterogeneity of mouse pluripotent stem cells with distinct functional and epigenetic states, Cell Stem Cell, 3 (2008), 391-401. doi: 10.1016/j.stem.2008.07.027. [12] T. Hong, K. Watanabe and C. Ta, et al., An ovol2-zeb1 mutual inhibitory circuit governs bidirectional and multi-step transition between epithelial and mesenchymal states, PLoS Comput Biol, 11 (2015), e1004569. doi: 10.1371/journal.pcbi.1004569. [13] T. Hong, C. Oguz and J. J. Tyson, A mathematical framework for understanding four-dimensional heterogeneous differentiation of CD4+ T cells, Bulletin of Mathematical Biology, 77 (2015), 1046-1064. doi: 10.1007/s11538-015-0076-6. [14] R. Y. Huang, M. K. Wong and T. Z. Tan, et al., An EMT spectrum defines an anoikis-resistant and spheroidogenic intermediate mesenchymal state that is sensitive to e-cadherin restoration by a src-kinase inhibitor, saracatinib (AZD0530), Cell Death Dis, 4 (2013), e915. doi: 10.1038/cddis.2013.442. [15] M. K. Jolly, D. Jia and M. Boareto, et al., Coupling the modules of EMT and stemness: A tunable 'stemness window' model, Oncotarget, 6 (2015), 25161-25174. doi: 10.18632/oncotarget.4629. [16] R. Kalluri and R. A. Weinberg, The basics of epithelial-mesenchymal transition, The Journal of Clinical Investigation, 119 (2009), 1420-1428. [17] J. Keizer, Statistical Thermodynamics of Nonequilibrium Processes, Springer-Verlag, 1987. doi: 10.1007/978-1-4612-1054-2. [18] R. Kubo, The fluctuation-dissipation theorem, Reports on Progress in Physics, 29 (1966), 255-284. doi: 10.1088/0034-4885/29/1/306. [19] D. A. Lawson, N. R. Bhakta and K. Kessenbrock, et al., Single-cell analysis reveals a stem-cell program in human metastatic breast cancer cells, Nature, 526 (2015), 131-135. doi: 10.1038/nature15260. [20] J. Lei, S. A. Levin and Q. Nie, Mathematical model of adult stem cell regeneration with cross-talk between genetic and epigenetic regulation, Proc Natl Acad Sci U S A, 111 (2014), E880-E887. doi: 10.1073/pnas.1324267111. [21] W. A. Lim, C. M. Lee and C. Tang, Design principles of regulatory networks: Searching for the molecular algorithms of the cell, Mol Cell, 49 (2013), 202-212. doi: 10.1016/j.molcel.2012.12.020. [22] X. Liu, S. Johnson and S. Liu, et al., Nonlinear Growth Kinetics of Breast Cancer Stem Cells: Implications for Cancer Stem Cell Targeted Therapy, Sci Rep, 2013. [23] W. C. Lo, C. S. Chou and K. K. Gokoffski, et al., Feedback regulation in multistage cell lineages, Math Biosci Eng, 6 (2009), 59-82. doi: 10.3934/mbe.2009.6.59. [24] M. Lu, M. K. Jolly and H. Levine, et al., MicroRNA-based regulation of epithelial-hybrid-mesenchymal fate determination, Proc Natl Acad Sci U S A, 110 (2013), 18144-18149. doi: 10.1073/pnas.1318192110. [25] S. A. Mani, W. Guo and M. J. Liao, et al., The epithelial-mesenchymal transition generates cells with properties of stem cells, Cell, 133 (2008), 704-715. doi: 10.1016/j.cell.2008.03.027. [26] K. V. Price, R. M. Storn and J. A. Lampinen, Differential Evolution: A Practical Approach to Global Optimization, Springer, Berlin, 2005. [27] Y. Shen, C. Shi and W. Wei, et al., The heterogeneity and dynamic equilibrium of rat embryonic stem cells, Cell Res, 21 (2011), 1143-1147. doi: 10.1038/cr.2011.98. [28] M. S. Sosa, P. Bragado and J. A. Aguirre-Ghiso, Mechanisms of disseminated cancer cell dormancy: An awakening field, Nat Rev Cancer, 14 (2014), 611-622. doi: 10.1038/nrc3793. [29] W. L. Tam and R. A. Weinberg, The epigenetics of epithelial-mesenchymal plasticity in cancer, Nature Medicine, 19 (2013), 1438-1449. doi: 10.1038/nm.3336. [30] X. J. Tian, H. Zhang and J. Xing, Coupled reversible and irreversible bistable switches underlying TGF-$\beta$-induced epithelial to mesenchymal transition, Biophysical journal, 105 (2013), 1079-1089. [31] J. J. Tyson and B. Novak, Functional motifs in biochemical reaction networks, Annu Rev Phys Chem, 61 (2010), 219-240. doi: 10.1146/annurev.physchem.012809.103457. [32] N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, $3^{rd}$ edition, Elsevier, Amsterdam, 2007. [33] L. Wang, J. Xin and Q. Nie, A critical quantity for noise attenuation in feedback systems, PLoS Comput Biol, 6 (2010), e1000764, 17 pp. doi: 10.1371/journal.pcbi.1000764. [34] W. Weston, J. Zayas and R. Perez, et al., Dynamic equilibrium of heterogeneous and interconvertible multipotent hematopoietic cell subsets, Sci Rep, 4 (2014), 5199. doi: 10.1038/srep05199. [35] X. Ye, W. L. Tam and T. Shibue, et al., Distinct EMT programs control normal mammary stem cells and tumour-initiating cells, Nature, 525 (2015), 256-260. doi: 10.1038/nature14897. [36] J. Zhang, X. J. Tian and H. Zhang, et al., TGF-$\beta$-induced Epithelial-To-Mesenchymal Transition Proceeds Through Stepwise Activation of Multiple Feedback Loops, Science Signaling, 2014. [37] L. Zheng, M. Chen and Q. Nie, External noise control in inherently stochastic biological systems, J Math Phys, 53 (2012), 115616, 13 pp. doi: 10.1063/1.4762825. [38] , Differential Evolution (DE) for Continuous Function Optimization (an algorithm by Kenneth Price and Rainer Storn),, Accessed in May 2016. Available from: , (2016).
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