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Stochastic dynamics of cell lineage in tissue homeostasis
1. | Department of Mathematics, University of California, Irvine, Irvine, CA 92697, USA |
2. | Department of Mathematics, University of California, Riverside, Riverside, CA 92507, USA |
3. | Department of Mathematics, Department of Developmental and Cell Biology, University of California, Irvine, Irvine, CA 92697, USA |
During epithelium tissue maintenance, lineages of cells differentiate and proliferate in a coordinated way to provide the desirable size and spatial organization of different types of cells. While mathematical models through deterministic description have been used to dissect role of feedback regulations on tissue layer size and stratification, how the stochastic effects influence tissue maintenance remains largely unknown. Here we present a stochastic continuum model for cell lineages to investigate how both layer thickness and layer stratification are affected by noise. We find that the cell-intrinsic noise often causes reduction and oscillation of layer size whereas the cell-extrinsic noise increases the thickness, and sometimes, leads to uncontrollable growth of the tissue layer. The layer stratification usually deteriorates as the noise level increases in the cell lineage systems. Interestingly, the morphogen noise, which mixes both cell-intrinsic noise and cell-extrinsic noise, can lead to larger size of layer with little impact on the layer stratification. By investigating different combinations of the three types of noise, we find the layer thickness variability is reduced when cell-extrinsic noise level is high or morphogen noise level is low. Interestingly, there exists a tradeoff between low thickness variability and strong layer stratification due to competition among the three types of noise, suggesting robust layer homeostasis requires balanced levels of different types of noise in the cell lineage systems.
References:
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M. Acar, J. T. Mettetal and A. Van Oudenaarden, Stochastic switching as a survival strategy in fluctuating environments, Nature genetics, 40 (2008), 471. |
[2] |
D. Austin, M. Allen, J. McCollum, R. Dar, J. Wilgus, G. Sayler, N. Samatova, C. Cox and M. Simpson, Gene network shaping of inherent noise spectra, Nature, 439(2006), 608. |
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S. V. Avery, Microbial cell individuality and the underlying sources of heterogeneity, Nature Reviews Microbiology, 4 (2006), 577. |
[4] |
A. Becskei and L. Serrano, Engineering stability in gene networks by autoregulation, Nature, 405 (2000), 590. |
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W. J. Blake, G. Balaázsi, M. A. Kohanski, F. J. Isaacs, K. F. Murphy, Y. Kuang, C. R. Cantor, D. R. Walt and J. J. Collins,
Phenotypic consequences of promoter-mediated transcriptional noise, Molecular Cell, 24 (2006), 853-865.
|
[6] |
T. Borovski, E. M. Felipe De Sousa, L. Vermeulen and J. P. Medema,
Cancer stem cell niche: The place to be, Cancer Research, 71 (2011), 634-639.
|
[7] |
C.-S. Chou, W.-C. Lo, K. K. Gokoffski, Y.-T. Zhang, F. Y. Wan, A. D. Lander, A. L. Calof and Q. Nie,
Spatial dynamics of multistage cell lineages in tissue stratification, Biophysical Journal, 99 (2010), 3145-3154.
|
[8] |
F. Doetsch,
A niche for adult neural stem cells., Development, 13 (2003), 543-550.
|
[9] |
H. Du, Y. Wang, D. Haensel, B. Lee, X. Dai and Q. Nie, Multiscale modeling of layer formation in epidermis, PLoS Computational Biology, 14 (2018), e1006006. |
[10] |
A. D. Economou, A. Ohazama, T. Porntaveetus, P. T. Sharpe, S. Kondo, M. A. Basson, A. Gritli-Linde, M. T. Cobourne and J. B. Green, Periodic stripe formation by a Turing mechanism operating at growth zones in the mammalian palate, Nature Genetics, 44 (2012), 348. |
[11] |
M. B. Elowitz, A. J. Levine, E. D. Siggia and P. S. Swain,
Stochastic gene expression in a single cell, Science, 297 (2002), 1183-1186.
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[12] |
L. Gammaitoni, P. Haänggi, P. Jung and F. Marchesoni, Stochastic resonance, Reviews of Modern Physics, 70 (1998), 223. |
[13] |
H. Ge, H. Qian and X. S. Xie, Stochastic phenotype transition of a single cell in an intermediate region of gene state switching, Physical Review Letters, 114 (2015), 078101. |
[14] |
J. Hasty, J. Pradines, M. Dolnik and J. J. Collins,
Noise-based switches and amplifiers for gene expression., Proceedings of the National Academy of Sciences, 97 (2000), 2075-2080.
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[15] |
D. Huh and J. Paulsson, Non-genetic heterogeneity from stochastic partitioning at cell division, Nature Genetics, 43 (2011), 95. |
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A. Jentzen and P. E. Kloeden, Taylor Approximations for Stochastic Partial Differential Equations, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2011.
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[17] |
M. Kærn, T. C. Elston, W. J. Blake and J. J. Collins, Stochasticity in gene expression: From theories to phenotypes, Nature Reviews Genetics, 6 (2005), 451. |
[18] |
D. C. Kirouac, G. J. Madlambayan, M. Yu, E. A. Sykes, C. Ito and P. W. Zandstra, Cell-cell interaction networks regulate blood stem and progenitor cell fate, Molecular Systems Biology, 5 (2009), 293. |
[19] |
P. E. Kloeden, The Numerical Solution of Stochastic Differenttial Equations, Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-662-12616-5. |
[20] |
A. D. Lander,
Pattern, growth, and control, Cell, 144 (2011), 955-969.
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[21] |
A. D. Lander, K. K. Gokoffski, F. Y. Wan, Q. Nie and A. L. Calof, Cell lineages and the logic of proliferative control, PLoS Biology, 7 (2009), e1000015. |
[22] |
A. D. Lander, J. Kimble, H. Clevers, E. Fuchs, D. Montarras, M. Buckingham, A. L. Calof, A. Trumpp and T. Oskarsson, What does the concept of the stem cell niche really mean today?, BMC Biology, 10 (2012), 19. |
[23] |
A. Li, S. Figueroa, T.-X. Jiang, P. Wu, R. Widelitz, Q. Nie and C.-M. Chuong, Diverse feather shape evolution enabled by coupling anisotropic signalling modules with self organizing branching programme, Nature Communications, 8 (2017), ncomms14139. |
[24] |
L. Li and T. Xie,
Stem cell niche: Structure and function, Annu. Rev. Cell Dev. Biol., 21 (2005), 605-631.
|
[25] |
C.-M. Lin, T. X. Jiang, R. E. Baker, P. K. Maini, R. B. Widelitz and C.-M. Chuong,
Spots and stripes: pleomorphic patterning of stem cells via p-ERK-dependent cell chemotaxis shown by feather morphogenesis and mathematical simulation, Developmental Biology, 334 (2009), 369-382.
|
[26] |
W.-C. Lo, C.-S. Chou, K. K. Gokoffski, F. Y.-M. Wan, A. D. Lander, A. L. Calof and Q. Nie,
Feedback regulation in multistage cell lineages, Mathematical Biosciences and Engineering: MBE, 6 (2009), 59-82.
doi: 10.3934/mbe.2009.6.59. |
[27] |
F. Luciani, D. Champeval, A. Herbette, L. Denat, B. Aylaj, S. Martinozzi, R. Ballotti, R. Kemler, C. R. Goding and F. De Vuyst,
Biological and mathematical modeling of melanocyte development, Development, 138 (2011), 3943-3954.
|
[28] |
A. Marciniak-Czochra, T. Stiehl, A. D. Ho, W. Jaäger and W. Wagner,
Modeling of asymmetric cell division in hematopoietic stem cells-regulation of self-renewal is essential for efficient repopulation, Stem Cells and Development, 18 (2009), 377-386.
|
[29] |
H. H. McAdams and A. Arkin,
Stochastic mechanisms in gene expression, Proceedings of the National Academy of Sciences, 94 (1997), 814-819.
|
[30] |
S. McCroskery, M. Thomas, L. Maxwell, M. Sharma and R. Kambadur,
Myostatin negatively regulates satellite cell activation and self-renewal, The Journal of Cell Biology, 162 (2003), 1135-1147.
|
[31] |
M. D. McDonnell and D. Abbott, What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology, PLoS Computational Biology, 5 (2009), e1000348, 9pp.
doi: 10.1371/journal.pcbi.1000348. |
[32] |
F. L. Moolten and N. L. Bucher,
Regeneration of rat liver: Transfer of humoral agent by cross circulation, Science, 158 (1967), 272-274.
|
[33] |
K. A. Moore and I. R. Lemischka,
Stem cells and their niches, Science, 311 (2006), 1880-1885.
|
[34] |
J. Ovadia and Q. Nie,
Numerical Methods for Two-Dimensional Stem Cell Tissue Growth, Journal of Scientific Computing, 58 (2014), 149-175.
doi: 10.1007/s10915-013-9728-6. |
[35] |
J. Ovadia and Q. Nie,
Stem cell niche structure as an inherent cause of undulating epithelial morphologies., Biophysical Journal, 104 (2013), 237-246.
|
[36] |
C. Rackauckas, T. Schilling and Q. Nie,
Mean-independent noise control of cell fates via intermediate states, iScience, 3 (2018), 11-20.
|
[37] |
C. V. Rao, D. M. Wolf and A. P. Arkin, Control, exploitation and tolerance of intracellular noise, Nature, 420 (2002), 231. |
[38] |
J. Raspopovic, L. Marcon, L. Russo and J. Sharpe,
Digit patterning is controlled by a Bmp-Sox9-Wnt Turing network modulated by morphogen gradients, Science, 345 (2014), 566-570.
|
[39] |
T. Ruiz-Herrero, K. Alessandri, B. V. Gurchenkov, P. Nassoy and L. Mahadevan,
Organ size control via hydraulically gated oscillations, Development, 144 (2017), 4422-4427.
|
[40] |
M. L. Simpson, C. D. Cox, M. S. Allen, J. M. McCollum, R. D. Dar, D. K. Karig and J. F. Cooke,
Noise in biological circuits, Wiley Interdisciplinary Reviews: Nanomedicine and Nanobiotechnology, 1 (2009), 214-225.
|
[41] |
C. L. Stokes, D. A. Lauffenburger and S. K. Williams,
Migration of individual microvessel endothelial cells: stochastic model and parameter measurement, Journal of Cell Science, 99 (1991), 419-430.
|
[42] |
M. Thattai and A. Van Oudenaarden,
Stochastic gene expression in fluctuating environments, Genetics, 167 (2004), 523-530.
|
[43] |
T. Tumbar, G. Guasch, V. Greco, C. Blanpain, W.E. Lowry, M. Rendl and E. Fuchs,
Defining the epithelial stem cell niche in skin, Science, 303 (2004), 359-363.
|
[44] |
L. Wang, J. Xin and Q. Nie, A critical quantity for noise attenuation in feedback systems, PLoS Computational Biology, 6 (2010), e1000764, 17pp.
doi: 10.1371/journal.pcbi.1000764. |
[45] |
Q. Wang, W. R. Holmes, J. Sosnik, T. Schilling and Q. Nie, Cell sorting and noise-induced cell plasticity coordinate to sharpen boundaries between gene expression domains, PLoS Computational Biology, 13 (2017), e1005307. |
[46] |
H.-H. Wu, S. Ivkovic, R. C. Murray, S. Jaramillo, K. M. Lyons, J. E. Johnson and A. L. Calof,
Autoregulation of neurogenesis by GDF11, Neuron, 37 (2003), 197-207.
|
[47] |
T.-H. Yen and N. A. Wright,
The gastrointestinal tract stem cell niche, Stem Cell Reviews, 2 (2006), 203-212.
|
[48] |
J. Zhang, C. Niu, L. Ye, H. Huang, X. He, W.-G. Tong, J. Ross, J. Haug, T. Johnson and J. Q. Feng, Identification of the haematopoietic stem cell niche and control of the niche size., Nature, 425(2003), 836. |
[49] |
L. Zhang, K. Radtke, L. Zheng, A. Q. Cai, T. F. Schilling and Q. Nie, Noise drives sharpening of gene expression boundaries in the zebrafish hindbrain, Molecular Systems Biology, 8 (2012), 613. |
show all references
References:
[1] |
M. Acar, J. T. Mettetal and A. Van Oudenaarden, Stochastic switching as a survival strategy in fluctuating environments, Nature genetics, 40 (2008), 471. |
[2] |
D. Austin, M. Allen, J. McCollum, R. Dar, J. Wilgus, G. Sayler, N. Samatova, C. Cox and M. Simpson, Gene network shaping of inherent noise spectra, Nature, 439(2006), 608. |
[3] |
S. V. Avery, Microbial cell individuality and the underlying sources of heterogeneity, Nature Reviews Microbiology, 4 (2006), 577. |
[4] |
A. Becskei and L. Serrano, Engineering stability in gene networks by autoregulation, Nature, 405 (2000), 590. |
[5] |
W. J. Blake, G. Balaázsi, M. A. Kohanski, F. J. Isaacs, K. F. Murphy, Y. Kuang, C. R. Cantor, D. R. Walt and J. J. Collins,
Phenotypic consequences of promoter-mediated transcriptional noise, Molecular Cell, 24 (2006), 853-865.
|
[6] |
T. Borovski, E. M. Felipe De Sousa, L. Vermeulen and J. P. Medema,
Cancer stem cell niche: The place to be, Cancer Research, 71 (2011), 634-639.
|
[7] |
C.-S. Chou, W.-C. Lo, K. K. Gokoffski, Y.-T. Zhang, F. Y. Wan, A. D. Lander, A. L. Calof and Q. Nie,
Spatial dynamics of multistage cell lineages in tissue stratification, Biophysical Journal, 99 (2010), 3145-3154.
|
[8] |
F. Doetsch,
A niche for adult neural stem cells., Development, 13 (2003), 543-550.
|
[9] |
H. Du, Y. Wang, D. Haensel, B. Lee, X. Dai and Q. Nie, Multiscale modeling of layer formation in epidermis, PLoS Computational Biology, 14 (2018), e1006006. |
[10] |
A. D. Economou, A. Ohazama, T. Porntaveetus, P. T. Sharpe, S. Kondo, M. A. Basson, A. Gritli-Linde, M. T. Cobourne and J. B. Green, Periodic stripe formation by a Turing mechanism operating at growth zones in the mammalian palate, Nature Genetics, 44 (2012), 348. |
[11] |
M. B. Elowitz, A. J. Levine, E. D. Siggia and P. S. Swain,
Stochastic gene expression in a single cell, Science, 297 (2002), 1183-1186.
|
[12] |
L. Gammaitoni, P. Haänggi, P. Jung and F. Marchesoni, Stochastic resonance, Reviews of Modern Physics, 70 (1998), 223. |
[13] |
H. Ge, H. Qian and X. S. Xie, Stochastic phenotype transition of a single cell in an intermediate region of gene state switching, Physical Review Letters, 114 (2015), 078101. |
[14] |
J. Hasty, J. Pradines, M. Dolnik and J. J. Collins,
Noise-based switches and amplifiers for gene expression., Proceedings of the National Academy of Sciences, 97 (2000), 2075-2080.
|
[15] |
D. Huh and J. Paulsson, Non-genetic heterogeneity from stochastic partitioning at cell division, Nature Genetics, 43 (2011), 95. |
[16] |
A. Jentzen and P. E. Kloeden, Taylor Approximations for Stochastic Partial Differential Equations, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2011.
doi: 10.1137/1.9781611972016. |
[17] |
M. Kærn, T. C. Elston, W. J. Blake and J. J. Collins, Stochasticity in gene expression: From theories to phenotypes, Nature Reviews Genetics, 6 (2005), 451. |
[18] |
D. C. Kirouac, G. J. Madlambayan, M. Yu, E. A. Sykes, C. Ito and P. W. Zandstra, Cell-cell interaction networks regulate blood stem and progenitor cell fate, Molecular Systems Biology, 5 (2009), 293. |
[19] |
P. E. Kloeden, The Numerical Solution of Stochastic Differenttial Equations, Springer-Verlag, Berlin, 1992.
doi: 10.1007/978-3-662-12616-5. |
[20] |
A. D. Lander,
Pattern, growth, and control, Cell, 144 (2011), 955-969.
|
[21] |
A. D. Lander, K. K. Gokoffski, F. Y. Wan, Q. Nie and A. L. Calof, Cell lineages and the logic of proliferative control, PLoS Biology, 7 (2009), e1000015. |
[22] |
A. D. Lander, J. Kimble, H. Clevers, E. Fuchs, D. Montarras, M. Buckingham, A. L. Calof, A. Trumpp and T. Oskarsson, What does the concept of the stem cell niche really mean today?, BMC Biology, 10 (2012), 19. |
[23] |
A. Li, S. Figueroa, T.-X. Jiang, P. Wu, R. Widelitz, Q. Nie and C.-M. Chuong, Diverse feather shape evolution enabled by coupling anisotropic signalling modules with self organizing branching programme, Nature Communications, 8 (2017), ncomms14139. |
[24] |
L. Li and T. Xie,
Stem cell niche: Structure and function, Annu. Rev. Cell Dev. Biol., 21 (2005), 605-631.
|
[25] |
C.-M. Lin, T. X. Jiang, R. E. Baker, P. K. Maini, R. B. Widelitz and C.-M. Chuong,
Spots and stripes: pleomorphic patterning of stem cells via p-ERK-dependent cell chemotaxis shown by feather morphogenesis and mathematical simulation, Developmental Biology, 334 (2009), 369-382.
|
[26] |
W.-C. Lo, C.-S. Chou, K. K. Gokoffski, F. Y.-M. Wan, A. D. Lander, A. L. Calof and Q. Nie,
Feedback regulation in multistage cell lineages, Mathematical Biosciences and Engineering: MBE, 6 (2009), 59-82.
doi: 10.3934/mbe.2009.6.59. |
[27] |
F. Luciani, D. Champeval, A. Herbette, L. Denat, B. Aylaj, S. Martinozzi, R. Ballotti, R. Kemler, C. R. Goding and F. De Vuyst,
Biological and mathematical modeling of melanocyte development, Development, 138 (2011), 3943-3954.
|
[28] |
A. Marciniak-Czochra, T. Stiehl, A. D. Ho, W. Jaäger and W. Wagner,
Modeling of asymmetric cell division in hematopoietic stem cells-regulation of self-renewal is essential for efficient repopulation, Stem Cells and Development, 18 (2009), 377-386.
|
[29] |
H. H. McAdams and A. Arkin,
Stochastic mechanisms in gene expression, Proceedings of the National Academy of Sciences, 94 (1997), 814-819.
|
[30] |
S. McCroskery, M. Thomas, L. Maxwell, M. Sharma and R. Kambadur,
Myostatin negatively regulates satellite cell activation and self-renewal, The Journal of Cell Biology, 162 (2003), 1135-1147.
|
[31] |
M. D. McDonnell and D. Abbott, What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology, PLoS Computational Biology, 5 (2009), e1000348, 9pp.
doi: 10.1371/journal.pcbi.1000348. |
[32] |
F. L. Moolten and N. L. Bucher,
Regeneration of rat liver: Transfer of humoral agent by cross circulation, Science, 158 (1967), 272-274.
|
[33] |
K. A. Moore and I. R. Lemischka,
Stem cells and their niches, Science, 311 (2006), 1880-1885.
|
[34] |
J. Ovadia and Q. Nie,
Numerical Methods for Two-Dimensional Stem Cell Tissue Growth, Journal of Scientific Computing, 58 (2014), 149-175.
doi: 10.1007/s10915-013-9728-6. |
[35] |
J. Ovadia and Q. Nie,
Stem cell niche structure as an inherent cause of undulating epithelial morphologies., Biophysical Journal, 104 (2013), 237-246.
|
[36] |
C. Rackauckas, T. Schilling and Q. Nie,
Mean-independent noise control of cell fates via intermediate states, iScience, 3 (2018), 11-20.
|
[37] |
C. V. Rao, D. M. Wolf and A. P. Arkin, Control, exploitation and tolerance of intracellular noise, Nature, 420 (2002), 231. |
[38] |
J. Raspopovic, L. Marcon, L. Russo and J. Sharpe,
Digit patterning is controlled by a Bmp-Sox9-Wnt Turing network modulated by morphogen gradients, Science, 345 (2014), 566-570.
|
[39] |
T. Ruiz-Herrero, K. Alessandri, B. V. Gurchenkov, P. Nassoy and L. Mahadevan,
Organ size control via hydraulically gated oscillations, Development, 144 (2017), 4422-4427.
|
[40] |
M. L. Simpson, C. D. Cox, M. S. Allen, J. M. McCollum, R. D. Dar, D. K. Karig and J. F. Cooke,
Noise in biological circuits, Wiley Interdisciplinary Reviews: Nanomedicine and Nanobiotechnology, 1 (2009), 214-225.
|
[41] |
C. L. Stokes, D. A. Lauffenburger and S. K. Williams,
Migration of individual microvessel endothelial cells: stochastic model and parameter measurement, Journal of Cell Science, 99 (1991), 419-430.
|
[42] |
M. Thattai and A. Van Oudenaarden,
Stochastic gene expression in fluctuating environments, Genetics, 167 (2004), 523-530.
|
[43] |
T. Tumbar, G. Guasch, V. Greco, C. Blanpain, W.E. Lowry, M. Rendl and E. Fuchs,
Defining the epithelial stem cell niche in skin, Science, 303 (2004), 359-363.
|
[44] |
L. Wang, J. Xin and Q. Nie, A critical quantity for noise attenuation in feedback systems, PLoS Computational Biology, 6 (2010), e1000764, 17pp.
doi: 10.1371/journal.pcbi.1000764. |
[45] |
Q. Wang, W. R. Holmes, J. Sosnik, T. Schilling and Q. Nie, Cell sorting and noise-induced cell plasticity coordinate to sharpen boundaries between gene expression domains, PLoS Computational Biology, 13 (2017), e1005307. |
[46] |
H.-H. Wu, S. Ivkovic, R. C. Murray, S. Jaramillo, K. M. Lyons, J. E. Johnson and A. L. Calof,
Autoregulation of neurogenesis by GDF11, Neuron, 37 (2003), 197-207.
|
[47] |
T.-H. Yen and N. A. Wright,
The gastrointestinal tract stem cell niche, Stem Cell Reviews, 2 (2006), 203-212.
|
[48] |
J. Zhang, C. Niu, L. Ye, H. Huang, X. He, W.-G. Tong, J. Ross, J. Haug, T. Johnson and J. Q. Feng, Identification of the haematopoietic stem cell niche and control of the niche size., Nature, 425(2003), 836. |
[49] |
L. Zhang, K. Radtke, L. Zheng, A. Q. Cai, T. F. Schilling and Q. Nie, Noise drives sharpening of gene expression boundaries in the zebrafish hindbrain, Molecular Systems Biology, 8 (2012), 613. |








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