Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Feedback regulation in multistage cell lineages

1. Departments of Mathematics, University of California, Irvine, CA
2. Center for Mathematical and Computational Biology, Department of Mathematics, University of California, Irvine, CA 92697-3875
3. Developmental and Cell Biology, University of California, Irvine, CA

Studies of developing and self-renewing tissues have shown that differentiated cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor (transit amplifying; TA) cell stages, which ultimately give rise to terminally differentiated (TD) cells. In several cases, self-renewal and differentiation of stem and progenitor cells within such lineages have been shown to be under feedback regulation. Together, the existence of multiple cell stages within a lineage and complex feedback regulation are thought to confer upon a tissue the ability to autoregulate development and regeneration, in terms of both cell number (total tissue volume) and cell identity (the proportions of different cell types, especially TD cells, within the tissue). In this paper, we model neurogenesis in the olfactory epithelium (OE) of the mouse, a system in which the lineage stages and mediators of feedback regulation that govern the generation of terminally differentiated olfactory receptor neurons (ORNs) have been the subject of much experimental work. Here we report on the existence and uniqueness of steady states in this system, as well as local and global stability of these steady states. In particular, we identify parameter conditions for the stability of the system when negative feedback loops are represented either as Hill functions, or in more general terms. Our results suggest that two factors -- autoregulation of the proliferation of transit amplifying (TA) progenitor cells, and a low death rate of TD cells -- enhance the stability of this system.
  Article Metrics

Keywords cell lineage; olfactory epithelium; neurogenesis; terminally differentiated cell; feedback; transit amplifying cell; modeling; stability; neuronal progenitor; stem cell

Citation: Wing-Cheong Lo, Ching-Shan Chou, Kimberly K. Gokoffski, Frederic Y.-M. Wan, Arthur D. Lander, Anne L. Calof, Qing Nie. Feedback regulation in multistage cell lineages. Mathematical Biosciences and Engineering, 2009, 6(1): 59-82. doi: 10.3934/mbe.2009.6.59


This article has been cited by

  • 1. Eliedonna Cacao, Francis A. Cucinotta, Modeling Impaired Hippocampal Neurogenesis after Radiation Exposure, Radiation Research, 2016, 185, 3, 319, 10.1667/RR14289.S1
  • 2. Arjen van Ooyen, Using theoretical models to analyse neural development, Nature Reviews Neuroscience, 2011, 12, 6, 311, 10.1038/nrn3031
  • 3. Frederic Michon, Andrew H. Jheon, Kerstin Seidel, Ophir D. Klein, , Stem Cells in Craniofacial Development and Regeneration, 2013, 315, 10.1002/9781118498026.ch17
  • 4. Xinfeng Liu, Sara Johnson, Shou Liu, Deepak Kanojia, Wei Yue, Udai P. Singh, Qian Wang, Qi Wang, Qing Nie, Hexin Chen, Nonlinear Growth Kinetics of Breast Cancer Stem Cells: Implications for Cancer Stem Cell Targeted Therapy, Scientific Reports, 2013, 3, 1, 10.1038/srep02473
  • 5. Ang Li, Yung-Chih Lai, Seth Figueroa, Tian Yang, Randall B. Widelitz, Krzysztof Kobielak, Qing Nie, Cheng Ming Chuong, Deciphering principles of morphogenesis from temporal and spatial patterns on the integument, Developmental Dynamics, 2015, 244, 8, 905, 10.1002/dvdy.24281
  • 6. Oliver J. Maclaren, Helen M. Byrne, Alexander G. Fletcher, Philip K. Maini, Models, measurement and inference in epithelial tissue dynamics, Mathematical Biosciences and Engineering, 2015, 12, 6, 1321, 10.3934/mbe.2015.12.1321
  • 7. T. Stiehl, A. Marciniak-Czochra, Mathematical Modeling of Leukemogenesis and Cancer Stem Cell Dynamics, Mathematical Modelling of Natural Phenomena, 2012, 7, 1, 166, 10.1051/mmnp/20127199
  • 8. Gentian Buzi, Arthur D Lander, Mustafa Khammash, Cell lineage branching as a strategy for proliferative control, BMC Biology, 2015, 13, 1, 10.1186/s12915-015-0122-8
  • 9. H. Cho, K. Ayers, L. de Pills, Y.-H. Kuo, J. Park, A. Radunskaya, R. C. Rockne, Modelling acute myeloid leukaemia in a continuum of differentiation states, Letters in Biomathematics, 2018, 1, 10.1080/23737867.2018.1472532
  • 10. Jienian Yang, David E. Axelrod, Natalia L. Komarova, Determining the control networks regulating stem cell lineages in colonic crypts, Journal of Theoretical Biology, 2017, 429, 190, 10.1016/j.jtbi.2017.06.033
  • 11. Sarah M. Roy, Dominik Wodarz, Tissue architecture, feedback regulation, and resilience to viral infection, Journal of Theoretical Biology, 2014, 340, 131, 10.1016/j.jtbi.2013.09.011
  • 12. Julie Wells, Briana Lee, Anna Qianyao Cai, Adrine Karapetyan, Wan-Ju Lee, Elizabeth Rugg, Satrajit Sinha, Qing Nie, Xing Dai, Ovol2 Suppresses Cell Cycling and Terminal Differentiation of Keratinocytes by Directly Repressing c-MycandNotch1, Journal of Biological Chemistry, 2009, 284, 42, 29125, 10.1074/jbc.M109.008847
  • 13. H. Youssefpour, X. Li, A.D. Lander, J.S. Lowengrub, Multispecies model of cell lineages and feedback control in solid tumors, Journal of Theoretical Biology, 2012, 304, 39, 10.1016/j.jtbi.2012.02.030
  • 14. Zheng Sun, Natalia L. Komarova, Stochastic modeling of stem-cell dynamics with control, Mathematical Biosciences, 2012, 240, 2, 231, 10.1016/j.mbs.2012.08.004
  • 15. Svetoslav Nikolov, Mukhtar Ullah, Momchil Nenov, Julio Vera Gonzalez, Peter Raasch, Olaf Wolkenhauer, , Medical Advancements in Aging and Regenerative Technologies, 2013, chapter 3, 53, 10.4018/978-1-4666-2506-8.ch003
  • 16. Catherine Ha Ta, Qing Nie, Tian Hong, Controlling stochasticity in epithelial-mesenchymal transition through multiple intermediate cellular states, Discrete and Continuous Dynamical Systems - Series B, 2016, 21, 7, 2275, 10.3934/dcdsb.2016047
  • 17. C. Calmelet, A. Prokop, J. Mensah, L. J. McCawley, P. S. Crooke, Modeling the Cancer Stem Cell Hypothesis, Mathematical Modelling of Natural Phenomena, 2010, 5, 3, 40, 10.1051/mmnp/20105304
  • 18. Jeremy Ovadia, Qing Nie, Stem Cell Niche Structure as an Inherent Cause of Undulating Epithelial Morphologies, Biophysical Journal, 2013, 104, 1, 237, 10.1016/j.bpj.2012.11.3807
  • 19. G. Jamróz, Measure-transmission metric and stability of structured population models, Nonlinear Analysis: Real World Applications, 2015, 25, 9, 10.1016/j.nonrwa.2015.02.008
  • 20. Wei-Ting Yeh, Hsuan-Yi Chen, A minimal spatial cell lineage model of epithelium: tissue stratification and multi-stability, New Journal of Physics, 2018, 20, 5, 053051, 10.1088/1367-2630/aac2ad
  • 21. Xiufang Chen, Yue Wang, Tianquan Feng, Ming Yi, Xingan Zhang, Da Zhou, The overshoot and phenotypic equilibrium in characterizing cancer dynamics of reversible phenotypic plasticity, Journal of Theoretical Biology, 2016, 390, 40, 10.1016/j.jtbi.2015.11.008
  • 22. Ignacio A. Rodriguez-Brenes, Dominik Wodarz, Natalia L. Komarova, Characterizing inhibited tumor growth in stem-cell-driven non-spatial cancers, Mathematical Biosciences, 2015, 270, 135, 10.1016/j.mbs.2015.08.009
  • 23. A. Q. Cai, Y. Peng, J. Wells, X. Dai, Q. Nie, Multi-scale Modelling for Threshold Dependent Differentiation, Mathematical Modelling of Natural Phenomena, 2009, 4, 4, 103, 10.1051/mmnp/20094403
  • 24. Dominik Wodarz, Effect of cellular de-differentiation on the dynamics and evolution of tissue and tumor cells in mathematical models with feedback regulation, Journal of Theoretical Biology, 2018, 448, 86, 10.1016/j.jtbi.2018.03.036
  • 25. Philipp Getto, Anna Marciniak-Czochra, Yukihiko Nakata, Maria dM. Vivanco, Global dynamics of two-compartment models for cell production systems with regulatory mechanisms, Mathematical Biosciences, 2013, 245, 2, 258, 10.1016/j.mbs.2013.07.006
  • 26. A.A. Jermusyk, G.T. Reeves, , Encyclopedia of Cell Biology, 2016, 63, 10.1016/B978-0-12-394447-4.40010-6
  • 27. Arthur D. Lander, Pattern, Growth, and Control, Cell, 2011, 144, 6, 955, 10.1016/j.cell.2011.03.009
  • 28. William R. Holmes, Qing Nie, Interactions and Tradeoffs Between Cell Recruitment, Proliferation, and Differentiation Affect CNS Regeneration, Biophysical Journal, 2014, 106, 7, 1528, 10.1016/j.bpj.2014.02.010
  • 29. A. Di Garbo, M. D. Johnston, S. J. Chapman, P. K. Maini, Variable renewal rate and growth properties of cell populations in colon crypts, Physical Review E, 2010, 81, 6, 10.1103/PhysRevE.81.061909
  • 30. Hugh R. MacMillan, Michael J. McConnell, Seeing beyond the average cell: branching process models of cell proliferation, differentiation, and death during mouse brain development, Theory in Biosciences, 2011, 130, 1, 31, 10.1007/s12064-010-0107-7
  • 31. Ignacio A. Rodriguez-Brenes, Dominik Wodarz, , , 2018, 10.1016/bs.host.2018.05.004
  • 32. Jianfeng Jiao, Min Luo, Ruiqi Wang, Feedback regulation in a stem cell model with acute myeloid leukaemia, BMC Systems Biology, 2018, 12, S4, 10.1186/s12918-018-0561-2
  • 33. Jinzhi Lei, Simon A. Levin, Qing Nie, Mathematical model of adult stem cell regeneration with cross-talk between genetic and epigenetic regulation, Proceedings of the National Academy of Sciences, 2014, 111, 10, E880, 10.1073/pnas.1324267111
  • 34. Philipp Getto, Anna Marciniak-Czochra, , Mammary Stem Cells, 2015, Chapter 15, 247, 10.1007/978-1-4939-2519-3_15
  • 35. Marek Kimmel, , A Systems Biology Approach to Blood, 2014, Chapter 7, 119, 10.1007/978-1-4939-2095-2_7
  • 36. Erica Manesso, José Teles, David Bryder, Carsten Peterson, Dynamical modelling of haematopoiesis: an integrated view over the system in homeostasis and under perturbation, Journal of The Royal Society Interface, 2013, 10, 80, 20120817, 10.1098/rsif.2012.0817
  • 37. Marissa Renardy, Alexandra Jilkine, Leili Shahriyari, Ching-Shan Chou, Control of cell fraction and population recovery during tissue regeneration in stem cell lineages, Journal of Theoretical Biology, 2018, 445, 33, 10.1016/j.jtbi.2018.02.017
  • 38. Piotr Gwiazda, Grzegorz Jamróz, Anna Marciniak-Czochra, Models of Discrete and Continuous Cell Differentiation in the Framework of Transport Equation, SIAM Journal on Mathematical Analysis, 2012, 44, 2, 1103, 10.1137/11083294X
  • 39. Chiara Fornari, Marco Beccuti, Stefania Lanzardo, Laura Conti, Gianfranco Balbo, Federica Cavallo, Raffaele A. Calogero, Francesca Cordero, Anita B. Hjelmeland, A Mathematical-Biological Joint Effort to Investigate the Tumor-Initiating Ability of Cancer Stem Cells, PLoS ONE, 2014, 9, 9, e106193, 10.1371/journal.pone.0106193
  • 40. Mao-Xiang Wang, Yu-Qiang Ma, Pik-Yin Lai, Regulatory effects on the population dynamics and wave propagation in a cell lineage model, Journal of Theoretical Biology, 2016, 393, 105, 10.1016/j.jtbi.2015.12.035
  • 41. Qing Nie, Maksim V. Plikus, Equal opportunities in stemness, Nature Cell Biology, 2019, 21, 8, 921, 10.1038/s41556-019-0366-6

Reader Comments

your name: *   your email: *  

Copyright Info: 2009, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved