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2009, 6(1): 59-82. doi: 10.3934/mbe.2009.6.59

Feedback regulation in multistage cell lineages

Wing-Cheong Lo 1, , Ching-Shan Chou 2, , Kimberly K. Gokoffski 3, , Frederic Y.-M. Wan 1, , Arthur D. Lander 3, , Anne L. Calof 3, and  Qing Nie 1,

1. 

Departments of Mathematics, University of California, Irvine, CA, United States, United States
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, United States, United States, United States

Received  August 2008 Revised  September 2008 Published  December 2008

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.
Keywords: cell lineage, olfactory epithelium, neurogenesis, terminally differentiated cell, feedback, transit amplifying cell, modeling, stability, neuronal progenitor, stem cell.
Mathematics Subject Classification: 92C15,92C37,34D23.
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 & Engineering, 2009, 6 (1) : 59-82. doi: 10.3934/mbe.2009.6.59
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