Abstract
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.
Highlights
Tissue development is charged with the difficult task of specifying correct types of terminally differentiated (TD) cells, at the same time it must specify correct numbers and proportions of the various TD and progenitor cell types that compose the tissue
Studies of mouse olfactory epithelium (OE) have supported the view that olfactory receptor neurons (ORNs) derive from a multistage lineage with three proliferating cell types: (1) self-renewing stem cells, which give rise to (2) transit amplifying (TA) progenitors that can be identified by their expression of the proneural gene Mash1
For a simplified system with a constant stem cell population size, the conditions for the existence, uniqueness, local and global stability of the steady state were derived for negative feedback represented in terms of both general decreasing functions and Hill functions
Summary
Tissue development is charged with the difficult task of specifying correct types of terminally differentiated (TD) cells (whose function typically characterizes the tissue), at the same time it must specify correct numbers and proportions of the various TD and progenitor cell types that compose the tissue. Studies of mouse OE have supported the view that ORNs derive from a multistage lineage with three proliferating cell types (reviewed in [5]): (1) self-renewing stem cells, which give rise to (2) TA progenitors that can be identified by their expression of the proneural gene Mash. We study a system with a constant stem cell population, and two feedbacks on proliferation of TA cells For this simplified system, the existence and uniqueness of the steady state, and local and global stability of the steady state are analyzed.
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