對於生物組織的調控(regulation)與型態生成(morphogenesis)，空間訊息以及細胞系(cell lineage)的考量是不可或缺的。同時，組織回到其恆穩狀態(steady state)的弛豫過程(relaxation process)目前仍然沒有被很好的了解。如果存在著生理上的或者力學上的機制可以驅使組織變得不穩定，那麼這就有可能是組織癌化(carcinogenesis)的一種途徑。為了研究這些問題，我們首先研究細胞系群集動力學(population dynamics)的一般性質。我們發現一般而言，細胞系系統可以容許存在多重的恆穩狀態，而這有或許可以關聯到組織的發育或者癌化。其次，我們針對一個簡化的複層上皮組織(stratified epithelium)模型來研究組織回到其恆穩狀態的弛豫動力學。藉由考量到組織的力學性質－例如黏滯係數(viscosity)－可能與不同細胞間的比例有關係，我們發現當黏滯係數在組織中並非均勻時，一個新的組織不穩定機制有可能會發生。因為過去只有少部分的研究有同時考量空間訊息以及細胞系，我們在此針對連續自我更新(continuous self-renewal)的組織建構了一個空間細胞系模型。我們發現當我們有興趣的時間尺度遠大於細胞週期時間(cell cycle time)，則組織的動力學表現得像是低雷諾數(low-Reynolds number)的流體，同時該流體的黏滯係數與不同細胞間的比例有關。在這個一般的空間細胞系模型的框架下，我們亦發現一個複層上皮組織的存在不可或缺的需要型態生成素(morphogen)的參與。這個模型亦允許存在多重複層上皮組織的恆穩狀態，在未來我們可以研究這些可能的恆穩狀態之間的躍遷以及競爭的過程。

It has been known that both spatial information and cell lineage are important in the regulation and morphogenesis of biological tissues. The relaxation dynamics of a tissue toward its steady state is still poorly understood. Furthermore, if there exists physiological or even mechanical mechanism that drives a tissue unstable, it could be a route toward carcinogenesis. To study these problems, we first study the general properties of a cell lineage population dynamics. We find that in general cell lineage systems allow the existence of multiple steady states, and this could be related to tissue development and carcinogenesis. Second, we study the relaxation dynamics of a tissue toward its steady state by a simplified model of stratified epithelium. By taking into account the fact that the mechanical properties of a tissue, for example viscosity, should depend on the local cell composition, we show that a new instability can happen due to the heterogeneous viscosity in the tissue. Since only few of past studies have taken both spatial information and cell lineage into account simultaneously, we construct a spatial cell lineage model for a continuous self-renewal tissue. We show that a tissue behaves as a low Reynolds number fluid on time scales large compare to cell cycle time with a viscosity depending on local cell composition. In the framework of this general spatial cell lineage model, the effect of morphogen is needed for stratified epithelium steady state to exist. Also, this model allows multiple stratified epithelium steady state, so the process of transition and competition between these steady states can be studied in the future.

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