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How to balance the size of exponentially growing cells has always been a focus of biologists. Recent experiments have uncovered that the cell is divided into two daughter cells only when the level of time-keeper protein reaches a fixed threshold and cell division in prokaryote is not completely symmetric. The timing of cell division is essentially random because gene expression is stochastic, but cells seen to manage to have precise timing of cell division events. Although the inter-cellular variability of gene expression has attracted much attention, the randomness of event timing has been rarely studied. In our analysis, the timing of cell division is formulated as the first-passage time (denoted by FPT) for time-keeper protein’s level to cross a critical threshold firstly, we derive exact analytical formulae for the mean and noise of FPT based on stochastic gene expression model with asymmetric cell division. The results of numerical simulation show that the regulatory factors (division rate, newborn cell size, exponential growth rate and threshold) have significant influence on the mean and noise of FPT. We also show that both the increase of division rate and newborn cell size could reduce the mean of FPT and increase the noise of FPT, the larger the exponential growth rate is, the smaller the mean and noise of FPT will be; and the larger the threshold value is, the higher the mean of FPT is and the lower the noise is. In addition, compared with symmetric division, asymmetric division can reduce the mean of FPT and improve the noise of FPT. In summary, our results provide insight into the relationship between regulatory factors and FPT and reveal that asymmetric division is an effective mechanism to shorten the mean of FPT.

New data have recently accumulated on how stem cell behave, self-renew and differentiate. Many studies have also focused on defining stem cells, and determination of the properties, including the mode of cell division and polarity, and regulatory environment(s) of both embryonic and tissue-specific stem cells in the last decades. In the lung, recent data show evidences that lung epithelial stem and progenitor cells are polarized, highly mitotic, have characteristic perpendicular cell divisions, and show a mode of division that is similar to other systems. They further show that the asymmetric division is probably the common mode of division in the mitotically dividing distal epithelial stem and progenitor cells of the embryonic lung. Both symmetric and asymmetric mode of cell divisions are tightly regulated in different stem cell types during tissue development and morphogenesis. How to choose between a symmetric and asymmetric cell division is one of the major questions in the stem cell field. It largely affects tissue development, morphogenesis and disease in different organs since improper asymmetric divisions badly affect organ morphogenesis, whereas uncontrolled symmetric division can lead to tumor formation. Moreover, the proper balance between self-renewal and differentiation of lung epithelial stem and progenitor cells is absolutely required for maintaining normal lung morphogenesis and for lung repair and regeneration since a deficiency of this balance probably can lead to a premature or injured lung. Therefore, identification of lung-specific stem cell types, understanding their behavior, and how they balance their self-renewal and differentiation could lead to the identification of innovative solutions for restoring normal lung morphogenesis and/or regeneration and repair of the lung. Furthermore, understanding the molecular mechanisms that control the asymmetrical cell division and both cell polarity and fate of lung epithelial stem and progenitor cells can help identifying new targets for prevention and rescuing lethal lung diseases in infants and children, and for regeneration of injured lungs. In this chapter, we will discuss recently accumulated data on the lung cell polarity, and the mode of division of lung epithelial stem and progenitor cells. In addition, we will describe the functions of Numb in stem cell fate and mode of division, and compare cell polarity and mode of division in the lung stem cells with other systems, as well as discuss the regulatory mechanisms of lung stem cell polarity, fate, behavior and mode of division.