Loeffler M, Grossmann B
Medizinische Klinik I, Köln, Germany.
J Theor Biol. 1991 May 21;150(2):175-91. doi: 10.1016/s0022-5193(05)80330-3.
The intestinal epithelium is one of the most rapidly regenerating tissues in mammals. Cell production takes place in the intestinal crypts which contain about 250 cells. Only a minority of 1-60 proliferating cells are able to maintain a crypt over a long period of time. However, so far attempts to identify these stem cells were unsuccessful. Therefore, little is known about their cellular growth and selfmaintenance properties. On the other hand, the crypts appear to exhibit a life cycle which starts by fission of existing crypts and ends by fission or extinction. Data on these processes have recently become available. Here, we demonstrate how these data on the life cycle of the macroscopic crypt structure can be used to derive a quantitative model of the microscopic process of stem cell growth. The model assumptions are: (1) stem cells undergo a time independent supracritical Markovian branching process (Galton-Watson process); (2) a crypt divides if the number of stem cells exceeds a given threshold and the stem cells are distributed to both daughter crypts according to binomial statistics; (3) the size of the crypt is proportional to the stem cell number. This model combining two different stochastic branching processes describes a new class of processes whose stationary stability and asymptotic behavior are examined. This model should be applicable to various growth processes with formation of subunits (e.g. population growth with formation of colonies in biology, ecology and sociology). Comparison with crypt data shows that intestinal stem cells have a probability of over 0.8 of dividing asymmetrically and that the threshold number should be 8 or larger.
肠上皮是哺乳动物中再生速度最快的组织之一。细胞生成发生在肠隐窝中，每个肠隐窝约含250个细胞。在这250个细胞中，只有少数1 - 60个增殖细胞能够长期维持一个隐窝。然而，到目前为止，识别这些干细胞的尝试均未成功。因此，人们对它们的细胞生长和自我维持特性知之甚少。另一方面，隐窝似乎呈现出一个生命周期，始于现有隐窝的分裂，终于分裂或消亡。关于这些过程的数据最近已可得。在此，我们展示了如何利用这些关于宏观隐窝结构生命周期的数据来推导干细胞生长微观过程的定量模型。该模型假设如下：（1）干细胞经历一个与时间无关的超临界马尔可夫分支过程（高尔顿 - 沃森过程）；（2）当干细胞数量超过给定阈值时，隐窝分裂，且干细胞根据二项式统计分布到两个子隐窝中；（3）隐窝的大小与干细胞数量成正比。这个结合了两种不同随机分支过程的模型描述了一类新的过程，我们对其平稳稳定性和渐近行为进行了研究。该模型应适用于各种形成亚单位的生长过程（例如生物学、生态学和社会学中形成菌落的种群增长）。与隐窝数据的比较表明，肠干细胞不对称分裂的概率超过0.8，且阈值数量应为8个或更多。
