Bjerknes M
Department of Anatomy and Cell Biology, University of Toronto, Ontario, Canada.
J Theor Biol. 1996 Feb 21;178(4):381-5. doi: 10.1006/jtbi.1996.0034.
In general, it is presumed that colonic epithelial stem cells are the principal cell type at risk of incurring the series of somatic mutations leading to carcinoma, since all other epithelial cell types are short-lived. Mutant stem cell clonal expansion increases the risk for subsequent mutations and is therefore a potentially important step in carcinogenesis. The stem cells reside in colonic crypts, simple tubular foldings of the epithelium, and thus counting crypts provides an indirect means to determine stem cell numbers. The normal crypt population is known to expand through a process of crypt replication and this is thought to result in a corresponding expansion of the epithelial stem cell population. A simple mathematical model of the population dynamics of normal and mutant crypts (crypts containing mutant stem cells) is developed and used to estimate a lower bound on the relative rate of expansion of the mutant stem cell population. The model predicts that if mutant and normal crypt populations expand at the same rate, and if the mutation rate is small relative to the rate of growth, then the fraction of clusters of mutant crypts composed of only a single mutant crypt should steadily decrease with age towards one-half. Aberrant crypts are easily recognizable lesions in human colon which have frequently been shown to contain cells with K-ras and occasionally APC gene mutations. Application of the model to recent counts of aberrant crypt cluster sizes indicate that the aberrant crypt population, and the contained mutant stem cell population, is expanding substantially faster than normal.
一般来说，人们推测结肠上皮干细胞是发生导致癌症的一系列体细胞突变的主要风险细胞类型，因为所有其他上皮细胞类型寿命较短。突变干细胞的克隆扩增增加了后续突变的风险，因此是致癌过程中一个潜在的重要步骤。干细胞存在于结肠隐窝中，即上皮的简单管状褶皱，因此计算隐窝数量提供了一种间接确定干细胞数量的方法。已知正常隐窝群体通过隐窝复制过程进行扩增，并且这被认为会导致上皮干细胞群体相应地扩增。建立了一个关于正常和突变隐窝（含有突变干细胞的隐窝）群体动态的简单数学模型，并用于估计突变干细胞群体相对扩增率的下限。该模型预测，如果突变和正常隐窝群体以相同速率扩增，并且如果突变率相对于生长速率较小，那么仅由单个突变隐窝组成的突变隐窝簇的比例应随着年龄稳步下降至二分之一。异常隐窝是人类结肠中易于识别的病变，经常被证明含有具有K-ras突变且偶尔具有APC基因突变的细胞。将该模型应用于最近对异常隐窝簇大小的计数表明，异常隐窝群体以及其中所含的突变干细胞群体的扩增速度比正常情况快得多。
