Program in Molecular and Computational Biology, Department of Biological Sciences, University of Southern California, Los Angeles, CA 90089, USA.
BMC Cancer. 2010 Jan 5;10:3. doi: 10.1186/1471-2407-10-3.
The purpose of this article is to present a relatively easy to understand cancer model where transformation occurs when the first cell, among many at risk within a colon, accumulates a set of driver mutations. The analysis of this model yields a simple algebraic equation, which takes as inputs the number of stem cells, mutation and division rates, and the number of driver mutations, and makes predictions about cancer epidemiology.
The equation [p = 1 - (1 - (1 - (1 - u)d)k)Nm ] calculates the probability of cancer (p) and contains five parameters: the number of divisions (d), the number of stem cells (N x m), the number of critical rate-limiting pathway driver mutations (k), and the mutation rate (u). In this model progression to cancer "starts" at conception and mutations accumulate with cell division. Transformation occurs when a critical number of rate-limiting pathway mutations first accumulates within a single stem cell.
When applied to several colorectal cancer data sets, parameter values consistent with crypt stem cell biology and normal mutation rates were able to match the increase in cancer with aging, and the mutation frequencies found in cancer genomes. The equation can help explain how cancer risks may vary with age, height, germline mutations, and aspirin use. APC mutations may shorten pathways to cancer by effectively increasing the numbers of stem cells at risk.
The equation illustrates that age-related increases in cancer frequencies may result from relatively normal division and mutation rates. Although this equation does not encompass all of the known complexity of cancer, it may be useful, especially in a teaching setting, to help illustrate relationships between small and large cancer features.
本文旨在介绍一个相对易于理解的癌症模型，其中当结肠内众多风险细胞中的第一个细胞积累了一组驱动突变时，就会发生转化。对该模型的分析产生了一个简单的代数方程，该方程将干细胞数量、突变和分裂率以及驱动突变数量作为输入，并对癌症流行病学做出预测。
该方程[p=1-(1-(1-(1-u)d)k)Nm]计算癌症的概率（p），包含五个参数：分裂次数（d）、干细胞数量（Nxm）、关键限速途径驱动突变数量（k）和突变率（u）。在这个模型中，癌症“起始”于受孕，突变随着细胞分裂而积累。当单个干细胞中首先积累了临界数量的限速途径突变时，就会发生转化。
当应用于几个结直肠癌数据集时，与隐窝干细胞生物学和正常突变率一致的参数值能够匹配癌症随年龄增长的增加，以及在癌症基因组中发现的突变频率。该方程可以帮助解释癌症风险如何随年龄、身高、种系突变和阿司匹林使用而变化。APC 突变可能通过有效增加风险干细胞的数量来缩短癌症的途径。
该方程表明，与年龄相关的癌症频率增加可能是由于相对正常的分裂和突变率所致。尽管该方程没有包含癌症所有已知的复杂性，但它可能在教学环境中特别有用，有助于说明小的和大的癌症特征之间的关系。
