Saiga T, Horie K, Tabuchi K, Midorikawa O
Exp Pathol. 1985;28(1):21-30. doi: 10.1016/s0232-1513(85)80028-1.
We established mathematical models for the cell variation seen in a heterogeneous malignant cell population, with the supposition that it occurs as the result of the competition between two types of cells, (A) and (B), leading to a change of stem cells. Models I and II: In the case of differences in the ability of (A) and (B) cells to adapt themselves to an environment, the proportion of cells which are less adaptable to the environment decreases exponentially and eventually disappears. Model III supposes that under certain environmental conditions, the two types of cells exist simultaneously in fixed proportions, and transformations of (B) cell to (A) cell and of (A) cell to (B) cell occur at a certain rate but are independent of each other. This process is considered to follow the Markov's chain theory. Based on this supposition, we established Model III and introduced the concept of "coefficient of cell variation". We found that Model III fits the process of cell variation seen in m cell line and we calculated the coefficients of cell variation seen in this cell line in different environments. The possible mechanism of the cell variation of this cell line is discussed.
我们建立了异质性恶性细胞群体中细胞变异的数学模型，假设其是由两种类型的细胞（A）和（B）之间的竞争导致干细胞变化而产生的。模型I和II：在（A）和（B）细胞适应环境能力存在差异的情况下，对环境适应性较差的细胞比例呈指数下降并最终消失。模型III假设在特定环境条件下，两种类型的细胞以固定比例同时存在，并且（B）细胞向（A）细胞以及（A）细胞向（B）细胞的转化以一定速率发生，但相互独立。该过程被认为遵循马尔可夫链理论。基于此假设，我们建立了模型III并引入了“细胞变异系数”的概念。我们发现模型III符合m细胞系中观察到的细胞变异过程，并计算了该细胞系在不同环境中观察到的细胞变异系数。讨论了该细胞系细胞变异的可能机制。
