Mathematical models of cell variation seen in a heterogeneous malignant cell population.

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.