Biomathematics Research Centre, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.
Bull Math Biol. 2012 Oct;74(10):2510-34. doi: 10.1007/s11538-012-9764-7. Epub 2012 Aug 23.
Cell cycle times are vital parameters in cancer research, and short cell cycle times are often related to poor survival of cancer patients. A method for experimental estimation of cell cycle times, or doubling times of cultured cancer cell populations, based on addition of paclitaxel (an inhibitor of cell division) has been proposed in literature. We use a mathematical model to investigate relationships between essential parameters of the cell division cycle following inhibition of cell division. The reduction in the number of cells engaged in DNA replication reaches a plateau as the concentration of paclitaxel is increased; this can be determined experimentally. From our model we have derived a plateau log reduction formula for proliferating cells and established that there are linear relationships between the plateau log reduction values and the reciprocal of doubling times (i.e. growth rates of the populations). We have therefore provided theoretical justification of an important experimental technique to determine cell doubling times. Furthermore, we have applied Monte Carlo experiments to justify the suggested linear relationships used to estimate doubling time from 5-day cell culture assays. We show that our results are applicable to cancer cell populations with cell loss present.
细胞周期时间是癌症研究中的重要参数，细胞周期时间较短通常与癌症患者的生存率较差有关。文献中提出了一种基于添加紫杉醇（一种细胞分裂抑制剂）来估算细胞周期时间或培养的癌细胞群体倍增时间的实验方法。我们使用数学模型来研究细胞分裂周期在抑制细胞分裂后的基本参数之间的关系。随着紫杉醇浓度的增加，参与 DNA 复制的细胞数量减少达到一个平台期；这可以通过实验来确定。我们从模型中推导出了增殖细胞的平台对数减少公式，并建立了平台对数减少值与倍增时间的倒数（即群体的增长率）之间的线性关系。因此，我们为确定细胞倍增时间的重要实验技术提供了理论依据。此外，我们还进行了蒙特卡罗实验，以验证从 5 天细胞培养实验中估算倍增时间所使用的建议线性关系。我们表明，我们的结果适用于存在细胞丢失的癌细胞群体。
