Nádas A, Goncharova E I, Rossman T G
Nelson Institute of Environmental Medicine, New York University Medical Center, New York 10016, USA.
Environ Mol Mutagen. 1996;28(2):90-9. doi: 10.1002/(SICI)1098-2280(1996)28:2<90::AID-EM4>3.0.CO;2-I.
Certain mathematical artifacts which had been appended by others to Luria and Delbrück's [Genetics 28: 491-511, 1943] model of spontaneous mutagenesis in bacterial populations have added confusion to the modeling and measurement of spontaneous mutation rates. Additional confusion arises when models which had been tuned for experiments with bacterial cultures grown from a small inoculum are adapted for use with mammalian cell cultures grown from a large initial population. As one consequence, biologists still tend to grow the large number of parallel cultures required by the fluctuation test in order to avoid large errors due to the high variability in the number of mutants in a growing culture. By avoiding models with infinite mean values and certain mathematical approximations that lead to conceptual and practical difficulties, the large variance of the number of mutants can be avoided (and the precision of the estimated mutation rate controlled) through the use of sufficiently large initial cell populations. A direct consequence is that simpler experiments with fewer cultures may suffice. In this paper, after a discussion of the confusions, we extend our previous approach [Rossman et al.: Mutat Res 328:21-30, 1995] by giving improved formulas for the standard error of the estimated mutation rate. The improvement results from using a more inclusive model based on consideration of the variability due to both the biological phenomenon of the growing culture (growth and mutation) and the protocols used for selection (sampling and plating efficiency). Also included is the situation where the initial cell population is not assumed to be free of mutants but the initial mutant fraction is measured instead. These standard error formulas are useful in planning experiments that yield mutation rate estimates with planned precision and for comparing and testing hypotheses about mutation rates in two or more populations which are grown under different conditions.
其他人附加到卢里亚和德尔布吕克[《遗传学》28: 491 - 511, 1943]细菌群体自发诱变模型上的某些数学产物，给自发突变率的建模和测量带来了混乱。当针对从小接种量培养的细菌培养物实验进行调整的模型被用于从大量初始群体培养的哺乳动物细胞培养物时，会产生更多混乱。结果之一是，生物学家仍然倾向于进行波动试验所需的大量平行培养，以避免由于生长培养物中突变体数量的高度变异性而导致的大误差。通过避免具有无限均值的模型以及某些导致概念和实际困难的数学近似，通过使用足够大的初始细胞群体，可以避免突变体数量的大方差（并控制估计突变率的精度）。直接结果是，用更少培养物进行的更简单实验可能就足够了。在本文中，在讨论了这些混乱之后，我们扩展了我们之前的方法[罗斯曼等人:《突变研究》328:21 - 30, 1995]，给出了估计突变率标准误差的改进公式。这种改进源于使用了一个更具包容性的模型，该模型考虑了生长培养物的生物学现象（生长和突变）以及选择所使用的方案（采样和平板接种效率）导致的变异性。还包括初始细胞群体不被假定为无突变体而是测量初始突变体比例的情况。这些标准误差公式在规划能够以计划精度产生突变率估计值的实验以及比较和检验关于在不同条件下生长的两个或更多群体中突变率的假设时很有用。
