Bacterial growth

I will return now to the question of mutation rate estimation in bacterial cultures. Luria-Delbrück fluctuation analysis is generally used to estimate the rate of so-called growth-dependent mutations in bacterial cultures. These are to be distinguished from adaptive mutations that occur in slowly growing cultures, in which little cell division takes place (1997). The distinction seems to be mostly in terms of the mutational mechanism. In the first case, the spectrum of observed genetic changes seems to be much more heterogeneous, and thus believed to occur via multiple mechanisms, whereas adaptive mutations are similar in various cells or systems, and have been related to recD gene activity.

Restricting ourselves to mutations that occur in growing cultures, we saw that the assumption that underlies the L-D distribution of mutants, namely that the cell cycle time is exponentially distributed, results in underestimation of the mutation rate. In the above sections I provided improved methods that take into account the cell-cycle time distribution. There are a number of other sources of errors that I would like to briefly discuss here.

In my simulations, I can precisely count the mutants when the culture reaches size N. In fluctuation analysis experiments, one cannot decide individually for each cell whether its phenotype is wildtype or mutant. The number of mutants is estimated by taking a sample of the culture, growing it on a selective environment, that only supports the growth of the mutants, and counting the number of colonies. Each colony is assumed to have been seeded by one mutant cell. Jones et al. (1994) discusses to a large extent the statistical complications associated with estimating the number of mutants in the culture. One issue which is not addressed in their study, is the assumption that the cells were in exponential growth over the whole period of the experiment. Such a condition is difficult to ensure. After growing exponentially, a bacterial culture generally experiences significant cell death, after which a stationary phase settles in. Although I will not go into the details of correcting for the cell death at the end of the exponential phase, as this would require detailed knowledge of the mechanisms involved, I will outline the procedure for a simple case. The basic assumption would be that death affects with equal probability wildtype and mutant cells. Then what we need to know in order to infer the mutation rate is the cell-cycle time distribution, and the counts of viable and dead cells at the time of mutant detection. The distribution of mutants in the final culture can be obtain from the convolution of the distribution at the end of exponential expansion and the hypergeometric distribution, corresponding to the sampling realized by the death process. That is, if mutants and wildtype cells are equally likely to be affected by death, the set of viable cells is essentially a sample, without replacement, of the cells at the end of the phase of exponential growth.

I believe that at this moment we have the basic components for an accurate method for mutation rate estimation in bacterial cultures. Automating this method is one of my topics of future work.