The main inspiration for this thread came from an article I ran across in a Google search. The primer boils down a >30 page paper beautifully, and it also explains the basics of what a Poisson distribution is.
I have been a huge fan of this experiment for decades because it is one of those classic experiments that combines simplicity with deep insight. The question that Salvador Luria Max Delbruck faced was how phage resistance operated in E. coli (phage are viruses that kill bacteria). As the paper above describes, the two main hypotheses were acquired immunity and immunity by mutation. This question was being asked in an era before the discovery of DNA, so it wasn’t as simple as sequencing a gene. This didn’t stop Luria and Delbruck from solving the problem, however.
The inspiration for the experiments and model is part of the legend of this experiment. Luria was at a faculty mixer, and part of the entertainment was slot machines. Luria suddenly realized that beneficial mutations could be modeled like slot machine jackpots. The winners could be found by challenging the bacteria with phage, so they had the basics of an experimental design. They could use a Poisson distribution to model the population, so they also had a statistical model. With these two things in hand, an experimental design and a statistical model, Luria and his colleague Delbruck set forth on testing the two hypotheses.
In this post, I will focus on the experimental design which is often called the fluctuation test. The experiments starts by streaking bacteria on a plate and selecting a single colony of E. coli. Each colony was founded by a single bacterium, so all descendants should be genetically identical except for any mutations that occur along the way.
That single colony is used to start some liquid culture which is grown overnight in order to have enough bacteria to work with. The next day, a small volume of that liquid culture is used to start multiple parallel cultures. Once those have multiplied for a while they are spread on agar plates that contain phage.
What do the two hypotheses, acquired immunity and immunty by mutation, predict when it comes to these plates? Like any good experiment, the two hypotheses make very different predictions. The acquired immunity hypothesis predicts that you should see about the same number of bacteria on each plate from each parallel culture since all bacteria should have the same innate mechanism of immunity if that is how it works. The immunity by mutation hypothesis predicts that you can see wildly different numbers of colonies on the plates since the mutation can happen in an early generation and produce many resistant bacteria, happen in a later generation and produce relatively few bacteria, or not occur at all and produce no resistant colonies.
So what did they see?
In the first two columns you will see that some of the cultures had no resistant bacteria, some had a handful, and a few had many. This is what we would expect to see in the case of immunity by mutation.