In the experiment of Luria and Delbruck described earlier, 20 culture tubes (0.2 ml) were used for study of mutations for resistance against T
_{1}phage. In this case 11 out of 21 tubes had no mutant cells. If frequencies of culture tubes showing 1, 2, 3, ... 100 (or more) mutant colonies are worked out, they exhibit a
Poisson distribution (mean frequency of class with no mutations = 11/20). In Figure 21.2, it can be seen that when we start with one cell, number of cell divisions =
n - 1 (
n = number of cells at the end). Therefore, if
n is very high (10
^{8 }per ml) relative to very small original number, then
n gives a sufficiently accurate estimate of cell divisions. Now, if mutation rate per cell division is assumed to be μ, mutation events per tube will be μx
n = μ
n. According to Poisson distribution
f_{(0) }=
e^{-m} = e
^{-μn}. Therefore,
f_{(0)} = 11/20 = 0.55 = e
^{-μ(0.2x 108)}; (as in e raised to - μ(0.2x 10
^{8})) which gives μ = 3 x 10
^{-8} mutations per cell division. Mutation frequency, on the other hand is calculated as (mutants in all 20 tubes)/ (20 x 0.2 x 10
^{8}), which was found to be 5.7 x 10
^{-7 }per cell (for Poisson Distribution, consult
Linkage and Crossing Over in Diploid Organisms (Higher Eukaryotes))