Question

In a bacterial culture in which all cells are unable to synthesize leucine (leu'), a potent mutagen is added, and the cells are allowed to undergo one round of replication. At that point, samples are taken, a series of dilutions is made, and the cells are plated on either minimal medium or minimal medium containing leucine. The first culture condition (minimal medium) allows the growth of only leu' cells, while the second culture condition (minimal medium with leucine added) allows growth of all cells. The results of the experiment are as follows: $$\begin{array}{lcc} \text { Culture Condition } & \text { Dilution } & \text { Colonies } \\ \text { Minimal medium } & 10^{-1} & 18 \\ \text { Minimal medium + leucine } & 10^{-7} & 6 \end{array}$$ What is the rate of mutation at the locus associated with leucine biosynthesis?

Short answer

Answer: The rate of mutation at the locus associated with leucine biosynthesis is 3 x $$10^{-6}$$.

Step-by-step solution

Identify the correct formula for calculating the rate of mutation

To find the rate of mutation, we will use the following formula: Rate of mutation = $$\frac{\text{Number of mutants}}{\text{Total number of cells plated}}$$

Calculate the number of mutants

The number of mutants can be determined from the minimal medium culture condition, as it allows the growth of only leu' cells. There were 18 colonies grown in the minimal medium at a dilution of $$10^{-1}$$. Number of mutants = Colonies grown in minimal medium x Dilution factor Number of mutants = 18 x $$10^{1}$$ = 180

Calculate the total number of cells plated

The total number of cells plated can be determined from the minimal medium + leucine culture condition, as it allows growth of all cells. There were 6 colonies grown in the minimal medium + leucine at a dilution of $$10^{-7}$$. Total number of cells plated = Colonies grown in minimal medium + leucine x Dilution factor Total number of cells plated = 6 x $$10^{7}$$ = 60,000,000

Calculate the rate of mutation

Now that we have the number of mutants (180) and the total number of cells plated (60,000,000), we can calculate the rate of mutation using the formula from Step 1. Rate of mutation = $$\frac{\text{Number of mutants}}{\text{Total number of cells plated}}$$ Rate of mutation = $$\frac{180}{60,000,000}$$ = 3 x $$10^{-6}$$ Therefore, the rate of mutation at the locus associated with leucine biosynthesis is 3 x $$10^{-6}$$.