# Calculate Mutant Frequency: Lac Operon Mutations

• mastiffcacher
In summary, Homework Statement The student is trying to calculate the mutant frequency from a bacterial culture and is confused about what the appropriate equation is. The student is unsure if they have understood correctly, but they believe that the equation should be the number of mutants/the number of cells, not the number of mutants/the number of cell divisions.
mastiffcacher

## Homework Statement

I have to calculate the mutant frequency from a bacterial culture. We were looking at mutations in the lac operon due to the ability to easily see when the mutation occurred. A lac- culture was plated on lacXMM and TSA. The number of revertants on the lacXMM was calculated to be 2.6x10^4 and the number of colonies was 2.26x10^9 on the TSA. These numbers were calculated after an overnight incubation period.

## Homework Equations

2^x=N where N is the number of cells and x is the number of cell divisions

mutant frequency= # mutants/# of cell divisions

## The Attempt at a Solution

Here is my problem. When I use the formulas given to me, I get the # of cell divisions to be 31.07 and a mutant frequency of 836.7. I am not quite sure what this number means. Last week, we were told that we could just use the # of CFU on lacXMM/ # of CFU on TSA. We were told that this was acceptable due to the number of cell divisions being high and that this somehow equaled out. I am not sure what was meant. When I simply do it this way, I get 1.1x10^-5 which I assume means that there are 1.1x10^-5 mutations per cell division.

So which way is correct and why exactly? The second answer is more in line with what I would think that the correct answer is but then why is the other formula the one that I find when I try and look it up? Any insight would be appreciated.

mastiffcacher said:
2^x=N where N is the number of cells and x is the number of cell divisions

mutant frequency= # mutants/# of cell divisions

I am not sure if I have understood correctly (I am not even sure what lacXMM is), but are you sure this is the equation for mutant frequency? The number of cell divisions does not tell you, on its own, the number of cells present - you can have two rounds of cell division and consequently four thousand cells, if you started with 1000 cells. To me, the equation would make more sense if it was the number of mutants/the number of cells, not the number of mutants/the number of cell divisions.
I may be mistaken, but I hope this is of some help.

Sorry it took a little bit to respond but I got busy at school. I was think the same way you were and was confused. As it is explained to me, the number of cell divisions is needed to determine the total cells over time. Since there were so many cells present, we were told to use # of mutants/ # of colonies on the standard plates. Everyone got the same answers so it must have been right. We were told that we actually calculated %mutants but that it would be close to the frequency due to the high cell populations.

And to clarify what lacXMM is, it is an agar plate that is made with 1X M9 minimal media that has been enriched with lactose at low levels (such as 5mM, 10mM, 2mM...). The X refers to X-Gal which acts as a screening tool for functioning LacZ products. It acts as a substrate that can be broken down releasing indole I think but anyway turns the colonies blue. X-Gal is also added to the lactose and M9 media to form a screening media for cells that mutated to a lacI positive mutant.

## What is the Lac Operon and why is it important in genetics?

The Lac Operon is a group of genes in bacteria that are responsible for metabolizing lactose. It is important in genetics because it was one of the first genetic systems to be fully understood and is still studied today as a model for gene regulation.

## How do mutations in the Lac Operon affect the function of the genes?

Mutations in the Lac Operon can cause changes in the function of the genes, either by disrupting the normal function of the genes or by altering the regulation of gene expression. For example, a mutation in the operator region can prevent the repressor protein from binding, leading to constitutive expression of the genes.

## What factors affect the frequency of Lac Operon mutations?

The frequency of Lac Operon mutations can be affected by various factors such as exposure to mutagens, DNA repair mechanisms, and the rate of DNA replication. Additionally, the location of the mutation within the Lac Operon can also impact the frequency, as mutations in certain regions may be more likely to occur than others.

## How is mutant frequency calculated in the Lac Operon?

Mutant frequency is calculated by dividing the number of mutant cells by the total number of cells in a population. This can be determined through various methods such as colony counting or DNA sequencing. The resulting frequency is typically expressed as a percentage or a fraction.

## Why is it important to calculate mutant frequency in the Lac Operon?

Calculating mutant frequency in the Lac Operon allows us to assess the rate of mutation in this genetic system and understand the impact of various factors on this rate. It can also help us identify potential mutations that may have occurred and track changes in the frequency over time. This information is valuable in studying the genetic stability and adaptability of organisms.

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