Hong Life CalculatorsUnderstanding the mutation frequency calculator — concept and principle
This calculator finds the mutant frequency of a bacterial or yeast culture, the proportion of mutant cells at the moment of plating, from colony counts on selective and non-selective plates with their volumes and dilutions. It also gives the two titres and how many cells there are per mutant. Microbiology and genetics labs use it.
How it is calculated
Titre = colonies ÷ volume plated (mL) × 10^x, where 10^−x is the dilution
Mutant frequency = mutant titre ÷ viable titre
One mutant in every … cells = 1 ÷ frequency; per 10⁸ cells = frequency × 10⁸
The principle
Selective plates allow only mutants to grow, so they count mutant cells; non-selective plates count all viable cells. Each colony comes from one cell, so colonies divided by the volume plated and corrected for dilution give cells per millilitre. The ratio of the two is the fraction of the population that carries the mutation. Frequency is not the same as mutation rate: a mutation early in growth can produce a large clone, a "jackpot", so frequencies vary widely between parallel cultures.
Worked example
Default inputs: 42 colonies on selective plates (0.1 mL, undiluted); 180 colonies on non-selective plates (0.1 mL, 10⁻⁶ dilution).
- Mutant titre = 42 ÷ 0.1 × 10⁰ = 420 per mL.
- Viable titre = 180 ÷ 0.1 × 10⁶ = 1,800,000,000 per mL.
- Mutant frequency = 420 ÷ 1.8 × 10⁹ = 2.333 × 10⁻⁷, or 23.33 per 10⁸ cells.
- That is one mutant in every 4,285,714 cells.
| Dilution of the non-selective plating (10^−x, enter x) | Mutant frequency |
|---|---|
| 1.5 | 0.007379 |
| 3 | 0.0002333 |
| 4.5 | 0.000007379 |
| 6 | 2.333e-7 |
| 7.5 | 7.379e-9 |
| 9 | 2.333e-10 |
| 12 | 2.333e-13 |
How to read the result
Compare frequencies only between cultures grown and plated the same way. A higher frequency after a treatment suggests a mutagenic effect, but because of jackpots you need several replicate cultures and a statistical comparison. To estimate the rate per cell division, use a fluctuation test.
Common mistakes
- Entering the dilution factor instead of its exponent.
- Using plates with too few or too many colonies to count reliably.
- Treating frequency as mutation rate.
- Forgetting that both titres must refer to the same culture at the same time.
Frequently asked questions
What is the difference between mutant frequency and mutation rate?
Frequency is the share of mutants present; rate is the chance of a new mutation per cell division.
Why do parallel cultures give different frequencies?
An early mutation can grow into a large clone, a jackpot.
How do I enter a 10⁻⁶ dilution?
Enter 6 as the exponent.
What if no mutants grow?
Report the frequency as less than the value for one colony.
Sources: W. A. Rosche and P. L. Foster, "Determining mutation rates in bacterial populations", Methods 20, 4–17 (2000)