Hong Life CalculatorsUnderstanding the mutation rate calculator — concept and principle
This calculator estimates the mutation rate per cell per division from a Luria–Delbrück fluctuation test, using either the p₀ method (the share of cultures with no mutants) or the Lea–Coulson median method. It also gives the expected number of mutations per culture and checks whether p₀ is in the reliable range. Microbial geneticists use it to measure spontaneous and induced mutation rates.
How it is calculated
p₀ method: p₀ = cultures without mutants ÷ total cultures; m = −ln p₀
Median method: m solves r̃ ÷ m − ln m = 1.24, where r̃ is the median number of mutants per culture
Mutation rate μ = m ÷ N_t
- N_t is the final number of viable cells per culture (entered in millions), roughly the number of cell divisions in the culture.
The principle
In a fluctuation test many small cultures are grown in parallel from few cells and each is plated entirely on selective medium. Mutations happen at random during growth, so the number of mutation events per culture follows a Poisson distribution with mean m. The chance of a culture having none is e^(−m), so the fraction of empty cultures gives m directly. A culture that grows to N_t cells has gone through about N_t divisions, so m ÷ N_t is the rate per division. Luria and Delbrück used this design in 1943 to show that mutations arise before selection, not because of it.
Worked example
Default inputs: p₀ method, 30 cultures, 12 without mutants, 200 million cells per culture.
- p₀ = 12 ÷ 30 = 0.4.
- m = −ln 0.4 = 0.9163 mutations per culture.
- μ = 0.9163 ÷ (200 × 10⁶) = 4.581 × 10⁻⁹ per cell per division.
- p₀ lies within 10–80%: yes — reliable range.
| Final viable cells per culture (millions) | Mutation rate (per cell per division) |
|---|---|
| 50 | 1.833e-8 |
| 100 | 9.163e-9 |
| 150 | 6.109e-9 |
| 200 | 4.581e-9 |
| 250 | 3.665e-9 |
| 300 | 3.054e-9 |
| 400 | 2.291e-9 |
How to read the result
Bacterial mutation rates for a single gene are typically very small numbers like this one. The p₀ method works best when p₀ is between about 0.1 and 0.8; if almost all cultures have mutants, use fewer cells or the median method. Some authors report rates per generation using m × ln 2 ÷ N_t, so state which convention you use.
Common mistakes
- Plating only part of each culture without correcting.
- Using too few parallel cultures, which gives a poor estimate of p₀.
- Confusing mutant frequency with mutation rate.
- Mixing conventions (per division versus per generation).
Frequently asked questions
Why is the p₀ method reliable only between 10% and 80%?
Outside that range, a few cultures more or less change ln p₀ a lot, so the estimate is noisy.
What is a fluctuation test?
Many parallel cultures plated on selective medium to count mutants in each.
What does the median method use?
The median number of mutant colonies, useful when most cultures have mutants.
Why divide by the final cell number?
It approximates the number of cell divisions in the culture.
Sources: S. E. Luria and M. Delbrück, Genetics 28, 491–511 (1943) · D. E. Lea and C. A. Coulson, J. Genet. 49, 264–285 (1949) · W. A. Rosche and P. L. Foster, Methods 20, 4–17 (2000)