Fluctuation Tests

This protocol is for doing a Luria-Delbrck fluctuation test to measure the rate at which mutations occur that enable growth on selective agar. This measurement can be used for determining whether a strain is a hypermutator. The colonies isolated on selective agar can also be analyzed by sequencing to determine what types of mutations are responsible for enabling growth.

Fluctuation tests commonly used on REL606-derived strains

mutation type examples nonselective media selective media
Reversion of auxotrophy Ara→Ara+ marker change MG MA
Antibiotic resistance Rifampicin, Nalidixic Acid, Spectinomycin LB LB + antibiotic
Phage resistance T4, T5 LB LB + top agar + phage
REL606-derived strains are resistant to streptomycin and phage T6.

If using D-cycloserine, minimal medium is necessary.

For these experiments we generally use 12 selective plates and 3 count plates per test strain. This is sufficient for resolving differences in mutation rates on the order of 10-fold. For measuring differences in mutation rate that are only 2- to 3-fold, we generally scale this up to 48 selective plates and 12 count plates per test strain. Making accurate comparisons of mutation rates on this scale is difficult. When comparing two strains and looking for very small changes, fluctuation tests for all strains should be done at the same time to avoid any number of confounding factors such as subtle differences in media, how long plates are incubated, whether very small colonies are counted as mutants, etc. Freshly prepared antibiotic and phage stocks should always be used.

Day 2: Revive Test Strains / Prepare Media

  • Start LB cultures of each E. coli strain to be tested by inoculating a scrape of ice or 5 l from the freezer stock into 10 ml of LB in a 50 ml Erlenmeyer flask.
  • Grow cultures overnight at 37C with orbital shaking at 120 rpm.
  • Prepare and pour 12-48 selective plates and 4-12 nonselective plates for each strain to be tested. See media recipes and antibiotic stock solutions

Day 1: Precondition Test Strains

  • Transfer 100 l of the overnight culture into 10 ml of saline. Mix by vortexing. Transfer 100 l from dilution in saline to 10 ml of DM25 in a 50 ml Erlenmeyer flask. (This is a total 10,000× dilution from the LB culture.)
  • Grow cultures overnight at 37C with orbital shaking at 120 rpm.

Day 0: Growth of Independent Cultures

  • Make a dilution of the overnight DM25 culture (through an intermediate tube of saline if necessary) into DM supplemented with an appropriate concentration of glucose (see below) such that the final concentration is 5000 cells / ml (1000 cells / 200 l). 20 ml of this master inoculum mix is sufficient for nearly 100 tubes (plenty for any experiment).
  • Aliquot 200 l of the master inoculum mix into as many 150 mm × 17 mm test tubes as you will be plating on nonselective AND selective media PLUS a few spare tubes. For example, 12 nonselective plates + 48 selective plates + 6 extra = 66 tubes. Use a repeat pipettor if there are many samples. Be sure to include a blank of your DM glucose media to test for contamination.
  • Grow these test tubes exactly 24 hours at 37C with 160 rpm orbital shaking. Be careful about packing too many racks of test tubes close to each other as this can block air flow in some incubators and prevent proper circulation and temperature control. We have had cases of tubes on one side of the incubator being heated until they entirely evaporated.
  • Plate 40 l of the master inoculum mix for each test strain on nonselective media to measure how many cells were actually in your inocula.

When determining what concentration of glucose you should use in the DM to give a high enough number of cells to produce mutants in a 200 l culture. Keep in mind that:

  1. Yields of REL606 in DM glucose media are approximately linear with the limiting glucose concentration between DM25 (0.0025% w/v glucose) and DM2000 (0.2% w/v glucose). DM25 gives 5×107 cells / ml and DM2000 gives 4×109 cells / ml. Evolved strains from the long-term evolution experiment generally yield half these densities, even as early as 2,000 generations. Concentrations of glucose greater than that in DM2000 (0.2% w/v glucose) do not give more cells, as other components of the media, aeration, and waste buildup become limiting.
  2. As a general rule of thumb, the expected average number of mutants per plate will be the total number of cells plated multiplied by the mutation rate. If you are measuring a mutation rate of 5×1010 per cell division and plate 109 cells, then you would expect 0.5 mutants per plate. Keep the expected number of colonies ≥0.5, since you need at least a few plates with mutants (not all empty plates) to get a reasonable estimate of the mutation rate, and ≤50 so that "jackpot" plates that sometimes occur with many more colonies will still be countable.
  3. It is best to try to use the same glucose concentration for all test strains if you are making comparisons of mutation rates, but this may not be possible (for example, wild-type versus a mutT or mutS mutator).
  4. Because the inoculum is so small (~1,000 cells). You may need to grow certain strains that normally grow to saturation in 24 hrs for longer, to reach the maximum cell density and have enough total cells per culture to see mutants.

DM glucose REL606 density (cells/ml) evolved strain (cells/ml) expected mutation rate example
DM10 2×107 1×107 2.5×108 to 2.5×106 phage T6 resistance
DM25 5×107 2.5×107 1×108 to 1×106  
DM50 1×108 5×107 5×109 to 5×107  
DM100 2×108 1×108 2.5×109 to 2.5×107  
DM250 5×108 2.5×108 1×109 to 1×107 rifampicin resistance
DM500 1×109 5×108 5×1010 to 5×108  
DM1000 2×109 1×109 2.5×1010 to 2.5×108 Ara→Ara+
DM2000 4×109 2×109 1×1010 to 1×108  
Most mutators that we see in the long-term lines increase the mutation rate by 10- to 100-fold.

Day 1: Plating of Independent Cultures

  • Make appropriate dilutions of the cultures that will be used for "count plates" that enumerate the total number of cells in each of the independent cultures. Plate the volume required to get 100-200 colonies from these dilutions on nonselective media. When making these dilutions, it is best to transfer the entire culture in each culture tube to the first dilution tube (some evaporation may occur that makes taking a certain number of microliters inconsistent from tube to tube).
  • Incubate all nonselective plates at 37C for 24 hours.
  • Plate the entire volume (now slightly less than 200 l due to evaporation) from the other cultures on selective plates.
  • Incubate all selective plates at 37C for 48-72 hours depending on the selective agent.

Counting Plates

  • On Day 2, count the nonselective plates.
  • On Days 3 and 4, count the selective plates.
    • Depending on the selection, there may be a range of mutants that quickly and slowly form colonies due to different mutations. In some cases these are so distinct that they can be counted separately.
    • It can sometimes be difficult to decide on whether small pinpricks are colonies or where in a gradation of colonies of different sizes to draw a cutoff after 2 days. In general, it is best to decide on an objective size cutoff and then to incubate one further day to 3 days total and see if at this point all colonies are now distinct.
  • Streak out to single colonies on selective agar any mutants that you are saving for further experiments or to sequence. Be aware that compensatory mutations may arise quickly during further growth when there is a fitness cost for antibiotic resistance.

Calculating Mutation Rates

Special Case: Zero mutants observed

If you observe zero mutants in all of your cultures, the MSS fluctuation test calculator will not work. However, you can use a variation of the mathematics of the p0 method to calculate an upper 95% confidence bound on the mutation rate.

The 95% confidence interval on p0, the proportion of T total cultures tested with zero mutants observed can be calculated in R as:

> binom.test(0,T)

Then use the 95%+ value of p0 in the standard formula to get m = ln p 0. And the mutation rate is m divided by the number of cells per population.


  1. Luria SE, Delbrck M. (1943) Mutations of bacteria from virus sensitivity to virus resistance. Genetics 28, 491511.
  2. Rosche WA, Foster PL. (2000) Determining mutation rates in bacterial populations. Methods 20:4-17. «PubMed»
  3. Hall BM, Ma CX, Liang P, Singh KK (2009) Fluctuation AnaLysis CalculatOR: a web tool for the determination of mutation rate using Luria-Delbrck fluctuation analysis. Bioinformatics 25:1564-5.
  4. Lenski RE. LTEE Checking for Contamination «webpage»
  5. Baisa G, Stabo NJ, Welcha RA (2013) Characterization of Escherichia coli D-Cycloserine Transport and Resistant Mutants. Journal of Bacteriology 195:138999.
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