ProtocolsFluctuationTests < Lab

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---+!! Fluctuation Tests

%TOC%

---++ Introduction

This protocol is for doing a Luria-Delbrück 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. For the right kind of selection, this can give information about the mutation spectrum.

*Fluctuation tests commonly used on REL606-derived strains* 
%TABLE{headeralign="left,center,center,center" dataalign="left,center,center,center" valign="bottom"}%
| *mutation type* | *examples* | *nonselective media* | *selective media* |
| Reversion of auxotrophy | Ara<sup>&ndash;</sup>&rarr;Ara<sup>+</sup> 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.

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.

---++ Experimental Procedure

---+++ Day &ndash;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 µl from the freezer stock into 10 ml of LB in a 50 ml Erlenmeyer flask.
   * Grow cultures overnight at 37°C 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 [[ProtocolsMediaRecipes][media recipes]] and [[ProtocolsAntibioticStockSolutions][antibiotic stock solutions]]

---+++ Day &ndash;1: Precondition Test Strains

   * Transfer 100 µl of the overnight culture into 10 ml of saline. Mix by vortexing. Transfer 100 µl 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 37°C with orbital shaking at 120 rpm.

   %ICON{"warning"}% *Preconditioning is important even if LB will be used in the fluctuation test. Suggested dilution is 1,000 to 10,000.* 

---+++ 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 µl). 20 ml of this master inoculum mix is sufficient for nearly 100 tubes (plenty for any experiment).
   * Aliquot 200 µl 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 37°C 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 µl 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 µl 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 5×10<sup>7</sup> cells / ml and DM2000 gives 4×10<sup>9</sup> 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.
   1 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 5×10<sup>&ndash;10</sup> per cell division and plate 10<sup>9</sup> cells, then you would expect 0.5 mutants per plate. Keep the expected number of colonies &ge;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 &le;50 so that "jackpot" plates that sometimes occur with many more colonies will still be countable. (General info on ideal CFU's for plate counts --&gt; https://search.proquest.com/docview/896470363?pq-origsite=gscholar)
   1 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).
   1 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. %ENDCOLOR%

%TABLE{headeralign="left,center,center,center,left" dataalign="left,center,center,center,left" valign="bottom"}%
| *DM glucose* | *REL606 density (cells/ml)* | *evolved strain (cells/ml)* | *expected mutation rate* | *example* |
| DM10 | 2×10<sup>7</sup> | 1×10<sup>7</sup> | 2.5×10<sup>&ndash;8</sup> to 2.5×10<sup>&ndash;6</sup> | phage T6 resistance |
| DM25 | 5×10<sup>7</sup> | 2.5×10<sup>7</sup> | 1×10<sup>&ndash;8</sup> to 1×10<sup>&ndash;6</sup> | |
| DM50 | 1×10<sup>8</sup> | 5×10<sup>7</sup> | 5×10<sup>&ndash;9</sup> to 5×10<sup>&ndash;7</sup> | |
| DM100 | 2×10<sup>8</sup> | 1×10<sup>8</sup> | 2.5×10<sup>&ndash;9</sup> to 2.5×10<sup>&ndash;7</sup> | |
| DM250 | 5×10<sup>8</sup> | 2.5×10<sup>8</sup> | 1×10<sup>&ndash;9</sup> to 1×10<sup>&ndash;7</sup> | rifampicin resistance |
| DM500 | 1×10<sup>9</sup> | 5×10<sup>8</sup> | 5×10<sup>&ndash;10</sup> to 5×10<sup>&ndash;8</sup> | |
| DM1000 | 2×10<sup>9</sup> | 1×10<sup>9</sup> | 2.5×10<sup>&ndash;10</sup> to 2.5×10<sup>&ndash;8</sup> | Ara<sup>&ndash;</sup>&rarr;Ara<sup>+</sup> |
| DM2000 | 4×10<sup>9</sup> | 2×10<sup>9</sup> | 1×10<sup>&ndash;10</sup> to 1×10<sup>&ndash;8</sup> | |
 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 ([[https://advanced.bact.wisc.edu/instr/book/displayarticle/103][Click here for cell count and dilution basics]]). 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). 
      * For count plates, you will likely need to do 2X 1:100 dilutions and plate between 200-50 microliters. You should have three 10 ml saline tubes (your first tube with your entire culture and 2X 1:100 dilutions).
      * Use the following formula to help you calculate your total population of cells, based on the dilution scheme discussed above = (volume of tube 1) x (dilution) x (1/volume plated in microliters)

   * Incubate all nonselective plates at 37°C for 24 hours.
   * Plate the entire volume (now slightly less than 200 µl due to evaporation) from the other cultures on selective plates.
   * Incubate all selective plates at 37°C 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.

---++ Data Analysis: Calculating Mutation Rates

There are a few different ways to calculate mutation rates from your results.

---+++ Run the analysis in R using Fluxxer.R / rSalvador (preferred)

   * Download the script =fluxxer.R= ([[https://github.com/barricklab/barricklab/blob/master/fluxxer.R][direct link]]) from the [[https://github.com/barricklab/barricklab][Barricklab GitHub Repository]].
   * This script uses the [[https://github.com/eeeeeric/rSalvador][rSalvador package]] to calculate mutation rates. Please cite rSalvador if you use =fluxxer.R=!
   * This file is an R script that can be run at the command line like an executable. You can put it in your =$PATH= or directly invoke it with a command like: =$ ./fluxxer.R=.
   * Run the command with no arguments or inspect the header of the R file using a text editor or RStudio to learn about the input file format and command line options.
   * An example input file =fluxxer_example_input.csv= ([[https://github.com/barricklab/barricklab/blob/master/fluxxer_example_input.csv][direct link]]) that you can use as as template for entering your data in the correct format is available in the [[https://github.com/barricklab/barricklab][Barricklab GitHub Repository]]
   * Here is a command line that you could use to analyze =fluxxer_example_input.csv=. The =-c= option performs an optional calculation of the significance of the difference in mutation rates between each pair of strains.

%CODE{"bash"}%
fluxxer.R -i fluxxer_example_input.csv -o fluxxer_example_output -c
%ENDCODE%

---+++ mlemur (preferred as well, plus easier install and analysis)

You can use the [[https://github.com/krystianll/mlemur][mlemur user interface]] to analyze groups of samples.
   * You must install the software using R.  After install, you will be able to open the software and easily plug in your data and analyze.
   * The software allows you to designate the starting population sizes, dilutions performed, fitness of mutants, etc.
   * Output will include mutation rates, 95% confidence intervals, predicted number of mutation events, etc.


---+++ FALCOR Web Tool (prior method - information may be out of date)

You can use the [[https://lianglab.brocku.ca/FALCOR/][FALCOR web tool]] to analyze individual samples.
   * Use the setting "MSS Maximum Likelihood Estimator" to calculate the mutation rate from your data. 
   * You must use a browser that allows Java code to execute. (Firefox but not Chrome will work, for example.)
   * The default java security settings will block the application from running, producing a non-helpful error message of: "application blocked by security settings". To over come this, open the java control panel [[http://java.com/en/download/help/jcp_security.xml][(Information on how to access the java control panel can be found here.)]] , and add the website address (http://www.keshavsingh.org/protocols/FALCOR.html) to the exception site list. This is a better way of letting the Java code run than lowering your overall security settings which can be very dangerous. 

---+++ 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 p<sub>0</sub> method to calculate an upper 95% confidence bound on the mutation rate.

The 95% confidence interval on p<sub>0</sub>, the proportion of T total cultures tested with zero mutants observed can be calculated in R as:

%CODE{"python"}%
> binom.test(0,T)
%ENDCODE%

Then use the 95%+ value of p<sub>0</sub> in the standard formula to get m = &ndash;ln p <sub>0</sub>. And the mutation rate is m divided by the number of cells per population.

---++ References

   1 Luria SE, Delbrück M. (1943) Mutations of bacteria from virus sensitivity to virus resistance. _Genetics_ *28*, 491&ndash;511.
   1 Rosche WA, Foster PL. (2000) Determining mutation rates in bacterial populations. _Methods_ *20*:4-17. [[http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=ShowDetailView&TermToSearch=10610800][«PubMed»]]
   1 Hall BM, Ma CX, Liang P, Singh KK (2009) Fluctuation AnaLysis CalculatOR: a web tool for the determination of mutation rate using Luria-Delbrück fluctuation analysis. _Bioinformatics_ *25*:1564-5.
   1 Lenski RE. LTEE Checking for Contamination [[http://myxo.css.msu.edu/ecoli/contam.html][«webpage»]]
   1 Baisa G, Stabo NJ, Welcha RA (2013) Characterization of Escherichia coli D-Cycloserine Transport and Resistant Mutants. _Journal of Bacteriology_ *195*:1389&ndash;99.
   1 &#321;azowski, K. (2023). Efficient, robust, and versatile fluctuation data analysis using MLE MUtation Rate calculator (mlemur). Mutation Research/Fundamental and Molecular Mechanisms of Mutagenesis, 826, 111816. [[https://doi.org/10.1016/j.mrfmmm.2023.111816][link to article]]
This topic: Lab > WebHome > ProtocolsFluctuationTests
Topic revision: r30 - 2025-08-01 - TylerDeJong