# Gumbel¶

The Gumbel can be used to determine which genes are essential in a single condition. It does a gene-by-gene analysis of the insertions at TA sites with each gene, makes a call based on the longest consecutive sequence of TA sites without insertion in the genes, calculates the probability of this using a Bayesian model.

Note

Intended only for Himar1 datasets.

## How does it work?¶

This method for identifying essential genes is based on analyzing ‘gaps’, or consecutive sequences of TA sites lacking insertions. The statistical significance of the length of a gap is determined using the Gumbel distribution, which is a form of an Extreme-Value distribution.

For a formal description of how this method works, see our paper [DeJesus2013]:

DeJesus, M.A., Zhang, Y.J., Sassettti, C.M., Rubin, E.J., Sacchettini, J.C., and Ioerger, T.R. (2013). Bayesian analysis of gene essentiality based on sequencing of transposon insertion libraries. Bioinformatics, 29(6):695-703.

Update (2021) - Binomial

Since the Gumbel method depends on the overall saturation (percent of TA sites with insertions), it can sometimes call a lot of smaller genes ‘Uncertain’. This might reduce the total number of essentials detected. For example, if the saturation is ~30%, no genes with fewer than ~10 TA sites might confidently be labeled as Essential. In particular, there are often genes with no insertions that look like they should obviously be called essential, and yet, they are too short to be confidently called essential in low-saturation datasets by the conservative Gumbel model.

To compensate for this, we have added a simple Binomial model for detecting small genes totally lacking insertions (described in (Choudhery et al, 2021)). In the output file, they are labled as ‘EB’ to distinguish them from essentials (E) based on the Gumbel model. The EB genes supplement genes marked E by Gumbel, and the combination of the 2 groups (E and EB) should be considered as ‘essentials’. The number of genes in each category is reported in a table in the header of the output file, like this:

(for an M. tuberculosis TnSeq dataset with 60% saturation:)
#Summary of Essentiality Calls:
#  E  =  551 (essential based on Gumbel)
#  EB =   94 (essential based on Binomial)
#  NE = 2829 (non-essential)
#  U  =  262 (uncertain)
#  S  =  254 (too short)

(for an M. tuberculosis TnSeq dataset with 40% saturation:)
#  E  =  194 (essential based on Gumbel)
#  EB =  315 (essential based on Binomial)
#  NE = 2441 (non-essential)
#  U  =  774 (uncertain)
#  S  =  266 (too short)


## Usage¶

> python3 transit.py gumbel <comma-separated .wig files> <annotation .prot_table or GFF3> <output file> [Optional Arguments]
Optional Arguments:
-s <integer>    :=  Number of samples. Default: -s 10000
-b <integer>    :=  Number of Burn-in samples. Default -b 500
-m <integer>    :=  Smallest read-count to consider. Default: -m 1
-t <integer>    :=  Trims all but every t-th value. Default: -t 1
-r <string>     :=  How to handle replicates. Sum or Mean. Default: -r Sum
-iN <float>     :=  Ignore TAs occuring at given percentage (as integer) of the N terminus. Default: -iN 0
-iC <float>     :=  Ignore TAs occuring at given percentage (as integer) of the C terminus. Default: -iC 0


## Parameters¶

• Samples: Gumbel uses Metropolis-Hastings (MH) to generate samples of posterior distributions. The default setting is to run the simulation for 10,000 iterations. This is usually enough to assure convergence of the sampler and to provide accurate estimates of posterior probabilities. Less iterations may work, but at the risk of lower accuracy.
• Burn-In: Because the MH sampler many not have stabilized in the first few iterations, a “burn-in” period is defined. Samples obtained in this “burn-in” period are discarded, and do not count towards estimates.
• Trim: The MH sampler produces Markov samples that are correlated. This parameter dictates how many samples must be attempted for every sampled obtained. Increasing this parameter will decrease the auto-correlation, at the cost of dramatically increasing the run-time. For most situations, this parameter should be left at the default of “1”.
• Minimum Read: The minimum read count that is considered a true read. Because the Gumbel method depends on determining gaps of TA sites lacking insertions, it may be susceptible to spurious reads (e.g. errors). The default value of 1 will consider all reads as true reads. A value of 2, for example, will ignore read counts of 1.
• Replicates: Determines how to deal with replicates by averaging the read-counts or summing read counts across datasets. This should not have an affect for the Gumbel method, aside from potentially affecting spurious reads.

## Outputs and diagnostics¶

The Gumbel method generates a tab-separated output file at the location chosen by the user. This file will automatically be loaded into the Results Files section of the GUI, allowing you to display it as a table. Alternatively, the file can be opened in a spreadsheet software like Excel as a tab-separated file. The columns of the output file are defined as follows:

ORF Gene ID.
Name Name of the gene.
Description Gene description.
k Number of Transposon Insertions Observed within the ORF.
n Total Number of TA dinucleotides within the ORF.
r Length of the Maximum Run of Non-Insertions observed.
s Span of nucleotides for the Maximum Run of Non-Insertions.
zbar Posterior Probability of Essentiality.
Call Essentiality call for the gene. Depends on FDR corrected thresholds. E=Essential U=Uncertain, NE=Non-Essential, S=too short

Note: Technically, Bayesian models are used to calculate posterior probabilities, not p-values (which is a concept associated with the frequentist framework). However, we have implemented a method for computing the approximate false-discovery rate (FDR) that serves a similar purpose. This determines a threshold for significance on the posterior probabilities that is corrected for multiple tests. The actual thresholds used are reported in the headers of the output file (and are near 1 for essentials and near 0 for non-essentials). There can be many genes that score between the two thresholds (t1 < zbar < t2). This reflects intrinsic uncertainty associated with either low read counts, sparse insertion density, or small genes. If the insertion_density is too low (< ~30%), the method may not work as well, and might indicate an unusually large number of Uncertain or Essential genes.

## Run-time¶

The Gumbel method takes on the order of 10 minutes for 10,000 samples. Run-time is linearly proportional to the ‘samples’ parameter, or length of MH sampling trajectory. Other notes: Gumbel can be run on multiple replicates; replicate datasets will be automatically merged.