CATH

CodeML/PAML

Install of PAML

Download it from here: http://abacus.gene.ucl.ac.uk/software/paml.html#download

Windows (The bin/ folder already contains windows executables):

cd paml4.6/

Linux:

cd paml4.5/
rm bin/*.exe
cd src
make -f Makefile
ls -l
rm *.o
mv baseml basemlg codeml pamp evolver yn00 chi2 ../bin
chmod +x ../bin/*

MacOSX:

cd paml4.6/
rm bin/*.exe
cd src
cc -O2 -o baseml baseml.c tools.c -lm
cc -O2 -o basemlg basemlg.c tools.c -lm
cc -O2 -o codeml codeml.c tools.c -lm
cc -O2 -o pamp pamp.c tools.c -lm
cc -O2 -o mcmctree mcmctree.c tools.c -lm
cc -O2 -o evolver evolver.c tools.c -lm
cc -O2 -o yn00 yn00.c tools.c -lm
cc -O2 -o chi2 chi2.c -lm
ls -l
rm *.o
mv baseml basemlg codeml pamp evolver yn00 chi2 ../bin
chmod +x ../bin/*

Theoretical principles of the Branch-site model

The selective pressure in protein coding genes can be detected within the framework of comparative genomics. The selective pressure is assumed to be defined by the ratio (ω) dN/dS. dS represents the synonymous rate (changing the amino acid) and dN the non-synonymous rate (keeping the amino acid). In the absence of evolutionary pressure, the synonymous rate and the non-synonymous rate are equal, so the dN/dS ratio is equal to 1. Under purifying selection, natural selection prevents the replacement of amino acids, so the dN will be lower than the dS, and dN/dS < 1. And under positive selection, the replacement rate of amino acid is favoured by selection, and dN/dS > 1.

CodeML and substitutions models:

CodeML is a program from the package PAML, based on Maximum Likelihood, and developed in the lab of Ziheng Yang, University College London.

It estimates various parameters (Ts/Tv, dN/dS, branch length) on the codon (nucleotide) alignment, based on a predefined topology (phylogenetic tree).

Different categories of codon models exist in CodeML:

The model 0 estimates a unique dN/dS ratio for the whole alignment. Not really interesting, except to define a null hypothesis to test against. The other branch models estimate different dN/dS among lineages (ie ASPM, a gene expressed in the brain of primates).
The site models estimate different dN/dS among sites (ie in the antigen-binding groove of the MHC).
The branch-site models estimate different dN/dS among sites and among branches. It can detect episodic evolution in protein sequences. IMHO, the most interesting model.

First, we have to define the branch where we think that position could have occurred. We will call this branch the “foreground branch” and all other branches in the tree will be the “background” branches. The background branches share the same distribution of ω = dN/dS value among sites, whereas different values can apply to the foreground branch.

To compute the likelihood value, two models are computed: a null model, in which the foreground branch may have different proportions of sites under neutral selection to the background (i.e. relaxed purifying selection), and an alternative model, in which the foreground branch may have a proportion of sites under positive selection.

As the alternative model is the general case, it is easier to present it first.

Four categories of sites are assumed in the branch-site model:

Sites with identical dN/dS in both foreground and background branches:

K0 : Proportion of sites that are under purifying selection (ω0 < 1) on both foreground and background branches.
K1 : Proportion of sites that are under neutral evolution (ω1 = 1) on both foreground and background branches.

Sites with different dN/dS between foreground and background branches:

K2a: Proportion of sites that are under positive selection (ω2 ≥ 1) on the foreground branch and under purifying selection (ω0 < 1) on background branches.
K2b: Proportion of sites that are under positive selection (ω2 ≥ 1) on the foreground branch and under neutral evolution (ω1 = 1) on background branches.

For each category, we get the proportion of sites and the associated dN/dS values.

In the null model, the dN/dS (ω2) is fixed to 1:

Sites with identical dN/dS in both foreground and background branches:

K0 : Sites that are under purifying selection (ω0 < 1) on both foreground and background branches.
K1 : Sites that are under neutral evolution (ω1 = 1) on both foreground and background branches.

Sites with different dN/dS between foreground and background branches:

K2a: Sites that are under neutral evolution (ω2 = 1) on the foreground branch and under purifying selection (ω0 < 1) on background branches.
K2b: Sites that are under neutral evolution (ω2 = 1) on the foreground branch and under neutral evolution (ω1 = 1) on background branches.

For each model, we get the log likelihood value (lnL1 for the alternative and lnL0 for the null models), from which we compute the Likelihood Ratio Test (LRT).

The 2×(lnL1-lnL0) follows a χ² curve with degree of freedom of 1, so we can get a p-value for this LRT.

Let's go in details.

Identification of positive seleciton in the serine/threonine-protein kinase gene family

In the evolution vertebrates, we would like to know if the branch leading to the Teleost fishes (genes A50 to A54) in the serine/threonine-protein kinase PAK 2 gene was under positive selection or not. And if yes, which residues were under positive selection.

We need four files to run CodeML (unzip them all):

The multiple nucleotide (CDS) alignment, in PHYLIP format. CodeML will strictly remove any position that contains at least one gap or an unknown “N” nucleotide: tf105351.eut.3.phy.zip
The phylogenetic tree in newick format, with the branch of interest specified by ”#1”(You can view it with NJplot or FigTree): tf105351.eut.3.53876.tree.zip
A command file where all parameters to run CodeML under the alternative model are specified: tf105351.eut.3.53876.ctl.zip
A command file where all parameters to run CodeML under the null model are specified: tf105351.eut.3.53876.fixed.ctl.zip

The tree looks like:

Execute CodeML

Run command file (alternative model):

We estimate the Ts/Tv ratio (fix_kappa = 0) and the dN/dS (fix_omega = 0). The branch-site model is specified by setting these two parameters:

model = 2 (different dN/dS for branches)
NSsites value to 2 (which allows 3 categories for sites: purifying, neutral and positive selection).

     seqfile = TF105351.Eut.3.phy            * sequence data file name
    treefile = TF105351.Eut.3.53876.tree     * tree structure file name
     outfile = TF105351.Eut.3.53876.mlc      * main result file name 

       noisy = 9   * 0,1,2,3,9: how much rubbish on the screen
     verbose = 1   * 1: detailed output, 0: concise output
     runmode = 0   * 0: user tree;  1: semi-automatic;  2: automatic
                   * 3: StepwiseAddition; (4,5):PerturbationNNI; -2: pairwise

     seqtype = 1   * 1:codons; 2:AAs; 3:codons-->AAs
   CodonFreq = 2   * 0:1/61 each, 1:F1X4, 2:F3X4, 3:codon table
       clock = 0   * 0: no clock, unrooted tree, 1: clock, rooted tree
      aaDist = 0   * 0:equal, +:geometric; -:linear, {1-5:G1974,Miyata,c,p,v}
       model = 2   * models for codons:
                   * 0:one, 1:b, 2:2 or more dN/dS ratios for branches
     NSsites = 2   * 0:one w; 1:NearlyNeutral; 2:PositiveSelection; 3:discrete;
                   * 4:freqs; 5:gamma;6:2gamma;7:beta;8:beta&w;9:beta&gamma;10:3normal
       icode = 0   * 0:standard genetic code; 1:mammalian mt; 2-10:see below
       Mgene = 0   * 0:rates, 1:separate; 2:pi, 3:kappa, 4:all
   fix_kappa = 0   * 1: kappa fixed, 0: kappa to be estimated
       kappa = 2   * initial or fixed kappa
   fix_omega = 0   * 1: omega or omega_1 fixed, 0: estimate
       omega = 1   * initial or fixed omega, for codons or codon-based AAs
       getSE = 0       * 0: don't want them, 1: want S.E.s of estimates
RateAncestor = 0       * (0,1,2): rates (alpha>0) or ancestral states (1 or 2)
  Small_Diff = .45e-6  * Default value.
   cleandata = 1       * remove sites with ambiguity data (1:yes, 0:no)?
 fix_blength = 0       * 0: ignore, -1: random, 1: initial, 2: fixed

Run command file (null model):

The command file for the null model is the same as for the alternative model, except for two parameters (in red):

The name of the output file (outfile) is different.
The dN/dS ratio is fixed to 1 (fix_omega = 1).

     seqfile = TF105351.Eut.3.phy               * sequence data file name
    treefile = TF105351.Eut.3.53876.tree        * tree structure file name
     outfile = TF105351.Eut.3.53876.fixed.mlc   * main result file name
 
       noisy = 9   * 0,1,2,3,9: how much rubbish on the screen
     verbose = 1   * 1: detailed output, 0: concise output
     runmode = 0   * 0: user tree;  1: semi-automatic;  2: automatic
                * 3: StepwiseAddition; (4,5):PerturbationNNI; -2: pairwise

     seqtype = 1   * 1:codons; 2:AAs; 3:codons-->AAs
   CodonFreq = 2   * 0:1/61 each, 1:F1X4, 2:F3X4, 3:codon table
       clock = 0   * 0: no clock, unrooted tree, 1: clock, rooted tree
      aaDist = 0   * 0:equal, +:geometric; -:linear, {1-5:G1974,Miyata,c,p,v}
       model = 2   * models for codons:
                   * 0:one, 1:b, 2:2 or more dN/dS ratios for branches
     NSsites = 2   * 0:one w; 1:NearlyNeutral; 2:PositiveSelection; 3:discrete;
                   * 4:freqs; 5:gamma;6:2gamma;7:beta;8:beta&w;9:beta&gamma;10:3normal
       icode = 0   * 0:standard genetic code; 1:mammalian mt; 2-10:see below
       Mgene = 0   * 0:rates, 1:separate; 2:pi, 3:kappa, 4:all
   fix_kappa = 0   * 1: kappa fixed, 0: kappa to be estimated
       kappa = 2   * initial or fixed kappa
   fix_omega = 1   * 1: omega or omega_1 fixed, 0: estimate               <- this line was changed, dN/dS is fixed to 1.
       omega = 1   * initial or fixed omega, for codons or codon-based AAs**    
       getSE = 0       * 0: don't want them, 1: want S.E.s of estimates
RateAncestor = 0       * (0,1,2): rates (alpha>0) or ancestral states (1 or 2)
  Small_Diff = .45e-6  * Default value.
   cleandata = 1       * remove sites with ambiguity data (1:yes, 0:no)?
 fix_blength = 0       * 0: ignore, -1: random, 1: initial, 2: fixed

Launch CodeML:

In MacOSX/Linux, this will look like:

codeml ./TF105351.Eut.3.53876.ctl
codeml ./TF105351.Eut.3.53876.fixed.ctl

In Windows:

codeml.exe TF105351.Eut.3.53876.ctl
codeml.exe TF105351.Eut.3.53876.fixed.ctl

Two mlc output files are produced (as it can take time, you can download them directly in the next step).:

Analyse results

Step 1) Assign significance of the detection of positive selection on the selected branch:

We retieve the likelihood values lnL1 and lnL0 from TF105351.Eut.3.53876.mlc and TF105351.Eut.3.53876.fixed.mlc files, respectively.

We retieve the number of parameters np1 and np0 from TF105351.Eut.3.53876.mlc and TF105351.Eut.3.53876.fixed.mlc files, respectively.

lnL(ntime: 41 np: 46): -4707.210163 +0.000000 (lnL1)
lnL(ntime: 41 np: 45): -4710.222252 +0.000000 (lnL0)

We can construct the LRT (you can use your favourite spreadsheet for that. Or even better with R):

ΔLRT = 2×(lnL1 - lnL0) = 2×(-4707.210163 - (-4710.222252)) = 6.024178

The degree of freedom is 1 (np1 - np0 = 46 - 45).

(With OpenOffice: 1-CHISQDIST(6.024178;1))

p-value = 0.014104 (under χ²) ⇒ significant!

A significant result with the branch-site codon model means that positive selection affected a subset of sites during a specific evolutionary time (also called episodic model of protein evolution).

Step 2) If significant, we can retrieve sites under positive selection

In the TF105351.Eut.3.53876.mlc, we can retrieve sites under positive selection using the Bayes Empirical Bayes (BEB) method:

    Positive sites for foreground lineages Prob(w>1):
        36 K 0.971*
       159 C 0.993**

Amino acids K and C refer to the first sequence in the alignment.

Position 36 has a high probability (97.1%) of being under positive selection. It shifted from a lysine to a glycine.
Position 159 has a very high probability (99.3%) of being under positive selection.

You can visualise the multiple in Jalview.

- Open Jalview

- Load TF105351.Eut.3.phy

- Then: Calculate→translate cDNA. (tips: by moving the pointer on the amino acids alignment, you can see the corresponding codon in the nucleotide alignment.