Assignment 12

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Introduction to Bayesian Analyses

In class we will use MrBayes3.2 as installed on the bioinformatics cluster. To start the program, move to the directory where your sequence data are located and type mb.

Skip this paragraph: MrBayes 3.1.2 for the iMacs in the classroom can be downloaded from HERE. Save it to your Desktop. Double-click on the "mrbayes-3.1.2.sit" archive to expand it. Inside the "mrbayes-3.1.2" folder you will find "MrBayes3.1.2" (not to be confused with "MrBayes3.1.2p" which is the parallel-processing version which runs on multiple CPUs). The latest version of the software for different operating systems is available here.

Intro Slides are here

Exercise 1:
The goal of this exercise is to learn how to use MrBayes to reconstruct phylogenies.

  1. Save the file ATPasSU_2014minus.nxs or ATPaseSU_2014plus.nxs into a folder on the cluster (using any of the file transfer program previously installed). The two data sets differ by the inclusion of the divergent flagellar assembly ATPases in the plus dataset. Arrange with your neighbor to work on different datasets. The dataset is of ATPase subunits you used earlier, but in the NEXUS format that MrBayes reads (the nexus format is used by PAUP and many other programs - it allows to pass trees and commands to the different programs -- clustal, seaview, and many other programs write nexus formated files, but often, you need to go into the file with a text editor and change things like the way gaps are treated, or the data type). You might need to rename the file after downloading. Have a look at the file in a text editor and make sure you know the name of the file and the directory where the file is stored (often difficulties arise because one program or the other has added an extension to the file). Start a terminal connection to the bioinformatics cluster, execute the qlogin command to be assigned to a compute node, change the directory to the directory where you stored the nexus files, and start MrBayes through typing mb at the commandline.

  2. At the MrBayes command prompt type "execute ATPaseSU_2014plus.nxs" OR "execute ATPaseSU_2014minus.nxs". This will load the data into the program.

  3. Here is an explanation of the commands at the end of sequence file in the MrBayes block:

    prset aamodelpr=fixed(jones) [this sets the substititution matrix to JTT, a mdern version of PAM]
    lset rates=gamma [this selects the gamma distribution to describe ASRV - this makes the program run a lot slower, you might not want to execute this option]
    mcmcp samplefreq=50 printfreq=50 [this sets the frequency with which the "robot" reports results to the screen and to the files (different files for parameters (.p) and trees (.t))]
    mcmcp savebrlens=yes [mcmcp sets parameters for the chain. savebrlens tells it to save the trees with branchlengths]
    [mcmcp] [if you use this command, it tells the program to save the files under a certain name. This is handy, if you want to read in data from a previous run, but it usually is easier to go with the default]
    mcmcp ngen=5000 [this sets the number of generations to run the chain for to 5000 generations]

    " prset" sets the priors for the model used to calculate likelihoods. In this case we choose the substitution parameters from the JTT amino acid substitution model (Jones et al., 1992).
    " mcmcp " sets parameters for Markov Chain Monte Carlo: we set to sample every 50 generation, to print results to a screen every 50th generation, run 2 chains simultaneously, start with random tree, and save branch lengths.
  4. Type "showmodel" to have MrBayes display the model you selected.

  5. At the MrBayes command prompt type "mcmc". This actually runs the chains, and we set it to run for 5000 generations. The program runs two analyses in parallel (by default each with 4 chains, and three of these chains are heated; it definitely is a good idea to run mb on a fast and remote computer). The smaller the reported average standard deviation of split frequencies is, the more reliable the result (i.e., your run is close enough to infinitely long). When the value is below .015, or when your patience is exhausted, terminate the run, by typing no at the prompt. Give it at least 5 minutes.

  6. Make sure you have typed "no" at the Continue with analysis? (yes/no): prompt.

  7. After the run is finished, the " sump " command will plot the logL vs. generation number, that allows to determine the necessary burnin (you want to discard those samples as "burnin" where the -logL is still rising steadily).
    To see the whole logL curve, you need to set the burnin fraction to .02 . (type help sump at the mb commandline). sump burninfrac=.02

    [Rather than using the sump command, you also can import the parameter file into EXEL and plot the logL values as a chart in EXEL. See below.]

    At the start of the run, the likelihood rapidly increases by orders of magnitude. If the first samples are included in the plot, one really cannot see if the likelihood values fluctuate around a constant
    value. You can exclude the first couple of samples by specifying a burnin or a burninfrac . (The new version of MrBayes uses a burnin of 25% by default.)

    sumt burnifrac =.25
    , where you need to substitute '.25' with the number you obtained in the previous step of the exercise. This command creates a consensus tree, and shows posterior probabilities of the clades. You can take a look at the tree on the screen, or in figtree, or njplot by loading the ATPaseSU_2013minus.nxs.con file into these programs.

    Which value did you use for the burnin/burninfraction?
    Which branch in the tree is the longest? (check the bipartition and branchlengths tables) How long is it?
    What is the measure?
    Are there features of the tree that you find surprising? If yes, what does this tell you about the posterior probabilities calculated by MrBayes?
    Can you explain in a few words, why is it important to exclude a 'burnin' from our analyses?
    Comparing your results with those from your neighbor, what is the maximum posterior probability separating the catalytic (A and beta) and non-catalytic (B and alppha) subunits for the plus and the minus datasets?

    Type " quit " at the prompt to exit MrBayes.

Exercise 2:

Parameter files from MrBayes runs of the same dataset divided into catalytic and regulatory subunits are here: cat reg. This model used on these datasets included among site rate variation calculated using a Gamma distribution.

This is the MrBayes block used:

begin mrbayes;
prset aamodelpr=fixed(jones);
mcmcp samplefreq=100 printfreq=100;
mcmcp savebrlens=yes;
mcmcp ngen=80000;
lset Rates=gamma;

Load these *.p files into Excel, remove the samples corresponding to the burnin (To discard the burnin: delete the 1st line, do a scatterplot of the first two columns, rescale y axis, decide the point from when on the points seem to scatter around a mean without slowly creeping upwards). To determine the 90% credibility intervals for the shape parameter, copy the column containing the shape parameter into a new spreadsheet, sort the column in ascending order (Select data you want to sort, and go to Data->Sort... ). After sorting, exclude 5% of the data on the top and on the bottom. The range of the remaining data gives you the 90% credibility interval. The run had been continued for a total of 160000 generations. (The consensus trees with posterior probabilities are here and here) What are the credibility intervals for the alpha shape parameter of the regulatory and the non-regulatory subunit respectively? (collaborate with your neighbor)


MrBayes by example: Identification of sites under positive selection in a protein


Professor Walter M. Fitch and assistant research biologist Robin M. Bush of UCI's Department of Ecology and Evolutionary Biology, working with researchers at the Centers for Disease Control and Prevention, studied the evolution of a prevalent form of the influenza A virus during an 11-year period from 1986 to 1997. They discovered that viruses having mutations in certain parts of an important viral surface protein were more likely than other strains to spawn future influenza lineages. Human susceptibility to infection depends on immunity gained during past bouts of influenza; thus, new viral mutations are required for new epidemics to occur. Knowing which currently circulating mutant strains are more likely to have successful offspring potentially may help in vaccine strain selection. The researchers' findings appear in the Dec. 3 issue of Science magazine.

Fitch and his fellow researchers followed the evolutionary pattern of the influenza virus, one that involves a never-ending battle between the virus and its host. The human body fights the invading virus by making antibodies against it. The antibodies recognize the shape of proteins on the viral surface. Previous infections only prepare the body to fight viruses with recognizable shapes. Thus, only those viruses that have undergone mutations that change their shape can cause disease. Over time, new strains of the virus continually emerge, spread and produce offspring lineages that undergo further mutations. This process is called antigenic drift. "The cycle goes on and on-new antibodies, new mutants," Fitch said.

The research into the virus' genetic data focused on the evolution of the hemagglutinin gene-the gene that codes for the major influenza surface protein. Fitch and fellow researchers constructed "family trees" for viral strains from 11 consecutive flu seasons. Each branch on the tree represents a new mutant strain of the virus. They found that the viral strains undergoing the greatest number of amino acid changes in specified positions of the hemagglutinin gene were most closely related to future influenza lineages in nine of the 11 flu seasons tested.

By studying the family trees of various flu strains, Fitch said, researchers can attempt to predict the evolution of an influenza virus and thus potentially aid in the development of more effective influenza vaccines.

The research team is currently expanding its work to include all three groups of circulating influenza viruses, hoping that contrasting their evolutionary strategies may lend more insight into the evolution of influenza.

Along with Fitch and Bush, Catherine A. Bender, Kanta Subbarao and Nancy J. Cox of the Centers for Disease Control and Prevention participated in the study.

A talk by Walter Fitch (slides and sound) is here



The goal of this exercise is to detect sites in hemmagglutinin that are under positive selection.

Since the analysis takes a very long time to run (several days), here are the saved results of the MrBayes run: Fitch_HA.nex.p , Fitch_HA.nex.t .

The original data file is flu_data.paup . The dataset is obtained from an article by Yang et al, 2000 . The File used for MrBayes is here

The MrBayes block used to obtain results above is:

begin mrbayes;
set autoclose=yes;
lset nst=2 rates=gamma nucmodel=codon omegavar=Ny98;
mcmcp samplefreq=500 printfreq=500;
mcmc ngen=500000;
sump burnin=50;
sumt burnin=50; end;

Selecting a nucmodel=codon with Omegavar=Ny98 specifies a model in which for every codon the ratio of the rate of non-synonymous to synonymous substitutions is considered. This ratio is called OMEGA. The Ny98 model considers three different omegas, one equal to 1 (no selection, this site is neutral); the second with omega < 1, these sites are under purifying selection; and the third with Omega >1, i.e. these sites are under positive or diversifying selection. (The problem of this model is that the there are only three distinct omegas estimated, and for each site the probability to fall into one of these three classes. If the omega>1 is estimated to be very large, because one site has a large omega, the other sites might not have a high probability to have the same omega, even though they might also be under positive selection. This leads to the site with largest omega to be identified with confidence, the others have more moderate probabilities to be under positive selection).

Note : Version 2.0 of Mr Bayes has a model that estimates omega for each site individually, the new version only allows the Ny98 model as described above..

  1. First, you need to detect how many generations to burn in (meaning the number of samples you will have to discard). Import the file Fitch_HA.nex.p.txt into Excel (link is above, open a new spreadsheet, select DATA, get external data, import text file (if your file does not have a txt extension, select enable all document types) -- select windows format, else defaults; (if you use an older version of Excel you need to import the file into two separate worksheets - it has too many columns; to import the remaining columns of the spreadsheet see 2. below) and plot # of generations versus -LnL values. Determine after how many generations the graph becomes "stationary". The burnin value is that number of generations divided by 50 (since only every 50th generation was sampled; i.e. the burnin value roughly is equal to the number of rows - not quite because there is a header). To more accurately determine the burnin, you need to rescale the Y-axis (click at the Y-axis -- if you aim accurately, you'll get a box that allows rescaling).
    The result (scatterplot of LogL versus generation) might look like this:

  2. Load Fitch_HA.nex.p into Excel. Go to Data->Get External Data->Import Text File. (In older versions of Excel, you need to load the data into 2 sheets, sincethe old Excel does not allow to load more than 256 columns per sheet. To load the data, create a new Excel spreadsheet. Go to Data->Get External Data->Import Text File , and load first 256 columns.

    Go to a separate sheet, and repeat "Get External Data" command to load the rest of the data, you need to block out (=select =make black) and exclude the first 256 columns (the last imported codon ended on nuc 555) -- you need to click the radio button AFTER you selected the columns to skip!). This file contains information for posterior probabilities for each codon (columns) at each sampled generation (rows).)

  3. Calculate average posterior probability for each site of being under positive selection (Do not forget to exclude first N rows as a burnin; you should have detected value of N in the first question of this exercise - to be clear on where the burnin ends, you might want to highlight the rows representing the burnin and select a different font color. (Use AVERAGE() function of Excel, enter the formula in a cell below the values for the individual trees -- starting in column pr+(1,2,3) -- copy the formula to all columns)

  4. Plot average posterior probability vs. site # . (select the row in which you calculated the averages, then click Graph, and select a bar graph). Write down the codon positions for a few sites with the highest posterior probability of being positively selected (the columns name pr+(1,2,3), pr+(4,5,6)....and so on. pr+(1,2,3) mean probability of codon #1 (nucleotide #1, #2 and #3) to be under positive selection))
  1. Determine the 90% credibility interval for the omega<1 value. To do this you sort posterior probability column in ascending order (Select data you want to sort, and go to Data->Sort... ). Again, do not forget to discard the burnin ; the easiest might be to actually delete it.. After sorting, exclude 5% of the data on the top and on the bottom. The range of the remaining data gives you the 90% confidence interval. (Enter answer in box below!)

  2. The structure of hemagglutinin has been crystallized and is publicly available through PDB. Download the PDB file here and examine it with SPDBV. Chain A of the PDB file corresponds to the sequences we did our analysis with (color the molecule according to chain). Below is a comparison of one of the sequences we used for analyses with the sequence for which the structure was determined:

    Using this alignment as a guide, map the site(s) which have the highest probability to belong to the class with omega>1. Where are these sites located in the protein? (Reminders: The position number in the nexus file corresponds to nucleotide sequence, the structure is based on the amino acid sequence - take the third codon position and divide by 3 to find the amino acid. You only want to be concerned with Chain A!)

    What is the 90% crediibility interval for the omega < 1? From your experience does this value indicate strong purifying selection?
    Which codon(s) showed signs of positive selection?
    Which position and which amino acid does this correspond to in the above alignment?
    Where is this aa located in the structure?


    Type logout to release the compute node form the queue.
    If you you encountered problems in your session, check the queue for abandoned sessions using the command qstat. If there are abandoned sessions under your account, kill them by deleting them from the queue by typing qdel job-ID, e.g. "qdel 40000" would delete Job # 40000


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