Assignment 12

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Likelihood ratio tests

Open seaview, and load ATPaseSU_2015plus.nxs.txt. Note that these sequences are already aligned. We want to calculate two likelihood values using Trees — PhyML:

1. Model:LG, Across site rate variation: None — we'll call this "LG"
2. Model:LG, Across site rate variation: Optimized (4) — we'll call this "LG+Gamma"

Collaborate with your neighbor to get likelihoods for LG and LG+Gamma (do one each). The log-likelihood score is shown in the tree building text window in seaview — once the computation is complete it appears as "Log likelihood of the current tree:".

One important condition that has to be fulfilled before one can use a Likelihood Ratio Test (LRT) to compare two models, is that the models should be "nested". This means that the simpler model must be a constrained version of the parameter-rich model. The likelihood ratio test is performed by doubling the difference in log-likelihood scores and comparing this test statistic with the critical value from a chi-squared distribution having degrees of freedom equal to the difference in the number of estimated parameters in the two models. The parameter-rich model will always have a better fit, due to the extra parameters and will therefore have the highest log-likelihood, so the difference should be a positive number. In this case there is 1 degree of freedom — the gamma shape parameter. Use this online chi-square calculator to determine the significance of the test.

Does the LG+Gamma model explain the data significantly better than an equal rates LG model? Why?

Open seaview, and load ATPaseSU_2015plus.phy.txt. Note that these sequences are already aligned (and there are no gaps!). We want to calculate two likelihood values using PhyML:

1. Model:WAG, Across site rate variation: None — we'll call this "WAG"
2. Model:WAG, Across site rate variation: Optimized (4) — we'll call this "WAG+Gamma"

Again, collaborate with your neighbor to get likelihoods for WAG and WAG+Gamma. Does the WAG+Gamma model explain the data significantly better than an equal rates WAG model? Why?

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.

Intro Slides are here

Exercise 2:
The goal of this exercise is to learn how to use MrBayes to reconstruct phylogenies.

1. Log on to the bbcsrv3.biotech.uconn.edu cluster using Bitvise SSH Client.
   
   
2. Save the file ATPaseSU_2015minus.nxs.txt or ATPaseSU_2015plus.nxs.txt into a folder on the cluster (e.g., save to Desktop, then use Bitvise SFTP). 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 (e.g., right-click the file, and Edit with Notepad++). On 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.
   
   
3. At the MrBayes command prompt type "execute ATPaseSU_2015plus.nxs.txt" OR "execute ATPaseSU_2015minus.nxs.txt". This will load the data into the program.
   
   
4. 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 modern 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 filename=ATPaseSU.nexus] [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.
   The MrBayes manual (pdf) , which incluedes tutorial sections, is here,
   
   
5. Type "showmodel" to have MrBayes display the model you selected.
   
   
6. 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.
   
   
7. Make sure you have typed "no" at the Continue with analysis? (yes/no): prompt.
   
   
8. 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 EXCEL and plot the logL values as a chart in EXCEL. See below.]
   [Or you can download the tracer application that can read the parameter files from MrBayes, and provides an easy intuitive and interactive way to evaluate these files with respect to burnin and confidence intervals]
   
   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.)
   
   Type
   sumt burninfrac =.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 by loading the ATPaseSU_2015minus.nxs.txt.con.tre file into the program.
   
   
9. Load the .p files into Excel or into tracer (local download link here) , and determine the mean, median and 95% credible interval for the Tree Length (TL) and shape parameter (gamma). (If you want .p, .t, and consensus trees from a longer mcmcm run download this file.)
   
   1) Which value did you use for the burnin/burninfraction?
   2) Which branch in the tree is the longest? (check the bipartition and branchlengths tables)
   3) How long is it?
   4) What is the measure?
   5) Are there features of the tree that you find surprising? If yes, what does this tell you about the posterior probabilities calculated by MrBayes?
   6) Can you explain in a few words, why is it important to exclude a 'burnin' from our analyses?
   7) Comparing your results with those from your neighbor, what is the posterior probability for the clann of the the catalytic (A and beta) and non-catalytic (B and alpha) subunits from the plus and the minus datasets?
   8) What explains the difference?
   9) What is the 95% credible interval for the shape parameter?
   
   
   
   Type " quit " at the prompt to exit MrBayes.

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

Background:

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.

Exercise3:

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.txt, Fitch_HA.nex.t.txt .

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:

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). Open the file Fitch_HA.nex.p.txt with Excel and plot # of generations versus -LnL values. Determine after how many generations the graph becomes "stationary" (hint: change the Y-axis bounds to "zoom in", e.g., -3300 min to -3200 max). 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. This file contains information for posterior probabilities for each codon (columns) at each sampled generation (rows). Scroll to the right to see these columns, starting with pr+(1,2,3), pr+(4,5,6), etc. 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)
   
   
3. 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))

5. Determine the 95% 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!)
   
   
6. 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 95% credibility interval for the omega < 1?
   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?
   

Finished?

Type logout to release the compute node from 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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