This example shows a method that can be used to investigate the significance of sequence alignments. The number of identities or positives in an alignment is not a clear indicator of a significant alignment. A permutation of a sequence from an alignment will have similar percentages of positives and identities when aligned against the original sequence. The score from an alignment is a better indicator of the significance of an alignment. This example uses the same Tay-Sachs disease related genes and proteins analyzed in the example Aligning Pairs of Sequences.

**Accessing NCBI Data from the MATLAB® Workspace**

In this example, you will work directly with protein data so use `getgenpept`

instead of `getgenbank`

to download the data from the NCBI site. First read the human protein information into MATLAB®.

```
humanProtein = getgenpept('NP_000511');
```

Results from a BLASTX search performed with this sequence showed that a Drosophila protein, GenPept accession number *AAM29423*, has some similarity to the human *HEXA* sequence. Use `getgenpept`

to download this sequence.

```
flyProtein = getgenpept('AAM29423');
```

For your convenience, previously downloaded sequences are included in a MAT-file. Note that data in public repositories is frequently curated and updated; therefore the results of this example might be slightly different when you use up-to-date datasets.

load('flyandhumanproteins.mat','humanProtein','flyProtein') seqdisp(humanProtein) seqdisp(flyProtein)

ans = >gi|189181666|gb|NP_000511.2| beta-hexosaminidase subunit alpha pre... 1 MTSSRLWFSL LLAAAFAGRA TALWPWPQNF QTSDQRYVLY PNNFQFQYDV SSAAQPGCSV 61 LDEAFQRYRD LLFGSGSWPR PYLTGKRHTL EKNVLVVSVV TPGCNQLPTL ESVENYTLTI 121 NDDQCLLLSE TVWGALRGLE TFSQLVWKSA EGTFFINKTE IEDFPRFPHR GLLLDTSRHY 181 LPLSSILDTL DVMAYNKLNV FHWHLVDDPS FPYESFTFPE LMRKGSYNPV THIYTAQDVK 241 EVIEYARLRG IRVLAEFDTP GHTLSWGPGI PGLLTPCYSG SEPSGTFGPV NPSLNNTYEF 301 MSTFFLEVSS VFPDFYLHLG GDEVDFTCWK SNPEIQDFMR KKGFGEDFKQ LESFYIQTLL 361 DIVSSYGKGY VVWQEVFDNK VKIQPDTIIQ VWREDIPVNY MKELELVTKA GFRALLSAPW 421 YLNRISYGPD WKDFYIVEPL AFEGTPEQKA LVIGGEACMW GEYVDNTNLV PRLWPRAGAV 481 AERLWSNKLT SDLTFAYERL SHFRCELLRR GVQAQPLNVG FCEQEFEQT ans = >gi|21064387|gb|AAM29423.1| RE17456p [Drosophila melanogaster]. 1 MSLAVSLRRA LLVLLTGAIF ILTVLYWNQG VTKAQAYNEA LERPHSHHDA SGFPIPVEKS 61 WTYKCENDRC MRVGHHGKSA KRVSFISCSM TCGDVNIWPH PTQKFLLSSQ THSFSVEDVQ 121 LHVDTAHREV RKQLQLAFDW FLKDLRLIQR LDYGGSSSEP TVSESSSKSR HHADLEPAAT 181 LFGATFGVKK AGDLTSVQVK ISVLKSGDLN FSLDNDETYQ LSTQTEGHRL QVEIIANSYF 241 GARHGLSTLQ QLIWFDDEDH LLHTYANSKV KDAPKFRYRG LMLDTSRHFF SVESIKRTIV 301 GMGLAKMNRF HWHLTDAQSF PYISRYYPEL AVHGAYSESE TYSEQDVREV AEFAKIYGVQ 361 VIPEIDAPAH AGNGWDWGPK RGMGELAMCI NQQPWSFYCG EPPCGQLNPK NNYTYLILQR 421 IYEELLQHTG PTDFFHLGGD EVNLDCWAQY FNDTDLRGLW CDFMLQAMAR LKLANNGVAP 481 KHVAVWSSAL TNTKRLPNSQ FTVQVWGGST WQENYDLLDN GYNVIFSHVD AWYLDCGFGS 541 WRATGDAACA QYRTWQNVYK HRPWERMRLD KKRKKQVLGG EVCMWTEQVD ENQLDNRLWP 601 RTAALAERLW TDPSDDHDMD IVPPDVFRRI SLFRNRLVEL GIRAEALFPK YCAQNPGECI

**A First Comparison and Global Alignment**

The first thing to do is to use `seqdotplot`

to see if there are any areas that are clearly aligned. This doesn't show any obvious alignments, but there are some areas of interest.

seqdotplot(humanProtein,flyProtein,3,2) title('Dot Plot of Two HexA-like Proteins'); ylabel('Human Protein');xlabel('Drosophila Protein');

Notice that there are a few diagonal stretches in the dot plot. This is not particularly good evidence of a significant global alignment, but you can try a global alignment using the function `nwalign`

. The BLOSUM50 scoring matrix is used by default.

```
[sc50,globAlig50] = nwalign(humanProtein,flyProtein);
fprintf('Score = %g \n',sc50)
showalignment(globAlig50);
```

Score = 49.6667

The sequence similarity is fairly low, so BLOSUM30 might be a more appropriate scoring matrix.

[sc30,globAlig30] = nwalign(humanProtein,flyProtein,'scoringmatrix','blosum30'); fprintf('Score = %g \n',sc30) showalignment(globAlig30);

Score = 82

This gives an alignment that has some areas of fairly strong similarity, but is this alignment statistically significant? One way to investigate whether this score is significant is to use Monte Carlo techniques. Given that the fly sequence was found using a BLAST search, there is some evidence that there is similarity between the two sequences. It is reasonable to expect the score for this alignment to be higher than the scores obtained from aligning random sequences of amino acids to the protein.

**Assessing the Significance of the Score**

To assess if the score is significant the first step is to make some random sequences that are similar to that of the fly protein. One way to do this is to take random permutations of the fly sequence. This can be done with the `randperm`

function. Then calculate the global alignment of these random sequences against the human protein and look at the statistical significance of the scores.

Initialize the state of the default random number generators to ensure that the figures and results generated match the ones in the HTML version of this example.

rng(0,'twister') n = 50; globalscores = zeros(n,1); flyLen = length(flyProtein.Sequence); for i = 1:n perm = randperm(flyLen); permutedSequence = flyProtein.Sequence(perm); globalscores(i) = nwalign(humanProtein,permutedSequence,'scoringmatrix','blosum30'); end

Now plot the scores as a bar chart. Note that because you are using randomly generated sequences.

figure buckets = ceil(n/5); hist(globalscores,buckets) hold on; stem(sc30,1,'k') title('Determining Alignment Significance using Monte Carlo Techniques'); xlabel('Score'); ylabel('Number of Sequences');

The scores of the alignments to the random sequences can be approximated by the type 1 extreme value distribution. Use the `evfit`

function from the Statistics and Machine Learning Toolbox™ to estimate the parameters of this distribution.

parmhat = evfit(globalscores)

parmhat = -31.7597 6.6440

Overlay a plot of the probability density function of the estimated distribution.

x = min(globalscores):max([globalscores;sc30]); y = evpdf(x,parmhat(1),parmhat(2)); [v, c] = hist(globalscores,buckets); binWidth = c(2) - c(1); scaleFactor = n*binWidth; plot(x,scaleFactor*y,'r'); hold off;

From this plot you can see that the global alignment (globAlig30) is clearly statistically significant.

**An Example Where the Score is Not Statistically Significant**

In FLYBASE web site you can search for all Drosophila beta-N-acetylhexosaminidase genes. The gene that you have been looking at so far is referenced as *CG8824*. Now you want to take a look at another similar gene, for instance *Hexo1*. See GO:0004563 for more information on these genes.

```
flyHexo1 = getgenpept('AAL28566');
```

The fly *Hexo1* aminoacid sequence is also provided in the MAT-file `flyandhumanproteins.mat`

.

load('flyandhumanproteins.mat','flyHexo1') seqdisp(humanProtein)

ans = >gi|189181666|gb|NP_000511.2| beta-hexosaminidase subunit alpha pre... 1 MTSSRLWFSL LLAAAFAGRA TALWPWPQNF QTSDQRYVLY PNNFQFQYDV SSAAQPGCSV 61 LDEAFQRYRD LLFGSGSWPR PYLTGKRHTL EKNVLVVSVV TPGCNQLPTL ESVENYTLTI 121 NDDQCLLLSE TVWGALRGLE TFSQLVWKSA EGTFFINKTE IEDFPRFPHR GLLLDTSRHY 181 LPLSSILDTL DVMAYNKLNV FHWHLVDDPS FPYESFTFPE LMRKGSYNPV THIYTAQDVK 241 EVIEYARLRG IRVLAEFDTP GHTLSWGPGI PGLLTPCYSG SEPSGTFGPV NPSLNNTYEF 301 MSTFFLEVSS VFPDFYLHLG GDEVDFTCWK SNPEIQDFMR KKGFGEDFKQ LESFYIQTLL 361 DIVSSYGKGY VVWQEVFDNK VKIQPDTIIQ VWREDIPVNY MKELELVTKA GFRALLSAPW 421 YLNRISYGPD WKDFYIVEPL AFEGTPEQKA LVIGGEACMW GEYVDNTNLV PRLWPRAGAV 481 AERLWSNKLT SDLTFAYERL SHFRCELLRR GVQAQPLNVG FCEQEFEQT

Repeat the process of generating a global alignment and then using random permutations of the amino acids to estimate the significance of the global alignment.

[Hexo1score,Hexo1Alignment] = nwalign(humanProtein,flyHexo1,'scoringmatrix','blosum30'); fprintf('Score = %g \n',Hexo1score) showalignment(Hexo1Alignment); Hexo1globalscores = zeros(n,1); flyLen = length(flyHexo1.Sequence); for i = 1:n perm = randperm(flyLen); permutedSequence = flyHexo1.Sequence(perm); Hexo1globalscores(i) = nwalign(humanProtein,permutedSequence,'scoringmatrix','blosum30'); end

Score = -72.2

Plot the scores, calculate the parameters of the distribution and overlay the PDF on the bar chart.

figure buckets = ceil(n/5); hist(Hexo1globalscores,buckets) title('Determining Alignment Significance using Monte Carlo Techniques'); xlabel('Score'); ylabel('Number of Sequences'); hold on; stem(Hexo1score,1,'c') parmhat = evfit(Hexo1globalscores) x = min(Hexo1globalscores):max([Hexo1globalscores;Hexo1score]); y = evpdf(x,parmhat(1),parmhat(2)); [v, c] = hist(Hexo1globalscores,buckets); binWidth = c(2) - c(1); scaleFactor = n*binWidth; plot(x,scaleFactor*y,'r'); hold off;

parmhat = -70.6926 7.0619

In this case it appears that the alignment is not statistically significant. Higher scoring alignments can easily be generated from a random permutation of the amino acids in the sequence. You can calculate an approximate p-value from the estimated extreme value CDF: However, far more than 50 random permutations are needed to get a reliable estimate of the extreme value pdf parameters from which to calculate a reasonably accurate p-value.

p = 1 - evcdf(Hexo1score,parmhat(1),parmhat(2))

p = 0.4458

One thing to notice is that the lengths of the two sequences are very different. The human *HEXA1* is 529 residues long and the fly *Hexo1* protein is only 383 residues in length. When you try to align these two sequences globally this difference in length means that a large number of gaps will have to be introduced into the sequence. This means that the significance of the scores will be heavily dependent on the `GAPOPEN`

and `EXTENDGP`

parameters. (See the help for `nwalign`

for more details.) Instead of using global alignment, in this case a better approach might be to look at the local alignment between the two sequences.

**Using Local Alignment and Randseq**

You will now repeat the process of estimating the significance of an alignment this time using local alignment and a slightly different method of generating the random sequences. Instead of simply permuting the letters in the sequence, an alternative is to draw a sequence from a multinomial distribution which is estimated from the fly protein sequence. You can do this using the `aacount`

and `randseq`

functions; the first estimates the amino acid frequencies of the query sequence and the later randomly creates new sequences based on this distribution.

[lscore,locAlig] = swalign(humanProtein,flyHexo1,'scoringmatrix','blosum30'); fprintf('Score = %g \n',lscore) showalignment(locAlig); localscores = zeros(n,1); aas = aacount(flyHexo1); for i = 1:n randProtein = randseq(flyLen,'FROMSTRUCTURE',aas); localscores(i) = swalign(humanProtein,randProtein,'scoringmatrix','blosum30'); end

Score = 152

Plot the scores, calculate the parameters of the distribution and overlay the PDF on the bar chart.

figure hist(localscores,buckets) title('Determining Alignment Significance using Monte Carlo Techniques'); xlabel('Score'); ylabel('Number of Sequences'); hold on; stem(lscore,1,'r') parmhat = evfit(localscores) x = min(localscores):max([localscores;lscore]); y = evpdf(x,parmhat(1),parmhat(2)); [v, c] = hist(localscores,buckets); binWidth = c(2) - c(1); scaleFactor = n*binWidth; plot(x,scaleFactor*y,'r'); hold off;

parmhat = 40.8331 3.9312

You might like to experiment to see if there are significant differences in the distribution of scores generated with `randperm`

and `randseq`

.

With the local alignment it appears that the alignment is statistically significant. In fact, looking at the local alignment shows a very good alignment for the full length of the *Hexo1* sequence.

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