Practical algorithms in Sequence Alignment

Sushmita RoyBMI/CS 576

www.biostat.wisc.edu/bmi576/sroy@biostat.wisc.edu

Sep 16th, 2014

Key concepts

• Assessing the significance of an alignment– Extreme value distribution gives an analytical form to

compute the significance of a score

• Heuristic algorithms– BLAST algorithm

Readings from book

• Chapter 2– Section 2.5– Section 2.7

RECAP: Four issues in sequence alignment

• Type• Algorithm• Score• Significance

Classical approach to assessing the significance of score

• Develop a “background” distribution of alignment score

• Assess the probability of observing our score S from this background distribution

Thought experiment for generating the background distribution

• Suppose we assume• Sequence lengths m and n• A particular substitution matrix and amino-acid

frequencies

• And we consider generating random sequences of lengths m and n and finding the best alignment of these sequences

• This will give us a distribution over alignment scores for random pairs of sequences

The extreme value distribution• Because we are picking the best alignments, we

want to know the distribution of max scores for alignments against a random set of sequences looks like

• The background distribution is given by an extreme value distribution (EVD)

• We need to assess the probability of observing a score of S or higher by random chance, that is, we need the form of the CDF: P(x>S)

Assessing significance of sequence score alignments

• It can be shown that the mean of optimal scores is

– K, λ estimated from the substitution matrix

• Probability of observing a score greater than S

• Substituting U into the equation

Need to speed up sequence alignment

• Consider the task of searching the RefSeq collection of sequences against a query sequence:– most recent release of DB contains 32,504,738 proteins– Entails 33,000,000*(300*300) matrix operations

(assuming query sequence is of length 300 and avg. sequence length is 300)

• O(mn) too slow for large databases with high query traffic• We will look at a heuristic algorithm to speed up the search

process

Heuristic alignment

• Heuristic algorithm: a problem-solving method which isn’t guaranteed to find the optimal solution, but which is efficient and finds good solutions

• Heuristic methods do fast approximation to dynamic programming– FASTA [Pearson & Lipman, 1988]– BLAST [Altschul et al., 1990; Altschul et al., Nucleic Acids

Research 1997]

BLAST: Basic Local Alignment Search Tool

• Altshul et al 1990– Cited >48,000 times!

• Key heuristics in BLAST– A good alignment is made up short stretches of matches:

seeds– Extend seeds to make longer alignments

• Key tradeoff made: sensitivity vs. speed• Used EVD theory for random sequence score• Works for both protein sequence and DNA sequence– Only scores differ

BLAST continued

• Two parameters control how BLAST searches the database– w: This specifies the length of words to seed the alignment– T: The smallest threshold of word pair match to be

considered in the alignment

Key steps of the BLAST algorithm

• For each query sequence1. Compile a list of high-scoring words of score at least T

• First generate words in the query sequence• Then find words that match query sequence words with score at

least T• Thus allows for inexact matches

2. Scan the database for hits of these words• Relies on indexing performed as pre-processing

3. Extend hits

Determining query words

Given:query sequence: QLNFSAGWword length w = 2 (default for protein usually w = 3)word score threshold T = 9

Step 1: determine all words of length w in query sequence

QL LN NF FS SA AG GW

Determining query words

Step 2: Determine all words that score at least T when compared to a word in the query sequence

QL QL=9LN LN=10NF NF=12, NY=9…SA none...

words fromquery sequence words with T≥9

Additional words potentially in database

Aminoacid substitution matrix

Scanning the database

• Search database for all occurrences of query words• Approach:– index database sequences into table of words

(pre-compute this)– index query words into table (at query time)

NPNSNTNWNY

QLNFSAGW

MFNYT, STNYD…

NPGAT, TSQRPNP…

query sequence

database sequences

• Extending a word hit to a larger alignment is straightforward

• Terminate extension when the score of the current alignment falls a certain distance below the best score found for shorter extensions

Extending a hit

Query sequence: Q L N F S ADB sequence: R L N Y S WScore: 1 4 5 3 4 -3Total: 1+4+5+3+4=17

How to choose w and T?

• Tradeoff between running time and sensitivity• Sensitivity

• T– small T: greater sensitivity, more hits to expand– large T: lower sensitivity, fewer hits to expand

• w– Larger w: fewer query word seeds, lower time for

extending, but more possible words (20w for AAs)

Updates to BLAST

• Two hit method– Lower the threshold but require two words to be on the

same diagonal and be no more than A characters apart

• Ability to handle gaps• Ability to handle position-specific score matrix

created from alignments generated from iteration i for iteration i+1

Altshul et al 1997

Two-hit method

Figure from Altshul et al 1997

+ Hits wit T>=13 (15 hits)

.Hits with T>=11 (22 hits)

Only these two are considered as they satisfy the two-hit method

Summary of BLAST

• T: Don’t consider seeds with score < T• Don’t extend hits when score falls below a specified

threshold• Pre-processing of database or query helps to improve

the running time

FASTA

• Starts with exact seed matches instead of inexact matches that satisfy a threshold

• Extends seeds (similar to BLAST)• Join high scoring seeds allowing for gaps• Re-align high scoring matches using dynamic

programming

Different versions of BLAST programs

Program Query Database

BLASTP Protein Protein

BLASTN DNA DNA

BLASTXTranslated

DNAProtein

TBLASTN ProteinTranslated

DNA

TBLASTXTranslated

DNATranslated

DNA

Sequence databases

• Web portals/Knowledge bases– NCBI: http://www.ncbi.nih.gov– EBI: http://www.ebi.ac.uk– Sanger: http://www.sanger.ac.uk– Each of these centers link to hundreds of databases

• Nucleotide sequences– Genbank– EMBL-EBI Nucleotide Sequence Database– Comprise ~8% of the total database (Nucleic Acid Research 2006

Database edition)

• Protein sequences– UniProtKB

Using BLAST

• http://blast.ncbi.nlm.nih.gov/Blast.cgi

• Will blast a DNA sequence against NCBI nucleotide database

• We will select– http://www.ncbi.nlm.nih.gov/nuccore/NG_000007.3?from

=70545&to=72150&report=fasta

Using BLAST

Choose the database

Enter the query sequence

Using BLASTThe sequence corresponds to the human HBB (hemoglobin) gene.

But we will select the mouse DB

Use Megablast (large word size)

Interpreting results

Assesses significance of a score. Related to P-value, but gives the expected number of alignments ofthis score value or higher.