• Summary Local and Global alignments
• FASTA and BLAST algorithms
• Evaluating significance of alignments

Global
Local
• Best score for aligning the full length sequences
• Dynamic programming
• Algorithm:
Needelman- Wunch
• Table cells are allowed any score
• Best score for aligning part of sequences
• Dynamic programming
• Algorithm:
Smith-Waterman
• Table cells never score below zero

ALIGN -- GLOBAL (N-W)/ LOCAL (S-W)
BLAST2SEQ – Only LOCAL using word match spidey -- aligns mRNAs to genomic sequence est2genome -- aligns ESTs to genomic sequence

>Human DNA
CATGCGACTGACcgacgtcgatcgatacgactagctagcATCGATCATA
>Human mRNA
CATGCGACTGACATCGATCATA
Biologically, indels occur in groups we want our gap score to reflect this

• Standard solution: affine gap model
– Once-off cost for opening a gap
– Lower cost for extending the gap
– Changes required to algorithm

• w x
= g + r(x-1)
• w x
: total gap penalty; g: gap open penalty; r: gap extend penalty;x: gap length
• gap penalty chosen
– Gaps not excluded
– Gaps not over included
– Typical Values: g=-12; r = -4

• Compute intensive
• Memory Intensive

• Complexity is determined by size of table
– Aligning a sequence of length m against one of length n requires calculating (m

n) cells
• Estimate: we calculate
10 8 cells per second
– Aligning two mRNA sequences of
8,000 bp requires 64,000,000 cells
– Aligning an mRNA and a
10 7 bp chromosome requires ~10 11 cells

•
Goal: Find homologue sequences in database to query input.

new sequence
?
Sequence Database
≈

•
Goal: Find homologue sequences in database to query input.
• Naïve solution:
Use exact algorithm to compare each sequence in the database to query.

• Human genome contains
3

10 9 base pairs
– Searching an mRNA against HG requires
~10 13 cells
-Even efficient exact algorithms will be extremely slow when preformed millions of times.
-Running the computations in parallel is expensive.

•
Solutions:
1. Use a heuristic (approximate) algorithm to discard most irrelevant sequences.
2. Perform the exact algorithm on the small group of remaining sequences.

• Homologous sequences are expected to contain common short segments (probably with substitutions, but without ins/dels)
• Preprocess database (DB) into new data structure to enable fast accession
• Remove low-complexity regions that are not useful for meaningful alignments

• AAAAAAAAAAA
• ATATATATATATA
• Transposable elements
(LINEs, SINEs)

Whats wrong with them?
produce artificial high scoring alignments.
So what do we do?: We apply Low Complexity masking to the query sequence

Complexity is calculated as: K=1/L log
N
(L!/Π n i all i
!)
Where N=4 in DNA (4 bases), L is the length of the sequence
And n i the number of each residue in the sequence
For the sequence GGGG:
L! =4x3x2x1=24 n g n c n a n t
=4
=0
=0
=0
Πn i
=24x1x1x1=24
K =1/4 log
4
(24/24)=0
For the sequence CTGA:
L! =4x3x2x1=24 ng =1 nc =1 na =1 nt =1
Πni =1x1x1x1
K =1/4 log
4
(24/1)=0.573

• FASTA (Lipman & Pearson 1985)
– First fast sequence searching algorithm for comparing a query sequence against a database
• BLAST - Basic Local Alignment Search
Technique (Altschul et al 1990)
– improvement of FASTA: Search speed, ease of use, statistical rigor
– Gapped BLAST (Altschul et al 1997)

• Common idea - a good alignment contains subsequences of absolute identity:
– First, identify very short (almost) exact matches.
– Next, the best short hits from the 1st step are extended to longer regions of similarity.
– Finally, the best hits are optimized using the Smith-
Waterman algorithm.

• Assumption: a good alignment probably matches some identical ‘words’
•
Example: Aligning a query sequence to a database
Database record:
ACTTGTAGATACAAAATGTG
Query sequence:
A-TTGTCG-TACAA-ATCTG
Matching words of size 4

• Preprocess of all the sequences in the database. Find short words and organize in dictionaries.
• Process the query sequence and prepare a dictionary.
– ATGGCTGCTCAAGT….
ATGG TGGC GGCT
… …
Query

FastA locates regions of the query sequence and the search set sequence that have high densities of exact word matches.
For DNA sequences the word length used is 6.
seq1 seq2

The 10 highest-scoring sequence regions are saved and re-scored using a scoring matrix.
seq1 seq2

FastA determines if any of the initial regions from different diagonals may be joined together to form an approximate alignment with gaps.
Only non-overlapping regions may be joined. seq1 seq2

The score for the joined regions is the sum of the scores of the initial regions minus a joining penalty for each gap.
seq1 seq2

• Apply an exact algorithm of local alignment on surviving records, computing the final alignment score.
• Calculate an Alignment score (S)
• Evaluate the statistical significance

Determine probability of alignment occurring at random
Random
Related
No Good Ideal

• A set of programs for database searching.
FastA EMBL

This format contains a one line header followed by lines of sequence data.
•Sequences in fasta formatted files are preceded by a line starting with a" >" symbol.
•The first word on this line is the name of the sequence.
•The remaining lines contain the sequence itself.
•Blank lines in a FASTA file are ignored,

• Output, general information:
–Z’ score = deviation (in sd) of the actual score from the mean of random scores
Z=(x-mean)/sd
– Opt: the number of optimized scores observed.
Lower limit
– E( ): the number of sequences expected in the score range.

• Developed to be as sensitive as FastA but much faster.
• Also searches for short words.
– Protein 3 letter words
– DNA 11 letter words .
– Words can be similar, not only identical

• Identity - CAT : CAT
• Similarity – CAT : CAT, CAY, HAT …
• But even CAT : XTX can be similar
• For each three letter word there are many similar words (depending on the alphabet).
• Similar words are only the ones that have a minimum cut-off score (T).
Y= C or T
H= A, C, T
X=A or T or C or G

• Find matching word pairs
• Extend word pairs as much as possible, i.e., as long as the total weight increases
• Result:
High-scoring Segment Pairs (HSPs)
THEFIRSTLINIHAV EAD REAMESIRPATRICKREAD
INVIEIAMD EAD MEATTNAMHEWASNINETEEN

• Try to connect HSPs by aligning the sequences in between them:
THEFIRSTLINIHAV EAD REA____M_ESIRPAT RIC KREAD
INVIEIAMD EAD MEATTNAMHEW___AS NIN ETEEN
The Gapped Blast algorithm allows several segments that are separated by short gaps to be connected together to one alignment

•
The score is a measure of the similarity of the query to the sequence shown.
•
The E-value is a measure of the reliability of the score.
•
E-value is the probability due to chance, that there is another alignment with a similarity greater than the given S score.

Score (S):

(identities + mismatches)-
 gaps
Bit score (S) :
– Similar to alignment score
– Normalized
– Higher means more significant

Expected # of alignments with score at least S
Increases linearly with length of query sequence
Increases linearly with length of database
Decreases exponentially with score of alignment m = length of query ; n= length of database ; s= score
–
K
,λ: statistical parameters dependent upon scoring system and background residue frequencies

• E values of less than 0.00001 show that sequences are almost always homologues.
• Greater E values, can represent homologues as well.
• Generally the decision whether an E-value is biologically significant depends on the size of database that is searched

• Gapped alignments use same statistics
•  and K cannot be easily estimated
• Empirical estimations and gap scores determined by looking at random alignments

• Blast is a family of programs :
BlastN , BlastP, BlastX , tBlastN , tBlastX
Query: DNA Protein
Database: DNA Protein
• BlastN - nt versus nt database
• BlastP - protein versus protein database
• BlastX - translated nt versus protein database
• tBlastN - protein versus translated nt database
• tBlastX - translated nt versus translated nt database

•
Output
– Graphical out put of top results
– The alignments for top scores
– Scores for each alignment:
1. E value
2. Bits score: a score normalized with respect to the scoring system. Can be used to compare different searches.