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Class 4: Sequence Alignment II Gaps, Heuristic SearchPowerPoint Presentation

Class 4: Sequence Alignment II Gaps, Heuristic Search

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### Class 4: Sequence Alignment IIGaps, Heuristic Search

.

Gaps

- Both alignments have the same number of matches and spaces but alignment 2 seems better
- Definition: A gap is any maximal, consecutive run of spaces in a single string.
- The length of a gap = the number of spaces in it

- Example 1 has 11 gaps, example 2 only 2 gaps
- Idea: develop alignment scores that take gaps (not spaces) into account

Biological Motivation

- Number of mutational events:
- A single gap – due to a single event that removed a number of residues
- Each gap – due to distinct, independent event

- Protein structure:
- Protein secondary structure consists of alpha helices, beta sheets and loops
- Loops of varying size can lead to very similar structure

cDNA Mataching

- cDNA is the sequence after splicing (introns have been removed) and editing
- We expect regions of high similarity, separated by long gaps

Gap Penalty Models (I)

Constant model

- Gives each gap a constant score, spaces are free
- Maximize:
- Time: O(mn)
- Works well with cDNA matching
Affine model

- Penalty for starting a gap + penalty for each additional space
- Each gap costs: Wg + qWs
- Maximize:
- Time: O(mn)
- Widely used

Gap Penalty Models (II)

Convex model

- Each extra space contributes less penalty
- Gap function is convex in its length
- Example: Ws + log(q)
- Time O(mnlogm)
- A better model of biology
General model

- The weight of a gap is some arbitrary w(q)
- Time O(mn2 + nm2)

Affine Weight Model

We divide all possible alignments of the prefixes s[1..i] and t[1..j] into 3 types

s: i

t: j

s: i-----

t: j

s: i

t: j-----

Affine Weight Model

Recurrence relations:

Wg+Ws

Ws

A

S(i,j)

S(i,j)

Wg+Ws

S(i,j)

C

Ws

Affine Weight ModelThis model has a natural explanation as a finite state automata

Alignment in Real Life

- One of the major uses of alignments is to find sequences in a “database”
- Such collections contain massive number of sequences (order of 106)
- Finding homologies in these databases with the standard dynamic programming can take too long
- Example:
- query protein : 232 AAs
- NR protein DB: 2.7 million sequences; 748 million AAs
- m*n = ~ 1.7 *1011cells !

Heuristic Search

- Instead, most searches rely on heuristic procedures
- These are not guaranteed to find the best match
- Sometimes, they will completely miss a high-scoring match
- We now describe the main ideas used by some of these procedures
- Actual implementations often contain additional tricks and hacks

Basic Intuition

- The main resource consuming factor in the standard DP is decision of where the gaps are. If there were no gaps, life was easy!
- Almost all heuristic search procedures are based on the observation that real-life well-matching pairs of sequences often do contain long strings with gap-less matches.
- These heuristics try to find significant local gap-less matches and then extend them.

Banded DP

- Suppose that we have two strings s[1..n] and t[1..m] such that nm
- If the optimal global alignment of s and t has few gaps, then path of the alignment will be close to the diagonal

s

t

Banded DP

- To find such a path, it suffices to search in a diagonal region of the matrix
- If the diagonal band has presumed width a, then the dynamic programming step takes O(an)
- Much faster than O(n2) of standard DP in this case

s

a

t

Banded DP

Problem (for local alignment):

- If we know that t[i..j] matches the query s[p..q], then we can use banded DP to evaluate quality of the match
- However, we do not know i,j,p,q !
- How do we select which sub-sequences to align using banded DP?

FASTA Overview

- Main idea:
Find (fast!) “good” diagonals and extend them to complete matches

- Suppose that we have a relatively long gap-less local match (diagonal):
…AGCGCCATGGATTGAGCGA…

…TGCGACATTGATCGACCTA…

- Can we find “clues” that will let us find it quickly?

t

Signature of a MatchAssumption: good matches contain several “patches” of perfect matches

AGCGCCATGGATTGAGCGA

TGCGACATTGATCGACCTA

FASTA

- Given s and t, and a parameter k
- Find all pairs (i,j) such that s[i..i+k] and t[j..j+k] match perfectly
- Locate sets of pairs that are on the same diagonal by sorting according to i-j thus…
- Locating diagonals that contain
many close pairs.

- This is faster than O(nm) !

s

i i+k

j

j+k

t

FASTA

- Extend the “best” diagonal matches to imperfect (yet ungapped) matches, compute alignment scores per diagonal. Pick the best-scoring matches.
- Try to combine close diagonals to potential gapped matches, picking the best-scoring matches.
- Finally, run banded DP on the regions containing these matches, resulting in several good candidate alignments.
- Most applications of FASTA use very small k(2 for proteins, and 4-6 for DNA)

BLAST Overview

- FASTA drawback is its reliance on perfect matches
- BLAST (Basic Local Alignment Search Tool) uses similar intuition, but relies on high scoringmatches rather than exact matches
- Given parameters: length k, and threshold T
- Two strings s and t of length k are a high scoring pair (HSP) if d(s,t) > T

High-Scoring Pair

- Given a query string s, BLAST construct all words w (“neighborhood words”), such that w is an HSP with a k-substring of s.
- Note: not all k-mers have an HSP in s

BLAST: phase 1

- Phase 1: compile a list of word pairs (k=3) above threshold T
- Example: for the following query:
…FSGTWYA… (query word is in green)

- A list of words (k=3) is:
- FSG SGT GTW TWY WYA
- YSG TGT ATW SWY WFA
- FTG SVT GSW TWF WYS

scores

GTW 6,5,11 22

neighborhood ASW 6,1,11 18

word hits ATW 0,5,11 16

> threshold NTW 0,5,11 16

GTY 6,5,2 13

GNW 10

neighborhood GAW 9

word hits

below threshold

(T=11)

BLAST: phase 2

- Search the database for perfect matches with neighborhoodwords. Those are “hits” for further alignment.
- We can locate seed words in a large database in a single pass, given the database is properly preprocessed (using hashing techniques).

t

Extending Potential Matches- Once a hit is found, BLAST attempts to find a local alignment that extends it.
- Seeds on the same diagonal tend to be combined (as in FASTA)

Two HSP diagonal

- An improvement: look for 2 HSPs on close diagonals
- Extend the alignment between them
- Fewer extensions considered
- There is a version of BLAST,
involving gapped

extensions.

- Generally faster then FASTA,
arguably better.

s

t

Blast Variants

- blastn (nucleotide BLAST)
- blastp (protein BLAST)
- tblastn (protein query, translated DB BLAST)
- blastx (translated query, protein DB BLAST)
- tblastx (translated query, translated DB BLAST)
- bl2seq (pairwise alignment)

Biological Databases

- Today, most of the biological information can be freely accessed on the web.
- One can:
- Search for information on a known gene
- Check if a sequence exists in a database
- Find a homologous protein, helping us guess:
- Structure
- Function

Databases and Tool

- Important gateways:
- National Center for Biotechnology (GenBank)
- http://www.ncbi.nlm.nih.gov/

- European Bioinformatics Institue (EMBL-Bank)
- http://www.ebi.ac.uk/

- Expert Protein Analysis System (SwissProt)
- http://www.expasy.org/
→ Different tools and DBs to allow biologists a rich suite of queries

- http://www.expasy.org/

- National Center for Biotechnology (GenBank)

Database Types

- Nucleotide DBs (GenBank, EMBL-Bank):
- Contain any and every type of DNA fragment:
- Full cDNA, ESTs, repeats, fragments

- “Dirty” and redundant

- Contain any and every type of DNA fragment:
- Protein DBs (SwissProt):
- Contain amino-acid sequences for full proteins
- High quality, strict screening process
- Lots of annotated information on each protein

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