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Class 4: Sequence Alignment II Gaps, Heuristic Search. Alignment with Gaps – Example. 1. 2. 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.

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Class 4 sequence alignment ii gaps heuristic search

Class 4: Sequence Alignment IIGaps, Heuristic Search


Class 4 sequence alignment ii gaps heuristic search

  • 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
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 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
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
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)

Indel model
Indel Model


Score: -6


Score: -6

Scoring Parameters

Match: +1

Indel: -2

Constant model
Constant Model


Score: -6


Score: 12

Scoring Parameters

Match: +1

Open gap: -2

Affine model
Affine Model


Score: -17


Score: 1

Scoring Parameters

Match: +1

Open gap: -2, each space: -1

Convex model
Convex Model


Score: -6


Score: ~7

Scoring Parameters

Match: +1

Open gap: -2, gap length: -logn

Affine weight model
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 model1
Affine Weight Model

Recurrence relations:

Affine weight model2
Affine Weight Model

Initial condition:

Optimal alignment:


Time: O(mn)

Space: O(mn)

Affine weight model3











Affine Weight Model

This model has a natural explanation as a finite state automata

Alignment in real life
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
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
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
Banded DP

  • Suppose that we have two strings s[1..n] and t[1..m] such that nm

  • If the optimal global alignment of s and t has few gaps, then path of the alignment will be close to the diagonal



Banded dp1
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




Banded dp2
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
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):



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

Signature of a match



Signature of a Match

Assumption: good matches contain several “patches” of perfect matches




  • 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) !


i i+k





  • 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
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
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
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:




Class 4 sequence alignment ii gaps heuristic search

BLAST: phase 1


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


Blast phase 2
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).

Extending potential matches



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
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


  • Generally faster then FASTA,

    arguably better.



Blast variants
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
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
Databases and Tool

  • Important gateways:

    • National Center for Biotechnology (GenBank)


    • European Bioinformatics Institue (EMBL-Bank)


    • Expert Protein Analysis System (SwissProt)


        → Different tools and DBs to allow biologists a rich suite of queries

Database types
Database Types

  • Nucleotide DBs (GenBank, EMBL-Bank):

    • Contain any and every type of DNA fragment:

      • Full cDNA, ESTs, repeats, fragments

    • “Dirty” and redundant

  • Protein DBs (SwissProt):

    • Contain amino-acid sequences for full proteins

    • High quality, strict screening process

    • Lots of annotated information on each protein