Sequence Alignment - Baylor ECSweb.ecs.baylor.edu/faculty/cho/3350/2_SequenceAlignment.pdf · PAM...

9/1/2015

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Young-Rae Cho

Associate Professor

Department of Computer Science

Baylor University

BINF 3350, Genomics and Bioinformatics

Sequence Alignment

BINF 3350, Chapter 4, Sequence Alignment

1. Sequence Alignment

2. Dynamic Programming

3. Scoring Alignments

4. Gap Penalty

5. Global vs. Local Alignment

6. Pairwise vs. Multiple Sequence Alignment

7. Sequence Homolog Search

8. Motif Search

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Sequence Homology

Homologs

Similar sequence and Common ancestor

Similar sequence and Same function (in divergent evolution)

Orthologs

Homologous sequences in different species by species divergence

Paralogs

Homologous sequences in the same species by gene duplication

Analogs

Similar sequence and No common ancestor (in convergent evolution)

Sequence Similarity

Importance of finding similar (DNA or protein) sequences

Evolutionary closeness

Relationship between sequences and evolution

Functional similarity

Relationship between sequences and functions

How to measure sequence similarity

(Method 1) Counting identical letters on each position

(Method 2) Inserting gaps to maximize the number of identical letters

Sequence alignment

A T G T T A T

T C G T A C T| | |

A T ‐ G T T A ‐ T

‐ T C G T ‐ A C T| | | | |

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Sequence Alignment

Sequence Alignment

Aligning two or more sequences to maximize their similarity including gaps

How to find sequence alignment?

(1) Measuring edit distance

Edit Distance (1)

Definition

Edit distance between two sequences x and y : the minimum number of

editing operations (insertion, deletion, substitution) to transform x into y

Example

x=“TGCATAT” (m=7), y=“ATCCGAT” (n=7)

TGCATAT

ATGCATATinsertion of “A”

ATCCATATsubstitution of “G” with “C”

ATCCGATATinsertion of “G”

ATCCGATTdeletion of “A”

ATCCGATdeletion of “T”

edit distance = 5 ?

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Edit Distance (2)

Example

x=“TGCATAT” (m=7), y=“ATCCGAT” (n=7)

Can it be done in 3 steps?

How to measure edit distance efficiently?

TGCATAT

ATGCATATinsertion of “A”

ATGCAATdeletion of “T”

ATCCAATsubstitute of “G” with “C”

ATCCGATsubstitute of “A” with “G”

edit distance = 4 ?

A T G T T A T G C A A T G T A C T T A

T C G T A C T C A G T T C A A G T C A

Edit Distance (3)

Example in 2-Row Representation

x=“ATCTGATG” (m=8), y=“TGCATAC” (n=7)

A T C T G A T G

T G C A T A C

x

y

4 matches

1 substitutions

3 insertions2 deletions

A T C T G A T G

T G C A T A C

x

y

4 matches4 insertions3 deletions

Edit distance = #insertions + #deletions + #substitutions

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Hamming Distance vs. Edit Distance

Hamming Distance

Compares the letters on the same position between two sequences

Not good to measure evolutionary distance between DNA sequences

Edit Distance

Compares the letters between two sequences after inserting gaps

Allows comparison of two sequences of different lengths

Good to measure evolutionary distance between DNA sequences

Example

x=“ATATATAT” , y=“TATATATA”

Hamming distance between x and y ?

Edit distance between x and y ?

Sequence Alignment

Sequence Alignment




(2) Finding longest common subsequence

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Longest Common Subsequence (1)

Subsequence of x

An ordered sequence of letters from x

Not necessarily consecutive

e.g., x=“ATTGCTA”, “AGCA” ?, “TCG” ?, “ATCT” ?, “TGAT” ?

Common Subsequence of x and y

e.g., x=“ATCTGAT” and y=“TGCATA”, “TCTA” ?, “TGAT” ?, “TATA” ?

Longest Common Subsequence (LCS) of x and y ?

Longest Common Subsequence (2)

Example

x=“ATCTGATG” (m=8), y=“TGCATAC” (n=7)

LCS of X and Y ?

2-row representation

How to find LCS efficiently?

A T G T T A T G C A A T G T A C T T A G A C T C A A G T G C C A T T T G A C

T C G T A C T C A G T T C A A G T C A G T T A C G A G T A C A T G C A A A C

A T G T T A T G C A A T G T A C T T A

T C G T A C T C A G T T C A A G T C A

A T G T T A T G C A

T C G T A C T C A G

A T G T T

T C G T A

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Sequence Alignment

Sequence Alignment




(2) Finding longest common subsequenceDynamic programming





4. Gap Penalty




8. Motif Search

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Definition

An algorithm to solve complex problems by breaking them down into simpler sub‐problems

The result of a sub‐problem is used to solve the next sub‐problem

Features

Optimization

• Finding an optimal solution

• Saving memory space

Examples

Binary search tree

Sequence alignment

Dynamic Programming

Edit Graph

2‐D grid structure having a diagonal

on the position of the same letter

Weight the diagonal lines as 1

Weight the other lines as 0

Goal

Finding the strongest path from

source to sink

Algorithm

(1) Compute the max score for each node

(The max score means the max counts of identical letters from source to each node)

(2) When reaching the sink, trace backward to find LCS

Dynamic Programming for Sequence Alignment

sink

source A T C G T A C

A

T

G

T

T

T

A

+1

+1

+1

+1

+1

+1

+1

+1

+1

+1

+1

+1

+1

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Example

Sequence Alignment

Sequence Alignment Example

source

sink

A T C G T A C

A

T

G

T

T

T

A

+1

+1

+1

+1

+1

+1

+1

+1

+1

+1

+1

+1

+1

0 0 0 0 0 0 0 0

0

0

0

0

0

0

0

1 1 1 1 1 1 1

1 2 2 2 2 2 2

1 2 2

4

3 3 3

1 2 3

3

4 4

1 2 2 3 4 4 4

1 2 2 3 4 5 5

1 2 2 3 4 5 5

2

A T C G T – A C –

A T – G T T A – T| | | | |

Example

X = “ATGCGT”, Y = “AGACAT”

Sequence Alignment

Quiz

sink

source A T G C G T

A

G

A

C

A

T

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4. Gap Penalty




8. Motif Search

Scoring Alignments: Percent Identity (1)

Identity

Degree of identical matches between sequences

Percent Identity

Percentage of identical matches

Dot-plot representations

Visualization method of identity

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Scoring Alignments: Percent Identity (2)

Dot-plot representations of self alignment

The background noise can be removed by setting a threshold of the min

identity score in a fixed window

Scoring Alignments: Percent Similarity

Percent Similarity

Percentage of similar amino acid pairs in biochemical structure (Protein)

Percentage of similar nucleotide pairs in biochemical structure (DNA)

Advanced Scoring Schemes

Varying scores in similarity of biochemical structures

Penalties (negative scores) for strong mismatches

Relative likelihood of evolutionary relationship

Probability of mutations

Minimum Acceptance Score

90% of sequence pairs with more than 30% sequence identity: homolog

20~30% sequence identity: twilight zone

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Substitution Matrices (1)

Substitution Matrix

Score matrix among nucleotides or amino acids

4 × 4 array representation for DNA sequences

or (4+1) × (4+1) array

20 × 20 array representation for protein sequences

or (20+1) × (20+1) array

Entry of δ(i,j) has the score between i and j,

i.e., the rate at which i is substituted with j over time


PAM (Point Accepted Mutations)

For protein sequence alignment

Amino acid substitution frequency in mutations

Logarithmic matrix of mutation probabilities

PAM120: Results from 120 mutations per 100 residues

PAM120 vs. PAM240

BLOSUM (Block Substitution Matrix)

For protein sequence alignment

Applied for local sequence alignments

Substitution frequencies between clustered groups

BLOSUM-62: Results with a threshold (cut-off) of 62% identity

BLOSUM-62 vs. BLOSUM-50

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Substitution Matrix Examples

BLOSUM-62 PAM120

Theory of Scoring Alignments

Random model

Non-random model

Odds ratio

Odds ratio for each position

Odds ratio for entire alignment

log-odds ratio (a score in a substitution matrix)

Expected score

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4. Gap Penalty




8. Motif Search

Gap Penalty (1)

Gaps

Contiguous sequence of spaces in one of the aligned sequences

Gaps inserted as the results of insertions and deletions (indels)

Gap Penalties

High penalties vs. Low penalties

Fixed penalties vs. Flexible penalties depending on residues

No penalty on start gaps and end gaps

Finding optimal number of gaps for the best score in sequence alignment

Dynamic Programming

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Gap Penalty (2)

Examples of high penalties and low penalties

Affine Gap Penalty (1)

Motivation

-σ for 1 gap (insertion or deletion)

-2σ for 2 consecutive gaps (insertions or deletions)

-3σ for 3 consecutive gaps (insertions or deletions), etc.

→ too severe penalty for a series of 100 consecutive gaps

Example

x=“ATAGC”, y=“ATATTGC”

x=“ATAGGC”, y=“ATGTGC”

single event

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Affine Gap Penalty (2)

Linear Gap Penalty

Score for a gap of length x : -σ x

Constant Gap Penalty

Score for a gap of length x : -ρ

Affine Gap Penalty

Score for a gap of length x : - (ρ + σ x)

ρ : gap opening penalty / σ : gap extension penalty ( ρ σ )





4. Gap Penalty




8. Motif Search

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Global vs. Local Alignment

Global Alignment

Finding sequence alignment across the whole length of sequences

Local Alignment

Finding significant similarity in a part of sequences

Example

x = “TCAGTGTCGAAGTTA”

y = “TAGGCTAGCAGTGTA”

T C A G – – T – G T C G A A G T – T A

T – A G G C T A G – C – A – G T G T A| | | | | | | | | | |

T C A G T G T C G A A G T T A

T A G G C T A G C A G T G T A| | | | | |

Dynamic Programming (Needleman-Wunch algorithm)

Dynamic Programming (Smith-Waterman algorithm)

Local Alignment Example

Local Alignment

Applied for multi-domain

protein sequences

Protein domain

• Basic functional block

• Evolutionary conserved

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4. Gap Penalty




8. Motif Search

Multiple Alignment (1)

Pairwise Alignment

Alignment of two sequences

Sometimes two sequences are functionally

similar or have common ancestor although

they have weak sequence similarity

Multiple Alignment

Alignment of three or more sequences simultaneously

Finds similarity which is invisible in pairwise alignment

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Multiple Alignment (2)

Example

Dynamic Programming ?

Computationally not acceptable

Need heuristic methods

Hierarchical Method (1)

Hierarchical Method

(1) Compares all sequences in pairwise alignments

(2) Creates a guide tree (hierarchy)

(3) Follows the guide tree for a series of

pairwise alignments

-

.17 –

.87 .28 –

.59 .33 .62 –

v1 v2 v3 v4 …

v1

v2

v3

v4

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Hierarchical Method (2)

Features

Also called progressive alignment

More intelligent strategy on each step

Use of consensus sequence to compare groups of sequences

Gaps are permanent (“once a gap, always a gap”)

Works well for close sequences

Application Tools

ClustalW

• Comparing residues one pair at a time and imposing gap penalties

DIALIGN

• Finding pairs of equal-length gap-free segments

Divide-and-Conquer Method

Process

Features

Fast aligning of long sequences

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Multiple Alignment Results

Examples

Summary of PSA & MSA Algorithms

Rigorous Algorithms

Heuristic Algorithms

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4. Gap Penalty




8. Motif Search

Searching Databases

Sequence Homolog Search

Search similar sequences to a query sequence in a database

Computational issues

• Dynamic programming (N-W / S-W algorithms) are rigorous

• But inefficient in searching a huge database

• Need heuristic approaches

Sequence Homolog Searching Tools

FASTA

BLAST

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FASTA (1)

FASTA

DNA / protein sequence alignment tool (local alignment)

Applies dynamic programming in scoring selected sequences

Heuristic method in candidate sequence search

Algorithm

(1) Finding all pairwise k-tuples (at least k contiguous matching residues)

(2) Scoring the k-tuples by a substitution matrix

(3) Selecting sequences with high scores for alignment

FASTA (2)

Indexing (or Hashing)

Indexing Process in FASTA

(1) Find all k-tuples from a query sequence and calculate ci

(2) Build an index table

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FASTA Package

FASTA package

ssearch : applies dynamic programming (S-W algorithm)

query sequence database

fasta protein protein

fasta DNA DNA

fastx / fasty DNA (all reading frames) protein

tfastx / tfasty protein DNA (all reading frames)

BLAST (1)

BLAST (Basic Local Alignment Search Tool)

DNA / protein sequence alignment tool

Finds local alignments

Heuristic method in sequence search

Runs faster than FASTA

Algorithm

(1) Makes a list of words (word pairs) from the query sequence

(2) Chooses high-scoring words

(3) Searches database for matches (hits) with the high-scoring words

(4) Extends the matches in both directions to find high-scoring segment pair

(HSP)

(5) Selects the sequence which has two or more HSPs for S-W alignment

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BLAST (2)

Deterministic Finite Automata (DFA)

DFA Analysis Process in BLAST

(1) Build DFA using high-scoring words

(2) Read sequences in database and trace DFA

(3) Output the positions for hits

BLAST Package

BLAST programs

query sequence database

blastp protein protein

blastn DNA DNA

blastx DNA (all reading frames) protein

tblastn protein DNA (all reading frames)

tblastx DNA (all reading frames) DNA (all reading frames)

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Search Results

BLAST Search Results

FASTA Search Results

E-value

E-value

Average number of alignments with a score of at least S that would be

expected by chance alone in searching a database of n sequences

Ranges of E-value:

High alignment score S

Low alignment score S

Factors

• Alignment score

• The number of sequences in the database

• Sequence length

Default E-value threshold: 0.01 ~ 0.001

Low E-value

High E-value

0 ~ n

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Filtering

Low-Complexity Region

Highly biased amino acid composition

Lowers significant hits in sequence alignment

BLAST filters the query sequence for low-complexity regions and mark “X”

Summary of Homolog Search Algorithms

Rigorous Algorithms

Heuristic Algorithms

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4. Gap Penalty




8. Motif Search

Motifs

Motifs

Short sequence patterns

Functionally related sequences share similarly distributed patterns (motifs)

of critical functional residues

Types of Motif Search

Search a query sequence in a motif database

Search a pattern in a sequence database

Find a pattern from a set of sequences

Motif Finding

Consensus method by global multiple alignment

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Motif Search Tools (1)

BLOCKS

Logos

• Size of letters: conservation levels

• Color of letters: biochemical properties

Motif Search Tools (2)

MEME

Summary motif information

• Location of motifs in sequences

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Motif Databases

PROSITE

Code for patterns

• Each letter represents an amino acid residue

• All positions are separated by “-”

Code description Example

X any amino acid G-X-L-M-S-A-D-F-F-F

[] two or more possible amino acid G-[LI]-L-M-S-A-D-F-F-F

{} disallowed amino acid G-[LI]-L-M-S-A-{RK}-F-F-F

(n) repetition by n of the amino acid G-[LI]-L-M-S-A-{RK}-F(3)

(n,m) a range: only allowed with X G-[LI]-L-M-S-A-{RK}-X(1,3)

Sequence Alignment - Baylor ECSweb.ecs.baylor.edu/faculty/cho/3350/2_SequenceAlignment.pdf · PAM...

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