Example Mitochondrial cytochrome b –

transport electrons From NCBI protein web page, search

for cytb and Loxodonta africana (African elephant) Elephas maximus (Indian elephant) Mammuthus primigenius (Siberian wooly Mammoth)

Which modern elephant is closer to a mammoth ?

Use clustalW to do the alignment

Chap. 3: Sequence Alignment

>0012AAX12542.1| cytochrome b [Elephas maximus]MTHTRKSHPLFKIINKSFIDLPTPSNISTWWNFGSLLGACLITQILTGLFLAMHYTPDTMTAFSSMSHICRDVNYGWIIRQLHSNGASIFFLCLYTHIGRNIYYGSYLYSETWNTGIMLLLITMATAFMGYVLPWGQMSFWGATVITNLFSAIPYIGTNLVEWIWGGFSVDKATLNRFFAFHFILPFTMVALAGVHLTFLHETGSNNPLGLTSDSDKIPFHPYYTIKDFLGLLILILLLLLLALLSPDMLGDPDNYMPADPLNTPLHIKPEWYFLFAYAILRSVPNKLGGVLALLLSILILGLMPLLHTSKHRSMMLRPLSQVLFWALTMDLLMLTWIGSQPVEYPYIAIGQMASILYFSIILAFLPIAGMIENYLIK

>gi|56578537|gb|AAW01445.1| cytochrome b [Loxodonta africana]MTHIRKSYPLLKIINKSFIDLPTPSNISAWWNFGSLLGACLITQILTGLFLAMHYTPDTMTAFSSMSHICRDVNYGWIIRQLHSNGASIFFLCLYTHIGRNIYYGSYLYSETWNTGIMLLLITMATAFMGYVLPWGQMSFWGATVITNLFSAIPYIGTNLVEWIWGGFSVDKATLNRFFALHFILPFTMTALAGVHLTFLHETGSNNPLGLTSDSDKIPFHPYYTIKDFLGLLILILLLLLLALLSPDMLGDPDNYMPADPLNTPLHIKPEWYFLFAYAILRSVPNKLGGVLALFLSILILGLMPLLHTSKYRSMMLRPLSQVLFWTLTMDLLMLTWIGSQPVEYPYTIIGQMASILYFSIILAFLPIAGMIENYLIK

>gi|2924604|dbj|BAA25008.1| cytochrome b [Mammuthus primigenius]MTHIRKSHPLLKILNKSFIDLPTPSNISTWWNFGSLLGACLITQILTGLFLAMHYTPDTMTAFSSMSHICRDVNYGWIIRQLHSNGASIFFLCLYTHIGRNIYYGSYLYSETWNTGIMLLLITMATAFMGYVLPWGQMSFWGATVITNLFSAIPYIGTDLVEWIWGGFSVDKATLNRFFALHFILPFTMIALAGVHLTFLHETGSNNPLGLTSDSDKIPFHPYYTIKDFLGLLILILFLLLLALLSPDMLGDPDNYMPADPLNTPLHIKPEWYFLFAYAILRSVPNKLGGVLALLLSILILGIMPLLHTSKHRSMMLRPLSQVLFWTLATDLLMLTWIGSQPVEYPYIIIGQMASILYFSIILAFLPIAGMIENYLIK

Pairwise sequence alignment is the most fundamental operation of bioinformatics

It is used to decide if two proteins (or genes) are related structurally or functionally

It is used to identify domains or motifs that are shared among proteins

It is the basis of BLAST searching (next) It is used in the analysis of genomes

Globin Globins carry oxygens and are first proteins to be

sequenced Hemoglobins – in read blood cell Myoglobin – in muscle cells of mammals Leghemoglobin – in legumes (beans, etc.)

Globin

(a)Myoglobin(b)Tetrameric hemoglobin(c) Beta globin subunit(d)Myoglobin & beta globin

Similarity and Homology Similarity

Observation or measurement of resemblance, independent of the source of the resemblance

Can be observed now but involves no historical hypothesis

Homology Specifies that sequences and the organisms

descended from a common ancestor Implies that similarities are shared ancestral

characteristics Cannot make the assertion of homology from

historical evidence, and thus is an inference from observations of similarity

Homology Similarity attributed to descent from a common

ancestor Two types of homology

Orthologs Homologous sequences in different species that arose from a

common ancestral gene during speciation; may or may not be responsible for a similar function.

Paralogs Homologous sequences within a single species that arose by

gene duplication.

Orthologs:members of a gene (protein)family in variousorganisms.This tree showsglobin orthologs.

Paralogs: members of a gene (protein) family within aspecies. This tree shows human globin paralogs.

Orthologs and paralogs are often viewed in a single tree

Globin phylogeny by Dayhoff (1972)

Globin phylogeny by Dayhoff in evolutionary time (1972)

Direct Alignment

Given two sequences +1 if letters in the same positions match -1, otherwise

Extremely simple, but what if there is a gap? Gap when a base is inserted or deleted (indel) Maybe only in biological data Maybe more significant mutation – give more

negative score as a penalty

RNDKPFSTARNRNQKPKWWTA+ + - + +- - - - - -

Visual Alignment -- Dotplot

A seq. in x axis and the other in y axis Dot on a crosspoint if

identical in both sequences

view

Special Dotplot

Periodic Palindrome

Sequence Alignment Direct alignment

An alignment with gaps

What is the criteria for a good alignment ? Use score to check for optimality May not produce a unique optimal alignment

g c t g a a c gc t a t a a t c

g c t g - a a - c - g- - c t - a t a a t c

g c t g - a a - c g- c t a t a a t c -

Calculation of an alignment score

General approach to pairwise alignment

Given two sequences Select an algorithm that generates a score Allow gaps (insertions, deletions) Score reflects degree of similarity Alignments can be global or local Estimate probability that the alignment occurred by

chance

Pairwise alignment: protein sequencescan be more informative than DNA

protein is more informative (20 vs 4 characters); many amino acids share related biophysical properties

codons are degenerate: changes in the third position often do not alter the amino acid that is specified

protein sequences offer a longer “look-back” time DNA sequences can be translated into protein, and then

used in pairwise alignments Many times, DNA alignments are appropriate when

to confirm the identity of a cDNA to study noncoding regions of DNA to study DNA polymorphisms example: Neanderthal vs modern human DNA

Genetic Code

Scoring Matrix Dotplot

Incredibly useful in identifying biological significance and interesting regions

Do not privde a measure of statistical similarity A numerical method

Not just provide position-by-position overlap But provide the nature and characteristics of residues

being aligned Scoring matrices

Empirical weighting schemes

Scoring Matrix Three biological factors in constructing a

scoring matrix Conservation

Account for conservation between proteins, but provide a way to assess conservation substitutions

Score represents what residues are capable of substitution for other residues while not adversely affecting the function of the native protein (determined by charge, size, hydrophobicity, etc.)

Frequency Reflect how often residues occur among

proteins Rare residues are given more weight

Evolution By design, implicitly represent evolutionary

patterns Review

http://books.google.com/books?hl=en&lr=&id=9p3E2sS1aJUC&oi=fnd&pg=PA73&ots=eJ0lzjEg_b&sig=Fl2kBl5QBq7VIoy-eDgDqXhaZ14#v=onepage&q&f=false

Scoring Matrix Log-Odds Score

qij : prob. of how often i and j are seen aligned pi: prob. of observing AA I among all proteins

sij = log(qij/ pipj)

score Represent the ratio of observed versus random

frequency of substitutign i by j Positive score – two residues are replaced more often

than by chance Negative – less likely to substitute than by chance

Scoring Matrix Nucleotides

AAs More complicated in 20x20

Other Scores

Gap penalty Gap initiation and extension

Clustal-W recommends use of identity matrix For DNA sequences

1 for a match, 0 for a mismatch, gap penalty of 10 for initiation and 0.1 for extension per residue

For AA sequences BLOSUM62 matrix for substitution, gap penalty

of 11 for initiation and 1 for extension per residue

a a a g a a aa a a – a a a

a a a g g g a a aa a a - - - a a a

Pairwise Alignment: Global and Local Given a scoring scheme, find alignments

maximizing the score Global

Entire sequence of protein or DNA sequence Needleman and Wunsch (dynamic

programming) Local

Focus on regions of greatest similarity Smith and Waterman In general, preferable to Global Alignment

Because only portions of proteins align

Global and Local in Dotplot

Dynamic Programming

Guaranteed to yield an optimal global alignment Drawback – many alignments may give the same

optimal score and none of them may correspond to biologically correct alignment W.Fitch and T.Smith found 17 alignments of alpha- and

beta-chains of chicken haemoglobin, one of which is correct based on structures

Drawback – complexity O(nm) for sequences of length n and m

Dynamic Programming

Rock removal game Two piles of rocks, each with 10 rocks A and B alternatively remove one rock from a

single pile or one rock each from both piles Player who remove the last rock(s) wins the game

Use reduction strategy starting with smaller problems

Consider 2+2 problem A removes one rock each, B removes one rock

each A removes one rock, B takes one rock from the

same pile B wins

3+3 problem ?

Rock Removal with 10+10 ↑ A takes one from pile X ← A takes one from pile Y A takes one from each pile * A will lose

Manhattan Tourist Problem

Visit as many tourist sites in a Manhattan grid Move to the east

or south only Start at upper

left corner End at # 15,

lower right corner

Problem Statement

Given a weighted grid G with two vertices (nodes) for a source and a sink

Find the longest path in a weighted grid

Weight: # of attraction sites on an edge (link)

Each vertex (node) can be identified by (i,j) Source at (0,0) Sink at (n, m)

3 2 4

1 0 2 43 2 4

4 6 5 20 7 3

4 4 5 23 3 0

Solution

Define si,j: the longest path from source to vertex (i,j) (0 ≤ i < n, 0 ≤ j < m)

Solve for smaller problems first

Solving for s0,j and si,0 is easy

3 2 4

1 0 2 43 2 4

4 6 5 20 7 3

4 4 5 23 3 0

0 3 5 9

1

5

9

(0,0)

Solution (2)

Iteratively solve for neighboring nodes si,1

si,2, etc.

si,j = max[si-1,j + weight on edge between (i-1,j) and (i,j),

si,j-1 + weight on edge between (i,j-1) and (i,j)]

3 2 4

1 0 2 43 2 4

4 6 5 20 7 3

4 4 5 23 3 0

0 3 5 9

1

5

9

(0,0)

4

10

14

(1,0)

(2,0)

(3,0)

(0,1)

Algorithm Algorithm

Given Weast(i,j) and Wsouth(i,j),

s0,0 = 0

for i =1 to n si,0 = si-1,0 + Wsouth(i,0)

for j =1 to n s0,j = s0,j-1 + Weast(0,j)

for i =1 to n for j = 1 to m

si,j = max[si-1,j + Wsouth(i,j),

si,j-1 + Weast(i,j)]

return sn,m

General Graph Problem

Not regular with two inputs (indegree) and two outputs (outdegree) at a node

Directed Acyclic Graph DAG: Directed Acyclic Graph

G = (V, E) Longest Path Problem

sv = max(su + weight from u to v) over all u which are Predecessor(v)

Predecessor relationship has to be established ahead of the time

57 3

5v

u1

u2

u3

Graph Problem applied to Alignment Measure of similarity

Hamming distance: equal-length sequences Levenshtein or edit distance, 1966

unequal-length sequence Min. # of ‘edit operations’ (insertion,

deletion, alteration of a single character in either sequence) required to change one string into the other

e.g.

Levenshtein distance = 3

a g – t c cc g c t c a

Edit Distance and Alignment

Two strings, v and w Gaps are allowed in string, except that two gaps

are not allowed at the same char positions

Each char in a string is represented by positions in the original string without gaps v: (1 2 2 3 4 5 6 7 7) w: (1 2 3 4 5 5 6 6 7)

For both strings, (0

0) (11) (2

2) (23) (3

4) (45) (5

5) (66) (7

6) (77)

Represents a path in a grid

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

Edit Distance

Vertex (i,j) corresponds to (i

j) for (vi, wj) G = (V, E) Longest Path Problem

sv = max(su + weight from u to v) over all u, Predecessor(v)

Predecessor relationship has to be established ahead of the time

Global Alignment

A string has a sequence of characters drawn from an alphabet A of size k

Scoring matrix, δ, of (k+1)x(k+1) Problem Statement

Given two strings, v and w, and a scoring matrix δ,

Find the longest (max. score) path

Dynamic programming kernel Recurrence relationship

si-1, j + δ(vi, -)si, j = max [ si, j-1 + δ(-, wj) ] si-1, j-1 + δ(vi, wj)

Global Alignment

Example of scoring matrix Match: +1; mismatch: -μ; indels: -σ

Indels are frequent, and gap penalties proportional to indel sizes are considered to be severe Affine gap penalties soften the penalty rate Can be linear, -(a + bx) for the indel length of x

si-1, j - σsi-1, j = max [ si, j-1 - σ ] si-1, j-1 + 1, if vi=wj

si-1, j-1 - μ, otherwise

Needleman-Wunsch, 1970

Setting up a matrix

Setting up a matrix

Scoring the matrix

Identifying the optimal alignment

Local Alignment

Global sequence alignment is useful for alignment of sequences from the same protein family, for example

Substrings from two sequences may be highly conserved in biological applications Temple Smith and Michael Waterman, 1981 Biologically irrelevant diagonal matches are likely

to have a higher score

Local Alignment Problem Given two strings v and w, and a scoring

matrix δ Find substrings of v and w whose global

alignment is maximal among all substrings of v and w Seemingly harder, because the global alignment

is to find the longest path from (0,0) to (n,m), whereas the local alignment is to find the longest path among all paths between two arbitrary points, (i,j) to (i’, j’)

Add edges of weight 0 from (0,0) to every other vertex (vertex (0,0) is a predecessor of every vertex

Local Alignment Solution

Recurrence kernel becomes

Select the largest si, j

Other non-maximal local alignments may have biological significance Select k best nonoverlapping local alignments

si-1, j + δ(vi, -)si, j = max [ si, j-1 + δ(-, wj) ] si-1, j-1 + δ(vi, wj)

0