Applied Bioinformatics Week 3. Theory I Similarity Dot plot

Applied Bioinformatics

Week 3

Theory I

• Similarity

• Dot plot

3

Introduction to Bioinformatics http://www.personeel.unimaas.nl/Westra/Education/BioInf/slides_of_bioinformatics.htmLECTURE 3: SEQUENCE ALIGNMENT

3.2 On sequence alignment

Sequence alignment is the most important task in bioinformatics!

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http://www.personeel.unimaas.nl/Westra/Education/BioInf/slides_of_bioinformatics.htmLECTURE 3: SEQUENCE ALIGNMENT

3.2 On sequence alignment

Sequence alignment is important for:

* prediction of function* database searching* gene finding* sequence divergence* sequence assembly

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http://www.personeel.unimaas.nl/Westra/Education/BioInf/slides_of_bioinformatics.htmLECTURE 3: SEQUENCE ALIGNMENT

3.3 On sequence similarity

Homology: genes that derive from a common ancestor-gene are called homologs

Orthologous genes are homologous genes in different organisms

Paralogous genes are homologous genes in one organism that derive from gene duplication

Gene duplication: one gene is duplicated in multiple copies that therefore free to evolve and assume new functions

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http://www.personeel.unimaas.nl/Westra/Education/BioInf/slides_of_bioinformatics.htm

HOMOLOGOUS and PARALOGOUS

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HOMOLOGOUS and PARALOGOUS

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HOMOLOGOUS and PARALOGOUS versus ANALOGOUS

? globin

plants

Ath-g

analogs

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http://www.personeel.unimaas.nl/Westra/Education/BioInf/slides_of_bioinformatics.htmLECTURE 3: SEQUENCE ALIGNMENT: sequence similarity

Causes for sequence (dis)similarity

mutation: a nucleotide at a certain location is replaced by another nucleotide (e.g.: ATA → AGA)

insertion: at a certain location one new nucleotide is inserted inbetween two existing nucleotides (e.g.: AA → AGA)

deletion: at a certain location one existing nucleotide is deleted (e.g.: ACTG → AC-G)

indel: an insertion or a deletion

Similarity

• We can only measure current similarity

• We can form hypothesi

Similarity Searching

• DotPlot

• Needleman-Wunsch

• Smith-Waterman

• FASTA

• BLAST

Dot Plot

• Writing one sequence horizontally

• Writing the other vertically

• At each intersection with equal nucleotides make a dot in the matrix

Dot Plot

Dot Plot

• Messy?

• Strong similarities can be visually enhanced

• Select a window size and a similarity score for that window (e.g. 10 and 8)

• Create a new matrix with dots where the window score >= 8

Dot Plot

Dot Plot Interpretation

Creating a Dot Plot

End Theory I

• Mindmapping

• 10 min break

Practice I

• Dot plot

Dot Plot

• ACGTGTGCGTTTGAAC• GGGTGTTCGTTTAAAC• Make a Dot plot for the two sequences above• Use a window of 3 to refine the view• Can you use Excel?

• Get any two DNA sequences and try the tool below– http://www.vivo.colostate.edu/molkit/dnadot/


• DotPlot


• Smith-Waterman

• FASTA

• BLAST

DefinitionsOptimal alignment - one that exhibits the

most correspondences. It is the alignment with the highest score. May or may not be biologically meaningful.

Global alignment - Needleman-Wunsch (1970) maximizes the number of matches between the sequences along the entire length of the sequences.

Local alignment - Smith-Waterman (1981) gives the highest scoring local match between two sequences.

How can we find an optimal alignment?

• ACGTCTGATACGCCGTATAGTCTATCTCTGAT---TCG-CATCGTC--T-ATCT

• How many possible alignments?

C(27,7) gap positions = ~888,000 possibilities

• Dynamic programming: The Needleman & Wunsch algorithm

1 27

Time Complexity

Consider two sequences:AAGT

AGTC

How many possible alignments the 2 sequences have?

2n2nnn = (2n)!/(n!)= (2n)!/(n!)2 2 = = (2(22n 2n //n ) = n ) = (2(2nn))

= 70

Scoring a sequence alignment

• Match/mismatch score: +1/+0• Open/extension penalty: –2/–1ACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || ||||||||----CTGATTCGC---ATCGTCTATCT

• Matches: 18 × (+1)• Mismatches: 2 × 0• Open: 2 × (–2)• Extension: 5 × (–1)

Score = +9Score = +9

Pairwise Global Alignment

• Computationally:

– Given:

a pair of sequences (strings of characters)

– Output:

an alignment that maximizes the similarity

Needleman-Wunsch Alg









• Which Alignment is better?

• For scoring use:– Match 1– Mismatch 0– Gap open -2– Gap extension -1

• How can substitution matrices be integrated?

Needleman & Wunsch

• Place each sequence along one axis• Place score 0 at the up-left corner• Fill in 1st row & column with gap penalty multiples• Fill in the matrix with max value of 3 possible moves:

– Vertical move: Score + gap penalty– Horizontal move: Score + gap penalty– Diagonal move: Score + match/mismatch score

• The optimal alignment score is in the lower-right corner• To reconstruct the optimal alignment, trace back where the

max at each step came from, stop when hit the origin.

Three steps in Needleman-Wunsch Algorithm

• Initialization

• Scoring

• Trace back (Alignment)

• Consider the two DNA sequences to be globally aligned are:

ATCG (x=4, length of sequence 1)

TCG (y=3, length of sequence 2)

Pooja Anshul Saxena, University of Mississippi

Scoring Scheme

• Match Score = +1

• Mismatch Score = -1

• Gap penalty = -1

• Substitution Matrix

A C G T

A 1 -1 -1 -1

C -1 1 -1 -1

G -1 -1 1 -1

T -1 -1 -1 1


Initialization Step

• Create a matrix with X +1 Rows and Y +1 Columns

• The 1st row and the 1st column of the score matrix are filled as multiple of gap penalty

T C G

0 -1 -2 -3

A -1

T -2

C -3

G -4Pooja Anshul Saxena, University of Mississippi

Scoring• The score of any cell C(i, j) is the maximum of:

scorediag = C(i-1, j-1) + S(i, j) = -1

scoreup = C(i-1, j) + g = -2

scoreleft = C(i, j-1) + g = -2

where S(i, j) is the substitution score for letters i and j, and g is the gap penalty

T C G

0 -1 -2 -3

A -1 -1

T -2

C -3

G -4

Max -> C(i,j)

S(T,A)

Scoring ….• Example:

The calculation for the cell C(2, 2):

scorediag = C(i-1, j-1) + S(I, j) = 0 + -1 = -1

scoreup = C(i-1, j) + g = -1 + -1 = -2

scoreleft = C(i, j-1) + g = -1 + -1 = -2T C G

0 -1 -2 -3

A -1 -1

T -2

C -3

G -4


Scoring ….

• Final Scoring Matrix

T C G

0 -1 -2 -3

A -1 -1 -2 -3

T -2 0 -1 -2

C -3 -1 1 0

G -4 -2 0 2


Trace back

• The trace back step determines the actual alignment(s) that result in the maximum score

• There are likely to be multiple maximal alignments

• Trace back starts from the last cell, i.e. position X, Y in the matrix

• Gives alignment in reverse order


Trace back ….

• There are three possible moves: diagonally (toward the top-left corner of the matrix), up, or left

• Trace back takes the current cell and looks to the neighbor cells that could be direct predecessors. This means it looks to the neighbor to the left (gap in sequence #2), the diagonal neighbor (match/mismatch), and the neighbor above it (gap in sequence #1). The algorithm for trace back chooses as the next cell in the sequence one of the possible predecessors


Trace back ….

• The only possible predecessor is the diagonal match/mismatch neighbor. If more than one possible predecessor exists, any can be chosen. This gives us a current alignment of

Seq 1: G |

Seq 2: G

T C G

0 -1 -2 -3

A -1 -1 -2 -3

T -2 0 -1 -2

C -3 -1 1 0

G -4 -2 0 2


Trace back ….• Final Trace back

Best Alignment:A T C G | | | |_ T C G

T C G

0 -1 -2 -3

A -1 -1 -2 -3

T -2 0 -1 -2

C -3 -1 1 0

G -4 -2 0 2



• DotPlot


• Smith-Waterman

• FASTA

• BLAST

Local Alignment

• Problem first formulated:– Smith and Waterman (1981)

• Problem:– Find an optimal alignment

between a substring of s and a substring of t

• Algorithm:– is a variant of the basic algorithm

for global alignment

Motivation• Searching for unknown domains or motifs

within proteins from different families– Proteins encoded from Homeobox genes (only

conserved in 1 region called Homeo domain – 60 amino acids long)

– Identifying active sites of enzymes

• Comparing long stretches of anonymous DNA• Querying databases where query word much

smaller than sequences in database• Analyzing repeated elements within a single

sequence

Smith-Waterman Alg

• Very similar to Needleman-Wunsch

• Determines local instead of global alignment

• Scores can drop and increase

• Alignments are calculated between 0 and 0 scores

Three steps in Smith-Waterman Algorithm

• Initialization

• Scoring

• Trace back (Alignment)

• Consider the two DNA sequences to be globally aligned are:

ATCG (x=4, length of sequence 1)

TCG (y=3, length of sequence 2)


Scoring Scheme

• Match Score = +1

• Mismatch Score = -1

• Gap penalty = -1

• Substitution Matrix

A C G T

A 1 -1 -1 -1

C -1 1 -1 -1

G -1 -1 1 -1

T -1 -1 -1 1


Initialization Step

• Create a matrix with X +1 Rows and Y +1 Columns

• The 1st row and the 1st column of the score matrix are filled with 0s

T C G

0 0 0 0

A 0

T 0

C 0

G 0Pooja Anshul Saxena, University of Mississippi

Scoring

• The score of any cell C(i, j) is the maximum of:scorediag = C(i-1, j-1) + S(I, j)scoreup = C(i-1, j) + gscoreleft = C(i, j-1) + g

And0(here S(I, j) is the substitution score for letters i and j, and g is the gap penalty)


Scoring ….• Example:

The calculation for the cell C(2, 2):

scorediag = C(i-1, j-1) + S(I, j) = 0 + -1 = -1

scoreup = C(i-1, j) + g = 0 + -1 = -1

scoreleft = C(i, j-1) + g = 0 + -1 = -1

T C G

0 0 0 0

A 0 0

T 0

C 0

G 0


Scoring ….

• Final Scoring Matrix

Note: It is not mandatory that the last cell has the maximum alignment score!

T C G

0 0 0 0

A 0 0 0 0

T 0 1 0 0

C 0 0 2 1

G 0 0 1 3


Trace back

• The trace back step determines the actual alignment(s) that result in the maximum score

• There are likely to be multiple maximal alignments

• Trace back starts from the cell with maximum value in the matrix

• Gives alignment in reverse order


Trace back ….

• There are three possible moves: diagonally (toward the top-left corner of the matrix), up, or left

• Trace back takes the current cell and looks to the neighbor cells that could be direct predecessors. This means it looks to the neighbor to the left (gap in sequence #2), the diagonal neighbor (match/mismatch), and the neighbor above it (gap in sequence #1). The algorithm for trace back chooses as the next cell in the sequence one of the possible predecessors. This continues till cell with value 0 is reached.


Trace back ….

• The only possible predecessor is the diagonal match/mismatch neighbor. If more than one possible predecessor exists, any can be chosen. This gives us a current alignment of

Seq 1: G |

Seq 2: G

T C G

0 0 0 0

A 0 0 0 0

T 0 1 0 0

C 0 0 2 1

G 0 0 1 3


Trace back ….• Final Trace back

Best Alignment:T C G | | |T C G

T C G

0 0 0 0

A 0 0 0 0

T 0 1 0 0

C 0 0 2 1

G 0 0 1 3


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http://www.personeel.unimaas.nl/Westra/Education/BioInf/slides_of_bioinformatics.htmLECTURE 3: GLOBAL ALIGNMENT

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http://www.personeel.unimaas.nl/Westra/Education/BioInf/slides_of_bioinformatics.htmLECTURE 3: GLOBAL ALIGNMENT

Significance of Sequence Alignment

• Consider randomly generated sequences. What distribution do you think the best local alignment score of two sequences of sample length should follow?

1. Uniform distribution

2. Normal distribution

3. Binomial distribution (n Bernoulli trails)

4. Poisson distribution (n, np=)

5. others

Extreme Value Distribution

• Yev = exp(- x - e-x )

-5 0 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Extreme Value Distribution vs. Normal Distribution

-5 0 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-5 0 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

“Twilight Zone”

-5 0 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Some proteins with less than 15% similarity have exactly the same 3-D structure while some proteins with 20% similarity have different structures. Homology/non-homology is never granted in the twilight zone.

End of Theoretical Part 2

• Mindmapping

• 10 min break

Needleman-Wunsch

• ACGTGTGCGTTTGAAC• GGGTGTAGTCGTTTAAAC

• Apply the Needleman-Wunsch algorithm to these two sequences

• Score the alignments

Alignments

• Explanation for alignment algorithms– http://baba.sourceforge.net/

• Alignment of 2 sequences– http://www.expasy.org/tools/sim-prot.html

• Get any two amino acid sequences and try– http://bioinformatics.iyte.edu.tr/SmithWaterman/

Documents

Applied Bioinformatics Week 3. Theory I Similarity Dot plot