Applied Bioinformatics Week 3
Applied Bioinformatics
Week 3
Theory I
• Similarity
• Dot plot
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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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http://www.personeel.unimaas.nl/Westra/Education/BioInf/slides_of_bioinformatics.htm
HOMOLOGOUS and PARALOGOUS
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http://www.personeel.unimaas.nl/Westra/Education/BioInf/slides_of_bioinformatics.htm
HOMOLOGOUS and PARALOGOUS versus ANALOGOUS
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Ath-g
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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/
Similarity Searching
• DotPlot
• Needleman-Wunsch
• 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
Needleman-Wunsch Alg
Needleman-Wunsch Alg
Needleman-Wunsch Alg
Needleman-Wunsch Alg
Needleman-Wunsch Alg
Needleman-Wunsch Alg
Needleman-Wunsch Alg
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
Pooja Anshul Saxena, University of Mississippi
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
Pooja Anshul Saxena, University of Mississippi
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
Pooja Anshul Saxena, University of Mississippi
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
Pooja Anshul Saxena, University of Mississippi
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
Pooja Anshul Saxena, University of Mississippi
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
Pooja Anshul Saxena, University of Mississippi
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
Pooja Anshul Saxena, University of Mississippi
Similarity Searching
• DotPlot
• Needleman-Wunsch
• 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)
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
Pooja Anshul Saxena, University of Mississippi
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)
Pooja Anshul Saxena, University of Mississippi
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
Pooja Anshul Saxena, University of Mississippi
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
Pooja Anshul Saxena, University of Mississippi
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
Pooja Anshul Saxena, University of Mississippi
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.
Pooja Anshul Saxena, University of Mississippi
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
Pooja Anshul Saxena, University of Mississippi
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
Pooja Anshul Saxena, University of Mississippi
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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/