1. Dot plots Dynamic Programming
Sequence Alignment I
Dot plots
Dynamic Programming

2. Why align sequences? conserved sequencesconserved function
Assess ancestry among homologs (sequences with common ancestory) to help in gene finding and annotation
Find consensus motifs among related sequences (e.g., regulatory and structural regions)
Estimate the rate of evolution

3. Definitions

4. Definitions

5. Problem

6. Are the sequences related?

7. Types of Alignment
Local
Global
Gap-free
Gapped

8. Methods of Alignment
Dot matrix
Dynamic programming
K-tuple

9. Dot plots To evaluate/visualize similarity between two sequences
Create a matrix when sequence 1 is a row vector and sequence 2 is a column vector.

10. Dot plot (identity matrix)

11. Self-alignment

12. Self-alignment with sliding window

13. Self-alignment with sliding window

14. Dotmatrix A T C 1 G
Seq1 = ‘ATCAA’
Seq2 = ‘ATCGA’

15. Function dotplot1.m function [dotmatrix]=dotplot1(seq1,seq2)
OUTPUT: [dotmatrix] is an n x m matrix with 1s and 0s, where 0 means a mismatch and 1 means a match between two nucleotides
INPUT: seq1 and seq2 are strings made of a,t,c, or g. (seq1 is a row vector 1 x m; and seq2 is a column vector (n x1).

16. Run dotplot1.m Place dotplot1.m into your directory.
Open a Matlab session.
Open the file named dotplot1.m under the file option.
Define seq1 and seq2 as the following; and run the program:
>> seq1 = ‘attataagg’
>> seq2 = ‘attataggg’
>> [dotmatrix] = dotplot1(seq1,seq2)
Next, copy and paste each line of the dotplot1.m on the command window without using ; to track what the program is doing.

17. Dot plot Seq1='attataagg‘ Seq2='attataggg' A match is red (=1);
a mismatch is blue (=0)

18. Dot plot with sliding windows
Sliding windows consider more than one position at a time.
Similarity cutoffs (threshold) also allow to get rid of positions with low similarity across the window.
Sliding window can reduce the noise in the dot plot.

19. Dot plot with sliding windows
Use a sliding window of size w, for example w =3, such that only positions with w number of consecutive matches along the diagonal count. A T C 1 G A T C 3 G 

20. Dot plot with sliding windows3 3

21. Dot plot with sliding windows3 3 3 2

22. Dot plot with sliding windowsA T C 3 2 G

23. Function dotplot2.m Introduced two variables:
function [dotmatrix,dot]=dotplot1(seq1,seq2,w,t)
Introduced two variables:
W = size of the sliding window
T = threshold, number of matches along the diagonal to assume a match.

24. Function dotplot2.m Worksheet (due end of lecture)
Examine the code in dotplot2.m to see what commands have been used to slide the window and count the number of consecutive matches. Briefly write down your assessment.
Type in different sequences for seq1 and seq2 (no longer than 30) and try two different w and t values to run dotplot2.m

25. Dot plot with sliding windows
Seq1='attataagg‘
Seq2='attataggg'
A match is red; a mismatch is blue
Sliding window size = 1
Threshold is 1
Sliding window size = 3
Threshold is 2
Sliding window size = 3
Threshold is 3
Seq1='attataagg’
Seq2='attataggg'
Seq1='attataagg’
Seq2='attataggg'

26. Alignment Is a pairwise match between the characters of each sequence.
A true alignment reflects evolutionarily common ancestry (homology).

27. Changes that occur in sequences
A mutation that replaces one character with another is a substitution.
An insertion that adds one or more positions and a deletion that deletes one or more positions are known as indels (gaps)

28. Alignment example:
AATCTATA
AAGATA

29. Gap-free alignment: match and mismatch
An alignment receives for each aligned pair of identical residues (the match score) and the penalty for aligned pair of nonidentical residues (mismatch score).
  n
match score; if seq1=seq2
mismatch score; if seq1seq2
where n is the length of the longer sequence.

30. Gap-free alignment example:
AATCTATA
AAGATA
Alignment scores would be 4, 1, 3, respectively; if the match score is 1 and mismatch score is 0.

31. Gaps
Indels complicate alignments by increasing the number of possible alignments between two or more sequences.

32. Alignment: match, mismatch, and gap penalty
An alignment receives a score for each aligned pair of identical residues (the match score) and the penalty for aligned pair of nonidentical residues (mismatch score), and a penalty for insertion of gaps.
  n
gap penalty; if seq1 = ‘-’ or seq2 = ‘-’
match score; if no gaps and seq1=seq2
mismatch score; if no gaps and seq1seq2
where n is the length of the longer sequence.

33. Gap-free alignment example:
AATCTATA
AAG-AT-A
AA-G-ATA
AA--GATA
Alignment scores would be 1, 3, 3, respectively; if the match score is 1; mismatch score is 0; and gap penalty is -1.

34. Origination and Length Penalties
Simple gap penalties lead to many optimal alignments (those having the same score).
Mutations are rare, invoking fewest number of unlikely events is evolutionarily sound.
3-nt indel would be more common than multiple single indels.

35. Origination and Length Penalties
Origination penalty: starting a new series of gaps in one of the sequences being aligned.
Length penalty: number of sequential missing characters.

36. Gap-free alignment example:
AATCTATA
AAG-AT-A
AA-G-ATA
AA--GATA
Alignment scores would be -3, -1, +1, respectively;
if the match score is 1; mismatch score is 0; and origination penalty is -2 and length penalty is -1.

37. Scoring matrices
Mismatch penalty can be used to provide further discrimination:
Two protein sequences, one of which has an alanine in a given position: A substitution to valine (another small hydrophobic aa) would have less impact than a change to lysine (a large, charged residue).
One can weigh these substitutions differently based on the likelihood of occurrence over time or based on other characteristics.

38. Scoring matrices
A scoring matrix is used to score each nongap position in the alignment.
Nucleotide sequences
Amino acid sequences

39. Identity matrix

40. Scoring matrices for DNA sequences5 -4 A T C G 1 -5 -1
BLAST matrix
Transition/Transversion matrix

41. Scoring Matrices
Need to know the frequency of one amino acid substituting for another versus that event happening by chance alone based on frequency of occurrence of each amino acid:
odds ratio = P(ab)/q(a)*q(b)

42. Scoring matrices for amino acids
Blosum
PAM (point accepted mutation)

43. Alignment and score for aa

44. BLOSUM
Ungapped alignments of related proteins are grouped using clustering techniques, substitution rates between clusters are calculated.
A BLOSUM-62 matrix is appropriate for comparing sequences of approximately 62% sequence similarity.

45. PAM matrices

46. PAM matrices

47. PAM-1

48. PAM1(multiplied by 10000)

49. PAM1*PAM1=PAM2

50. PAM250 = PAM1250

51. The Point-Accepted-Mutation (PAM) model of evolution and the PAM scoring matrix
Observed %
Difference
Evolutionary Distance
In PAMs 1 5 10 20 40 50 60 70 80 1 5 11 23 56 80
112
159
246

52. Final Scoring Matrix is the Log-Odds Scoring Matrix
S (a,b) = 10 log10(Mab/Pb)
Replacement amino acid
Original amino acid
Frequency of amino acid b
Mutational probability matrix number

53. PAM unit
PAM-1 is 1 substitution per 100 residues.

54. Point accepted mutation (PAM) matrix
Calculated by observing the substitutions that occur in alignments between similar sequences with very high (>85%) identity.

55. Construct a multiple sequence alignment
ACGCTAFKI
GCGCTAFKI
ACGCTAFKL
GCGCTGFKI
GCGCTLFKI
ASGCTAFKL
ACACTAFKL

56. Construct a multiple sequence alignment
A phylogenetic tree is created indicating the order in which various substitutions taken place.
AG
IL
AG
AL
CS
GA

57. Generating PAM matrix
For each amino acid, the frequency with which it is substituted by every other amino acid is calculated. Substitutions are considered symmetric: AG counts as GA
For example for FGA count all AG and GA substitutions.

58. Construct a multiple sequence alignment
FGA = AG AG GA = 3
AG
IL
AG
AL
CS
GA

59. Relative mutability, mi
Number of times the amino acid is substituted by any other amino acid in the phylogenetic tree.
This number is then divided by the total number of mutations that could have affected the residue.
This denominator is the total number of subs across entire tree times two, multiplied by freq. of the amino acid, times a scaling factor

60. Construct a multiple sequence alignment
FGA = AG AG GA = 3
AG
IL
AG
AL
CS
GA

61. Relative mutability of A: mA
Total of 4 mutations involving A.
Total number mutations in the entire tree is 6 should be multiplied by two = 6 x 2 = 12
Relative frequency of A residues (10 As out of 7x9=63 residues) is 10/63 =
Thus mA = 4/12 x x 100 =

62. Mutation probability of A to G: MGA
mA = 4/12 x x 100 =
MGA = mA multiplied by #(AG and GA subs) and then this is divided by #(all subs involving A)
MGA = ( x 3)/4 =

63. Scoring matrix: RGA
log(Mij/fi), where Mij mutation probability of ij and fi equals to relative frequency of j type residue. For example f(G) = 10/63 =
RGA = log(MGA/f(G)) = log(0.0156/0.1587)
= -1.01

64. PAM matrix calculator

65. Choice of matrix PAM vs. BLOSUM:
polar residues are less variable in BLOSUM
Since PAM is based on pairs of entire sequences with less than 15% divergence, most of the variations counted are in surface loop regions, regions under low evolutionary constraints. Asn is one of the most mutable residues.
BLOSUM matrices are based on conserved regions of more distantly related proteins and thus ignore residues in surface loop regions. The mutability of Asn is close to the average mutability.
Surface loop regions preferentially contain polar residues
Thus, BLOSUM matrices strongly overestimate the conservation of polar residues relative to PAM matrices.
Matrix Conservation polar/apolar
PAM 0.49
BLOSUM 0.93

66. Choice of matrix
General: the choice of matrix should be governed by the use to which the matrix is put.
Searches for distantly similar sequences, in which only the BLOCKS are likely to be conserved should rely on BLOSUM matrices.
Complete alignments of globular protein sequences should use PAM matrices.
Proteins with extensive transmembrane helices should be aligned using the transmembrane matrix.

67. Choice of matrix

68. Dynamic Programming
Exhaustive search: search all possible alignments: NOT FEASIBLE
Dynamic programming: a method of breaking a problem apart into reasonably sized subproblems and using these partial results to compute the final answer.
Needleman and Wunsch

69. How to start the alignment?
How to break down the problem:
Seq1 = ‘CACGA’
Seq2 = ‘CGA’
Three possible ways to start the problem:
C of seq1 and C of seq2 match
C ACGA
C GA
A gap is inserted into 1st position of seq1
- CACGA
A gap is inserted into 1st position of seq2
- CGA

70. How to end the alignment?
If we knew the score for the best alignment, we can track back the steps to reach to the best score.
Use a table to store each step of the alignment to refer back later on.
Depends on storing partial sequence alignments so you don’t do it again and again.

71. Dynamic Programming

72. Partial scores table A C T G -1 -2 -3 -4 -5 -6 -7-1 -2 -3 -4 -5 -6 -7
Initialize a matrix where seq1 is on the rows and seq2 is on the colums
Fill in the first row and first column with multiples of gap penalty, in this case it equals to -1.

73. Partial scores table A C T G -1 -2 -3 -4 -5 1 -6 -7
Start with the first residue of each sequence:
Should A match A?
The alignment score between A of seq1 and A of seq2 can come from:
diagonal: match (+1) or mismatch (0)
From top means a gap (-1) inserted in the first sequence (from left to right)
From left means that a gap (-1) is inserted in the second sequence (from top to bottom)
SELECT THE MAXIMUM AMONG THREE A C T G -1 -2 -3 -4 -5 1 -6 -7

74. Partial scores table A C T G -1 -2 -3 -4 -5 1 -6 -7
Continue towards right
Does A match C
diagonal: match (+1) or mismatch (0)
From top means a gap (-1) inserted in the first sequence (from left to right)
From left means that a gap (-1) is inserted in the second sequence (from top to bottom) A C T G -1 -2 -3 -4 -5 1 -6 -7

75. Partial scores table A C T G -1 -2 -3 -4 -5 1 -6 -7
Continue towards right
Does A match T
diagonal: match (+1) or mismatch (0)
From top means a gap (-1) inserted in the first sequence (from left to right)
From left means that a gap (-1) is inserted in the second sequence (from top to bottom) A C T G -1 -2 -3 -4 -5 1 -6 -7

76. Partial scores table A C T G -1 -2 -3 -4 -5 1 -6 -7
Continue towards right
Does A match C
diagonal: match (+1) or mismatch (0)
From top means a gap (-1) inserted in the first sequence (from left to right)
From left means that a gap (-1) is inserted in the second sequence (from top to bottom) A C T G -1 -2 -3 -4 -5 1 -6 -7

77. Partial scores table A C T G -1 -2 -3 -4 -5 1 -6 -7
Continue towards right
Does A match G
diagonal: match (+1) or mismatch (0)
From top means a gap (-1) inserted in the first sequence (from left to right)
From left means that a gap (-1) is inserted in the second sequence (from top to bottom) A C T G -1 -2 -3 -4 -5 1 -6 -7

78. Partial scores table A C T G -1 -2 -3 -4 -5 1 -6 -7
Go to second row and continue towards right
Does C match A
diagonal: match (+1) or mismatch (0)
From top means a gap (-1) inserted in the first sequence (from left to right)
From left means that a gap (-1) is inserted in the second sequence (from top to bottom) A C T G -1 -2 -3 -4 -5 1 -6 -7

79. Partial scores table A C T G -1 -2 -3 -4 -5 1 2 -6 -7
Continue towards right
Does C match C
diagonal: match (+1) or mismatch (0)
From top means a gap (-1) inserted in the first sequence (from left to right)
From left means that a gap (-1) is inserted in the second sequence (from top to bottom) A C T G -1 -2 -3 -4 -5 1 2 -6 -7

80. Partial scores table A C T G -1 -2 -3 -4 -5 1 2 -6 -7
Continue towards right
Does C match T
diagonal: match (+1) or mismatch (0)
From top means a gap (-1) inserted in the first sequence (from left to right)
From left means that a gap (-1) is inserted in the second sequence (from top to bottom) A C T G -1 -2 -3 -4 -5 1 2 -6 -7

81. Partial scores table A C T G -1 -2 -3 -4 -5 1 2 -6 -7
Continue towards right
Does C match C
diagonal: match (+1) or mismatch (0)
From top means a gap (-1) inserted in the first sequence (from left to right)
From left means that a gap (-1) is inserted in the second sequence (from top to bottom) A C T G -1 -2 -3 -4 -5 1 2 -6 -7

82. Partial scores table A C T G -1 -2 -3 -4 -5 1 2 -6 -7
Continue towards right
Does C match G
diagonal: match (+1) or mismatch (0)
From top means a gap (-1) inserted in the first sequence (from left to right)
From left means that a gap (-1) is inserted in the second sequence (from top to bottom) A C T G -1 -2 -3 -4 -5 1 2 -6 -7

83. Partial scores table A C T G -1 -2 -3 -4 -5 1 2 -6 -7-1 -2 -3 -4 -5 1 2 -6 -7
Fill in all cells in the partial scores table
While you fill in keep tract of from which direction you have carried away the scores from.

84. Partial scores table A C T G -1 -2 -3 -4 -5 1 2 -6 -7-1 -2 -3 -4 -5 1 2 -6 -7
Back trace your steps from the optimal alignment score.
Sometimes more than one optimal alignment is possible.

85. Partial scores table A C T G -1 -2 -3 -4 -5 1 2 -6 -7
From the end point: G
TCG
TAG
--TCG
AGTAG
AC—-TCG
ACAGTAG A C T G -1 -2 -3 -4 -5 1 2 -6 -7

86. Dynamic Programming

87. Dynamic Programming

88. Dynamic Programming

89. Dynamic Programming

90. Dynamic Programming
Mismatch between D and V is -3; gap is -8

91. Dynamic Programming

92. Dynamic Programming

93. Trace-back

94. Global alignments Needleman and Wunch algorithm is global:
compares two sequences in their entirety
a gap penalty is assessed regardless of whether gaps are located internally within a sequence, or at the end of one of both sequences.

95. Semi-global alignment
Terminal gaps are undermined because they are generally due to incomplete data and have no biological significance.
How is it different than the global algorithm?

96. Semi-global vs. global
In global a vertical move equals to a gap in the horizontal axis while a move to left equals to a gap in the vertical axis; they are both penalized.
If one allows initial gaps without penalty in the sequences, should set the first row and first column of the partial scores table to 0.

97. Semi-global alignmentC T G 1 2 3 4 5 6
Horizontal moves on the bottom row and vertical moves on the right most column are penalty free.

98. Semi-global alignment
ACACTGATCG
ACACTG----

99. Local alignment Smith-Waterman Algorithm
If you have a long sequence, and want to find any subsequences that are similar to any part of yeast genome.
Local alignment finds the best matching subsequences within two search sequences.

100. Modify global alignment algorithm
Smith-Waterman Algorithm
Place a zero in any position in the table if all of the other methods result in scores lower than zero.

101. Local Alignment

102. local alignment A C T G 1 2 3 4

103. Multiple Sequence Alignment

104. GAPS

105. Use align1 to align: enter x and y in the command line (>>)
>> x='ggagaggat'
x =
ggagaggat
>> y='ccagacct'
y =
ccagacct
>> align1

106. Use align1 to align: enter x and y in the command line (>>)
xalign =
ggagaggat
yalign =
ccagacc-t

107. Use alignloc1 to align: type in alignloc1 at the >>
xalign =
aga
yalign =

108. What is different? No gap penalty at the initiation
%Initial Conditions for matrices F and I:
for i = 2:M+1
F(i,1) = (i-1)*0
I(i,1) = 1 %I:vertical
end
for j = 2:N+1
F(1,j) = (j-1)*0
I(1,j) = 3 %I:horizontal

109. What is different? Maximization
[F(i,j) I(i,j)] = max([F(i-1,j)+g F(i-1,j-1)+w F(i,j-1)+g 0])

110. What is different? Find the max value of the F matrix
[Yj,fj]=max(max(F)) % find column id
[Yi,fi]=max(max(F')) % find row id
i=fi(1) % set current i
j=fj(1) % set current j

111. What is different? When maximum value is 0 then stop
if I(i,j) == 1
i = i-1
xrev(k) = x(i)
yrev(k) = '-'
elseif I(i,j) == 2
i = i-1; j = j-1
yrev(k) = y(j)
elseif I(i,j) == 3
j = j-1;
xrev(k) = '-'
else
break
end