S.Prasanth Kumar, S.Prasanth Kumar, BioinformaticianBioinformatician
Genomics
Sequence Alignment : Complete Coverage-ISequence Alignment : Complete Coverage-I
S.Prasanth Kumar Dept. of Bioinformatics Applied Botany Centre (ABC) Gujarat University, Ahmedabad, INDIA
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Alignment scoring schemes
Alignment of ATCGGATCT and ACGGACT
match: +2mismatch: -1indel –2
6 * 2 + 1 * -1 + 2 * -2 = 7
6 matches, 1 mismatch, and 2 indels
Optimal alignment of two sequences
Brute Force Method
Suppose there are two sequences X and Z to be aligned, where |X| = m and |Z| = nIf gaps are allowed in the sequences, then the potential length of both the first and second sequences is m+n.
2m+n subsequences with spaces for the sequence X2m+n subsequences with spaces for the sequence Z
Alignment = 2m+n * 2m+n = 2(2(m+n)) = 4m+n comparisons
Optimal alignment of two sequences
Dynamic Programming
DP align two sequences by beginning at the ends of the two sequences and attempting to align all possible pairs of characters (one from each sequence) using a scoring scheme for matches, mismatches, and gaps. The highest set of scores defines the optimal alignment between the two sequences
DP algorithms solve optimization problems by dividing theproblem into independent subproblems
Optimal alignment of two sequences
Dynamic Programming Matrix
s(aibj) = +5 if ai = bj (match score)s(aibj) = -3 if ai ≠ bj (mismatch score)w = -4 (gap penalty)
• Initialization• Matrix Fill (scoring)• Traceback (alignment)
Global Alignment: Needleman-Wunsch Algorithm
Initialization Step
Each row Si,0 is set to w * i Each column S0,j is set to w * j
Global Alignment: Needleman-Wunsch Algorithm
Matrix Fill Step
G-G match score = +5
Si,j = MAX [0 + 5, -4 + -4, -4 + -4] = MAX [ 5 , -8 , -8 ] = 5
Confusing ?
Diagonal + Match/Mismatch Score
Left + Gap penalty
Right + Gap penalty
Global Alignment: Needleman-Wunsch Algorithm
G-A mismatch score = -3
Si,j = MAX [-4 + -3, 5 + -4, -8 + -4] = MAX [ -7 , 1 , -12 ] = 1
Global Alignment: Needleman-Wunsch Algorithm
Trace backing
Easy ; Find the lowermost right corner and follow arrow
Global Alignment: Needleman-Wunsch Algorithm
5 – 3 + 5 – 4 + 5 + 5 – 4 + 5 – 4 – 4 + 5 = 11
Local Alignment: Smith-Waterman Algorithm
Initialization Step
Each row Si,0 is set to 0 Each column S0,j is set to 0
Same Rule Initialization different Trace backing need attention
Local Alignment: Smith-Waterman Algorithm
There are two cells having 14. There are multiple alignments producing the maximal alignment score What to consider ? Value in last row means aligned fully
Local Alignment: Smith-Waterman Algorithm
Two trace back pathway pointers
The two local alignments resulting in a score of 14
Local Alignment: Smith-Waterman Algorithm
5 matches, 1 mismatch, and 2 gaps
score = 5 *5 – 1 *3 – 2 *4 = 25 – 3 – 8 = 14
What in Next Coverage ?
Scoring Matrices: PAM & BLOSUMAssessing the significance of sequence alignments
Thank You For Your Attention !!!