Pairwise Sequence Alignment

WHAT?

WHAT? Given any two sequences (DNA or protein) Seq 1: Seq 2: CATATTGCAGTGGTCCCGCGTCAGGCT Seq 2: TAAATTGCGTGGTCGCACTGCACGCT we are interested to know to what extent they are similar? CATATTGCAGTGGTCCCGCGTCAGGCT TAAATTGCGT-GGTCGCACTGCACGCT

WHY?

Discover function Study evolution Find crucial features within a sequence Identify cause of diseases

Discover function Sequences that are similar probably have the same function

Study evolution If two sequences from different organisms are similar , they may have a common ancestor

Find crucial features Conservation of the IGFALS (Insulin-like growth factor) Between human and mouse. Regions in the sequences that are strongly conserved between different sequences can indicate their functional importance CATATTGCAGTGGTCCCGCGTCAGGCT TAAATTGCGT-GGTCGCACTGCACGCT

Identify cause of disease Comparison of sequences between individuals can detect changes that are related to diseases

Sickle Cell Anemia Due to 1 swapping an A for a T, causing inserted amino acid to be valine instead of glutamine in hemoglobin Image source: http://www.cc.nih.gov/ccc/ccnews/nov99/

Healthy Individual >gi|28302128|ref|NM_000518.4| Homo sapiens hemoglobin, beta (HBB), mRNA ACATTTGCTTCTGACACAACTGTGTTCACTAGCAACCTCAAACAGACACCATGGTGCATCTGACTCCTGA GGAGAAGTCTGCCGTTACTGCCCTGTGGGGCAAGGTGAACGTGGATGAAGTTGGTGGTGAGGCCCTGGGC AGGCTGCTGGTGGTCTACCCTTGGACCCAGAGGTTCTTTGAGTCCTTTGGGGATCTGTCCACTCCTGATG CTGTTATGGGCAACCCTAAGGTGAAGGCTCATGGCAAGAAAGTGCTCGGTGCCTTTAGTGATGGCCTGGC TCACCTGGACAACCTCAAGGGCACCTTTGCCACACTGAGTGAGCTGCACTGTGACAAGCTGCACGTGGAT CCTGAGAACTTCAGGCTCCTGGGCAACGTGCTGGTCTGTGTGCTGGCCCATCACTTTGGCAAAGAATTCA CCCCACCAGTGCAGGCTGCCTATCAGAAAGTGGTGGCTGGTGTGGCTAATGCCCTGGCCCACAAGTATCA CTAAGCTCGCTTTCTTGCTGTCCAATTTCTATTAAAGGTTCCTTTGTTCCCTAAGTCCAACTACTAAACT GGGGGATATTATGAAGGGCCTTGAGCATCTGGATTCTGCCTAATAAAAAACATTTATTTTCATTGC >gi|4504349|ref|NP_000509.1| beta globin [Homo sapiens] MVHLTPEEKSAVTALWGKVNVDEVGGEALGRLLVVYPWTQRFFESFGDLSTPDAVMGNPKVKAHGKKVLG AFSDGLAHLDNLKGTFATLSELHCDKLHVDPENFRLLGNVLVCVLAHHFGKEFTPPVQAAYQKVVAGVAN ALAHKYH

Diseased Individual >gi|28302128|ref|NM_000518.4| Homo sapiens hemoglobin, beta (HBB), mRNA ACATTTGCTTCTGACACAACTGTGTTCACTAGCAACCTCAAACAGACACCATGGTGCATCTGACTCCTGA GGTGAAGTCTGCCGTTACTGCCCTGTGGGGCAAGGTGAACGTGGATGAAGTTGGTGGTGAGGCCCTGGGC AGGCTGCTGGTGGTCTACCCTTGGACCCAGAGGTTCTTTGAGTCCTTTGGGGATCTGTCCACTCCTGATG CTGTTATGGGCAACCCTAAGGTGAAGGCTCATGGCAAGAAAGTGCTCGGTGCCTTTAGTGATGGCCTGGC TCACCTGGACAACCTCAAGGGCACCTTTGCCACACTGAGTGAGCTGCACTGTGACAAGCTGCACGTGGAT CCTGAGAACTTCAGGCTCCTGGGCAACGTGCTGGTCTGTGTGCTGGCCCATCACTTTGGCAAAGAATTCA CCCCACCAGTGCAGGCTGCCTATCAGAAAGTGGTGGCTGGTGTGGCTAATGCCCTGGCCCACAAGTATCA CTAAGCTCGCTTTCTTGCTGTCCAATTTCTATTAAAGGTTCCTTTGTTCCCTAAGTCCAACTACTAAACT GGGGGATATTATGAAGGGCCTTGAGCATCTGGATTCTGCCTAATAAAAAACATTTATTTTCATTGC >gi|4504349|ref|NP_000509.1| beta globin [Homo sapiens] MVHLTPVEKSAVTALWGKVNVDEVGGEALGRLLVVYPWTQRFFESFGDLSTPDAVMGNPKVKAHGKKVLG AFSDGLAHLDNLKGTFATLSELHCDKLHVDPENFRLLGNVLVCVLAHHFGKEFTPPVQAAYQKVVAGVAN ALAHKYH

How do sequences change?

Sequence Modifications Three types of changes Substitution (point mutation) Insertion Deletion Indel (replication slippage) TCCGT TCAGT TCAGT TCGAGT TCGT

In order to align two sequences we need a quantitive model to evaluate similarity between sequences. How do we quantitate sequence similarity ?

Substitutions Only not including indels Sequences compared base-by-base Count the number of matches and mismatches For example :Matches score +2, Mismatches score -1 TTCGTCGTAGTCGGCTCGACCTG GTACGTCTAGCGAGCGTGATCCT 9 matches +18 14 mismatches -14 Total score +4 A weak match

TT-CGTCGTAGTCG-GC-TCGACC-TG GTACGTC-TAG-CGAGCGT-GATCCT- Including Indels Create an ‘alignment’ Count matches within alignment Indels are scored as mismatches -1 TT-CGTCGTAGTCG-GC-TCGACC-TG GTACGTC-TAG-CGAGCGT-GATCCT- 17 matches +34 2 mismatches - 2 8 indels - 8 Total score +24 A strong match

Choosing an Alignment Many different alignments are possible Should consider all possible Take the best score found There may be more than one best alignment TT-CGTCGTAGTCG-GC-TCGACC-TG GTACGTC-TAG-CGAGCGT-GATCCT- +24 -TTCGT-CGTAGTC-GGCTCG-ACCTG GTAC-GTCTA-GCGAGCGT-GATCC-T

Why is it hard ? Alignment requires an algorithm that performs a number of comparisons roughly proportional to the square of the average sequence length n2.

Dynamic Programming A method for reducing a complex problem to a set of identical sub-problems The best solution to one sub-problem is independent from the best solution to the other sub-problem

Dynamic Programming A method for reducing a complex problem to a set of identical sub-problems The best solution to one sub-problem is independent from the best solution to the other sub-problem

What does it mean? If a path from X→Z passes through Y, the best path from X→Y is independent of the best path from Y→Z

Sequence Global Alignment Needleman-Wunsch Sequences: A = ACGCTG, B = CATGT A C G C T G 1 2 3 4 5 6 C 1 A 2 T 3 G 4 T Z 5

Example -1 2 2 3 4 5 -2 ? Sequences: A = ACGCTG, B = CATGT Score of best alignment between AC and CATG 2 …between ACG and CATG 2 3 4 5 -2 …between AC and CATGT Calculate score between ACG and CATGT ? Match:+2, Other:-1

Example 2 3 4 5 Align the next Insertion in the letter in the sequences Insertion in the first sequence (del) 3 5 2 3 4 5 - 5 Insertion in the Second sequence 3 -

Example 2 3 4 5 -1 2 1 -2 Sequences: A = ACGCTG, B = CATGT -1 from before plus -1 for mismatch of G against T  -2 2 from before plus -1 for mismatch of – against T  1 2 3 4 5 -1 2 -2 from before plus -1 for mismatch of G against –  -3 1 Cell gets highest score of -2,1,-3  1 -2 Sequences: A = ACGCTG, B = CATGT

Sequences: A = ACGCTG, B = CATGT Example 2 3 4 5 1 -1 2 -2 Sequences: A = ACGCTG, B = CATGT

A 1 C 2 G 3 4 T 5 6 0  C 1  A 2  T 3  G 4  T 5 

A 1 C 2 G 3 4 T 5 6 0  -1 C 1  A 2  T 3  G 4  T 5  A -

ACGCTG ------ A 1 C 2 G 3 4 T 5 6 0 -1 -2 -3 -4 -5 -6 C 1 A 2 T 3 G 4 A 1 C 2 G 3 4 T 5 6 0  -1 -2 -3 -4 -5 -6 C 1  A 2  T 3  G 4  T 5  ACGCTG ------

----- CATGT A 1 C 2 G 3 4 T 5 6 0 -1 -2 -3 -4 -5 -6 C 1 A 2 T 3 G 4 A 1 C 2 G 3 4 T 5 6 0  -1 -2 -3 -4 -5 -6 C 1  A 2  T 3  G 4  T 5  ----- CATGT

A 1 C 2 G 3 4 T 5 6 0  -1 -2 -3 -4 -5 -6 C 1  A 2  T 3  G 4  T 5  A C

A 1 C 2 G 3 4 T 5 6 0  -1 -2 -3 -4 -5 -6 C 1  A 2  T 3  G 4  T 5  AC -C

A 1 C 2 G 3 4 T 5 6 0  -1 -2 -3 -4 -5 -6 C 1  A 2  T 3  G 4  T 5  ACG -C-

ACGC ---C ACGC -C-- A 1 C 2 G 3 4 T 5 6 0 -1 -2 -3 -4 -5 -6 C 1 A 2 A 1 C 2 G 3 4 T 5 6 0  -1 -2 -3 -4 -5 -6 C 1  A 2  T 3  G 4  T 5  ACGC ---C ACGC -C--

A 1 C 2 G 3 4 T 5 6 0  -1 -2 -3 -4 -5 -6 C 1  A 2  T 3  G 4  T 5  ACG -CA

A 1 C 2 G 3 4 T 5 6 0  -1 -2 -3 -4 -5 -6 C 1  A 2  T 3  G 4  T 5 

A 1 C 2 G 3 4 T 5 6 0  -1 -2 -3 -4 -5 -6 C 1  A 2  T 3  G 4  T 5 

A 1 C 2 G 3 4 T 5 6 0  -1 C 1  A 2  T 3  G 4  T 5 

A 1 C 2 G 3 4 T 5 6 0  -1 C 1  A 2  T 3  G 4  T 5  ACGCTG- -C-ATGT

A 1 C 2 G 3 4 T 5 6 0  -1 C 1  A 2  T 3  G 4  T 5  ACGCTG- -CA-TGT

A 1 C 2 G 3 4 T 5 6 0  -1 C 1  A 2  T 3  G 4  T 5  -ACGCTG CATG-T-

Needleman-Wunsch Alignment Summary Needleman-Wunsch Alignment Global alignment between sequences Compare entire sequence against another Create scoring table Sequence A across top, B down left Cell at column i and row j contains the score of best alignment between the first i elements of A and the first j elements of B Global alignment score is bottom right cell

Global vs. Local alignment DorothyHodkin DorothyCrowfootHodkin DOROTHY HODGKIN Global alignment: DOROTHY--------HODGKIN DOROTHYCROWFOOTHODGKIN Local alignment:

Local Alignment Smith-Waterman Best score for aligning part of sequences Often beats global alignment score Global Alignment ATTGCAGTG-TCGAGCGTCAGGCT ATTGCGTCGATCGCAC-GCACGCT Local Alignment CATATTGCAGTGGTCCCGCGTCAGGCT TAAATTGCGT-GGTCGCACTGCACGCT

Global vs. Local alignment Alignment of two Genomic sequences >Human DNA CATGCGACTGACcgacgtcgatcgatacgactagctagcATCGATCATA >Mouse DNA CATGCGTCTGACgctttttgctagcgatatcggactATCGATATA

Global vs. Local alignment Alignment of two Genomic sequences Global Alignment Human:CATGCGACTGACcgacgtcgatcgatacgactagctagcATCGATCATA Mouse:CATGCGTCTGACgct---ttttgctagcgatatcggactATCGAT-ATA ****** ***** * *** * ****** *** Human:CATGCGACTGAC Mouse:CATGCGTCTGAC Human:ATCGATCATA Mouse:ATCGAT-ATA Local Alignment

Global vs. Local alignment Alignment of two Genomic DNA and mRNA >Human DNA CATGCGACTGACcgacgtcgatcgatacgactagctagcATCGATCATA >Human mRNA CATGCGACTGACATCGATCATA

Global vs. Local alignment Alignment of two Genomic DNA and mRNA Global Alignment DNA: CATGCGACTGACcgacgtcgatcgatacgactagctagcATCGATCATA mRNA:CATGCGACTGAC---------------------------ATCGATCATA ************ ********** DNA: CATGCGACTGAC mRNA:CATGCGACTGAC DNA: ATCGATCATA mRNA:ATCGATCATA Local Alignment