Pair-wise Sequence Alignment Introduction to bioinformatics 2007 Lecture 5 C E N T R F O R I N T E G R A T I V E B I O I N F O R M A T I C S V U E

“Nothing in Biology makes sense except in the light of evolution” (Theodosius Dobzhansky ( )) “Nothing in bioinformatics makes sense except in the light of Biology” Bioinformatics

The Genetic Code

A protein sequence alignment MSTGAVLIY--TSILIKECHAMPAGNE GGILLFHRTHELIKESHAMANDEGGSNNS * * * **** *** A DNA sequence alignment attcgttggcaaatcgcccctatccggccttaa att---tggcggatcg-cctctacgggcc---- *** **** **** ** ******

Searching for similarities What is the function of the new gene? The “lazy” investigation (i.e., no biologial experiments, just bioinformatics techniques): – Find a set of similar protein sequences to the unknown sequence – Identify similarities and differences – For long proteins: first identify domains

Is similarity really interesting?

Evolutionary and functional relationships Reconstruct evolutionary relation: Based on sequence -Identity (simplest method) -Similarity Homology (common ancestry: the ultimate goal) Other (e.g., 3D structure) Functional relation: Sequence Structure Function

Common ancestry is more interesting: Makes it more likely that genes share the same function Homology: sharing a common ancestor – a binary property (yes/no) – it’s a nice tool: When (an unknown) gene X is homologous to (a known) gene G it means that we gain a lot of information on X: what we know about G can be transferred to X as a good suggestion. Searching for similarities

How to go from DNA to protein sequence A piece of double stranded DNA: 5’ attcgttggcaaatcgcccctatccggc 3’ 3’ taagcaaccgtttagcggggataggccg 5’ DNA direction is from 5’ to 3’

How to go from DNA to protein sequence 6-frame translation using the codon table (last lecture): 5’ attcgttggcaaatcgcccctatccggc 3’ 3’ taagcaaccgtttagcggggataggccg 5’

Bioinformatics tool Data Algorithm Biological Interpretation (model) tool

Example today: Pairwise sequence alignment needs sense of evolution Global dynamic programming MDAGSTVILCFVG MDAASTILCGSMDAASTILCGS Amino Acid Exchange Matrix Gap penalties (open,extension) Search matrix MDAGSTVILCFVG- MDAAST-ILC--GS Evolution

How to determine similarity? Frequent evolutionary events: 1. Substitution 2. Insertion, deletion 3. Duplication 4. Inversion Evolution at work We’ll only use these Z X Y Common ancestor, usually extinct available

Alignment - the problem Operations: –substitution, –Insertion –deletion GTACT--C GGA-TGAC algorithmsforgenomes |||||||||| algorithms4genomes Algorithmsforgenomes ||||||| algorithms4genomes algorithmsforgenomes ||||||||||? ||||||| algorithms4--genomes

A protein sequence alignment MSTGAVLIY--TSILIKECHAMPAGNE GGILLFHRTHELIKESHAMANDEGGSNNS * * * **** *** A DNA sequence alignment attcgttggcaaatcgcccctatccggccttaa att---tggcggatcg-cctctacgggcc---- *** **** **** ** ******

– Substitution (or match/mismatch) DNA proteins – Gap penalty Linear: gp(k)=ak Affine: gp(k)=b+ak Concave, e.g.: gp(k)=log(k) The score for an alignment is the sum of the scores of all alignment columns Dynamic programming Scoring alignments

– Substitution (or match/mismatch) DNA proteins – Gap penalty Linear: gp(k)=  k Affine: gp(k)=  +  k Concave, e.g.: gp(k)=log(k) The score for an alignment is the sum of the scores over all alignment columns Dynamic programming Scoring alignments / Gap length penalty affine concave linear, General alignment score: S a,b =

Substitution Matrices: DNA define a score for match/mismatch of letters Simple: Used in genome alignments: ACGT A1 C 1 G 1 T 1 ACGT A C G T

Substitution matrices for a.a. Amino acids are not equal: 1.Some are similar and easily substituted: biochemical properties structure 2.Some mutations occur more often due to similar codons The two above give us substitution matrices orange: nonpolar and hydrophobic. green: polar and hydrophilic magenta box are acidic light blue box are basic

BLOSUM 62 substitution matrix

Constant vs. affine gap scoring Seq1G T A - -G - T - A Seq2- - A T G- A T G - Const-2 –2 1 –2 –2 (SUM = -7)-2 – –2 (SUM = -7) Affine – (SUM = -7)-3 – –3 (SUM = -11)‏ -2 extensionintro Gap Scoring -3Affine -2Constant …and +1 for match

Dynamic programming Scoring alignments 101 Amino Acid Exchange Matrix Affine gap penalties (open, extension) 20  20 Score: s(T,T)+s(D,D)+s(W,W)+s(V,L)-P o -2P x + +s(L,I)+s(K,K) T D W V T A L K T D W L - - I K

Amino acid exchange matrices How do we get one? And how do we get associated gap penalties? First systematic method to derive a.a. exchange matrices by Margaret Dayhoff et al. (1968) – Atlas of Protein Structure 20  20

A 2 R -2 6 N D C Q E G H I L K M F P S T W Y V A R N D C Q E G H I L K M F P S T W Y V PAM250 matrix amino acid exchange matrix (log odds) Positive exchange values denote mutations that are more likely than randomly expected, while negative numbers correspond to avoided mutations compared to the randomly expected situation

Amino acids are not equal: 1. Some are easily substituted because they have similar: physico-chemical properties structure 2. Some mutations between amino acids occur more often due to similar codons The two above observations give us ways to define substitution matrices Amino acid exchange matrices

Pair-wise alignment Combinatorial explosion - 1 gap in 1 sequence: n+1 possibilities - 2 gaps in 1 sequence: (n+1)n - 3 gaps in 1 sequence: (n+1)n(n-1), etc. 2n (2n)! 2 2n = ~ n (n!) 2   n 2 sequences of 300 a.a.: ~10 88 alignments 2 sequences of 1000 a.a.: ~ alignments! T D W V T A L K T D W L - - I K

Technique to overcome the combinatorial explosion: Dynamic Programming Alignment is simulated as Markov process, all sequence positions are seen as independent Chances of sequence events are independent –Therefore, probabilities per aligned position need to be multiplied –Amino acid matrices contain so-called log-odds values (log 10 of the probabilities), so probabilities can be summed

To perform statistical analyses on messages or sequences, we need a reference model. The model: each letter in a sequence is selected from a defined alphabet in an independent and identically distributed (i.i.d.) manner. This choice of model system will allow us to compute the statistical significance of certain characteristics of a sequence, its subsequences, or an alignment. Given a probability distribution, P i, for the letters in a i.i.d. message, the probability of seeing a particular sequence of letters i, j, k,... n is simply P i P j P k ···P n. As an alternative to multiplication of the probabilities, we could sum their logarithms and exponentiate the result. The probability of the same sequence of letters can be computed by exponentiating log P i + log P j + log P k + ··· + log P n. In practice, when aligning sequences we only add log-odds values (residue exchange matrix) but we do not exponentiate the final score. To say the same more statistically…

Sequence alignment History of Dynamic Programming algorithm 1970 Needleman-Wunsch global pair-wise alignment Needleman SB, Wunsch CD (1970) A general method applicable to the search for similarities in the amino acid sequence of two proteins, J Mol Biol. 48(3): Smith-Waterman local pair-wise alignment Smith, TF, Waterman, MS (1981) Identification of common molecular subsequences. J. Mol. Biol. 147,

Pairwise sequence alignment Global dynamic programming MDAGSTVILCFVG MDAASTILCGSMDAASTILCGS Amino Acid Exchange Matrix Gap penalties (open,extension) Search matrix MDAGSTVILCFVG- MDAAST-ILC--GS Evolution

Global dynamic programming i-1 i j-1 j H(i,j) = Max H(i-1,j-1) + S(i,j) H(i-1,j) - g H(i,j-1) - g diagonal vertical horizontal Value from residue exchange matrix This is a recursive formula

Global alignment The Needleman-Wunsch algorithm Goal: find the maximal scoring alignment Scores: m match, -s mismatch, -g for insertion/deletion Dynamic programming –Solve smaller subproblem(s)‏ –Iteratively extend the solution The best alignment for X[1…i] and Y[1…j] is called M[i, j] X 1 … X i X i Y 1 … - Y j-1 Y j -

The algorithm Y[1…j - 1] Y[j] X[1…i - 1] X[i] Y[1…j-1]Y[j] X[1…i] - Y[1…j] - X[1…i-1] X[i] M[i, j-1] - gM[i-1, j] - g M[i-1, j-1] + m - s M[i,j] = Goal: find the maximal scoring alignment Scores: m match, -s mismatch, -g for insertion/deletion The best alignment for X[1…i] and Y[1…j] is called M[i, j] 3 ways to extend the alignment

The algorithm – final equation M[i, j] = M[i, j- 1 ] – g M[i- 1, j] – g M[i- 1, j- 1 ] + score(X[i],Y[j])‏ jj-1 i-1 i max * * -g X 1 …X i-1 X i Y 1 …Y j-1 Y j X 1 …X i - Y 1 …Y j-1 Y j X 1 …X i-1 X i Y 1 …Y j - Corresponds to:

Example: global alignment of two sequences Align two DNA sequences: –GAGTGA –GAGGCGA (note the length difference)‏ Parameters of the algorithm: –Match: score(A,A) = 1 –Mismatch: score(A,T) = -1 –Gap: g = -2 M[i, j] = M[i, j- 1 ] – 2 M[i- 1, j] – 2 M[i- 1, j- 1 ] ± 1 max

The algorithm. Step 1: init Create the matrix Initiation –0 at [0,0] –Apply the equation… M[i, j] = M[i, j- 1 ] – 2 M[i- 1, j] – 2 M[i- 1, j- 1 ] ± 1 max jj ii A G C G G A G 0 - AGTGAG-

The algorithm. Step 1: init Initiation of the matrix: –0 at pos [0,0] –Fill in the first row using the “  ” rule –Fill in the first column using “  ” M[i, j] = M[i, j- 1 ] – 2 M[i- 1, j] – 2 M[i- 1, j- 1 ] ± 1 max j i

The algorithm. Step 2: fill in Continue filling in of the matrix, remembering from which cell the result comes (arrows)‏ M[i, j] = M[i, j- 1 ] – 2 M[i- 1, j] – 2 M[i- 1, j- 1 ] ± 1 max j i

The algorithm. Step 2: fill in We are done… Where’s the result? M[i, j] = M[i, j- 1 ] – 2 M[i- 1, j] – 2 M[i- 1, j- 1 ] ± 1 max j i The lowest-rightmost cell

The algorithm. Step 3: traceback Start at the last cell of the matrix Go against the direction of arrows Sometimes the value may be obtained from more than one cell (which one?)‏ j i M[i, j] = M[i, j- 1 ] – 2 M[i- 1, j] – 2 M[i- 1, j- 1 ] ± 1 max

The algorithm. Step 3: traceback Extract the alignments j i GAGT-GA GAGGCGA GA-GTGA GAGGCGA a b a)‏ b)‏ The ‘low’ and the ‘high’ road You can also jump from the high to the low road in the middle (following the arrow): to what alignment does that lead?

Affine gaps M[i, j] = I x [i-1, j- 1 ] I y [i- 1, j-1] M[i- 1, j- 1 ] max score(X[i], Y[j]) + I x [i, j] = M[i, j-1] + g o I x [i, j- 1 ] + g e max I y [i, j] = M[i-1, j] + g o I y [i-1, j] + g x max Penalties: g o - gap opening (e.g. -8)‏ g e - gap extension (e.g. -1)‏ X 1 … - Y 1 … Y j X 1 …X i - Y 1 …Y j-1 Y j X 1 … - - Y 1 …Y j-1 Y j X1… XiY1… YjX1… XiY1… home: think of boundary values M[*,0], I[*,0] etc.

Semi-global pairwise alignment Global alignment: all gaps are penalised Semi-global alignment: N- and C-terminal (5’ and 3’) gaps (end-gaps) are not penalised MSTGAVLIY--TS GGILLFHRTSGTSNS End-gaps

Variation on global alignment Global alignment: previous algorithms is called global alignment, because it uses all letters from both sequences. CAGCACTTGGATTCTCGG CAGC-----G-T----GG Semi-global alignment: don’t penalize for end gaps CAGCA-CTTGGATTCTCGG ---CAGCGTGG

Semi-global pairwise alignment Applications of semi-global: – Finding a gene in genome – Placing marker onto a chromosome – One sequence much longer than the other Danger: really bad alignments for divergent sequences (particularly if gap penalties are high) Protein sequences have N- and C-terminal amino acids that are often small and hydrophilic, and so these ends match seq X: seq Y:

Semi-global alignment Ignore 5’ or N- terminal end gaps –First row/column set to 0 Ignore C-terminal or 3’ end gaps –Read the result from last row/column T G A - GTGAG

Take-home messages Homology Why are we interested in similarity? Pairwise alignment: global alignment and semi-global alignment Three types of gap penalty regimes: linear, affine and concave Make sure you can calculate alignment using the DP algorithm