Patterns, Profiles, and

Transcription

1 Patterns, Profiles, and Mltiple l Alignments

2 Otline Profiles, Position Specific Scoring Matrices Profile Hidden Markov Models Alignment of Profiles Mltiple Alignment Algorithms Problem definition Can we se Dynamic Programming to solve MSA? Progressive Alignment ClstalW Scoring Mltiple Alignments Entropy Sm of Pairs SP Score Seqence Pattern Discovery

3 Mltiple Seqences Up to this point we have considered pairwise relationships between seqences Protein families contain mltiple l seqences E.g. Globins Conserved, important regions A common task is to find ot whether a new seqence can be inclded in a protein family or not. We can then assign a fnction and predict 3D strctre

4 Profile Representation of Mltiple Seqences - A G G C T A T C A C C T G T A G C T A C C A G C A G C T A C C A G C A G C T A T C A C G G C A G C T A T C G C G G A C G T

5 Profile Representation of Mltiple Seqences - A G G C T A T C A C C T G T A G C T A C C A G C A G C T A C C A G C A G C T A T C A C G G C A G C T A T C G C G G A C G T Earlier, we were aligning a seqence against a seqence Can we align a seqence against a profile in order to find ot whether this seqence belongs to that protein family?

6 PSSM Position Specific Scoring Matrices The profile representation of a protein family can be a considered as the coefficients of a scoring matrix which give amino acid preferences for each alignment position separately How to obtain PSSMs? From a given mltiple alignment of seqences Database searches where a set of database proteins are aligned to the qery i.e. reference seqence

7 How to obtain PSSMs? Sppose we have a mltiple alignment of N seqences. To obtain the vales of the PSSM matrix m,b, we can se the techniqe we have sed to align a seqence to a profile and se the freqencies of amino acids at each colmn as coefficients: n, b = m,, a N f, b = f s, b a, b reside types b

8 A better way to weigh reside preferences It is better to give preferred resides extra weight, becase reside types rarely fond are probably highly disfavored at that colmn Use logarithmic weighting: m, a ln1 f n, b s f =, b a, ln1/ N + 1, b reside N + 1 = b types b

9 Using log-odds odds ratios We can also se a techniqe similar to the constrction of the common scoring matrices m, a = log q, a p a If sfficient data is available: q = f, a, a

10 If sfficient data is not available q,a will case problems Amino acids that do not occr in a colmn will case a score of - A simple soltion: assme at least one occrrence of each reside type q, a = N n, a + 1 N + 20 These additional conts are called psedoconts.

11 A better formla Incorporate backgrond amino acid composition q, a n + β p =, a N + β a β is the total nmber of psedoconts in a colmn. Can be adjsted based on the amont of data available.

12 Viewing Profiles/PSSMs as logos I Reside contribtion at each position: = log 2 20 H f, a I H, a = f, a log 2 f a ed

13 Profile Hidden Markov Models Using HMMs to represent a profile and to align a seqence to a profile

14 Hidden Markov Model Hidden Markov models are probabilistic finite state machines. A hidden Markov model λ is determined by the following parameters: A set of finite nmber of states: S i, 1 i N The probability of starting in state S i, π i The transition probability from state S i to S j, a ij The emission probability density of a symbol ω in state S i

15 What is hidden? With a hidden Markov model, we sally model a temporal process whose otpt we can observe bt do not know the actal nderlying mathematical or physical model. We try to model this process statistically. Here the states of the hidden Markov model are hidden to s. We assme that there is some nderlying model or some logic that prodces a set of otpt signals.

16 Problems associated with HMMs There are three typical qestions one can ask regarding HMMs: Given the parameters of the model, compte the probability of a particlar otpt seqence. This problem is solved by the forward-backward procedre. Given the parameters of the model, find the most likely seqence of hidden states that cold have generated a given otpt seqence. This problem is solved by the Viterbi algorithm. Given an otpt seqence or a set of sch seqences, find the most likely set of state transition and otpt probabilities. In other words, train the parameters of the HMM given a dataset of otpt seqences. This problem is solved by the Bam-Welch algorithm.

17 Example from Wikipedia Yo have a fi friend to whom yo talk lkdaily on the phone. Yor fi friend is only interested in three activities: walking in the park, shopping, and cleaning his apartment. The choice of what to do is determined exclsively by the weather on a given day. Yo have no definite information abot the weather where yor friend lives, bt yo know general trends. Based on what he tells yo he did each day, yo try to gess what the weather mst have been like. Th t t t "R i " d "S " b t t b There are two states, "Rainy" and "Snny", bt yo cannot observe them directly, that is, they are hidden from yo. On each day, there is a certain chance that yor friend will perform one of the following activities, depending on the weather: "walk", "shop", or "clean". Since yor friend tells yo abot his activities, those are the observations.

18 Example from Wikipedia Yo know the general weather trends in the area, and what yor friend likes to do on the average. In other words, the parameters of the HMM are known. walk: 0.1 shop: 0.4 clean: walk: 0.6 shop: 0.3 clean: Rainy Snny start

19 Example from Wikipedia Now, yo talked to yor friend for three days, and he told yo that on the first day walked, the next day he shopped and the last day he cleaned. What is the most likely seqence of days that cold have prodced this otcome? Solved by the Viterbi algorithm What is the overall probability bilit of the observations? Solved by forward-backward algorithm walk: walk: 0.6 shop: 0.4 shop: 0.3 clean: 0.5 clean: start t Rainy Snny

20 HMMs to represent a family of seqences Given a mltiple alignment of seqences, we can se an HMM to model the seqences. Each colmn of the alignment may be represented by a hidden state that prodced that colmn. Insertions and deletions can be represented by other states.

21 Profile HMMs from alignments A given mltiple seqence alignment may be sed to get the following HMM.

22 Profile HMMs The strctre of the profile HMM is given by: From: simple.png There are match, insert, and delete states. Given a mltiple seqence alignment we can easily determine the HMM parameters no Bam-Welch needed in this case

23 Profile HMMS The strctre is of profile HMMs is sally fixed following some biological observations:

24 Variants for non-global alignments Local alignments flanking model Emission prob. in flanking states se backgrond vales p a. a Looping prob. close to 1, e.g. 1- η for some small η. D j I j M j Begin End Q Q

25 Variants for non-global alignments Overlap alignments Only transitions to the first model state are allowed. When expecting to find either present as a whole or absent Transition to first delete state allows missing first reside D j Q I j Q Begin M j End

26 Variants for non-global alignments Repeat alignments Transition from right flanking state back to random model Can find mltiple matching segments in qery string D j I j M j Begin Q End

27 Determining the states of the HMM The strctre is sally fixed and only the nmber of match states is to be determined An alignment colmn with no gaps can be considered as a match state. An alignment colmn with a majority of gaps can be considered an insert state. Usally a threshold on the gap proportion is determined to find the match states

28 Determining the transition probabilities The transition probabilities from a state always add p to 1 except the end state which do not have any transitions from it. t, v = w 1

29 Determining the transition probabilities Cont all the transitions on the given mltiple alignment from an alignment position or state and se them in the following eqation to find transition probabilities from a state t, v = m w, v m,w,

30 Determining the emission probabilities Determining the emission probabilities Emission probabilities in a match or insert state also adds p to 1. = a M M n a e, + = a n M a e 1, b b M M n a e, + = b b M M n a e 20, Using psedoconts a I p a e =

31 Psedoconts in HMMs If we do not observe a certain amino acid at a colmn of an MSA the emission probability is 0 for that amino acid. This strategy will give 0 probability to sch seqences. However, we do not want to do that, i.e., we do not want to miss seqences that may be biologically important becase of only one mismatch Soltion: Add hypothetical occrrences of those amino acids into the colmns. E.g, assme a backgrond distribtion for each colmn. The actal appearances of amino acids at a colmn pdate the backgrond distribtion.

32 Example withot psedoconts

33 Example with psedoconts

34 Scoring a seqence against a profile HMM Given a profile HMM, any given path throgh the model will emit a seqence with an associated probability The path probability is the prodct of all transition and emission probabilities along the path.

35 Scoring a seqence against a profile HMM Given a qery seqence sing algorithms similar to DP for seqence alignment we can compte the most probable path that will emit that qery seqence Viterbi algorithm The probability that the given qery seqence is emitted by that HMM is given by the sm of all probabilities over all possible paths forward/backward algorithms.

36 Viterbi algorithm It is a dynamic programming algorithm. It is based on the following assmptions: At any time the process we are modeling is in some state We have finite nmber of states Each state prodces a single otpt Compting the most likely hidden seqence p to a certain point t mst depend only on the observed event at point t, and the most likely seqence at point t 1. These assmptions are satisfied by a first order HMM.

37 Viterbi DP recrrence relations Viterbi DP recrrence relations M M t x v =,, max i I i M i M i M M I t x v M M t x v x e x v, i D M D t x v =,, max 1 1 i I i M x i I I I t x v I M t x v p x v i i 1 i M D M t x v =,, max i D i M i D D D t x v D M t x v x v

38 Viterbi algorithm Using these eqations we can fill in a partial scores table v of size Initialization: length qery x nmber of states in HMM set v Start = 1, v = 0 for all states H lti l i b biliti ill However, mltiplying many probabilities will lead to very small nmbers for long seqences. Therefore se log of probabilities instead and convert prodcts to smmation

39 Viterbi DP recrrence relations Viterbi DP recrrence relations + log log M M t x v =, log log, log log max log log i I i M i M i M M I t x v M M t x v x e x v +, log log i D M D t x v =, log log, log log max log log 1 1 i I i M x i I I I t x v I M t x v p x v i i + log log 1 i M D M t x v + + =, log log, log log max log i D i M i D D D t x v D M t x v x v

40 Forward algorithm Forward and backward algorithms are sed to compte the probability of the seqence being emitted from an HMM by smming p the probabilities over all possible paths. Modification on Viterbi DP eqations: Instead of sing max, sm all options

41 Forward algorithm Forward algorithm, [ 1 1 i M i M i M M M t x f x e x f + =,, [ i I i M i M i M M I t x f f f + + ], i D M D t x f + ],, [ 1 1 i I i M x i I I I t x f I M t x f p x f i + = ] [ D D t f D M t f f + ],, [ i D i M i D D D t x f D M t x f x f + =

42 Searching a database Given the hidden Markov model for a protein family. We can evalate all the seqences in a database in terms of how likely they cold have been prodced by this HMM model. This likelihood score can be sed to find new protein seqences as candidate members for that protein family. We can se the Viterbi algorithm or the forward/backward algorithms to compte the probability. bilit

43 Finding the HMM for a protein family Given a set of seqences, can we find the parameters of an HMM withot performing a mltiple seqence alignment first? Yes. We can se the Bam-Welch algorithm However, we have to decide first How many match states are there?

44 Bam-Welch Algorithm The Bam-Welch algorithm is an expectationmaximization EM algorithm. It can compte maximm likelihood estimates and posterior mode estimates for the parameters transition and emission probabilities of an HMM, when given only emissions as training data.

45 Available profile HMM tools SAM HMMER2 and many others

46 Mltiple alignment algorithms One of the most essential tools in moleclar biology Finding highly conserved sbregions or embedded patterns of a set of biological seqences Conserved regions sally are key fnctional regions, prime targets for drg developments Estimation of evoltionary distance between seqences Prediction of protein secondary/tertiary ti strctre t Practically sefl methods only since 1987 D. Sankoff Before 1987 they were constrcted by hand Dynamic programming is expensive

47 Mltiple Seqence Alignment MSA What is mltiple seqence alignment? Given k seqences: VTISCTGSSSNIGAGNHVKWYQQLPG VTISCTGTSSNIGSITVNWYQQLPG LRLSCSSSGFIFSSYAMYWVRQAPG LSLTCTVSGTSFDDYYSTWVRQPPG PEVTCVVVDVSHEDPQVKFNWYVDG ATLVCLISDFYPGAVTVAWKADS AALGCLVKDYFPEPVTVSWNSG VSLTCLVKGFYPSDIAVEWESNG

48 Mltiple Seqence Alignment MSA An MSA of these seqences: VTISCTGSSSNIGAG-NHVKWYQQLPG VTISCTGTSSNIGS--ITVNWYQQLPG LRLSCSSSGFIFSS--YAMYWVRQAPG LSLTCTVSGTSFDD--YYSTWVRQPPG PEVTCVVVDVSHEDPQVKFNWYVDG-- ATLVCLISDFYPGA--VTVAWKADS-- AALGCLVKDYFPEP--VTVSWNSG--- VSLTCLVKGFYPSD--IAVEWESNG--

49 Mltiple Seqence Alignment MSA An MSA of these seqences: VTISCTGSSSNIGAG-NHVKWYQQLPG VTISCTGTSSNIGS--ITVNWYQQLPG LRLSCSSSGFIFSS--YAMYWVRQAPG LSLTCTVSGTSFDD--YYSTWVRQPPG PEVTCVVVDVSHEDPQVKFNWYVDG-- ATLVCLISDFYPGA--VTVAWKADS-- AALGCLVKDYFPEP--VTVSWNSG--- VSLTCLVKGFYPSD--IAVEWESNG-- Conserved resides

50 Mltiple Seqence Alignment MSA An MSA of these seqences: VTISCTGSSSNIGAG-NHVKWYQQLPG VTISCTGTSSNIGS--ITVNWYQQLPG LRLSCSSSGFIFSS--YAMYWVRQAPG LSLTCTVSGTSFDD--YYSTWVRQPPG PEVTCVVVDVSHEDPQVKFNWYVDG-- ATLVCLISDFYPGA--VTVAWKADS-- AALGCLVKDYFPEP--VTVSWNSG--- VSLTCLVKGFYPSD--IAVEWESNG-- Conserved regions

51 Mltiple Seqence Alignment MSA An MSA of these seqences: VTISCTGSSSNIGAG-NHVKWYQQLPG VTISCTGTSSNIGS--ITVNWYQQLPG LRLSCSSSGFIFSS--YAMYWVRQAPG LSLTCTVSGTSFDD--YYSTWVRQPPG PEVTCVVVDVSHEDPQVKFNWYVDG-- ATLVCLISDFYPGA--VTVAWKADS-- AALGCLVKDYFPEP--VTVSWNSG--- VSLTCLVKGFYPSD--IAVEWESNG-- Patterns? Positions 1 and 3 are hydrophobic resides

52 Mltiple Seqence Alignment MSA An MSA of these seqences: VTISCTGSSSNIGAG-NHVKWYQQLPG VTISCTGTSSNIGS--ITVNWYQQLPG LRLSCSSSGFIFSS--YAMYWVRQAPG LSLTCTVSGTSFDD--YYSTWVRQPPG PEVTCVVVDVSHEDPQVKFNWYVDG-- ATLVCLISDFYPGA--VTVAWKADS-- AALGCLVKDYFPEP--VTVSWNSG--- VSLTCLVKGFYPSD--IAVEWESNG-- Conserved resides, regions, patterns

53 MSA Warnings MSA algorithms work nder the assmption that they are aligning related seqences They will align ANYTHING they are given, even if nrelated If it jst looks wrong it probably is

54 Generalizing the Notion of Pairwise Alignment Alignment of 2 seqences is represented as a 2-row matrix In a similar way, we represent alignment of 3 seqences as a 3-row matrix A T _ G C G _ A _ C G T _ A A T C A C _ A Score: more conserved colmns, better alignment

55 Alignments = Paths in k dimensional grids Align 3 seqences: ATGC, AATC,ATGC A -- T G C A A T -- C -- A T G C

56 Alignment Paths A -- T G C x coordinate A A T -- C -- A T G C

57 Alignment Paths A -- T G C A A T -- C x coordinate y coordinate -- A T G C

58 Alignment Paths A -- T G C A A T -- C A T G C x coordinate y coordinate z coordinate Reslting path in x,y,z space: 0,0,0 1,1,0 1,2,1,,,,, 2,3,2,, 3,3,3,, 4,4,4,,

59 Aligning Three Seqences Same strategy as aligning two seqences Use a 3-D Dmatrix, with each axis representing a seqence to align For global alignments, go from sorce to sink sorce sink

60 2-D Dvs3D 3-D Alignment Grid V W 2-D alignment matrix 3-D alignment matrix

61 2-D cell verss 3-D Alignment Cell In 2-D, 3 edges in each nit sqare In 3-D, 7 edges in each nit cbe

62 Architectre of 3-D Alignment Cell i-1,j-1,k-1 i-1,j,k-1 i-1,j-1,k i-1,j,k i,j-1,k-1 i,j,k-1 i,j-1,k,j, i,j,k

63 Mltiple Alignment: Dynamic Programming s i,j,k = max s i-1,j-1,k-1 + δv i, w j, k s i-1,j-1,k + δ v i, w j, _ s i-1,j,k-1 1jk1 + δ v i, _, k s i,j-1,k-1 + δ _, w j, k s i-1,j,k 1jk + δ v i, _, _ s i,j-1,k + δ _, w j, _ s i,j,k-1 + δ _, _, k cbe diagonal: no indels face diagonal: one indel edge diagonal: two indels δx, y, z isanentryinthe3-d in the scoring matrix

64 Mltiple Alignment: Rnning Time For 3 seqences of length n, the rn time is 7n 3 ; On 3 For k seqences, bild a k-dimensional matrix, ti with rn time 2 k -1n k ; O2 k n k Conclsion: dynamic programming approach for alignment between two seqences is easily extended d to k seqences bt it is impractical de to exponential rnning time

65 Mltiple Alignment Indces Pairwise Alignments Every mltiple alignment indces pairwise alignments Indces: x: AC-GCGG-C y: AC-GC-GAG z: GCCGC-GAG x: ACGCGG-C; x: AC-GCGG-C; y: AC-GCGAG y: ACGC-GAC; z: GCCGC-GAG; z: GCCGCGAG

66 Reverse Problem: Constrcting Mltiple Alignment from Pairwise Alignments Given 3 arbitrary pairwise alignments: x: ACGCTGG-C; x: AC-GCTGG-C; y: AC-GC-GAG y: ACGC--GAC; z: GCCGCA-GAG; z: GCCGCAGAG can we constrct a mltiple alignment that indces can we constrct a mltiple alignment that indces them?

67 Reverse Problem: Constrcting Mltiple Alignment from Pairwise Alignments Given 3 arbitrary pairwise alignments: x: ACGCTGG-C; x: AC-GCTGG-C; y: AC-GC-GAG y: ACGC--GAC; z: GCCGCA-GAG; z: GCCGCAGAG can we constrct a mltiple alignment that indces them? NOT ALWAYS Pairwise alignments may be inconsistent

68 Inferring Mltiple Alignment from Pairwise Alignments From an optimal mltiple alignment, we can infer pairwise alignments between all pairs of seqences, bt they are not necessarily optimal It is difficlt to infer a good mltiple alignment from optimal pairwise alignments between all seqences

69 Combining Optimal Pairwise Alignments into Mltiple Alignment Can combine pairwise alignments into mltiple alignment Can not combine pairwise alignments into mltiple alignment

70 Consenss String of a Mltiple Alignment - A G G C T A T C A C C T G T A G C T A C C A G C A G C T A C C A G C A G C T A T C A C G G C A G C T A T C G C G G C A G - C T A T C A C - G G Consenss String: C A G C T A T C A C G G The consenss string S M derived from mltiple alignment M is the concatenation of the consenss characters for each colmn of M. The consenss character for colmn i is the character that minimizes the smmed distance to it from all the characters in colmn i. i.e., if match and mismatch scores are eqal for all symbols, the majority symbol is the consenss character

71 Profile Representation of Mltiple Alignment - A G G C T A T C A C C T G T A G C T A C C A G C A G C T A C C A G C A G C T A T C A C G G C A G C T A T C G C G G A C G T

72 Profile Representation of Mltiple Alignment - A G G C T A T C A C C T G T A G C T A C C A G C A G C T A C C A G C A G C T A T C A C G G C A G C T A T C G C G G A C G T Earlier, we were aligning a seqence against a seqence Can we align a seqence against a profile? Can we align a profile against a profile?

73 Aligning alignments Given two alignments, can we align them? x GGGCACTGCAT y GGTTACGTC-- Alignment 1 z GGGAACTGCAG w GGACGTACC-- Alignment 2 v GGACCT-----

74 Aligning alignments Given two alignments, can we align them? Hint: se alignment of corresponding profiles x GGGCACTGCAT y GGTTACGTC-- z GGGAACTGCAG w GGACGTACC-- v GGACCT----- Combined Alignment

75 Mltiple Alignment: Greedy Approach Choose most similar pair of strings and combine into a profile, thereby redcing alignment of k seqences to an alignment of of k-1 seqences/profiles. Repeat This is a heristic greedy method 1 = ACGTACGTACGT 1 = ACg/tTACg/tTACg/cT k 2 = TTAATTAATTAA 3 = ACTACTACTACT 2 = TTAATTAATTAA k = CCGGCCGGCCGG k-1 k = CCGGCCGGCCGG

76 Greedy Approach: Example Consider these 4 seqences s1 s2 s3 s4 GATTCA GTCTGA GATATT GTCAGC

77 Greedy Approach: Example cont d There are = 6 possible alignments s2 GTCTGA s4 GTCAGC score = 2 s1 GAT-TCA s2 G-TCTGA score = 1 s1 GAT-TCA TCA s3 GATAT-T score = 1 s1 GATTCA-- s4 G T-CAGCscore = 0 s2 G-TCTGA s3 GATAT-T score = -1 s3 GAT-ATT ATT s4 G-TCAGC score = -1

78 Greedy Approach: Example cont d s2 s4 s 2 and s 4 are closest; combine: GTCTGA GTCAGC s 2,4 profile GTCt/aGa/cA / new set of 3 seqences: s 1 s 3 s 2,4 GATTCA GATATT GTCt/aGa/c

79 Progressive Alignment Progressive alignment is a variation of greedy algorithm with a somewhat more intelligent strategy for choosing the order of alignments. Progressive alignment works well for close seqences, bt deteriorates for distant seqences Gaps in consenss string are permanent Use profiles to compare seqences

80 Star alignment Heristic method for mltiple l seqence alignments Select a seqence c as the center of the star For each seqence x 1,, x k sch that index i c, perform a Needleman-Wnsch global alignment Aggregate alignments with the principle once a gap, always a gap.

81 Choosing a center Try them all and pick the one which h is most similar il to all of the seqences Let Sx i,xx j be the optimal score between seqences x i and x j. Calclate all Ok 2 alignments, and choose as x c the seqence x i that maximizes the following Σ Sx i,x j j i

82 Star alignment example MPE MSKE S 1 : MPE s 1 s 3 S 2 :MKE MKE M-KE S 3 : MSKE S s 4 : SKE SKE s 2 M-PE M-PE MPE M-KE M-KE s 4 MKE MSKE MSKE S-KE MKE

83 Analysis Assming all seqences have length n Ok 2 n 2 to calclate center Step i of iterative pairwise alignment takes Oi n n time two strings of length n and i n Ok 2 n 2 overall cost

84 ClstalW Most poplar mltiple alignment tool today W stands for weighted different parts of alignment are weighted differently. Three-step process 1. Constrct pairwise alignments 2. Bild Gide Tree by Neighbor Joining method 3. Progressive Alignment gided by the tree - The seqences are aligned progressively according to the branching order in the gide tree

85 Step 1: Pairwise Alignment Aligns each seqence again each other giving a similarity matrix Similarity = exact matches / seqence length percent identity v 1 v 2 v 3 v 4 v 1 - v v v means 17 % identical ca

86 Step 2: Gide Tree Create Gide Tree sing the similarity matrix ClstalW ses the neighbor-joining method Gide tree roghly reflects evoltionary g y y relations

87 Step 2: Gide Tree cont d v 1 v 2 v 3 v 4 v 1 v 3 v 1 - v 4 v v 2 v v Calclate: v 1,3 = alignment v 1, v 3 v 1,3,4 = alignmentv 1,3,v 4 v 1,2,3,4 = alignmentv 1,3,4,v 2

88 Step 3: Progressive Alignment Start by aligning the two most similar seqences Following the gide tree, add in the next seqences, aligning to the existing alignment Insert gaps as necessary FOS_RAT PEEMSVTS-LDLTGGLPEATTPESEEAFTLPLLNDPEPK-PSLEPVKNISNMELKAEPFD PSLEPVKNISNMELKAEPFD FOS_MOUSE PEEMSVAS-LDLTGGLPEASTPESEEAFTLPLLNDPEPK-PSLEPVKSISNVELKAEPFD FOS_CHICK SEELAAATALDLG----APSPAAAEEAFALPLMTEAPPAVPPKEPSG--SGLELKAEPFD FOSB_MOUSE PGPGPLAEVRDLPG-----STSAKEDGFGWLLPPPPPPP LPFQ FOSB_HUMAN PGPGPLAEVRDLPG-----SAPAKEDGFSWLLPPPPPPP LPFQ LPFQ.. : **. :.. *:.* *. * **: Dots and stars show how well-conserved a colmn is.

89 ClstalW: another example S 1 S 2 S 3 S 4 ALSK TNSD NASK NTSD

90 ClstalW example S 1 S 2 S 3 S 4 ALSK TNSD NASK NTSD All pairwise alignments S 1 S 2 S 3 S 4 S S S S 4 0 Distance Matrix

91 ClstalW example S 1 S 2 S 3 S 4 ALSK TNSD NASK NTSD All pairwise alignments S 1 S 2 S 3 S 4 S3 S Neighbor 3 S Joining S S 2 S S S 4 0 Rooted Tree Distance Matrix S 1

92 ClstalW example S 1 ALSK Mltiple Alignment Steps S 2 TNSD S 3 NASK 1. Align S 1 with S 3 2. Align S NTSD 2 with S 4 S 4 All pairwise alignments 3. Align S 1, S 3 with S 2, S 4 S 1 S 2 S 3 S 4 S3 S Neighbor 3 S Joining S S 2 S S S 4 0 Rooted Tree Distance Matrix S 1

93 ClstalW example -ALSK Mltiple Alignment Steps S ALSK 1. Align S 1 with S 1 -ALSK NA-SK 3 S 2 TNSD -TNSD S 3 NASK NA-SK -TNSD 2. Align S 2 with S NT-SD 4 NTSD NT-SD S 4 All pairwise alignments Mltiple Alignment 3. Align S 1, S 3 with S 2, S 4 S 1 S 1 S 2 S 3 S 4 S S S S 4 0 Neighbor Joining Rooted Tree S 3 S 2 S 4 Distance Matrix

94 Other progressive approaches PILEUP Similar to CLUSTALW Uses UPGMA to prodce tree

95 Problems with progressive alignments Depend on pairwise alignments If seqences are very distantly related, mch higher likelihood of errors Care mst be made in choosing scoring matrices and penalties

96

97 Iterative refinement in progressive alignment Another problem of progressive alignment: Initial alignments are frozen even when new evidence comes Example: x: GAAGTT y: GAC-TT Frozen! z: GAACTG GTACTG w: GTACTG Now clear that correct y = GA-CTT

98 Evalating mltiple alignments Balibase benchmark Thompson, 1999 De-facto standard for assessing the qality of a mltiple alignment tool Manally refined mltiple seqence alignments Qality measred by how good it matches the core blocks Another benchmark: SABmark benchmark Based on protein strctral families

99 Scoring mltiple alignments Ideally, a scoring scheme shold Penalize variations in conserved positions higher Relate seqences by a phylogenetic tree Tree alignment Usally assme Independence of colmns Qality comptation Entropy-based scoring Compte the Shannon entropy of each colmn Sm-of-pairs SP score

100 Mltiple Alignments: Scoring Nmber of matches mltiple longest common sbseqence score Entropy score Sm of pairs SP-Score