Multiple Sequence Alignment

Home , BLOSUM, Clustal, MAFFT, Sequence alignment

Bioinformatics Algorithms

David Hoksza http://siret.ms.mff.cuni.cz/hoksza Outline

• Motivation • Algorithms

• Scoring functions • exhaustive • multidimensional dynamic programming

• heuristics • progressive alignment • iterative alignment/refinement • block(local)-based alignment Multiple sequence alignment (MSA)

• Goal of MSA is to find “optimal” mapping of a set of sequences

• Homologous residues (originating in the same position in a common ancestor) among a set of sequences are aligned together in columns

• Usually employs multiple pairwise alignment (PA) computations to reveal the evolutionarily equivalent positions across all sequences Motivation

• Distant homologues • faint similarity can become apparent when present in many sequences • motifs might not be apparent from pairwise alignment only

• Detection of key functional residues • amino acids critical for function tend to be conserved during the evolution and therefore can be revealed by inspecting sequences within given family

• Prediction of secondary/tertiary structure

• Inferring evolutionary history

4 Representation of MSA

• Column-based representation

• Profile representation (position specific scoring matrix)

• Sequence logo Manual MSA

• High quality MSA can be carried out automatic MSA algorithms by hand using expert knowledge • specific columns • BAliBASE • highly conserved residues • https://lbgi.fr/balibase/ • buried hydrophobic residues • PROSITE • secondary structure (especially in RNA • http://prosite.expasy.org/ alignment) • Pfam • expected patterns of insertions and • http://pfam.sanger.ac.uk/ deletions • TIGRFAM • http://www.jcvi.org/cgi- bin/tigrfams/index.cgi • Tedious, but • … (some databases are semi-automatic • high-quality source of family and many of the databases construct the information MSA from the structure information) • a benchmark for evaluation of Scoring

• How to score an MSA?

푺 푨 = 푮 + ෍ 푪푺(푨풊)

• 퐴푖 … 푖-th column • 퐶푆(퐴푖) … score of the 푖-th column • 퐺 … gap function (assumes linear or constant gap penalty)

• the score assumes independent columns

• Two score types are usually considered • minimum entropy (ME) • sum of pairs (SP) Minimum entropy (1)

• ME aims to minimize entropy of each column

• columns with low entropy (can be expressed with only few bits) are good for the alignment

• the more bits we need to express a column, the more divers the column is Minimum entropy (2)

• Probability of a column • assumption of independency between columns and residues within columns 풄풊풂 푷 푨풊 = ෑ 풑풊풂 풂 0 퐴푖 [푗] ≠ 푎 • 푐푖푎…observed counts for residue 푎 in 푖-th column 푐푖푎 = σ푗 ൝ 1 퐴푖 푗 = 푎 • 퐴푖 [푗]… 푗-th symbol in 푖-th column • 푝푖푎… probability of residue 푎 in column 푖

푪푴푬 푨풊 = − ෍ 풄풊풂 퐥퐨퐠 풑풊풂 푴푬 = ෍ 푪푴푬(푨풊) 풂 풊 • completely conserved column would score 0 Sum of pairs

• Sum of scores of all possible pairs in a multiple alignment 푨 for a particular scoring matrix • Score for each column is computed as the sum of all pairs of position in that column • Column scores are then summed to get the SP-score |퐴| |퐴|

푆푃 퐴 = ෍ 퐶푆푃 퐴푖 = ෍ ෍ 휎(퐴푖 푘 , 퐴푖 푙 ) 푖=1 푖=1 푘<푙

• 퐴푖 [푘]… 푘-th symbol in 푖-th column • 휎(푥, 푦) … PAM or BLOSUM values for the residue 푥 and 푦 G K N SP - Example T R N S H E • BLOSUM 62 scoring matrix -1 +1 +6 6 SP score drawback • Alignment of 푵 sequences, all containing leucine at given position from functional reasons • BLOSUM62 matrix 흈 푳, 푳 = ퟒ → 푺푷 푨풊 = ퟒ × 푵(푵 − ퟏ)/ퟐ • Let us replace one of the leucines with glycine (incorrect alignment) 흈 푳, 푮 = −ퟒ → the score decreases by ퟖ × (푵 − ퟏ) • 푺푷 푨풊 is worse by a fraction of 8×(푁−1) ퟒ = 4×푁(푁−1)/2 푵 • Relative difference in score between the correct alignment and incorrect alignment decreases with the number of sequences in the alignment • BUT increasing the number of sequences (evidence) should give us more increased relative difference Multidimensional dynamic programming (1)

• Generalization of pairwise dynamic programming • 3 sequences: ATGC, AATC,TTGC

0 1 1 2 3 4 x coordinate A - T G C 0 1 2 3 3 4 y coordinate A A T - C 0 0 1 2 3 4 z coordinate - T T G C

• Resulting path • (0,0,0) → (1,1,0) → (1,2,1) → (2,3,2) → (3,3,3) → (4,4,4) Multidimensional dynamic programming (2)

• Let us assume linear gap penalty model (not affine)

• 훾 푔 = 푔푑 for a gap of length 푔 and gap cost 푑

• initialization and backtracking are analogous with the 2D case Multidimensional dynamic programming (3)

• 3 edges • 7 edges Computational complexity of MDP

• Computation of each cell of the DP matrix takes ퟐ푵 − ퟏ (all possible combinations of gaps column)

• Let us assume all the sequences have approximately the same length 푳

• Memory complexity 푶 푳푵 • Time complexity 푶 ퟐ푵푳푵 MDP - exercise

• Let’s have sequence of length 50 • Comparison of a pair of sequences using DP takes 0,1s

• What is the time needed to compare 4 sequences?

• Let’s say we have 1000 years and average sequence length is 50. • How many sequence can afford to compare? Heuristic Algorithms

• Progressive alignment methods • iterative building of the alignment • Block-based alignment • Feng & Doolittle • local alignment built by identifying • ClustalW, Clustal Omega blocks of ungapped MSA identified and assembled • Consistency-based methods • DIALIGN • T-Coffee • Mix of approaches • Iterative refinement • MAFFT, MUSCLE • alignment built and then refined be realigning the constituent sequences • Barton & Sternberg Progressive alignment

• Framework • First, two sequences are aligned using standard pairwise alignment • The remaining sequences are taken one by one and aligned to the previous ones • Repeated until all sequences are aligned

• Parameters • The order in which the sequences are be aligned • Whether only one alignment is kept and sequences are added to it or whether also an alignment can be aligned to another alignment (as if a tree was being built) • The process used to align and score sequences or alignments against the existing ones Star alignment

• N sequences 풔ퟏ, … , 풔푵 to be aligned

1. Pick 풔풊 as a starting sequence – center

2. Compute all optimal global alignments between 풔풊 and 풔풋, 푗 ≠ 푖

3. Successively merge sequences into the arising MSA • once a gap always a gap rule • if a gap is introduced into the MSA it stays there forever SA – example (1)

S1: ATTGCCATT ATTGCC-ATT-- S2: ATGGCCATT ATTGCCATT ATGGCC-ATT-- S3: ATCCAATTTT ATGGCCATT ATTGCCGATT-- S4: ATCTTCTT ATCTTC--TT-- S5: ATTGCCGATT ATC-CA-ATTTT

ATTGCC-ATT ATTGCCATT-- ATTGCCATT ATTGCCGATT ATC-CAATTTT

ATTGCCATT ATCTTC-TT

credit: Xingquan Zhu, Florida Atlantic University SA – example (2)

pairwise alignment multiple alignment ATTGCCATT ATTGCCATT 1. ATGGCCATT ATGGCCATT ATTGCCATT-- ATTGCCATT-- 2. ATGGCCATT-- ATC-CAATTTT ATC-CAATTTT ATTGCCATT-- ATTGCCATT ATGGCCATT-- 3. ATCTTC-TT ATC-CAATTTT ATCTTC-TT-- ATTGCC-ATT-- ATGGCC-ATT-- ATTGCC-ATT 4. ATC-CA-ATTTT ATTGCCGATT ATCTTC--TT-- ATTGCCGATT-- SA - choosing the center

• Compute all pairwise alignment and pick sequence 풔풊 with maximum σ풋≠풊 풔(풔풊, 풔풋) • Choosing the sequence which is most similar to all the rest

• Compute all pairwise alignments and compute MSA for every 풔풊 and pick the best SA – time complexity

• Average sequence length 퐿

• One global alignment computation in 퐎(푳ퟐ)

• 푘 sequences → 퐎(풌ퟐ푳ퟐ) pairwise computations

• 푙 … upper bound on the MSA length → 퐎(풍풌) for MSA construction

푂 푘2퐿2 + 푙푘 = 푶(풌ퟐ푳ퟐ) SA - exercise

• Compute SP for the constructed MSA

• Compute SA for the previous example but add sequences to the MSA in different order. Does the order of addition impacts the score?

• Compute MSA starting with S5. Does the score change?

ATTGCC-ATT ATGGCC-ATT AT--CCAATTTT AT--CTTCTT ATTGCCGATT ATTGCCGATT ATTGCCGATT-- ATTGCCGATT Feng & Doolittle (1)

푆 푎,푎 +푆 푏,푏 • 푆 푎, 푏 = 푚푎푥 2 1. Calculate a distance matrix from all-to-all pairwise • 푆푟푎푛푑 is an expected score alignments (푁(푁 − 1)/2) obtained by randomization • 푆푒푓푓 can be viewed as normalized 2. Convert raw alignment scores into (evolutionary) distances percentage similarity which decreases roughly exponentially to 0 with increasing evolutionary distance. • –log makes the measure linear with 푆표푏푠−푆푟푎푛푑 • 퐷 = − log 푆푒푓푓 × 100 = − log × 100 evolutionary distance 푆푚푎푥−푆푟푎푛푑

3. Construct a guide tree from the distance matrix using Fitch & Margoliash algorithm 4. Align child nodes of each parent (can be sequence- sequence, sequence-MSA, MSA-MSA) in the order they were added to the tree

source: Feng, Da-Fei, and Russell F. Doolittle. "Progressive sequence alignment as a prerequisitetto correct phylogenetic trees." Journal of molecular evolution 25.4 (1987): 351-360. Feng & Doolittle (2)

• Sequence-sequence is aligned using classical dynamic programming

• Sequence-MSA – sequence is aligned with each sequence in the group and the highest scoring alignment defines how the sequence is added to the group

• MSA-MSA – as in previous case but all pairs of sequences are tested

• When a sequence is added to a group, neutral symbol X is introduced instead of the gap position • allows to align gap positions • neutral – anything aligned with X scores 0 • side effect – the gaps in two MSAs tend to come together in the resulting MSA Profile/MSA Alignment

• When adding a sequence to a group it is desirable to take into account the MSA built so far • mismatches at highly conserved positions should be penalized more • 2 MSA (profiles) of 푁 sequences, one from 1. . 푛, second 푛 + 1. . 푁

෍ 푺 푨 풊 = ෍ ෍ 흈(푨풌 풊 , 푨풍 풊 ) 풊 풊 풌<풍≤푵

= ෍ ෍ 흈(푨풌 풊 , 푨풍 풊 ) + ෍ ෍ 흈(푨풌 풊 , 푨풍 풊 ) + ෍ ෍ 흈(푨풌 풊 , 푨풍 풊 ) 풊 풌<풍≤풏 풊 풏<풌<풍≤푵 풊 풌≤풏,풏<풍≤푵 • The score of the σ푖 σ푘<푙≤푁 휎(퐴푘 푖 , 퐴푙 푖 ) consists of the in-group scores plus between group scores • when aligning the profiles we can use standard dynamic programming where columns are aligned against columns using the in-between scores • → using position-specific information from the group’s multiple alignment ClustalW

• Similar to Feng & Doolittle but uses profile-based building

1. Calculate matrix from all-to-all pairwise alignments (푁(푁 − 1)/2)

2. Convert raw alignment similarity scores into evolutionary distances

3. Construct a guided tree from the distance matrix using neighbor joining algorithm

4. Progressively align the nodes in order of decreasing similarity, using sequence-sequence, sequence-profile, and profile-profile alignment ClustalW - Alignment

column-based global alignment

standard global alignment ClustalW – heuristics (1)

• Weighting of subsequences to compensate for biased representation in large subfamilies – compensates defects of sum-of-pairs scoring • sequence contributions to the MSA are weighted by their relationships in the predicted evolutionary tree

• Closely related sequences BLOSUM 80 – distant sequences BLOSUM 50

• Position-specific gap open profile penalties multiplied by a modifier being function of the residues observed at the position • comes from structure-based alignments ClustalW – heuristics (2)

• Gap penalties are higher if there are no gaps at given position but some exist at nearby positions • force the gaps to be in the same places

• Guide tree can be adjusted on the fly to postpone aligning low-similar sequences up to the point where more information is present

• … Clustal Omega

• ClustalW does not scale well for a big number (thousands) of sequences • Bottleneck is the guide tree construction → 푂(푀 × 푁2) • Clustal Omega algorithm • mBed algorithm-based for guide tree construction • emBedding of each sequence in a space of 푛 dimensions where n is proportional to log N • Each sequence replaced by an 푛 element vector, where each element is the distance to one of 푛 reference sequences • Clustering of the vectors by UPGMA or K-means • Alignments of profiles using hidden Markov models (HHalign package)

• Additional features • Adding sequences to existing alignments • External profiles - HMM profile from sequences homologous to the input set which can be used in MSA construction

33 Progressive alignment drawbacks

• Drawback of the progressive methods is the greedy nature of the algorithm • once an error, always an error

• Solutions • Iterative approach • Tries to correct mistakes in the initial alignment … which might happen easily if pairwise sequence similarity is too low

• Consistency-based approach • Tries to avoid mistakes in advance

34 T-Coffee

• A progressive alignment with the ability to consider information from all of the sequences during each alignment step, not just those being aligned at that stage (consistency)

• Tackles ClustalW drawback T-Coffee algorithm (1)

1. Primary library generation • Generate primary libraries of sequence alignments (using several methods) • For each pair compute weights based on percent identity (shorter sequence) • Merge the primary libraries – pairs of aligned residues get a weight equal to the sum of the weights 2. Extended library generation • For each pair of sequences try to align them using an intermediate sequence • Score each pair of residues by the lower of the two weights and sum the weights for that residue pair over all triplets 3. Progressive alignment • Guided tree is used to build the multiple alignment • A pair of sequences is aligned using dynamic programming with weights based on the extended library • When aligning two sets of sequences, averaged library weights are used T-Coffee algorithm (2)

77+88 = 165 Iterative refinement

• Once an error, always an error • when a sequence is added to a MSA it cannot be changed later on (holds also for consistency-based approaches) • dependence on the initial alignment

• Idea behind iterative refinement methods • optimal solution can be obtained by iterative improvement of suboptimal solutions

• First, a suboptimal solution is identified by a fast heuristic method and then possibly improved by iterative removal and re-addition of the sequences Barton-Sternberg

1. Find the highest scoring pair of sequences and align them using the pairwise dynamic programming 2. Identify most similar remaining sequence with respect to the existing profile and align it using sequence-profile alignment 3. Repeat step 2 until all sequences are aligned

4. Remove sequence 풔ퟏ and realign it to the profile by profile-sequence alignment. Repeat for 풔ퟐ, … , 풔푵 5. Repeat step 4 for a fixed number of times or until convergence Block-based alignment

• Both progressive and iterative methods assume that all parts of all sequences are consistent with a global alignment • not every position in the alignment has to correspond to a homologous site in all sequences

• Block-based solution approach to the problem of global alignment by • splitting sequences into blocks • aligning the blocks • merging block alignments DIALIGN

• Alignment constructed from gap-free local alignments between pairs of sequences • based on diagonals in the dynamic programming matrix • Procedure • align all possible pairs of sequences • determine all diagonals and assign weights • for a diagonal 퐷 of length 푙, score 풔 is obtained from substitution matrix • determine length-independent weight as 풘 푫 = − 퐥퐨퐠 푷(풍, 풔), where 푷(풍, 풔) is the probability that diagonal of sequence of length 풍 will have score at least 풔 • build MSA by adding consistent diagonals in order of decreasing weight (and overlap with other diagonals) • explore unaligned regions and include them if possible DIALIGN - Example

atctaatagttaaactcccccgtgcttag