Outline • Alignment of pairs of sequence • Local and global alignments • Methods of alignments • Dot matrix analysis • Dynamic programming approach • Use of scoring matrices and gap penalties • Scoring matrices -- PAM and BLOSUM
What is sequence alignment? • Sequence alignment is a way of arranging the sequences of DNA, RNA or protein to identify regions of similarity that may be a consequence of functional, structural or evolutionary relationships between the sequences. • The procedure of comparing two (pair-wise alignment) or more multiple sequences is to search for a series of individual characters or patterns that are in the same order in the sequences. • There are two types of alignment: local and global.
Global alignment vs Local alignment • Global alignment is attempting to match as much of the sequence as possible. The tool for Global alignment is based on Needleman-Wunsch algorithm. • Local alignment is to try to find the regions with highest density of matches. The tool for local alignment is based on Smith-Waterman. • Both algorithms are derivates from the basic dynamic programming algorithm. L G P S S K Q T G K G S - S R I W D N Global alignment L N - I T K S A G K G A I M R L G D A - - - - - - - T G K G - - - - - - - - Local alignment - - - - - - - A G K G - - - - - - - -
Why do sequence alignment? • Sequence alignment is useful for discovering structural, functional and evolutionary information in biological sequences. • Sequences that are very much alike may have similar secondary and 3D structure, similar function and likely a common ancestral sequence. It is extremely unlikely that such sequences obtained similarity by chance. -- For DNA molecules with n nucleotides such probability is very low P = 4-n. -- For proteins with n nucleotides, the probability even much lower P = 20 –n. • Sequence alignment makes the following tasks easy: 1.annotation of new sequences; 2. modelling of protein structures; 3. design and analysis of gene expression experiments
Raw Data ???T C A T G C A T T G 2 matches, 0 gaps T C A T G | |C A T T G 3 matches (2 end gaps) T C A T G . | | | . C A T T G 4 matches, 1 insertion T C A - T G | | | | . C A T T G 4 matches, 1 insertion T C A T - G | | | | . C A T T G An example of aligning text strings
Terminologies of sequence comparison • Sequence identity -- exactly the same Amino Acid or Nucleotide in the same position. • Sequence similarity -- Substitutions with similar chemical properties. • Sequence homology -- general term that indicates evolutionary relatedness among sequences; we usually measure of percentage identity of sequence homology • Pairwise alignment -- used to find the best-matching piecewise (local) or global alignments of two query sequences. Pairwise alignments can only be used between two sequences at a time. • Multiple sequence alignment -- try to align all of the sequences in a given query set.
Methods of pairwise alignment • Dot matrix analysis • The dynamic programming (DP) algorithm • Word methods
What is Dot matrix analysis • A dot matrix analysis is a method for comparing two sequences to look for possible alignment (Gibbs and McIntyre 1970) • The algorithm for a dot matrix: 1. One sequence (A) is listed across the top of the matrix and the other (B) is listed down the left side 2. Starting from the first character in B, one moves across the page keeping in the first row and placing a dot in many column where the character in A is the same 3. The process is continued until all possible comparisons between A and B are made 4. Any region of similarity is revealed by a diagonal row of dots 5. Isolated dots not on diagonal represent random matches
What can Dot matrix analysis do? • It can detect of matching regions can be improved by filtering out random matches and this can be achieved by using a sliding window • It can be used to assess repetitiveness in a single sequence, such as direct and inverted repeats within the sequences
1st example of Dot matrix analysis: two identical sequences • http://arbl.cvmbs.colostate.edu/molkit/dnadot/index.html
2nd example of Dot matrix analysis: two very different sequences • http://arbl.cvmbs.colostate.edu/molkit/dnadot/index.html
3rd example of Dot matrix analysis: two similar sequences sequences • http://arbl.cvmbs.colostate.edu/molkit/dnadot/index.html
Dynamic programming algorithm • The approach compares every pair of characters in the two sequences and generates an alignment, which is the best or optimal. • The method can be useful in aligning nucleotide to protein sequences. • The method requires large amounts of computing power and is a highly computationally demanding because the nature of dynamic programming technique is recursion. • New algorithmic improvements as well as increasing computer capacity make possible to align a query sequence against a large DB in a few minutes. • Two approaches for dynamic programming: Top-down approach and Bottom-up.
The procedure of the dynamic programming algorithm • The alignment procedure depends upon scoring system based on probability that: 1) a particular amino acid pair is found in alignments of related proteins (pxy); 2) the same amino acid pair is aligned by chance (pxpy); 3) introduction of a gap would be a better choice as it increases the score. • A substitution matrix is composed of the ratio of the first two probabilities. There are many such matrices, two of them PAM and BLOSUM will be talked in next few slides. • The calculation of scores for the gap introduction and its extension is from the matrices and represent a prior knowledge and some assumptions. For example: one of them is quite simple, if negative cost of a gap is too high a reasonable alignment between slightly different sequences will be never achieved but if it is too low an optimal alignment is hardly possible. Other assumptions are based on sophisticated statistical procedures.
An example: scoring a sequence alignment with a gap penalty Sequence 1 V D S - C Y Sequence 2 V E S L C Y Score 4 2 4 -11 97 Score = sum of amino acid pair scores (26) minus single gap penalty (11) = 15 Note: 1. it is likely to have non-identical amino acids placed in the corresponding positions. 2. Scores gained by each match are not always the same, for instance two rare amino acids will score more than two common. 3. The alignment gap(s) may be introduced for optimising the score. Introduction of gaps causes penalties.
Steps for the dynamic programming algorithm • Score of new = Score of previous + Score of new • alignment alignment (A) aligned pair • V D S - C Y V D S - C Y • V E S L C Y V E S L C Y • 15 = 8 + 7 • 2.Score of = Score of previous + Score of new • alignment (A) alignment (B) aligned pair • V D S - C V D S - C • V E S L C V E S L C • 8 = -1 + 9 • 3. Repeat removing aligned pairs until end of alignments is reached
Why use a substitution matrix? • Determine likelihood of homology between two sequences. • Substitutions that are more likely should get a higher score, • Substitutions that are less likely should get a lower score.
How to calculate Scoring Matrices • Log-odds matrix where each cell gives the probability of aligning those two residues • Score of alignment = Sum of log-odds scores of residues • Score for each residue given by:
Types of Matrices • Percent Identity • Standard scoring matrix to align DNA sequences • PAM • Estimates the rate at which each possible residue in a sequence changes to each other residue over time • BLOSUM-X • Identifies sequences that are X% similar to the query sequence
Scoring matrices: PAM (Percent Accepted Mutation) and BLOSUM62 (BLOcks amino acid SUbstitution Matrices) Amino acids are grouped according to to the chemistry of the side group: (C) sulfhydryl, (STPAG)-small hydrophilic, (NDEQ) acid, acid amide and hydrophilic, (HRK) basic, (MILV) small hydrophobic, and (FYW) aromatic. Log odds values: +10 means that ancestor probability is greater, 0 means that the probability are equal, -4 means that the change is random. Thus the probability of alignment YY/YY is 10+10=20, whereas YY/TP is –3-5=-8, a rare and unexpected between homologous sequences. BLOSUM is based on local alignments. BLOSUM was first introduced in a paper by Henikoff and Henikoff. They scanned the for very conserved regions of protein families (that do not have gaps in the sequence alignment) and then counted the relative frequencies of amino acids and their substitution probabilities. Then, they calculated a log-odds score for each of the 210 possible substitutions of the 20 standard amino acids.
Word methods • Word methods, also known as k-tuple methods, are heuristic methods that are not guaranteed to find an optimal alignment solution, but are significantly more efficient than dynamic programming. • The typical tools used for this method is BLAST and FASTA.
The list of sequence alignment software • http://en.wikipedia.org/wiki/List_of_sequence_alignment_software