The document provides an extensive overview of sequence alignment in bioinformatics, explaining its definitions, significance, and methodologies. It details different types of alignments, including global, local, and multiple sequence alignments, as well as the algorithms used to perform them, such as Needleman-Wunsch and Smith-Waterman. It also discusses the concepts of similarity versus homology, the impact of mutations on sequence dissimilarity, and the computational complexity associated with alignment algorithms.

1. Introduction to sequence
Alignment

2. Outline
2
 Introduction-Definitions
 The need for sequence alignment
 Classification of sequence alignments
 The alignment problem-Complexity of alignment

3. Sequence Alignment
 Probably the most common
“experiment” done in biology today
 Formally considered an experiment
because you don’t know what you’ll get
until you perform the operation
 As an experiment, it is based on a
hypothesis; it uses a reproducible
technique and it generates results that
lead to conclusions or more
experiments

4. Fact:
Sequence comparisons
lie at the heart of all
bioinformatics

5. Sequence Alignment
Sequence alignment is the assignment of residue-
residue correspondences: It involves:
•- precise operators for alignment: matching, gaps
•- quantitative scoring system for matches and
gaps
•- systematic search among possible alignments
•- use alignment algorithms to find optimal
alignment

6. Algorithms
 An algorithm is a sequence of
instructions that one must perform in
order to solve a well-formulated
problem
 First you must identify exactly what the
problem is!
 A problem describes a class of
computational tasks. A problem for
instance is one particular input from
that task

7. Similarity versus Homology*
 Similarity refers to the
likeness or % identity
between 2 sequences
 Similarity means
sharing a statistically
significant number of
bases or amino acids
 Similarity does not
imply homology
 Homology refers to
shared ancestry
 Two sequences are
homologous if they
are derived from a
common ancestral
sequence
 Homology usually
implies similarity

8. Similarity versus
Homology*
 Similarity can be quantified
 It is correct to say that two
sequences are X% identical
 It is correct to say that two
sequences have a similarity score of
Z
 It is generally incorrect to say that
two sequences are X% similar

9. Homologues & All That*
 Homologue (or Homolog)
 Protein/gene that shares a common ancestor and which has
good sequence and/or structure similarity to another (general
term)
 Homology: genes that derive from a common ancestor-
these gene are called homologs
 Paralogue (or Paralog)
 A homologue which arose through gene duplication in the
same species/chromosome
 Paralogous genes are homologous genes in one organism
that derive from gene duplication
 Gene duplication: one gene is duplicated in multiple copies
that are therefore free to evolve and assume new functions
 Orthologue (or Ortholog)
 A homologue which arose through speciation (found in
different species)
 Orthologous genes are homologous genes in different
organisms

10. Mutations
 Causes for sequence (dis)similarity
 mutation: a nucleotide at a certain location is
replaced by another nucleotide (e.g.: ATA → AGA)
 insertion: at a certain location one new nucleotide is
inserted in between two existing
nucleotides
(e.g.: AA → AGA)
 deletion: at a certain location one existing
nucleotide
is deleted (e.g.: ACTG → AC-G)
 indel: an insertion or a deletion

11. Importance: Alignments tell us about...*
 Function or activity of a new gene/protein
 Structure or shape of a new protein
 Location or preferred location of a protein
 Stability of a gene or protein
 Origin of a gene or protein
 Origin or phylogeny of an organelle
 Origin or phylogeny of an organism

12. Sequence Complexity*
MCDEFGHIKLAN…. High Complexity
ACTGTCACTGAT…. Mid Complexity
NNNNTTTTTNNN…. Low Complexity

13. Assessing Sequence
Similarity
Rbn KETAAAKFERQHMD
Lsz KVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNT
Rbn SST SAASSSNYCNQMMKSRNLTKDRCKPMNTFVHESLA
Lsz QATNRNTDGSTDYGILQINSRWWCNDGRTP GSRN
Rbn DVQAVCSQKNVACKNGQTNCYQSYSTMSITDCRETGSSKY
Lsz LCNIPCSALLSSDITASVNC AKKIVSDGDGMNAWVAWR
Rbn PNACYKTTQANKHIIVACEGNPYVPHFDASV
Lsz NRCKGTDVQA WIRGCRL
is this alignment significant?

14. Is This Alignment
Significant?
Gelsolin 89 L G N E L S Q D E S G A A A I F T V Q L 108
Annexin 82 L P S A L K S A L S G H L E T V I L G L 101
154 L E K D I I S D T S G D F R K L M V A L 173
240 L E – S I K K E V K G D L E N A F L N L 258
314 L Y Y Y I Q Q D T K G D Y Q K A L L Y L 333
Consensus L x P x x x P D x S G x h x x h x V L L

15. Some Simple Rules**
 If two sequence are > 100 residues and
> 25% identical, they are likely related
 If two sequences are 15-25% identical
they may be related, but more tests are
needed
 If two sequences are < 15% identical they
are probably not related
 If you need more than 1 gap for every 20
residues the alignment is suspicious

16. Classifications of
sequence alignments
a) Global/local sequence alignment
b) Pairwise/multiple sequence
alignment

17. Global/local sequence alignment
1. Global alignment
- Input: treat the two sequences as potentially equivalent
- Goal: identify conserved regions and differences
- Algorithm: Needleman-Wunsch dynamic programming
- Applications:
- Comparing two genes with same function (in human vs.
mouse).
- Comparing two proteins with similar function.
Q: How similar are two sequences S1 and S2
Input: two sequences S1, S2 over the same alphabet
Output: two sequences S’1, S’2 of equal length
(S’1, S’2 are S1, S2 with possibly additional gaps)
Example:
 S1= GCGCATGGATTGAGCGA
 S2= TGCGCCATTGATGACC
 A possible alignment:
S’1= -GCGC-ATGGATTGAGCGA
S’2= TGCGCCATTGAT-GACC--

18. Global/local sequence alignment
2. Local alignment
- Input: The two sequences may or may not be related
- Goal: see whether a substring in one sequence aligns well with a
substring in the other
- Algorithm: Smith-Waterman dynamic programming
- Note: for local matching, overhangs at the ends are not treated as
gaps
- Applications:
- Searching for local similarities in large sequences
(e.g., newly sequenced genomes)
-Looking for conserved domains or motifs in two proteins
Q: Find the pair of substrings in two input sequences which have the
highest similarity
Input: two sequences S1, S2 over the same alphabet
Output: two sequences S’1, S’2 of equal length
(S’1, S’2 are substrings of S1, S2 with possibly additional gaps)
Example:
 S1= GCGCATGGATTGAGCGA
 S2= TGCGCCATTGATGACC
 A possible alignment:
S’1= ATTGA-G
S’2= ATTGATG

19. Global vs. Local Alignments
 Global alignment algorithms start at the
beginning of two sequences and add gaps
to each until the end of one is reached.
 Local alignment algorithms finds the
region (or regions) of highest similarity
between two sequences and build the
alignment outward from there.

20. Global/local sequence alignment
3. Semi-global alignment
- Input: two sequences, one short and one long
- Goal: is the short one a part of the long one?
- Algorithm: modification of Smith-Waterman
- Applications:
- Given a DNA fragment (with possible error), look for it in the genome
- Look for a well-known domain in a newly-sequenced protein.
4. Suffix-prefix alignment
- Input: two sequences (usually DNA)
- Goal: is the prefix of one the suffix of the other?
- Algorithm: modification of Smith-Waterman.
- Applications:
- DNA fragment assembly
5. Heuristic alignment
- Input: two sequences
- Goal: See if two sequences are "similar" or candidates for alignment
- Algorithms: BLAST, FASTA (and others)
- Applications:
- Search in large databases

21. Database search methods: Sequence Alignment
The most widely used local similarity algorithms are:
Smith-Waterman (http://www.ebi.ac.uk/MPsrch/)
Basic Local Alignment Search Tool (BLAST, http://www.ncbi.nih.gov)
Fast Alignment (FASTA, http://fasta.genome.jp; http://www.ebi.ac.uk/fasta33/;
http://www.arabidopsis.org/cgi-bin/fasta/nph-TAIRfasta.pl)

23. Which algorithm to use for database similarity
search?
BLAST > FASTA > Smith-Waterman (It is VERY SLOW and
uses a LOT OF COMPUTER POWER)
FASTA is more sensitive, misses less homologues
Smith-Waterman is even more sensitive.
BLAST calculates probabilities
FASTA more accurate for DNA-DNA search then BLAST

24. Pairwise/multiple sequence alignment
Multiple sequence alignment (MSA) can be seen as a generalization
of Pairwise Sequence Alignment - instead of aligning two sequences,
n sequences are aligned simultaneously, where n is > 2
Definition:
A multiple sequence alignment is an alignment of n > 2 sequences obtained
by inserting gaps (“-”) into sequences such that the resulting sequences have
all length L and can be arranged in a matrix of N rows and L columns where
each column represents a homologous position
Note: MSA applies both to nucleotide and amino acid sequences
To construct a multiple alignment, one may have to introduce gaps in sequences
at positions where there were no gaps in the corresponding pairwise alignment
 multiple alignments typically contain more gaps than any given pair of
aligned sequences
Multiple sequence alignment (MSA)
Pairwise sequence alignment
A pairwise sequence alignment is an alignment of 2 sequences
obtained by inserting gaps (“-”) such that the resulting sequences
have the same length and where each pair of residues represents a
homologous position

27. Keyword search vs. alignment
Keyword search
- keyword search is exact matching
- can be done quickly (straightforward scan)
- used in Entrez (for example)
Alignment
- non-exact, scored matching
- takes much more time
- used in tools like BLAST2, CLUSTALW

28. Why do we need (multiple) sequence alignment?
Multiple sequence alignment can help to develop a sequence “finger print” which allows the
identification of members of distantly related protein family (motifs)
Formulate & test hypotheses about protein 3-D structure
MSA can help us to reveal biological facts about proteins, e.g.:
(e.g. how protein function has changed or evolutionary pressure acting on a gene)
Crucial for genome sequencing:
-Random fragments of a large molecule are sequenced and those that overlap are
found by a multiple sequence alignment program.
- Sequence may be from one strand of DNA or the other, so complements of each
sequence must also be compared
- Sequence fragments will usually overlap, but by an unknown amount and in
some cases, one sequence may be included within another
- All of the overlapping pairs of sequence fragments must be assembled into large
composite genome sequence
To establish homology for phylogenetic analyses
Identify primers and probes to search for homologous sequences in other organisms

29. The alignment problem
Taxon A AGAC
Taxon B --AC
Taxon C AG--
Taxon A AGAC
Taxon C AG--
Taxon B --AC
Taxon B AC--
Taxon C AG--
Taxon A AGAC
Taxon B --AC
Taxon C --AG
Taxon A AGAC
It is not self-evident how these
sequences are to be aligned together.
Here are some possibilities:
How do we generate a multiple alignment? Given a pairwise alignment, just
add the third, then the fourth, and so on, until all have been aligned. Does it
work?
Example:
Taxon A AGAC
Taxon B --AC
Taxon A AGAC
Taxon C AG--
Taxon B AC
Taxon C AG
It depends not only on the various alignment parameters but also on the order in
which sequences are added to the multiple alignment

30. The alignment problem
What happens when a sequence alignment is wrong?
A B C A C B B C A
A: AGT
B: AT
C: ATC
A: AGT
B: A -T
C: ATC
A: AGT
B: AT -
C: ATC
A: AGT -
B: A -T -
C: A -TC

31. From pairwise to multiple alignments
In pairwise alignments, one has a two-dimensional matrix
with the sequences on each axis. The number of operations
required to locate the best “path” through the matrix is
approximately proportional to the product of the lengths of the
two sequences
A possible general method would be to extend the pairwise
alignment method into a simultaneous N-wise alignment, using
a complete dynamical-programming algorithm in N dimensions.
Algorithmically, this is not difficult to do
But what about execution time?

32. Algorithm Complexity ‘The big-O notation’
One of the most important properties of an algorithm is how its
execution time increases as the problem is made larger (e.g. more
sequences to align).
This is the so-called algorithmic (or computational) complexity of the
algorithm
There is a notation to describe the algorithmic complexity, called the
big-O notation.
If we have a problem size (number of input data points) n, then an
algorithm takes O(n) time if the time increases linearly with n. If the
algorithm needs time proportional to the square of n, then it is O(n2)
It is important to realize that an algorithm that is quick on small
problems may be totally useless on large problems if it has a bad O()
behavior. As a rule of thumb one can use the following
characterizations, where n is the size of the problem, and c is a
constant:

33. The big-O notation
•To compute a N-wise alignment, the algorithmic
complexity is something like O(c2n),
where c is a constant, and n is the number of
sequences
Example:
A pairwise alignment of two sequences [O(c2x2)], takes 1 second,
then four sequences [O(c2x4)], would take 104 seconds (2.8
hours), five sequences [O(c2x5)], 106 seconds (11.6 days), six
sequences [O(c2x6)], 108 seconds (3.2 years), seven sequences
[O(c2x7)], 1010 seconds (317 years), and so on
This is disastrous!

34. How to optimize alignment algorithms?
Use structural information:
- reading frame
- protein structure
-Sequence elements are not truly independent but
related by phylogeny
NK/-YLS
NK/-Y/FL/-S
NKYLSNYLS NFS NFLS
NFL/-S
N – Y L S
N K Y L S
N – F – S
N – F L S
Raw
Human N Y L S
Chimp N K Y L S
Gorilla N F S
Orangutan N F L S
Alignment
Human Chimp Gorilla Orangutan

36. How to optimize alignment algorithms?
Sequences often contain highly conserved regions
These regions can be used for an initial alignment
By analyzing a number of small, independent fragments,
the algorithmic complexity can be drastically reduced!

38. “Optimal” vs. “correct” alignment
For a given group of sequences, there is no single “correct”
alignment, only an alignment that is “optimal” according to some
set of calculations
This is partly due to:
- the complexity of the problem,
- limitations of the scoring systems used,
- our limited understanding of life and evolution
Success of the alignment will depend on the similarity of the
sequences. If sequence variation is great it will be very difficult to
find an optimal alignment

40. Sequence alignment and gaps
Gaps can occur:
Before the first character of a string
CTGCGGG---GGTAAT
|||| || ||
--GCGG-AGAGG-AA-
Inside a string
CTGCGGG---GGTAAT
|||| || ||
--GCGG-AGAGG-AA-
After the last character of a string
CTGCGGG---GGTAAT
|||| || ||
--GCGG-AGAGG-AA-
Note: In protein-coding nucleotide sequences most gaps have a length of 3N

41. Gap Penalties
In the MSA scoring scheme, a penalty is subtracted for each gap introduced
into an alignment because the gap increases uncertainty into an alignment
The gap penalty is used to help decide whether or not to accept a gap or
insertion in an alignment
Biologically, it should in general be easier for a sequence to accept a different
residue in a position, rather than having parts of the sequence chopped away
or inserted. Gaps/insertions should therefore be more rare than point
mutations (substitutions)
In general, the lower the gapping penalties, the more gaps and more
identities are detected but this should be considered in relation to biological
significance
Most MSA programs allow for an adjustment of gap penalties
Sequence alignment and gaps

42. END