1. Last lecture summary

2. Flavors of sequence alignment
pair-wise alignment × multiple sequence alignment
- párové/násobné zarovnání
- Sequences that are quite similar and approximately the same length are suitable candidates for global alignment.
- Local alignments are more suitable for aligning sequences that are similar along some of their lengths but dissimilar in others, sequences that differ in length, or sequences that share a conserved region or domain.

3. Flavors of sequence alignment
global alignment × local alignment
global
align entire sequence
stretches of sequence with the highest density of matches are aligned, generating islands of matches or subalignments in the aligned sequences
- párové/násobné zarovnání
- Sequences that are quite similar and approximately the same length are suitable candidates for global alignment.
- Local alignments are more suitable for aligning sequences that are similar along some of their lengths but dissimilar in others, sequences that differ in length, or sequences that share a conserved region or domain.
local

4. Evolution of sequences
The sequences are the products of molecular evolution.
When sequences share a common ancestor, they tend to exhibit similarity in their sequences, structures and biological functions.
DNA1
DNA2
Protein1
Protein2
- similar sequences produce similar proteins – this is probably the most powerful idea of bioinformatics because it enables us to make predictions. Often little is known about the function of new sequence from a genome sequencing program, but if similar sequences can be found in a database for which functional or structural information is available, then this can be used as the basis of a prediction of function or structure for the new sequence.
Sequence similarity
Similar 3D structure
Similar function
Similar sequences produce similar proteins
However, this statement is not a rule. See Gerlt JA, Babbitt PC. Can sequence determine function? Genome Biol. 2000;1(5) PMID:

5. Homology homology, orthology, paralogy How it happens?
orthologs – from different spcies, posses same function
paralogs – different function in the same organism
How it happens?
orthology – speciation
paralogy – gene duplication
gene duplication – unequal cross-over, chromosome replication, retrotrasposition
The degree of sequence conservation in the alignment reveals evolutionary relatedness of different sequences
The variation between sequences reflects the changes that have occurred during evolution in the form of substitutions and/or indels.

6. Scoring systems
DNA and protein sequences can be aligned so that the number of identically matching pairs is maximized.
Counting the number of matches gives us a score (3 in this case). Higher score means better alignment.
This procedure can be formalized using substitution matrix.
A T T G T
A – - G A C A T A T C G 1
Identity matrix

7. Scoring DNA sequence alignment
Match score: +1
Mismatch score: +0
Gap penalty: –1
ACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || |||||||| ----CTGATTCGC---ATCGTCTATCT
Matches: 18 × (+1)
Mismatches: 2 × 0
Gaps: 7 × (– 1)
Score = +11

8. Scoring DNA sequence alignment (2)
Match/mismatch score: +1/+0
Origination/length penalty: –2/–1
ACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || |||||||| ----CTGATTCGC---ATCGTCTATCT
Matches: 18 × (+1)
Mismatches: 2 × 0
Origination: 2 × (–2)
Length: 7 × (–1)
Score = +7

9. Substitution matrices
Should reflect:
Physicochemical properties of amino acids.
Different frequencies of individual amino acids occuring in proteins.
Interchangeability of the genetic code.
PAM
Manual alignments of 71 groups of very similar (at least 85% identity) protein sequences substitutions were found.
These mutations do not significantly alter the protein function. Hence they are called accepted mutations.
Two sequences are 1 PAM apart if they have 99% identical residues.
PAM1 matrix is the result of computing the probability of one substitution per 100 amino acids.
Higher PAM matrices

10. PAM 120 small, polar small, nonpolar polar or acidic basic
Zvelebil, Baum, Understanding bioinformatics.
PAM 120
Positive score – frequency of substitutions is greater than would have occurred by random chance.
Zero score – frequency is equal to that expected by chance.
Negative score – frequency is less than would have occurred by random chance.
small, polar
small, nonpolar
polar or acidic
basic
large, hydrophobic
aromatic

11. How to calculate score? substitution matrix 2 - BLOSUM62 shown here
Selzer, Applied bioinformatics.
How to calculate score?
substitution matrix 2
- BLOSUM62 shown here

12. New stuff

13. Protein vs. DNA sequences
Given the choice of aligning DNA or protein, it is often more informative to compare protein sequences.
There are several reasons for this:
Many changes in DNA do not change the amino acid that is specified.
Many amino acids share related biophysical properties. Though these amino acids are not identical, they can be more easily substituted each with other. These relationships can be accounted for using scoring systems.
When is it appropriate to compare nucleic sequences?
confirming the identity of DNA sequence in database search, searching for polymorphisms, confirming identity of cloned cDNA
When nucleotide sequence is analyzed, it is usually preferable to study the protein sequences.
Particularly 3rd position in codon does not change the coded amino acid.

14. Similarity vs. identity
Similarity refers to the percentage of aligned residues that can be more readily substituted for each other.
have similar physicochemical characteristics and
the selective pressure results in some mutations being accepted and others being eliminated
S = [(Ls × 2)/(La + Lb)] × 100
number of aligned residues
with similar characteristics
total lengths of each sequence

15. Homology vs. similarity
Two sequences are homologous when they descended from a common ancestor sequence.
Similarity can be quantified: “two sequences share 40% similarity”.
But NOT “two sequences share 40% homology”. Just “two sequences are homologous”
Qualitative statement
And it is a conclusion about a common ancestral relationship drawn from sequence similarity comparison
- homology is like pregnancy, you’re either pregnant, or you’re not. You are not pregnant for 80%

16. Gaps How will I score this alignment?
The gaps can’t be inserted freely.
Indels are relatively slow evolutionary processes.
And alignments with large gaps do not make biological sense.
Each gap is penalized – a gap penalty
The gap penalty is an adjustable parameter.
Let’s use the gap penalty equaling to -11.
V D S - C Y
V E S L C Y
V D S - C Y
V E S L C Y
S = – =15

17. Gap penalty Affine gap penalty
different for opening and extending
constant for extending
The gap penalty is high – fewer gaps will be inserted
If you’re searching for sequences that are a strict match for your query sequence, the gap penalty should be set high.
This will retrieve regions with very closely related sequences.
The gap penalty is low – more and larger gaps will be inserted
If you are searching for similarity between distantly related sequences, the gap penalty should be set low.

18. Percentage identity = 10%
High gap penalty. Gaps has been inserted only at the beginning and end.
Percentage identity = 10%
(B) Low gap penalty. More gaps. Percentage identity = 18%
Zvelebil, Baum, Understanding bioinformatics.

19. BLOSUM matrices I
BLOck SUbstitution Matrix by Henikoff and Henikoff, 1992.
They used the BLOCKS database containing multiple alignments of ungapped segments (blocks).
These alignments correspond to the most highly conserved regions of proteins.
Blocks are ungapped sequence motifs. Sequence motif is a conserved stretch of amino acids confering a specific function to a protein.
Any given protein can contain one or more blocks corresponding to its structural/functional motifs.
- Henikoff S, Henikoff JG. Amino acid substitution matrices from protein blocks. Proc Natl Acad Sci U S A Nov 15;89(22): PMID:

20. Blocks .
In BLOCKS Database ( Keyword Search search for cytosine and methylase. Block Maps – Graphical Map
At the top picture each sequence has 6 blocks.
Bottom are logos of each of six blocks.
A sequence logo is a graphical representation of aligned sequences where at each position the size of each residue is proportional to its frequency in that position and the total height of all the residues in the position is proportional to the conservation (information content) of the position. See paper Schneider TD, Stephens RM. Sequence logos: a new way to display consensus sequences. Nucleic Acids Res. 1990;18(20): PubMed PMID:
Right – sequences forming given block. Just a segment, not whole. And just two blocks out of six are shown

21. BLOSUM matrices II
Thus the Hanikoffs focused on substitution patterns only in the most conserved regions of a protein. These regions are (presumably) least prone to change.
The substitution patterns of 2000 blocks (block is the whole alignment, not individual sequences within it) representing more than 500 groups were examined, and BLOSUM matrices were generated.
Sequences sharing no more than 62% identity were used to calculate BLOSUM62 matrix.
Short and clear explanation of BLOSUM62 derivation: Eddy SR. Where did the BLOSUM62 alignment score matrix come from? Nat Biotechnol (8): PMID:

22. BLOSUM matrices III
BLOSUM matrices are based on entirely different type of sequence analysis (local ungapped alignment vs. global gapped alignment in PAM) and on a much larger data set than PAM.
All BLOSUM matrices are based on observed alignments. They are not based on extrapolations like PAM.
BLOSUM numbering system goes in reversing order as the PAM numbering system.
The lower the BLOSUM number, the more divergent sequence they represent.

23. PAM vs. BLOSUM I
However, you may ask a question which particular matrix should be used?
Dayhoff et al. (1978) defined terms protein families and superfamilies.
A protein family is formed by sequences 85% (or greater) identical to each other.
A protein superfamily is defined as sequences related from 30% or greater.
Superfamily may clearly contain many families.
These terms are widely used in contemporary literature, however with different meanings (we’ll come to that later).
BLOSUM can be compared with PAM using a measure of average information per residue pair in bit units called relative entropy. Relative entropy is 0 when the target (or observed) distribution of pair frequencies is the same as the background (or expected) distribution and increases as these two distributions become more distinguishable. Relative entropy was used by Altschul to characterize the Dayhoff matrices, which show a decrease with increasing PAM. For the BLOSUM series, relative entropy increases nearly linearly with increasing clustering percentage. Based on relative entropy, the PAM 250 matrix is comparable to BLOSUM 45 with relative entropy of =0.4 bit, while PAM 120 is comparable to BLOSUM 80 with relative entropy of =1 bit. BLOSUM 62 is intermediate in both clustering percentage and relative entropy (0.7 bit) and is comparable to PAM 160. Matrices with comparable relative entropies also have similar expected scores.
Altschul SF. Amino acid substitution matrices from an information theoretic perspective. J Mol Biol Jun 5;219(3): PMID:
Guidance in the choice of scoting matrix: Wheeler D. Selecting the right protein-scoring matrix. Curr Protoc Bioinformatics. 2002;Chapter 3:Unit

24. PAM vs. BLOSUM II – PAM
At the time of deriving PAM matrices, most known proteins were small, globular and hydrophilic. If resercher believes his protein contain substantial hydrophobic regions, PAM matrices are not that useful.
Most widely used is PAM250.
It is capable of detecting similarities in the 30% range (i.e. superfamilies).
Another point of view – PAM250 provides the best look-back in evolutionary time.
PAM250 is most effective if the goal is to know the widest possible range of proteins similar to the given protein.

25. PAM vs. BLOSUM III – PAM
Assume a protein is a known member of the serine protease family.
Using the protein as a query against protein databases with PAM 250 will detect virtually all serine proteases, but also considerable amount of irrelevant hits.
In this case, the PAM160 matrix should be used. It detects similarities in the 50% to 60% range (Altschul, 1991).
And to find only those proteins most similar (70% - 90%) to the query protein, use PAM40.
Let’s summarize:
Locate all potential similarities – PAM250
Determine if the protein belongs to the protein family – PAM160
Determine the most similar proteins – PAM40

26. PAM vs. BLOSUM IV – BLOSUM
Most widely used is BLOSUM62.
BLOSUM62 appears to be superior to PAM250 in detecting distant relationships even if the PAM method is updated with current data sets.
BLOSUM62 is capable of accurately detecting similarities down to the 30% range (superfamilies).
Determine if the protein belongs to protein family – BLOSUM80 (detects identities at the 50% level)
Determine the most similar proteins – BLOSUM90
- BLOSUM is better than PAM: Altschul, S.F Amino acid substitution matrices from an information theoretic perspective. J. Mol. Biol. 219:

27. Selecting an Appropriate Matrix
Best use
Similarity (%)
Pam40
Short highly similar alignments
70-90
PAM160
Detecting members of a protein family
50-60
PAM250
Longer alingments of more divergent sequences
~30
BLOSUM90
BLOSUM80
BLOSUM62
Most effective in finding all potential similarities
30-40
BLOSUM30
<30
Similarity column gives range of similarities that the matrix is able to best detect.

28. PAM vs. BLOSUM V – battle
Careful information theory analysis showed that the following matrices are equivalent:
PAM250 is equivalent to BLOSUM45
PAM160 is equivalent to BLOSUM62
PAM120 is equivalent to BLOSUM80
Compared to the PAM160 matrix, BLOSUM62 is less tolerant to substitutions involving hydrophilic amino acids, and more tolerant to substitutions involving hydrophobic amino acids.
Although both PAM250 and BLOSUM62 detect similarities at the 30% level, since BLOSUM uses much wider range of proteins, PAM250 is actually equivalent to BLOSUM45 when considering all proteins, not just those that are hydrophilic.
information theoretic analysis: Altschul, S.F Amino acid substitution matrices from an information theoretic perspective. J. Mol. Biol. 219: Henikoff, S. and Henikoff, J.G Amino acid substitution matrices from protein blocks. Proc. Natl. Acad. Sci. U.S.A. 89:

29. Scoring DNA Alignment
The concept of similarity has little relevance here.
Though transitions (R → R or Y → Y) occur more often than transversions (R → Y or Y → R), this is usually not helpful for sequence alignment.
Instead, concept of identity is used.
Frequencies of mutations are equal for all bases:
match score +5
mismatch score -4
gap penalty (usually a parameter)
opening -10
extending -2

30. Pairwise alignment algorithms
Dynamic programming
Slow, but formally optimizing
Heuristic methods
Efficient, but not as thorough
Word (also k-tuples) methods
Used in database searches
Dot plot (dot matrix)
Graphical way of comparing two sequences

31. Dynamic programming (DP)
General class of algorithms typically applied to optimization problems.
Recursive approach.
Original problem is broken into smaller subproblems and then solved.
Pieces of larger problem have a sequential dependency.
4th piece can be solved using solution of the 3rd piece, the 3rd piece can be solved by using solution of the 2nd piece and so on…

32. ABCDE PQRST A…D P…R We want to align two following sequences:
If you already have the optimal solution to:
A…D
P…R
then you know the next pair of characters will be either:
A…DE or A…D- or A…DE
P…RS P…RS P…R-
You can extend the match by determining which of these has the highest score.

33. Sequence B
Sequence A
Best previous alignment
New best alignment = previous best + local best
...

34. DP algorithms Global alignment - Needlman-Wunsch
Local alignment - Smith-Waterman
Guaranteed to provide the optimal alignment.
Disadvantages:
Slow due to the very large number of computational steps: O(n 2).
Computer memory requirement also increases with the square of the sequence lengths.
Therefore, it is difficult to use the method for very long sequences.
Many alignments may give the same optimal score. And none of these correspond to the biologically correct alignment.

35. Dot plot
Graphical method that allows the comparison of two biological sequences and identify regions of close similarity between them.
Also used for finding direct or inverted repeats in sequences.
Or for prediction regions in RNA that are self-complementary and therefore have potential to form secondary structures.
good resource on dot plots:

36. - Lines linking the dots in diagonals indicate sequence alignment
- Lines linking the dots in diagonals indicate sequence alignment. Diagonal lines above or below the main diagonal represent internal repeats of either sequence.

37. Self-similarity dot plot I
The DNA sequence EU compared against itself.
- a bit messy. So sliding window can be used.
Introduction to dot-plots, Jan Schulz

38. background
noise
gap
runs of
matched
residues

39. Self-similarity dot plot II
The DNA sequence EU compared against itself.
Window size = 16.
Linear color mapping
Introduction to dot-plots, Jan Schulz

40. Improving dot plot Sliding window – window size (lets say 11)
Stringency (lets say 7) – a dot is printed only if 7 out of the next 11 positions in the sequence are identical
Color mapping
Scoring matrices can be used to assign a score to each substitution. These numbers then can be converted to gray/color.

41. Interpretation of dot plot I
Plot two homologous sequences of interest. If they are similar – diagonal line will occur (matches).
frame shifts
mutations
gaps in diagonal
insertions
shift of main diagonal
deletions

42. Interpretation of dot plot II
Identify repeat regions (direct repeats, inverted repeats) – lines parallel to the diagonal line in self-similarity plot
Microsattelites and minisattelites (these are also called low-complexity regions) can be identified as “squares”.
Palindromatic sequences are shown as lines perpendicular to the main diagonal.
Plaindromatic sequence: V ELIPSE SPI LEV
Bioinformatics explained: Dot plots,

43. Repeats in dot plot direct repeats minisattelites inverted repeats
self-similarity dot plot of NA sequence ofhuman LDL receptor
window 23, stringency 7
inverted repeats
from the book Bioinformatics, David. M. Mount,

44. Interpretation of dot plot – summary
a-f) are self similiarity dot plots (T1=T2). g-h) are dot plots comparing two different sequences of similar length.
a) A continuous main diagonal shows perfect similarity for symbols with the same indices.
b) Parallels to the main diagonal indicate repeated regions in the same reading direction on different parts of the sequences. In this case a region D is found twice in the sequence (D1, D2, so called ‘duplications’).
c) Lines perpendicular to the main diagonal indicate palindromic areas. In this case the sequence is completely palindromic in the displayed area. As an example the latin sentence ‘SATOR AREPO TENET OPERA ROTAS’ might be consulted.
d) Partially palindromic sequence (For DNA sequences this refers to a perfect match of the normal strand with its reverse complement, which is frequently found for many transposable elements.
e) Bold blocks on the main diagonal indicate repetition of the same symbol in both sequences, e.g. (G)50, so called microsatellite repeats
f) Parallel lines indicate tandem repeats of a larger motif in both sequences, e.g. (AGCTCTGAC)20, so called minisatellite patterns. The distance between the diagonals equals the distance of the motif.
g) When the diagonal is a discontinuous line this indicates that the sequences T1 and T2 share a common source. In literal analyses we may have to deal with plagiarism or in DNA analyses sequences may be homologous because of a common ancestor. The number of interruptions increases with modifications on the text or the time of independent evolution and mutation rate.
h) Partial deletion in sequence 1 or insertion in sequence 2, so called ‘indel’. In protein coding sequences this can be often observed for many different types of domains, which got lost or substituted during evolution (Beaussart et al. 2007). Also comparing mRNA (cDNA) sequences without introns (T1) against the unspliced DNA sequence (T2) generally yields this picture.

45. Dot plot of the human genome
The draft assembly of chromosome 7, compared to the near complete Build34. Diagonals of the same slope but shifted from the main diagonal indicate order disagreements, diagonals with opposite slope represent inversions. The inset magnifies 500 kb covering 3 BACs at a finer resolution and revealing the central BAC was poorly assembled in the draft version.
A. M. Campbell, L. J. Heyer, Discovering genomics, proteomics and bioinformatics

46. Dot plot rules
Larger windows size is used for DNA sequences because the number of random matches is much greater due to the presence of only four characters in the alphabet.
A typical window size for DNA is 15, with stringency 10. For proteins the matrix has not to be filtered at all, or windows 2 or 3 with stringency 2 can be used.
If two proteins are expected to be related but to have long regions of dissimilar sequence with only a small proportion of identities, such as similar active sites, a large window, e.g., 20, and small stringency, e.g., 5, should be useful for seeing any similarity.

47. Dot plot advantages/disadvantages
All possible matches of residues between two sequences are found. It’s just up to you to choose the most significant ones.
Readily reveals the presence of insertions/deletions and direct and inverted repeats that are more difficult to find by the other, more automated methods.
Disadvantages: Most dot matrix computer programs do not show an actual alignment. Does not return a score to indicate how ‘optimal’ a given alignment is (no statistical significance that could be tested).