Last lecture summary
• identity vs. similarity
• homology vs. similarity
• gap penalty
• affine gap penalty
• gap penalty high
• fewer gaps, if investigating related sequences
• low
• more gaps, larger gaps, distantly related sequences
BLOSUM
• blocks
• focuse on substitution patterns only in blocks
• BLOSUM62 – 62, what does it mean?
• BLOSUM vs. PAM
• BLOSUM matrices are based on observed alignments
• BLOSUM numbering system goes in reversing order as the PAM
numbering system
Selecting an Appropriate Matrix
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
Short highly similar alignments
70-90
BLOSUM80
Detecting members of a protein family
50-60
BLOSUM62
Most effective in finding all potential similarities
30-40
BLOSUM30
Longer alingments of more divergent sequences
<30
Similarity column gives range of similarities that the matrix is able to best detect.
Dynamic programming (DP)
• Recursive approach, 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…
New best alignment = previous best + local best
Best previous alignment
Sequence A
...
...
...
...
Sequence B
If you already have the optimal solution to:
X…Y
A…B
then you know the next pair of characters will either be:
X…YZ
A…BC
or
X…YA…BC
or
X…YZ
A…B-
You can extend the match by determining which of these
has the highest score.
New stuff
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 selfcomplementary and therefore have potential to form
secondary structures.
Self-similarity dot plot I
The DNA sequence
EU127468.1 compared
against itself.
Introduction to dot-plots, Jan Schulz
http://www.code10.info/index.php?option=com_content&view=article&id=64:inroduction-to-dot-plots&catid=52:cat_coding_algorithms_dot-plots&Itemid=76
background
noise
gap
runs of
matched
residues
Self-similarity dot plot II
The DNA sequence
EU127468.1 compared
against itself.
Window size = 16.
Linear color mapping
Introduction to dot-plots, Jan Schulz
http://www.code10.info/index.php?option=com_content&view=article&id=64:inroduction-to-dot-plots&catid=52:cat_coding_algorithms_dot-plots&Itemid=76
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.
Interpretation of dot plot I
1. Plot two homologous sequences of interest. If they are
similar – diagonal line will occur (matches).
2. frame shifts
a) mutations
gaps in diagonal
b) insertions
shift of main diagonal
c) deletions
shift of main diagonal
http://ugene.unipro.ru/documentation/manual/plugins/dotplot/interpret_a_dotplot.html
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, http://www.clcbio.com/index.php?id=1330&manual=BE_Dot_plots.html
Repeats in dot plot
minisattelites
self-similarity dot plot of
NA sequence ofhuman
LDL receptor
window 23, stringency 7
direct repeats
inverted repeats
from the book Bioinformatics, David. M. Mount,
Interpretation of dot plot – summary
http://www.code10.info/index.php?option=com_content&view=article&id=64:inroduction-to-dot-plots&catid=52:cat_coding_algorithms_dot-plots&Itemid=76
Dot plot of the human genome
A. M. Campbell, L. J. Heyer, Discovering genomics, proteomics and bioinformatics
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.
Dot plot advantages/disadvantages
• Advantages:
• 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).
Homology vs. similarity again
• Just a reminder of the important concept in sequence
analysis – homology. It is a conclusion about a common
ancestral relationship drawn from sequence similarity.
• Sequence similarity is a direct result of observation from
the sequence alignment. It can be quantified using
percentages, but homology can not!
• It is important to understand this difference between
homology and similarity.
• If the similarity is high enough, a common evolutionary
relationship can be inferred.
Limits of the alignment detection
• However, what is enough? What are the detection limits of
pairwise alignments? How many mutations can occur
before the differences make two sequences
unrecognizable?
• Intuitively, at some point are two homologous sequences
too divergent for their alignment to be recognized as
significant.
• The best way to determine detection limits of pairwise
alignment is to use statistical hypothesis testing. See
later.
Twilight zone
• However, the level one can infer homologous relationship
depends on type of sequence (proteins, NA) and on the
length of the alignment.
• Unrelated sequences of DNA have at least 25% chance to be
identical. For proteins it is 5%. If gaps are allowed, this percentage
can increase up to 10-20%.
• The shorter the sequence, the higher the chance that some
alignment is attributable to random chance.
• This suggest that shorter sequences require higher cuttof
for inferring homology than longer sequences.
Essential bioinformatics, Xiong
Statistical significance
• Key question – Constitutes a given alignment evidence for
homology? Or did it occur just by chance?
• The statistical significance of the alignment (i.e. its score)
can be tested by statistical hypotheses testing.
Significance of global alignment I
• We align two proteins: human beta globin and myoglobin.
We obtain score S.
• And we want to know if such a score is significant or if it
appeared just by a chance. How to proceed?
• State H0
• two sequences are not related, score S represents a chance
occurrence
• State Ha
• Choose a significance level 𝛼
• What else do we have to know?
• statistics of distribution. i.e. what?
• sample mean, sample standard deviation
Significance of global alignment II
• How to determine the parameters of distribution?
• Compare S to scores of beta globin/myoglobin relative to a large
number of sequences of non-homologous proteins
• Compare with a set of randomly generated sequences.
• Keep the beta globin and randomly scramble the sequence of
myoglobin.
• Performing any of the previous, we obtain the sample
mean and sample standard deviation.
• A Z-score can be calculated. How?
𝑆−𝜇
𝑍=
𝜎
Significance of global alignment III
• For normal distribution, if Z=3 99.74% of the scores are
within how many stdev of the mean?
• three
• And the fraction of scores greater is?
1.0 − 0.9974 0.26
=
= 0.13%
2
2
• We can expect to see this particular high score by chance
about 1 time in 750 (1/750 ≈ 0.13%)
• 0.26% is represented as confidence level 𝛼 = 0.0026.
• In hypotheses testing, commonly used is 𝛼 = 0.05.
Significance of global alignment IV
• The problem with this approach is if the distribution is not
Gaussian.
• Then the estimated significance level will be wrong.
• Bad news – distribution of global alignments is generally
not Gaussian and no theory exists.
• Another consideration – problem of multiple comparisons
• If we compare query sequence to 1 million sequences in database,
we have a million chances to find a high scoring match. In such
case it is appropriate to adjust 𝛼 to more stringent level.
• Bonferroni correction –
𝛼
106
=
0.05
106
= 5 × 10−8
Significance of local alignment
• In contrast to global alignment there is a thorough
understanding of the distribution of scores.
• Key role play Extreme value distributions (EVD)
• Generate N data sets from the same distribution, create a
new data set that includes the maximum/minimum values
from these N data sets, the resulting data set can only be
described by one of the three distributions
• Gumbel, Fréchet, Weibull
• applications
• extreme floods, large wildfires
• large insurance losses
• size of freak waves
• sequence alignment 
Gumbel distribution
𝜌 𝑥 =
1
𝑥−𝜇
𝑥−𝜇
exp −
− exp
𝜎
𝜎
𝜎
𝜇 … location parameter
𝜎 or 𝛽 or 𝜆 … scale parameter
𝑥−𝜇
𝑃 𝑋 > 𝑥 = 1 − exp −exp −
𝜎
wikipedia.org
Statistical distribution of alignments
• local alignment
• analytical theory
• gapless – Gumbel, parameters can be evaluated analytically
• gapped – Gumbel, parameters must be obtained from simulations,
no analytical formulas
• global alignment
• no thorough theory, however empirical simulations show that the
distribution is also Gumbel