Sequencing genomes

hordeprobableBiotechnology

Oct 4, 2013 (4 years and 1 month ago)

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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.


4
th

piece can be solved using solution of the 3
rd

piece, the 3
rd

piece can be solved by using solution of
the 2
nd

piece and so on…


Sequence B

Sequence A

Best previous alignment

New best alignment = previous best + local best

...

...

...

...

If
you already have the optimal solution to:


X…Y


A…B

then you know the
next
pair of characters will either be
:



X…Y
Z

or

X…Y
-

or

X…Y
Z


A…B
C
A…B
C
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 self
-
complementary 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_d
ot
-
plots&Itemid=76

runs of

matched

residues

gap

background

noise

Self
-
similarity dot plot II

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_d
ot
-
plots&Itemid=76

The DNA sequence
EU127468.1 compared
against itself.


Window size = 16.

Linear color mapping

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 they
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

from the book Bioinformatics, David. M. Mount,

direct repeats

minisattelites

inverted repeats

self
-
similarity dot plot of
NA sequence ofhuman
LDL receptor


window 23, stringency 7

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_d
ot
-
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 2/3 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 alignmen
t. 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 detection of alignment


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.


The matched sequence reported e.g. by the search
program can be classified as TP (true positive, i.e. two
sequences are homologous) or as FP (false positive, i.e.
genuinely unrelated, aligned only by chance).


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 score is significant or if it
appeared just by chance. How to proceed?


State H
0



two sequences are not related, score
S

represents a chance
occurrence


State H
a


Choose a significance level



What else do we have to know?


s
tatistics 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?


𝑍
=
𝑆


𝜎




Significance
of global alignment
II
I


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
2
=
0
.
26
2
=
0
.
13%



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

=
0
.
0026
.


In hypotheses testing, commonly used is

=
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


to more stringent level
.


Bonferroni correction



𝛼
10
6
=
0
.
05
10
6
=
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
𝜎
exp

𝑥


𝜎

exp
𝑥


𝜎






… location parameter

𝜎
,

,


… scale parameter




𝑃
𝑋
>
𝑥
=
1

exp

exp

𝑥


𝜎

wikipedia.org

Statistical distribution of alignments


local alignment


analytical theory


gapless


Gumbel, parameters can be evaluated analytically


gapped


Gumbel, paramaters must be obtained from simulations,
no analytical formulas


global alignment


no thorough theory, however empirical simultions show that the
distribution is also Gumbel