Bioinformatica t3-scoringmatrices v2014

FBW
13-10-2014
Wim Van Criekinge

Wel les op 4 november en GEEN les op 18 november

Overview
• Introduction
– Short recap on databases
– Definitions
• Scoring Matrices
– Theoretical
– Empirial
• PAM (pam-simulator.pl)
• BLOSUM
• Pairwise alignment
– Dot-plots (dotplot-simulator.pl)
Overview

Major sites
NCBI - The National Center for Biotechnology Information
http://www.ncbi.nlm.nih.gov/
The National Center for Biotechnology Information (NCBI) at
the National Library of Medicine (NLM), a part of the National
Institutes of Health (NIH).
ExPASy - Molecular Biology Server
http://expasy.hcuge.ch/www/
Molecular biology WWW server of the Swiss Institute of
Bioinformatics (SIB). This server is dedicated to the analysis of
protein sequences and structures as well as 2-D PAGE
EBI - European Bioinformatics Institute
http://www.ebi.ac.uk/

Definitions
Identity
The extent to which two (nucleotide or amino acid)
sequences are invariant.
Homology
Similarity attributed to descent from a common ancestor.
RBP: 26 RVKENFDKARFSGTWYAMAKKDPEGLFLQDNIVAEFSVDETGQMSATAKGRVRLLNNWD- 84
+ K ++ + + GTW++MA+ L + A V T + +L+ W+
glycodelin: 23 QTKQDLELPKLAGTWHSMAMA-TNNISLMATLKAPLRVHITSLLPTPEDNLEIVLHRWEN 81

Definitions
Orthologous
Homologous sequences in different species
that arose from a common ancestral gene
during speciation; may or may not be responsible
for a similar function.
Paralogous
Homologous sequences within a single species
that arose by gene duplication.

Multiple sequence alignment of
glyceraldehyde- 3-phsophate dehydrogenases
fly GAKKVIISAP SAD.APM..F VCGVNLDAYK PDMKVVSNAS CTTNCLAPLA
human GAKRVIISAP SAD.APM..F VMGVNHEKYD NSLKIISNAS CTTNCLAPLA
plant GAKKVIISAP SAD.APM..F VVGVNEHTYQ PNMDIVSNAS CTTNCLAPLA
bacterium GAKKVVMTGP SKDNTPM..F VKGANFDKY. AGQDIVSNAS CTTNCLAPLA
yeast GAKKVVITAP SS.TAPM..F VMGVNEEKYT SDLKIVSNAS CTTNCLAPLA
archaeon GADKVLISAP PKGDEPVKQL VYGVNHDEYD GE.DVVSNAS CTTNSITPVA
fly KVINDNFEIV EGLMTTVHAT TATQKTVDGP SGKLWRDGRG AAQNIIPAST
human KVIHDNFGIV EGLMTTVHAI TATQKTVDGP SGKLWRDGRG ALQNIIPAST
plant KVVHEEFGIL EGLMTTVHAT TATQKTVDGP SMKDWRGGRG ASQNIIPSST
bacterium KVINDNFGII EGLMTTVHAT TATQKTVDGP SHKDWRGGRG ASQNIIPSST
yeast KVINDAFGIE EGLMTTVHSL TATQKTVDGP SHKDWRGGRT ASGNIIPSST
archaeon KVLDEEFGIN AGQLTTVHAY TGSQNLMDGP NGKP.RRRRA AAENIIPTST
fly GAAKAVGKVI PALNGKLTGM AFRVPTPNVS VVDLTVRLGK GASYDEIKAK
human GAAKAVGKVI PELNGKLTGM AFRVPTANVS VVDLTCRLEK PAKYDDIKKV
plant GAAKAVGKVL PELNGKLTGM AFRVPTSNVS VVDLTCRLEK GASYEDVKAA
bacterium GAAKAVGKVL PELNGKLTGM AFRVPTPNVS VVDLTVRLEK AATYEQIKAA
yeast GAAKAVGKVL PELQGKLTGM AFRVPTVDVS VVDLTVKLNK ETTYDEIKKV
archaeon GAAQAATEVL PELEGKLDGM AIRVPVPNGS ITEFVVDLDD DVTESDVNAA

This power of sequence alignments
• empirical finding: if two biological
sequences are sufficiently similar, almost
invariably they have similar biological
functions and will be descended from a
common ancestor.
• (i) function is encoded into sequence,
this means: the sequence provides the
syntax and
• (ii) there is a redundancy in the
encoding, many positions in the
sequence may be changed without
perceptible changes in the function, thus
the semantics of the encoding is robust.

A metric …
It is very important to realize, that all
subsequent results depend critically on just
how this is done and what model lies at the
basis for the construction of a specific
scoring matrix.
A scoring matrix is a tool to quantify how
well a certain model is represented in the
alignment of two sequences, and any result
obtained by its application is meaningful
exclusively in the context of that model.

Importance of scoring matrices
Scoring matrices appear in all analysis
involving sequence comparison.
 The choice of matrix can strongly influence
the outcome of the analysis.
 Scoring matrices implicitly represent a
particular theory of evolution.
 Understanding theories underlying a given
scoring matrix can aid in making proper
choice.
• Nucleic acid and Protein Scoring Matrices

Nucleic Acid Scoring Matrices
• Identity matrix (similarity) BLAST matrix (similarity)
A T C G A T C G
A 1 0 0 0 A 5 -4 -4 -4
T 0 1 0 0 T -4 5 -4 -4
C 0 0 1 0 C -4 -4 5 -4
G 0 0 0 1 G -4 -4 -4 5
• Transition/Transversion Matrix
A T C G
A 0 5 5 1
T 5 0 1 5
C 5 1 0 5
G 1 5 5 0
A and T
purine -pyrimidine
G and C
purine-pyrimidine

Transition/Transversion Matrix
• Nucleotide bases fall into two
categories depending on the ring
structure of the base. Purines
(Adenine and Guanine) are two ring
bases, pyrimidines (Cytosine and
Thymine) are single ring bases.
Mutations in DNA are changes in
which one base is replaced by
another.
• A mutation that conserves the ring
number is called a transition (e.g., A
-> G or C -> T) a mutation that
changes the ring number are called
transversions. (e.g. A -> C or A -> T
and so on).
A T C G
A 0 5 5 1
T 5 0 1 5
C 5 1 0 5
G 1 5 5 0

Transition/Transversion Matrix
• Although there are more ways to
create a transversion, the number
of transitions observed to occur in
nature (i.e., when comparing
related DNA sequences) is much
greater. Since the likelihood of
transitions is greater, it is
sometimes desireable to create a
weight matrix which takes this
propensity into account when
comparing two DNA sequences.
• Use of a Transition/Transversion
Matrix reduces noise in
comparisons of distantly related
sequences.
A T C G
A 0 5 5 1
T 5 0 1 5
C 5 1 0 5
G 1 5 5 0

Protein Scoring Matrices: Unitary Matrix
• The simplest metric in use is the
identity metric.
• If two amino acids are the same,
they are given one score, if they are
not, they are given a different score -
regardless, of what the replacement
is.
• One may give a score of 1 for
matches and 0 for mismatches - this
leads to the frequently used unitary
matrix

A R N D C Q E G H I L K M F P S T W Y V
A 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
R 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
N 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
D 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
C 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Q 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
E 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
G 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
H 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
I 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
L 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
K 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
M 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
F 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
T 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
W 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
Y 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
V 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

• The simplest matrix:
– High scores for Identities
– Low scores for non-identities
• Works for closely related proteins
• Or one could assign +6 for a match and -1 for
a mismatch, this would be a matrix useful for
local alignment procedures, where a negative
expectation value for randomly aligned
sequences is required to ensure that the score
will not grow simply from extending the
alignment in a random way.

A very crude model of an evolutionary
relationship could be implemented in a
scoring matrix in the following way: since
all point-mutations arise from nucleotide
changes, the probability that an observed
amino acid pair is related by chance,
rather than inheritance should depend on
the number of point mutations necessary
to transform one codon into the other.
A metric resulting from this model would
define the distance between two amino
acids by the minimal number of nucleotide
changes required.
Genetic Code Matrix

Genetic Code Matrix
The table is generated by calculating the minimum number of base changes required to
convert an amino acid in row i to an amino acid in column j.
Note Met->Tyr is the only change that requires all 3 codon positions to change.
A S G L K V T P E D N I Q R F Y C H M W Z B X
Ala = A O 1 1 2 2 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2
Ser = S 1 O 1 1 2 2 1 1 2 2 1 1 2 1 1 1 1 2 2 1 2 2 2
Gly = G 1 1 0 2 2 1 2 2 1 1 2 2 2 1 2 2 1 2 2 1 2 2 2
Leu = L 2 1 2 0 2 1 2 1 2 2 2 1 1 1 1 2 2 1 1 1 2 2 2
Lys = K 2 2 2 2 0 2 1 2 1 2 1 1 1 1 2 2 2 2 1 2 1 2 2
Val = V 1 2 1 1 2 0 2 2 1 1 2 1 2 2 1 2 2 2 1 2 2 2 2
Thr = T 1 1 2 2 1 2 0 1 2 2 1 1 2 1 2 2 2 2 1 2 2 2 2
Pro = P 1 1 2 1 2 2 1 0 2 2 2 2 1 1 2 2 2 1 2 2 2 2 2
Glu - E 1 2 1 2 1 1 2 2 0 1 2 2 1 2 2 2 2 2 2 2 1 2 2
Asp = D 1 2 1 2 2 1 2 2 1 O 1 2 2 2 2 1 2 1 2 2 2 1 2
Asn = N 2 1 2 2 1 2 1 2 2 1 O 1 2 2 2 1 2 1 2 2 2 1 2
Ile = I 2 1 2 1 1 1 1 2 2 2 1 0 2 1 1 2 2 2 1 2 2 2 2
Gln = Q 2 2 2 1 1 2 2 1 1 2 2 2 0 1 2 2 2 1 2 2 1 2 2
Arg = R 2 1 1 1 1 2 1 1 2 2 2 1 1 0 2 2 1 1 1 1 2 2 2
Phe = F 2 1 2 1 2 1 2 2 2 2 2 1 2 2 0 1 1 2 2 2 2 2 2
Tyr = Y 2 1 2 2 2 2 2 2 2 1 1 2 2 2 1 O 1 1 3 2 2 1 2
Cys = C 2 1 1 2 2 2 2 2 2 2 2 2 2 1 1 1 0 2 2 1 2 2 2
His = H 2 2 2 1 2 2 2 1 2 1 1 2 1 1 2 1 2 0 2 2 2 1 2
Met = M 2 2 2 1 1 1 1 2 2 2 2 1 2 1 2 3 2 2 0 2 2 2 2
Trp = W 2 1 1 1 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 0 2 2 2
Glx = Z 2 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 2 2 2 1 2 2
Asx = B 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 1 2 1 2 2 2 1 2
??? = X 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

This genetic code matrix already
improves sensitivity and specificity
of alignments from the identity
matrix.
The fact that the genetic code matrix
works to align related proteins, in
the same way that matrices derived
from amino-acid properties work
says something very interesting
about the genetic code: namely that
it appears to have evolved to
minimize the effects of point
mutations.
Genetic Code Matrix

• Simple identity, which scores only identical amino
acids as a match.
• Genetic code changes, which scores the
minimum number of nucieotide changes to change
a codon for one amino acid into a codon for the
other.
• Chemical similarity of amino acid side chains,
which scores as a match two amino acids which
have a similar side chain, such as hydrophobic,
charged and polar amino acid groups.
Overview

All proteins are polymers of the 20 naturally occuring
amino acids. They are listed here along with their
abbreviations :-
Alanine Ala A
Cysteine Cys C
Aspartic AciD Asp D
Glutamic Acid Glu E
Phenylalanine Phe F
Glycine Gly G
Histidine His H
Isoleucine Ile I
Lysine Lys K
Leucine Leu L
Methionine Met M
AsparagiNe Asn N
Proline Pro P
Glutamine Gln Q
ARginine Arg R
Serine Ser S
Threonine Thr T
Valine Val V
Tryptophan Trp W
TYrosine Tyr Y
Amino Acid Residues

All amino acids have the
same general formula
Amino Acid Residues

• Hydrophobic-aliphatic amino
acids: Their side chains consist of
non-polar methyl- or methylene-groups.
– These amino acids are usually located
on the interior of the protein as they
are hydrophobic in nature.
– All except for alanine are bifurcated. In
the cases of Val and Ile the bifurcation
is close to the main chain and can
therefore restrict the conformation of
the polypeptide by steric hindrance.
– red and blue atoms represent polar
main chain groups
Amino Acid Residues

• Hydrophobic-aromatic: Only
phenylalanine is entirely non-polar.
Tyrosine's phenolic side chain has a
hydroxyl substituent and tryptophan
has a nitrogen atom in its indole ring
sytem.
– These residues are nearly always found
to be largely buried in the hydrophobic
interior of a proteins as they are
prdeominantly non-polar in nature.
– However, the polar atoms of tyrosine
and tryptophan allow hydrogen bonding
interactions to be made with other
residues or even solvent molecules
Amino Acid Residues

Neutral-polar side chains: a number of
small aliphatic side chains containing polar
groups which cannot ionize readily.
– Serine and threonine possess hydroxyl groups in
their side chains and as these polar groups are
close to the main chain they can form hydrogen
bonds with it. This can influence the local
conformation of the polypeptide,
– Residues such as serine and asparagine are
known to adopt conformations which most other
amino acids cannot.
– The amino acids asparagine and glutamine
posses amide groups in their side chains which
are usually hydrogen-bonded whenever they
occur in the interior of a protein.
Amino Acid Residues

• Acidic amino acids: Aspartate and
glutamate have carboxyl side chains
and are therefore negatively charged
at physiological pH (around neutral).
– The strongly polar nature of these
residues means that they are most often
found on the surface of globular proteins
where they can interact favourably with
solvent molecules.
– These residues can also take part in
electrostatic interactions with positively
charged basic amino acids.
– Aspartate and glutamate also can take
on catalytic roles in the active sites of
enzymes and are well known for their
metal ion binding abilities
Amino Acid Residues

• Basic amino acids:
– histidine has the lowest pKa (around 6) and is
therefore neutral at around physiological pH.
• This amino acid occurs very frequently in enzyme
active sites as it can function as a very efficient
general acid-base catalyst.
• It also acts as a metal ion ligand in numerous
protein families.
– Lysine and arginine are more strongly basic and
are positively charged at physiological pH's. They
are generally solvated but do occasionally occur
in the interior of a protein where they are usually
involved in electrostatic interactions with
negatively charged groups such as Asp or Glu.
• Lys and Arg have important roles in anion-binding
proteins as they can interact electrostatically with
the ligand.
Amino Acid Residues

Conformationally important residues: Glycine and
proline are unique amino acids. They appear to
influence the conformation of the polypeptide.
• Glycine essentially lacks a side chain and therefore
can adopt conformations which are sterically
forbidden for other amino acids. This confers a high
degree of local flexibility on the polypeptide.
– Accordingly, glycine residues are frequently found in
turn regions of proteins where the backbone has to
make a sharp turn.
– Glycine occurs abundantly in certain fibrous proteins
due to its flexibility and because its small size allows
adjacent polypeptide chains to pack together closely.
• In contrast, proline is the most rigid of the twenty
naturally occurring amino acids since its side chain
is covalently linked with the main chain nitrogen
Amino Acid Residues

Here is one list where amino acids are
grouped according to the characteristics of
the side chains:
 Aliphatic - alanine, glycine, isoleucine,
leucine, proline, valine,
 Aromatic - phenylalanine, tryptophan,
tyrosine,
 Acidic - aspartic acid, glutamic acid,
 Basic - arginine, histidine, lysine,
 Hydroxylic - serine, threonine
 Sulphur-containing - cysteine,
methionine
 Amidic (containing amide group) -
asparagine, glutamine
Amino Acid Residues

Hydrophobicity matrix
R K D E B Z S N Q G X T H A C M P V L I Y F W
Arg = R 10 10 9 9 8 8 6 6 6 5 5 5 5 5 4 3 3 3 3 3 2 1 0
Lys = K 10 10 9 9 8 8 6 6 6 5 5 5 5 5 4 3 3 3 3 3 2 1 0
Asp = D 9 9 10 10 8 8 7 6 6 6 5 5 5 5 5 4 4 4 3 3 3 2 1
Glu = E 9 9 10 10 8 8 7 6 6 6 5 5 5 5 5 4 4 4 3 3 3 2 1
Asx = B 8 8 8 8 10 10 8 8 8 8 7 7 7 7 6 6 6 5 5 5 4 4 3
Glx = Z 8 8 8 8 10 10 8 8 8 8 7 7 7 7 6 6 6 5 5 5 4 4 3
Ser = S 6 6 7 7 8 8 10 10 10 10 9 9 9 9 8 8 7 7 7 7 6 6 4
Asn = N 6 6 6 6 8 8 10 10 10 10 9 9 9 9 8 8 8 7 7 7 6 6 4
Gln = Q 6 6 6 6 8 8 10 10 10 10 9 9 9 9 8 8 8 7 7 7 6 6 4
Gly = G 5 5 6 6 8 8 10 10 10 10 9 9 9 9 8 8 8 8 7 7 6 6 5
??? = X 5 5 5 5 7 7 9 9 9 9 10 10 10 10 9 9 8 8 8 8 7 7 5
Thr = T 5 5 5 5 7 7 9 9 9 9 10 10 10 10 9 9 8 8 8 8 7 7 5
His = H 5 5 5 5 7 7 9 9 9 9 10 10 10 10 9 9 9 8 8 8 7 7 5
Ala = A 5 5 5 5 7 7 9 9 9 9 10 10 10 10 9 9 9 8 8 8 7 7 5
Cys = C 4 4 5 5 6 6 8 8 8 8 9 9 9 9 10 10 9 9 9 9 8 8 5
Met = M 3 3 4 4 6 6 8 8 8 8 9 9 9 9 10 10 10 10 9 9 8 8 7
Pro = P 3 3 4 4 6 6 7 8 8 8 8 8 9 9 9 10 10 10 9 9 9 8 7
Val = V 3 3 4 4 5 5 7 7 7 8 8 8 8 8 9 10 10 10 10 10 9 8 7
Leu = L 3 3 3 3 5 5 7 7 7 7 8 8 8 8 9 9 9 10 10 10 9 9 8
Ile = I 3 3 3 3 5 5 7 7 7 7 8 8 8 8 9 9 9 10 10 10 9 9 8
Tyr = Y 2 2 3 3 4 4 6 6 6 6 7 7 7 7 8 8 9 9 9 9 10 10 8
Phe = F 1 1 2 2 4 4 6 6 6 6 7 7 7 7 8 8 8 8 9 9 10 10 9
Trp = W 0 0 1 1 3 3 4 4 4 5 5 5 5 5 6 7 7 7 8 8 8 9 10
•Physical/Chemical characteristics: Attempt to quantify some physical or chemical attribute of
•the residues and arbitrarily assign weights based on similarities of the residues in this chosen property.

Other similarity scoring matrices might be constructed from
any property of amino acids that can be quantified
- partition coefficients between hydrophobic and hydrophilic phases
- charge
- molecular volume
Unfortunately, …

AAindex
Amino acid indices and similarity matrices
(http://www.genome.ad.jp/dbget/aaindex.html)
List of 494 Amino Acid Indices in AAindex ver.6.0
• ANDN920101 alpha-CH chemical shifts (Andersen et al., 1992)
• ARGP820101 Hydrophobicity index (Argos et al., 1982)
• ARGP820102 Signal sequence helical potential (Argos et al., 1982)
• ARGP820103 Membrane-buried preference parameters (Argos et al., 1982)
• BEGF750101 Conformational parameter of inner helix (Beghin-Dirkx, 1975)
• BEGF750102 Conformational parameter of beta-structure (Beghin-Dirkx, 1975)
• BEGF750103 Conformational parameter of beta-turn (Beghin-Dirkx, 1975)
• BHAR880101 Average flexibility indices (Bhaskaran-Ponnuswamy, 1988)
• BIGC670101 Residue volume (Bigelow, 1967)
• BIOV880101 Information value for accessibility; average fraction 35% (Biou et al., 1988)
• BIOV880102 Information value for accessibility; average fraction 23% (Biou et al., 1988)
• BROC820101 Retention coefficient in TFA (Browne et al., 1982)
• BROC820102 Retention coefficient in HFBA (Browne et al., 1982)
• BULH740101 Transfer free energy to surface (Bull-Breese, 1974)
• BULH740102 Apparent partial specific volume (Bull-Breese, 1974)

Protein Eng. 1996 Jan;9(1):27-36.

acids as a match.
other.
• The Dayhoff percent accepted mutation (PAM)
family of matrices, which scores amino acid pairs
on the basis of the expected frequency of
substitution of one amino acid for the other during
protein evolution.
Overview

• In the absence of a valid model
derived from first principles, an
empirical approach
seems more appropriate to score
amino acid similarity.
• This approach is based on
the assumption that once the
evolutionary relationship of two
sequences is
established, the residues that did
exchange are similar.
Dayhoff Matrix

Model of Evolution:
“Proteins evolve through a succesion of
independent point mutations, that are
accepted in a population and
subsequently can be observed in the
sequence pool.”
Definition:
The evolutionary distance between two
sequences is the (minimal) number of
point mutations that was necessary to
evolve one sequence into the other
Overview

• The model used here states that
proteins evolve through a succesion of
independent point mutations, that are
accepted in a population and
subsequently can be observed in the
sequence pool.
• We can define an evolutionary
distance between two sequences as
the number of point mutations that was
necessary to evolve one sequence into
the other.
Principle

• M.O. Dayhoff and colleagues
introduced the term "accepted point
mutation" for a mutation that is stably
fixed in the gene pool in the course
of evolution. Thus a measure of
evolutionary distance between two
sequences can be defined:
• A PAM (Percent accepted mutation)
is one accepted point mutation on
the path between two sequences,
per 100 residues.
Overview

Principles of Scoring Matrix Construction
First step: finding “accepted mutations”
In order to identify accepted point
mutations, a complete phylogenetic
tree including all ancestral sequences
has to be constructed. To avoid a
large degree of ambiguities in this
step, Dayhoff and colleagues
restricted their analysis to sequence
families with more than 85% identity.

Identification of accepted point mutations:
•Collection of correct (manual) alignments
• 1300 sequences in 72 families
• closely related in order not to get multiply
changes at the same position
• Construct a complete phylogenetic tree including all
ancestral sequences.
• Dayhoff et al restricted their analysis to
sequence families with more than 85%
identity.
• Tabulate into a 20x20 matrix the amino acid pair
exchanges for each of the observed and inferred
sequences.
Overview

ACGH DBGH ADIJ CBIJ
/ /
/ /
B - C / A - D B - D / A - C
/ /
/ /
ABGH ABIJ
/
I - G /
J - H /
/
/
|
|
|
Overview

Dayhoff’s PAM1 mutation probability matrix (Transition Matrix)
A
Ala
R
Arg
N
Asn
D
Asp
C
Cys
Q
Gln
E
Glu
G
Gly
H
His
I
Ile
A 9867 2 9 10 3 8 17 21 2 6
R 1 9913 1 0 1 10 0 0 10 3
N 4 1 9822 36 0 4 6 6 21 3
D 6 0 42 9859 0 6 53 6 4 1
C 1 1 0 0 9973 0 0 0 1 1
Q 3 9 4 5 0 9876 27 1 23 1
E 10 0 7 56 0 35 9865 4 2 3
G 21 1 12 11 1 3 7 9935 1 0
H 1 8 18 3 1 20 1 0 9912 0
I 2 2 3 1 2 1 2 0 0 9872

PAM1: Transition Matrix
Ala Arg Asn Asp Cys Gln Glu Gly His Ile Leu Lys Met
Phe Pro Ser Thr Trp Tyr Val
A R N D C Q E G H I L K M F P S T W Y V
Ala A 9867 2 9 10 3 8 17 21 2 6 4 2 6 2 22 35 32 0 2 18
Arg R 1 9913 1 0 1 10 0 0 10 3 1 19 4 1 4 6 1 8 0 1
Asn N 4 1 9822 36 0 4 6 6 21 3 1 13 0 1 2 20 9 1 4 1
Asp D 6 0 42 9859 0 6 53 6 4 1 0 3 0 0 1 5 3 0 0 1
Cys C 1 1 0 0 9973 0 0 0 1 1 0 0 0 0 1 5 1 0 3 2
Gln Q 3 9 4 5 0 9876 27 1 23 1 3 6 4 0 6 2 2 0 0 1
Glu E 10 0 7 56 0 35 9865 4 2 3 1 4 1 0 3 4 2 0 1 2
Gly G 21 1 12 11 1 3 7 9935 1 0 1 2 1 1 3 21 3 0 0 5
His H 1 8 18 3 1 20 1 0 9912 0 1 1 0 2 3 1 1 1 4 1
Ile I 2 2 3 1 2 1 2 0 0 9872 9 2 12 7 0 1 7 0 1 33
Leu L 3 1 3 0 0 6 1 1 4 22 9947 2 45 13 3 1 3 4 2 15
Lys K 2 37 25 6 0 12 7 2 2 4 1 9926 20 0 3 8 11 0 1 1
Met M 1 1 0 0 0 2 0 0 0 5 8 4 9874 1 0 1 2 0 0 4
Phe F 1 1 1 0 0 0 0 1 2 8 6 0 4 9946 0 2 1 3 28 0
Pro P 13 5 2 1 1 8 3 2 5 1 2 2 1 1 9926 12 4 0 0 2
Ser S 28 11 34 7 11 4 6 16 2 2 1 7 4 3 17 9840 38 5 2 2
Thr T 22 2 13 4 1 3 2 2 1 11 2 8 6 1 5 32 9871 0 2 9
Trp W 0 2 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 9976 1 0
Tyr Y 1 0 3 0 3 0 1 0 4 1 1 0 0 21 0 1 1 2 9945 1
Val V 13 2 1 1 3 2 2 3 3 57 11 1 17 1 3 2 10 0 2 9901

Numbers of accepted point mutations (x10)
accumulated from closely related
sequences.
Fractional exchanges result when ancestral
sequences are ambiguous: the
probabilities are distributed equally
among all possibilities.
The total number of exchanges tallied was
1,572. Note that 36 exchanges were
never observed.
The Asp-Glu pair had the largest number of
exchanges
PAM1: Transition Matrix

Second step: Frequencies of Occurence
If the properties of amino acids differ and if
they occur with different frequencies, all
statements we can make about the average
properties of sequences will depend on the
frequencies of occurence of the individual
amino acids. These frequencies of
occurence are approximated by the
frequencies of observation. They are the
number of occurences of a given amino acid
divided by the number of amino-acids
observed.
The sum of all is one.

Amino acid frequencies
Second step: Frequencies of Occurence
1978 1991
L 0.085 0.091
A 0.087 0.077
G 0.089 0.074
S 0.070 0.069
V 0.065 0.066
E 0.050 0.062
T 0.058 0.059
K 0.081 0.059
I 0.037 0.053
D 0.047 0.052
R 0.041 0.051
P 0.051 0.051
N 0.040 0.043
Q 0.038 0.041
F 0.040 0.040
Y 0.030 0.032
M 0.015 0.024
H 0.034 0.023
C 0.033 0.020
W 0.010 0.014

Third step: Relative Mutabilities
• To obtain a complete picture of the
mutational process, the amino-acids that
do not mutate must be taken into account
too.
• We need to know: what is the chance, on
average, that a given amino acid will
mutate at all. This is the relative
mutability of the amino acid.
• It is obtained by multiplying the number
of observed changes by the amino acids
frequency of occurence.

Compute amino acid mutability, mj, i.e., the propability
of a given amino acid, j, to be replaced.
Aligned A D A
Sequences A D B
Amino Acids A B D
Observed Changes 1 1 0
Frequency of Occurence 3 1 2
(Total Composition)
Relative Mutability .33 1 0
Overview

1978 1991
A 100 100
C 20 44
D 106 86
E 102 77
F 41 51
G 49 50
H 66 91
I 96 103
K 56 72
L 40 54
M 94 93
N 134 104
P 56 58
Q 93 84
R 65 83
S 120 117
T 97 107
V 74 98
W 18 25
Y 41 50

Fourth step: Mutation Probability Matrix
• With these data the probability that an amino acid in
row i of the matrix will replace the amino acid in
column j can be calculated: it is the mutability of amino
acid j, multiplied by the relative pair exchange
frequency (the pair exchange frequency for ij divided
by the sum of all pair exchange frequencies for amino
acid i).
Mij= The mutation probability matrix gives the
probability, that an amino acid i will replace an amino
acid of type j in a given evolutionary interval, in two
related sequences
ADB
ADA
A D B
A
D
B
i
j

Fifth step: The Evolutionary Distance
• Since the represent the probabilites
for amino acids to remain
conserved, if we scale all cells of our
matrix by a constant factor we can
scale the matrix to reflect a specific
overall probability of change. We
may chose so that the expected
number of changes is 1 %, this
gives the matrix for the evolutionary
distance of 1 PAM.

6. Relatedness Odds
• By comparison, the probability that
that same event is observed by
random chance is simply given by
the frequency of occurence of
amino acid i
• Rij = probability that j replaces i in
related proteins
ran = probability that j replaces I by
chance (eg unrelated proteins)
• Pi
ran = fi = the frequency of
occurance of amino acid i
• Pi

Last step: the log-odds matrix
• Since multiplication is a computationally
expensive process, it is preferrable to add
the logarithms of the matrix elements. This
matrix, the log odds matrix, is the
foundation of quantitative sequence
comparisons under an evolutionary model.
• Since the Dayhoff matrix was taken as the
log to base 10, a value of +1 would mean
that the corresponding pair has been
observed 10 times more frequently than
expected by chance. A value of -0.2 would
mean that the observed pair was observed
1.6 times less frequently than chance
would predict.

• http://www.bio.brandeis.edu/InterpGenes/Proj
ect/align12.htm

A B C D E F G H I K L M N P Q R S T V W Y Z
0.4 0.0 -0.4 0.0 0.0 -0.8 0.2 -0.2 -0.2 -0.2 -0.4 -0.2 0.0 0.2 0.0 -0.4 0.2 0.2 0.0 -1.2 -0.6 0.0 A
0.5 -0.9 0.6 0.4 -1.0 0.1 0.3 -0.4 0.1 -0.7 -0.5 0.4 -0.2 0.3 -0.1 0.1 0.0 -0.4 -1.1 -0.6 0.4 B
2.4 -1.0 -1.0 -0.8 -0.6 -0.6 -0.4 -1.0 -1.2 -1.0 -0.8 -0.6 -1.0 -0.8 0.0 -0.4 -0.4 -1.6 0.0 -1.0 C
0.8 0.6 -1.2 0.2 0.2 -0.4 0.0 -0.8 -0.6 0.4 -0.2 0.4 -0.2 0.0 0.0 -0.4 -1.4 -0.8 0.5 D
0.8 -1.0 0.0 0.2 -0.4 0.0 -0.6 -0.4 0.2 -0.2 0.4 -0.2 0.0 0.0 -0.4 -1.4 -0.8 0.6 E
1.8 -1.0 -0.4 0.2 -1.0 0.4 0.0 -0.8 -1.0 -1.0 -0.8 -0.6 -0.6 -0.2 0.0 1.4 -1.0 F
1.0 -0.4 -0.6 -0.4 -0.8 -0.6 0.0 -0.2 -0.2 -0.6 0.2 0.0 -0.2 -1.4 -1.0 -0.1 G
1.2 -0.4 0.0 -0.4 -0.4 0.4 0.0 0.6 0.4 -0.2 -0.2 -0.4 -0.6 0.0 -0.4 H
1.0 -0.4 0.4 0.4 -0.4 -0.4 -0.4 -0.4 -0.2 0.0 0.8 -1.0 -0.2 -0.4 I
1.0 -0.6 0.0 0.2 -0.2 0.2 0.6 0.0 0.0 -0.4 -0.6 -0.8 0.1 K
1.2 0.8 -0.6 -0.6 -0.4 -0.6 -0.6 -0.4 0.4 -0.4 -0.2 -0.5 L
1.2 -0.4 -0.4 -0.2 0.0 -0.4 -0.2 0.4 -0.8 -0.4 -0.3 M
0.4 -0.2 0.2 0.0 0.2 0.0 -0.4 -0.8 -0.4 0.2 N
1.2 0.0 0.0 0.2 0.0 -0.2 -1.2 -1.0 -0.1 P
0.8 0.2 -0.2 -0.2 -0.4 -1.0 -0.8 0.6 Q
1.2 0.0 -0.2 -0.4 0.4 -0.8 0.6 R
0.4 0.2 -0.2 -0.4 -0.6 -0.1 S
0.6 0.0 -1.0 -0.6 -0.1 T
0.8 -1.2 -0.4 -0.4 V
3.4 0.0 -1.2 W
2.0 -0.8 Y
0.6 Z
PAM 1 Scoring Matrix

• Some of the properties go into the
makeup of PAM matrices are - amino
acid residue size, shape, local
concentrations of electric charge, van
der Waals surface, ability to form salt
bridges, hydrophobic interactions, and
hydrogen bonds.
– These patterns are imposed principally
by natural selection and only secondarily
by the constraints of the genetic code.
– Coming up with one’s own matrix of
weights based on some logical features
may not be very successful because your
logical features may have been over-written
by other more important
considerations.
Overview

• Two aspects of this process cause the
evolutionary distance to be unequal in
general to the number of observed
differences between the sequences:
– First, there is a chance that a certain
residue may have mutated, than reverted,
hiding the effect of the mutation.
– Second, specific residues may have
mutated more than once, thus the number
of point mutations is likely to be larger
than the number of differences between
the two sequences..

Experiment: pam-simulator.pl
• Initialize:
– Generate Random protein (1000 aa)
• Simulate evolution (eg 250 for PAM250)
– Apply PAM1 Transition matrix to each amino
acid
– Use Weighted Random Selection
• Iterate
– Measure difference to orginal protein

Weighted Random Selection
• Ala => Xxx (%)
A
R
N
D
C
Q
E
G
H
I
L
K
M
F
P
S
T
W
Y
V

PAM-Simulator
PAM-simulator
120
100
80
60
40
20
0
0 50 100 150 200 250 300
PAM
%identity

PAM-Simulator
PAM-Simulator
100
90
80
70
60
50
40
30
20
10
0
0 200 400 600 800 1000 1200 1400 1600 1800 2000
PAM
% identity

Some PAM values and their corresponding observed distances
PAM Value Distance(%)
80 50
100 60
200 75
250 85 <- Twilight zone
300 92
(From Doolittle, 1987, Of URFs and ORFs,
University Science Books)
•When the PAM distance value between two distantly related proteins nears the value 250 it
becomes difficult to tell whether the two proteins are homologous, or that they are two at
randomly taken proteins that can be aligned by chance. In that case we speak of the 'twilight
zone'.
•The relation between the observed percentage in distance of two sequences versus PAM
value. Two randomly diverging sequences change in a negatively exponential fashion. After
the insertion of gaps to two random sequences, it can be expected that they will be 80 - 90 %
dissimilar (from Doolittle, 1987 ).

• Creation of a pam series from evolutionary
simulations
• pam2=pam1^2
• pam3=pam1^3
• And so on…
• pam30,60,90,120,250,300
• low pam - closely related sequences
– high scores for identity and low scores for
substitutions - closer to the identity matrix
• high pam - distant sequences
– at pam2000 all information is degenerate except
for cysteins
• pam250 is the most popular and general
– one amino acid in five remains unchanged
(mutability varies among the amino acids)
Overview

Overview
250 PAM evolutionary distance
A R N D C Q E G H I L K M F P
Ala A 13 6 9 9 5 8 9 12 6 8 6 7 7 4 11
Arg R 3 17 4 3 2 5 3 2 6 3 2 9 4 1 4
Asn N 4 4 6 7 2 5 6 4 6 3 2 5 3 2 4
Asp D 5 4 8 11 1 7 10 5 6 3 2 5 3 1 4
Cys C 2 1 1 1 52 1 1 2 2 2 1 1 1 1 2
Gln Q 3 5 5 6 1 10 7 3 7 2 3 5 3 1 4
Glu E 5 4 7 11 1 9 12 5 6 3 2 5 3 1 4
Gly G 12 5 10 10 4 7 9 27 5 5 4 6 5 3 8
His H 2 5 5 4 2 7 4 2 15 2 2 3 2 2 3
Ile I 3 2 2 2 2 2 2 2 2 10 6 2 6 5 2
Leu L 6 4 4 3 2 6 4 3 5 15 34 4 20 13 5
Lys K 6 18 10 8 2 10 8 5 8 5 4 24 9 2 6
Met M 1 1 1 1 0 1 1 1 1 2 3 2 6 2 1
Phe F 2 1 2 1 1 1 1 1 3 5 6 1 4 32 1
Pro P 7 5 5 4 3 5 4 5 5 3 3 4 3 2 20
Ser S 9 6 8 7 7 6 7 9 6 5 4 7 5 3 9
Thr T 8 5 6 6 4 5 5 6 4 6 4 6 5 3 6
Trp W 0 2 0 0 0 0 0 0 1 0 1 0 0 1 0
Tyr Y 1 1 2 1 3 1 1 1 3 2 2 1 2 15 1
Val V 7 4 4 4 4 4 4 4 5 4 15 10 4 10 5
[column on left represents the replacement amino acid]
Mutation probability matrix for the evolutionary distance of 250 PAMs. To
simplify the appearance, the elements are shown multiplied by 100.
In comparing two sequences of average amino acid frequency at this
evolutionary distance, there is a 13% probability that a position
containing Ala in the first sequence will contain Ala in the second.
There is a 3% chance that it will contain Arg, and so forth.

A brief history of time (BYA)
Origin of
life
Origin of
eukaryotes insects
Fungi/animal
Plant/animal
Earliest
fossils
4 3 2 1 0
BYA

Margaret Dayhoff’s 34 protein superfamilies
Protein PAMs per 100 million years
Ig kappa chain 37
Kappa casein 33
Lactalbumin 27
Hemoglobin a 12
Myoglobin 8.9
Insulin 4.4
Histone H4 0.10
Ubiquitin 0.00

 Many sequences depart from average
composition.
 Rare replacements were observed too
infrequently to resolve relative
probabilities accurately (for 36 pairs no
replacements were observed!).
 Errors in 1PAM are magnified in the
extrapolation to 250PAM.
 Distantly related sequences usually
have islands (blocks) of conserved
residues. This implies that replacement
is not equally probable over entire
sequence.
Sources of error

acids as a match.
other.
• The Dayhoff percent accepted mutation (PAM)
family of matrices, which scores amino acid pairs
on the basis of the expected frequency of
substitution of one amino acid for the other during
protein evolution.
• The blocks substitution matrix (BLOSUM) amino
acid substitution tables, which scores amino acid
pairs based on the frequency of amino acid
substitutions in aligned sequence motifs called
blocks which are found in protein families
Overview

BLOSUM: Blocks Substitution Matrix
• Henikoff & Henikoff (Henikoff, S. &
Henikoff J.G. (1992) PNAS 89:10915-
10919)
• asking about the relatedness of distantly
related amino acid sequences ?
• They use blocks of sequence fragments
from different protein families which can
be aligned without the introduction of
gaps. These sequence blocks correspond
to the more highly conserved regions.

BLOSUM (BLOck – SUM) scoring
S = 3 sequences
W = 6 aa
N= (W*S*(S-1))/2 = 18 pairs
DDNAAV
DNAVDD
NNVAVV
Block = ungapped alignent
Eg. Amino Acids D N V A
a b c d e f
1
2
3

A. Observed pairs
a b c d e f
DDNAAV
DNAVDD
NNVAVV
1
2
3
D N A V
D
N
A
V
1
4
1
3
1
1
1
1
4 1
f fij
D N A V
D
N
A
V
.056
.222
.056
.167
.056
.056
.056
.056
.222 .056
gij
/18
Relative frequency table
Probability of obtaining a pair
if randomly choosing pairs
from block

B. Expected pairs A
DDDDD
NNNN
AAAA
VVVVV
DDNAAV
DNAVDD
NNVAVV
Pi
5/18
4/18
4/18
5/18
P{Draw DN pair}= P{Draw D, then N or Draw M, then D}
P{Draw DN pair}= PDPN + PNPD = 2 * (5/18)*(4/18) = .123
D N A V
D
N
A
V
.077
.123
.154
.123
.049
.123
.099
.049
.123 .049
eRandom rel. frequency table ij
Probability of obtaining a pair of
each amino acid drawn
independently from block

C. Summary (A/B)
sij = log2 gij/eij
(sij) is basic BLOSUM score matrix
Notes:
• Observed pairs in blocks contain information about
relationships at all levels of evolutionary distance
simultaneously (Cf: Dayhoffs’s close relationships)
• Actual algorithm generates observed + expected pair
distributions by accumalution over a set of approx. 2000
ungapped blocks of varrying with (w) + depth (s)

• blosum30,35,40,45,50,55,60,62,65,70,75,80,85,90
• transition frequencies observed directly by identifying
blocks that are at least
– 45% identical (BLOSUM45)
– 50% identical (BLOSUM50)
– 62% identical (BLOSUM62) etc.
• No extrapolation made
• High blosum - closely related sequences
• Low blosum - distant sequences
• blosum45  pam250
• blosum62  pam160
• blosum62 is the most popular matrix
The BLOSUM Series

• Church of the Flying Spaghetti Monster
• http://www.venganza.org/about/open-letter

• Which matrix should I use?
– Matrices derived from observed substitution data
(e.g. the Dayhoff or BLOSUM matrices) are
superior to identity, genetic code or physical
property matrices.
– Schwartz and Dayhoff recommended a mutation
data matrix for the distance of 250 PAMs as a
result of a study using a dynamic programming
procedure to compare a variety of proteins known
to be distantly related.
• The 250 PAM matrix was selected since in Monte
Carlo studies matrices reflecting this evolutionary
distance gave a consistently higher significance
score than other matrices in the range 0.750 PAM.
The matrix also gave better scores when compared
to the genetic code matrix and identity scoring.
Overview

Which matrix should I use?
• When comparing sequences that were not
known in advance to be related, for
example when database scanning:
– default scoring matrix used is the
BLOSUM62 matrix
– if one is restricted to using
only PAM scoring matrices, then
the PAM120 is recommended for
general protein similarity searches
• When using a local alignment method,
Altschul suggests that three matrices
should ideally be used: PAM40, PAM120
and PAM250, the lower PAM matrices will
tend to find short alignments of highly
similar sequences, while higher PAM
matrices will find longer, weaker local
alignments.

Rat versus
mouse RBP
Rat versus
bacterial
lipocalin

– Henikoff and Henikoff have compared the
BLOSUM matrices to PAM by evaluating how
effectively the matrices can detect known members
of a protein family from a database when searching
with the ungapped local alignment program
BLAST. They conclude that overall the BLOSUM
62 matrix is the most effective.
• However, all the substitution matrices investigated
perform better than BLOSUM 62 for a proportion of
the families. This suggests that no single matrix is
the complete answer for all sequence comparisons.
• It is probably best to compliment the BLOSUM 62
matrix with comparisons using 250 PAMS, and
Overington structurally derived matrices.
– It seems likely that as more protein three
dimensional structures are determined, substitution
tables derived from structure comparison will give
the most reliable data.
Overview

Dotplots
• What is it ?
– Graphical representation using two orthogonal
axes and “dots” for regions of similarity.
– In a bioinformatics context two sequence are
used on the axes and dots are plotted when a
given treshold is met in a given window.
• Dot-plotting is the best way to see all of the
structures in common between two
sequences or to visualize all of the repeated
or inverted repeated structures in one
sequence

Dot Plot References
Gibbs, A. J. & McIntyre, G. A. (1970).
The diagram method for comparing sequences. its use with
amino acid and nucleotide sequences.
Eur. J. Biochem. 16, 1-11.
Staden, R. (1982).
An interactive graphics program for comparing and aligning
nucleic-acid and amino-acid sequences.
Nucl. Acid. Res. 10 (9), 2951-2961.

Visual Alignments (Dot Plots)
• Matrix
– Rows: Characters in one sequence
– Columns: Characters in second sequence
• Filling
– Loop through each row; if character in row, col match, fill
in the cell
– Continue until all cells have been examined

Dotplot-simulator.pl
print " $seq1n";
for(my $teller=0;$teller<=$seq2_length;$teller++){
print substr($seq2,$teller,1);
$w2=substr($seq2,$teller,$window);
for(my $teller2=0;$teller2<=$seq_length;$teller2++){
$w1=substr($seq1,$teller2,$window);
if($w1 eq $w2){print "*";}else{print " ";}
}
print"n";
}

Overview
Window size = 1, stringency 100%

Noise in Dot Plots
• Nucleic Acids (DNA, RNA)
– 1 out of 4 bases matches at random
• Stringency
– Window size is considered
– Percentage of bases matching in the window is
set as threshold

Reduction of Dot Plot Noise
Self alignment of ACCTGAGCTCACCTGAGTTA

Dotplot-simulator.pl
Example: ZK822 Genomic and cDNA
Gene prediction:
How many exons ?
Confirm donor and aceptor sites ?
Remember to check the reverse complement !

• Regions of similarity appear
as diagonal runs of dots
• Reverse diagonals
(perpendicular to diagonal)
indicate inversions
• Reverse diagonals crossing
diagonals (Xs) indicate
palindromes
• A gap is introduced by each
vertical or horizontal skip
Overview

• Window size changes with goal
of analysis
– size of average exon
– size of average protein structural
element
– size of gene promoter
– size of enzyme active site
Overview

Rules of thumb
 Don't get too many points, about 3-
5 times the length of the sequence
is about right (1-2%)
 Window size about 20 for distant
proteins 12 for nucleic acid
 Check sequence vs. itself
 Check sequence vs. sequence
 Anticipate results
(e.g. “in-house” sequence vs genomic,
question)
Overview

Available Dot Plot Programs
Dotlet (Java Applet)
http://www.isrec.isb-sib.
ch/java/dotlet/Dotlet.
html

Dotter (http://www.cgr.ki.se/cgr/groups/sonnhammer/Dotter.html)

EMBOSS DotMatcher, DotPath,DotUp

Weblems
• W3.1: Why does 2 PAM, i.e. 1 PAM multiplied with itself,
not correspond to exactly 2% of the amino acids having
mutated, but a little less than 2% ? Or, in other words, why
does a 250 PAM matrix not correspond to 250% accepted
mutations ?
• W3.2: Is it biologically plausible that the C-C and W-W
entries in the scoring matrices are the most prominent ?
Which entries (or groups of entries) are the least prominent ?
• W3.3: What is OMIM ? How many entries are there ? What
percentage of OMIM listed diseases has no known (gene)
cause ?
• W3.4: Pick one disease mapped to chromosome Y from
OMIM where only a mapping region is known. How many
candidate genes can you find in the locus using ENSEMBL ?
Can you link ontology terms for the candidates to the disease
phenotype ?

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