Last lecture summary
Sequence alignment
• What is sequence alignment
• Three flavors of sequence alignment
• Point mutations, indels
Sequences
• 'Central dogma of bioinformatics'
• Sequences diverge
• Conserved residues
• The variation between sequences – changes occurred
during evolution in the form of substitutions (mutations)
and/or indels.
New stuff
Homology
• During the time period, the molecular sequences undergo
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random changes, some of which are selected during the
process of evolution.
Selected sequences accumulate mutations, they diverge
over time.
Two sequences are homologous when they are
descended from a common ancestor sequence.
Traces of evolution may still remain in certain portions of
the sequences to allow identification of the common
ancestry.
Residues performing key roles are preserved by natural
selection, less crucial residues mutate more frequently.
Orhology, paralogy I
• Orthologs – homologous proteins from different species
that possess the same function (e.g. corresponding
kinases in signal transduction pathway in humans and
mice)
• Paralogs – homologous proteins that have different
function in the same species (e.g. two kinases in different
signal transduction pathways of humans)
However, these terms are controversially discussed:
Jensen RA. Orthologs and paralogs - we need to get it right. Genome Biol. 2001;2(8), PMID: 11532207 and references therein
Orthology, paralogy II
• Orthologs – genes separated by the
event of speciation
• Sequences are direct descendants of a
common ancestor.
• Most likely have similar domain structure, 3D structure and
biological function.
• Paralogs – genes separated by the event of genetic
duplication
• Gene duplication: An extra copy of a gene. Gene duplication is a
key mechanism in evolution. Once a gene is duplicated, the
identical genes can undergo changes and diverge to create two
different genes.
http://www.globalchange.umich.edu/globalchange1/current/lectures/speciation/speciation.html
Gene duplication
1. Unequal cross-over
2. Entire chromosome is replicated twice
• This error will result in one of the daughter cells having an extra
copy of the chromosome. If this cell fuses with another cell during
reproduction, it may or may not result in a viable zygote.
3. Retrotransposition
• Sequences of DNA are copied to RNA and then back to DNA
instead of being translated into proteins resulting in extra copies of
DNA being present within cell.
Unequal cross-over
Homologous chromosomes are
misaligned during meiosis.
The probability of misalignment
is a function of the degree of
sharing the repetitive elements.
• Comparing sequences through alignment – patterns of
conservation and variation can be identified.
• 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.
• Identifying the evolutionary relationships between
sequences helps to characterize the function of unknown
sequences.
• Protein sequence comparison can identify homologous
sequences from common ancestor 1 billions year ago
(BYA). DNA sequences typically only 600 MYA.
The outline of sequence alignment
1. How to recognize which sequence alignment is better.
• Scoring system
• Scoring DNA alignment
• Scoring protein alignment – substitution matrices (PAM, BLOSUM)
2. How to perform sequence alignment.
• Algorithm
• Dot plot, dynamic programming, heuristic algorithms (BLAST)
Scoring sequence alignment
Scoring DNA alignment
Substitution matrix
• DNA and protein sequences can be aligned so that the
number of identically matching pairs is maximized.
A T T G - - - T
A – - G A C A T
• 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
Identity
matrix
T
C
A
1
T
0
1
C
0
0
1
G
0
0
0
G
1
Gaps or no gaps
Gapped DNA alignment (1)
• Match score:
• Mismatch score:
• Gap penalty:
+1
+0
–1
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ACGTCTGATACGCCGTATAGTCTATCT
||||| |||
|| ||||||||
----CTGATTCGC---ATCGTCTATCT
• Matches: 18 × (+1)
• Mismatches: 2 × 0
• Gaps: 7 × (– 1)
Score = +11
Length penalties
• We want to find alignments that are evolutionarily likely.
• Which of the following alignments seems more likely to
you?
ACGTCTGATACGCCGTATAGTCTATCT
ACGTCTGAT-------ATAGTCTATCT

ACGTCTGATACGCCGTATAGTCTATCT
AC-T-TGA--CG-CGT-TA-TCTATCT 
• We can achieve this by penalizing more for a new gap,
than for extending an existing gap
Gapped DNA alignment (2)
• Match/mismatch score:
• Origination/length penalty:
+1/+0
–2/–1
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ACGTCTGATACGCCGTATAGTCTATCT
||||| |||
|| ||||||||
----CTGATTCGC---ATCGTCTATCT
• Matches: 18 × (+1)
• Mismatches: 2 × 0
• Origination: 2 × (–2)
• Length: 7 × (–1)
Score = +7
Typical DNA Alignment Scoring
• Frequencies of mutations are equal for all bases:
• match score +5
• mismatch score -4
• gap penalty (usually a parameter)
• opening -10
• extending -2
Scoring protein alignment
Scoring protein alignment
• identity matrix: NAs – OK, proteins – not enough
• AAs are not exchanged with the same probability as can
be conceived theoretically.
• For example, substitution of aspartic acids D by glutamic
acid E is frequently observed. And change from aspartic
acid to tryptophan W is very rare.
D
E
W
Scoring protein alignment
• Why is that?
1. Triplet-based genetic code
GAT (D) → GAA (E), GAT (D) → TGG (W)
2. Both D and E have similar properties, but D and W differ
considerably. D is hydrophilic, W is hydrophobic, D → W
mutation can greatly alter 3D structure and
consequently function.
Genetic code
http://www.doctortee.com/dsu/tiftickjian/bio100/gene-expression.html
Substitution matrices for proteins
• Substitution (score) matrices show scores for amino acids
substitution. Higher score means higher probability of
mutation.
• Conservative substitutions – conserve the physical and
chemical properties of the amino acids, limit
structural/functional disruption
• Substitution matrices should reflect:
• Physicochemical properties of amino acids.
• Different frequencies of individual amino acids occuring in proteins.
• Interchangeability of the genetic code.
Protein substitution matrices – PAM
PAM matrices I
• How to assign scores? Let’s get nature – evolution –
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involved!
If you choose set of proteins with very similar sequences,
you can do alignment manually.
Also, if sequences in your set are similar, then there is a
high probability that amino acid difference are due to
single mutation.
From the frequencies of mutations in the set of similar
protein sequences probabilities of substitutions can be
derived.
This is exactly the approach take by Margaret Dayhoff in
1978 to construct PAM (Accepted Point Mutation)
matrices.
Dayhoff, M.O., Schwartz, R. and Orcutt, B.C. (1978). "A model of Evolutionary Change in Proteins". Atlas of protein sequence and structure
(volume 5, supplement 3 ed.). Nat. Biomed. Res. Found.. pp. 345–358.
PAM matrices II
• 71 gapless alignments of sequences with at least 85%
identity. 1572 substitutions were found.
• These mutations do not significantly alter the protein
function. Hence they are called accepted mutations
(accepted by natural selection).
• Probabilities that any one amino acid would mutate into
any other were calculated.
• From these probabilities, scores were derived.
Excellent discussion of the derivation and use of PAM matrices: George DG, Barker WC, Hunt LT. Mutation data matrix and its
uses. Methods Enzymol. 1990,183:333-51. PMID: 2314281.
PAM matrices III
• Dayhoff’s definition of accepted mutation was thus based
on empirically observed amino acids substitutions.
• The used unit is a PAM. Two sequences are 1 PAM apart
if they have 99% identical residues. i.e. from 100 residues,
one is mutated.
• PAM1 matrix represents probabilities of point mutations
over certain evolutionary time.
• in Drosophila 1 PAM corresponds to ~2.62 MYA
• in Human 1 PAM corresponds to ~4.58 MYA
Higher PAM matrices
• What to do if I want get probabilities over much longer
evolutionary time?
• Dayhoff proposed a model of evolution that is a Markov
process.
• A case of Markov process is a linear dynamical system.
Linear dynamical system I
A new species of frog has been introduced into an area where it
has too few natural predators. In an attempt to restore the
ecological balance, a team of scientists is considering
introducing a species of bird which feeds on this frog.
Experimental data suggests that the population of frogs and
birds from one year to the next can be modeled by linear
relationships. Specifically, it has been found that if the quantities
Fk and Bk represent the populations of the frogs and birds in the
kth year, then
𝐵𝑘+1 = 0.6𝐵𝑘 + 0.4𝐹𝑘
𝐹𝑘+1 = −0.35𝐵𝑘 + 1.4𝐹𝑘
The question is this: in the long run, will the introduction of the
birds reduce or eliminate the frog population growth?
Linear dynamical system II
𝐹𝑘+1
0.6
0.4 𝐹𝑘
=
𝐵𝑘+1
−0.35 1.4 𝐵𝑘
• So this system evolves in time according to x(k+1) = Ax(k).
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Such a system is called discrete linear dynamical
system, matrix A is called transition matrix.
If we need to know the state of the system in time k = 50,
we have to compute x(50) = A50 x(0).
And the same is true for Dayhoff’s model of evolution.
If we need to obtain probability matrices for higher
percentage of accepted mutations (i.e. covering longer
evolutionary time), we do matrix powers.
Let’s say we want PAM120. We do PAM1120.