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Evolution and Scoring Rules
Example Score = 5 x (# matches) + (-4) x (# mismatches) +
+ (-7) x (total length of all gaps)
Example Score = 5 x (# matches) + (-4) x (# mismatches) +
+ (-5) x (# gap openings) + (-2) x (total length of all gaps)
![Page 2: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/2.jpg)
![Page 3: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/3.jpg)
![Page 4: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/4.jpg)
Scoring Matrices
![Page 5: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/5.jpg)
Scoring Rules vs. Scoring Matrices Nucleotide vs. Amino Acid Sequence The choice of a scoring rule can strongly
influence the outcome of sequence analysis Scoring matrices implicitly represent a
particular theory of evolution Elements of the matrices specify the
similarity of one residue to another
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DNA: A T G C
1:1
RNA: A U G C
3:1
Protein: 20 amino acids
Transcription
Translation
Replication
Translation - Protein Synthesis: Every 3 nucleotides (codon) are translated into one amino acid
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Nucleotide sequence determines the amino acid sequence
![Page 8: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/8.jpg)
Translation - Protein Synthesis
5’ -> 3’ : N-term -> C-term RNA Protein
![Page 9: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/9.jpg)
![Page 10: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/10.jpg)
![Page 11: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/11.jpg)
Log Likelihoods used as Scoring Matrices:
PAM - % Accepted Mutations:1500 changes in 71 groups w/ > 85%
similarity
BLOSUM – Blocks Substitution Matrix:2000 “blocks” from 500 families
![Page 12: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/12.jpg)
Log Likelihoods used as Scoring Matrices:
BLOSUM
ji
ijij pp
pS 2log2
![Page 13: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/13.jpg)
Likelihood Ratio for Aligning a Single Pair of Residues
•Above: the probability that two residues are aligned by evolutionary descent
•Below: the probability that they are aligned by chance
•Pi, Pj are frequencies of residue i and j in all protein sequences (abundance)
ji
ijij pp
p
ji
jiS log
chance)by | withalignedPr(
ancestry)common | withalignedPr(log
![Page 14: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/14.jpg)
Likelihood Ratio of Aligning Two Sequences
tjsiij
ji
ij
ji
ij Spp
p
pp
p
ji
ji
,
loglog
chance)by | withalignedPr(
ancestry)common | withalignedPr(log
)chanceby |alignmentPr(
)ancestrycommon |alignmentPr(log
alignment of ratiolik log
![Page 15: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/15.jpg)
The alignment score of aligning two sequences is the log likelihood ratio of the alignment under two models Common ancestry By chance
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PAM and BLOSUM matrices are all log likelihood matrices
More specificly: An alignment that scores 6 means
that the alignment by common ancestry is 2^(6/2)=8 times as likely as expected by chance.
ji
ijij pp
pS 2log2
![Page 17: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/17.jpg)
BLOSUM matrices for Protein
S. Henikoff and J. Henikoff (1992). “Amino acid substitution matrices from protein blocks”. PNAS 89: 10915-10919
Training Data: ~2000 conserved blocks from BLOCKS database. Ungapped, aligned protein segments. Each block represents a conserved region of a protein family
![Page 18: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/18.jpg)
Constructing BLOSUM Matrices of Specific Similarities
Sets of sequences have widely varying similarity. Sequences with above a threshold similarity are clustered.
If clustering threshold is 62%, final matrix is BLOSUM62
![Page 19: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/19.jpg)
A toy example of constructing a BLOSUM matrix from 4
training sequences
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Constructing a BLOSUM matr.1. Counting mutations
![Page 21: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/21.jpg)
Constructing a BLOSUM matr.2. Tallying mutation frequencies
![Page 22: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/22.jpg)
Constructing a BLOSUM matr.3. Matrix of mutation probs.
![Page 23: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/23.jpg)
4. Calculate abundance of each residue (Marginal prob)
![Page 24: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/24.jpg)
5. Obtaining a BLOSUM matrix
![Page 25: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/25.jpg)
Constructing the real BLOSUM62 Matrix
![Page 26: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/26.jpg)
1.2.3.Mutation Frequency Table
1000ijP
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4. Calculate Amino Acid Abundance
acid aminoeach of likelihood marginal the: ip
![Page 28: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/28.jpg)
5. Obtaining BLOSUM62 Matrix
ji
ijij pp
pS 2log2
![Page 29: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/29.jpg)
![Page 30: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/30.jpg)
PAM Matrices (Point Accepted Mutations)
Mutations accepted by natural selection
![Page 31: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/31.jpg)
PAM Matrices Accepted Point Mutation Atlas of Protein Sequence and Structure,
Suppl 3, 1978, M.O. Dayhoff.
ed. National Biomedical Research Foundation, 1
Based on evolutionary principles
![Page 32: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/32.jpg)
Constructing PAM Matrix: Training Data
![Page 33: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/33.jpg)
PAM: Phylogenetic Tree
![Page 34: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/34.jpg)
PAM: Accepted Point Mutation
![Page 35: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/35.jpg)
Mutability
![Page 36: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/36.jpg)
Total Mutation Rate
is the total mutation rate of all amino acids
![Page 37: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/37.jpg)
Normalize Total Mutation Rate
![Page 38: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/38.jpg)
Mutation Probability Matrix Normalized
Such that the Total Mutation Rate is 1%
![Page 39: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/39.jpg)
Mutation Probability Matrix (transposed) M*10000
![Page 40: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/40.jpg)
-- PAM1 mutation prob. matr. --PAM2 Mutation Probability Matrix?
-- Mutations that happen in twice the evolution period of that for a PAM1
)1(M)2(M
![Page 41: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/41.jpg)
PAM Matrix: Assumptions
![Page 42: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/42.jpg)
In two PAM1 periods: {AR} = {AA and AR} or {AN and NR} or {AD and DR} or … or {AV and VR}
![Page 43: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/43.jpg)
period) 2ndin RPr(Dperiod)1st in DPr(A
period) 2ndin RPr(Nperiod)1st in NPr(A
period) 2ndin RPr(Aperiod)1st in A Pr(A
periods) 2in RAPr(
DRADNRANARAAAR PPPPPPP )2(
Entries in a PAM-2 Mut. Prob. Matr.
![Page 44: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/44.jpg)
PAM-k Mutation Prob. Matrix
KK MM
MMM
}{ )1()(
)1()1()2(
![Page 45: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/45.jpg)
PAM-1 log likelihood matrix
ji
ijij pp
PS
)1(
10log10
![Page 46: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/46.jpg)
PAM-k log likelihood matrix
ji
kij
ijk
pp
PS
)(
10)( log10
![Page 47: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/47.jpg)
PAM-250
![Page 48: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/48.jpg)
PAM60—60%, PAM80—50%, PAM120—40% PAM-250 matrix provides a better
scoring alignment than lower-numbered PAM matrices for proteins of 14-27% similarity
![Page 49: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/49.jpg)
Sources of Error in PAM
![Page 50: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/50.jpg)
Comparing Scoring MatrixPAM
Based on extrapolation of a small evol. Period
Track evolutionary origins Homologous seq.s during
evolution
BLOSUM Based on a range of
evol. Periods Conserved blocks Find conserved
domains
![Page 51: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/51.jpg)
Choice of Scoring Matrix
![Page 52: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/52.jpg)
Global Alignment with Affine Gaps
Complex Dynamic Programming
![Page 53: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/53.jpg)
Problem w/ Independent Gap Penalties The occurrence of x consecutive
deletions/insertions is more likely than the occurrence of x isolated mutations
We should penalize x long gap less than x
times of the penalty for one gap
![Page 54: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/54.jpg)
Affine Gap Penalty
w2 is the penalty for each gap w1 is the _extra_ penalty for the
1st gap
![Page 55: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/55.jpg)
Scoring Rule not Additive! We need to know if the current gap
is a new gap or the continuation of an existing gap
Use three Dynamic Programming matrices to keep track of the previous step
![Page 56: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/56.jpg)
S1 is the vertical sequenceS2 is the horizontal sequence (From Diagonal) a(i,j): current position
is a match (From Left) b(i,j): current position is a
gap in S1 (From Above) c(i,j): current position is a
gap in S2Filling the next element in each matrix
depends on the previous step, which is stored in the three matrices.
![Page 57: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/57.jpg)
![Page 58: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/58.jpg)
Last step a match
a gap in S2
a gap in S1
new gap in S2
a continued gap in S2
a gap in S2 following a gap in S1
![Page 59: Evolution and Scoring Rules Example Score = 5 x (# matches) + (-4) x (# mismatches) + + (-7) x (total length of all gaps) Example Score = 5 x (# matches)](https://reader035.vdocument.in/reader035/viewer/2022062518/56649e795503460f94b78847/html5/thumbnails/59.jpg)
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Decisions in Seq. Alignment Local or global alignment? Which program to use Type of scoring matrix Value of gap penalty
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Aij*10
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PAM-k log-likelihood matrix
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