1. Sequence evolution and homology identification
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2. Nucleotide substitution
- usually too slow to monitor directly…
spontaneous mutation rates? p
for mammalian nuclear DNA (regions not under functional constraint)
~ 4 x nt sub per site per year
... much higher for viruses
eg to nt sub per site per generation
… so use comparative analysis of 2 sequences which
share a common ancestor
determine number and nature of nt substitutions that have
occurred (ie measure degree of divergence)
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3. Potential pitfalls 1. Are all evolutionary changes being monitored?
- if closely-related, high probability only one change at any
given site…
but if distant, may have been multiple substitutions (“hits”)
at a site
- can use algorithms to correct for this
2. If indels between two sequences, can they be aligned
with confidence?
- algorithms with gap penalties
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4. 13 substitutions occurred but only 3 discovered by sequence comparison
Ancestral sequence
13 substitutions occurred but only 3 discovered by sequence comparison
Present day sequences
Fig. 3.6
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5. Multiple hits Page & Holmes Fig. 5.9
Homoplasy: same nt, but not directly inherited from ancestral sequence
(If comparing long stretches, highly unlikely they would have converged to the same sequence)
Page & Holmes Fig. 5.9
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6. Uncertainty in codon substitution
Pathway I: CCC(Pro)CCA(Pro) CAA(Gln)
Pathway II: CCC(Pro)CAC(His) CAA(Gln)
Is one pathway more likely than another?
p.82
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7. The purpose of sequence alignment
Identification of sequence homology and homologous sites
Homology: similarity that is the result of inheritance from a common ancestor (identification and analysis of homologies is central to phylogenetics).
An Alignment is an hypothesis of positional homology between bases/Amino Acids.
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8. Normal and Thalassemia HBb
----|----|----|----|----|----|----|----|----|----|----|----|--
Normal AUGGUGCACCUGACUCCUGAGGAGAAGUCUGCCGUUACUGCCCUGUGGGGCAAGGUGAACGU
Thalass. AUGGUGCACCUGACUCCUGAGGAGAAGUCUGCCGUUACUGCCCUGUGGGGCAAGGUGAACGU
**************************************************************
--|----|----|----|----|----|----|----|----|----|----|----|----
Normal GGAUGAAGUUGGUGGU-GAGGCCCUGGGCAGGUUGGUAUCAAGGUUACAAGACAGG......
Thalass. GGAUGAAGUUGGUGGUUGAGGCCCUGGGCAGGUUGGUAUCAAGGUUACAAGACAGG......
**************** ***************************************
Are the two genes homologous?
What evolutionary change can you infer from the alignment?
What is the consequence of the evolutionary change?
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9. Janeka, JE et al. 2007 Science 318:792
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10. What is an optimal alignment?
Alignment1: Favorite Favourite
Alignment2: ---Favorite Favourite--
Alignment3: Favorite Favourite
Alignment4: Favo-rite Favourite
An optimal alignment
One with maximum number of matches and minimum number of mismatches and gaps
Operational definition: one with highest alignment score given a particular scoring scheme (e.g., match: 2, mismatch: -1, gap: -2)
Which of the 4 alignments above is the optimal alignment?
Changing the scoring scheme may change the optimal alignment
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11. Importance of scoring schemes
Two alternative alignments: Alignment 1: ACCCAGGGCTTA ACCCGGGCTTAG Alignment 2: ACCCAGGGCTTA ACCC-GGGCTTAG
Scoring scheme 1: Match: 2, mismatch: 0, gap: -5
Scoring scheme 2: Match: 2, mismatch: -1, gap: -1
Which of the two is the optimal alignment according to scoring scheme 1? Which according to scoring scheme 2?
Importance of biological input
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12. Dynamic Programming Constant gap penalty: Scoring scheme:
Match (M): 2 Mismatch (MM): Gap (G): -2
For each cell, compute three values:
Upleft value + IF(Match, M, MM) Left value + G Up value + G
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13. Alignment with secondary structure
Sequences:
Seq1: CACGACCAATCTCGTG Seq2: CACGGCCAATCCGTG
Seq1: CACGA ||||| GUGCU
Seq2: CACGA ||||| GUGCU
Seq2: CACGG ||||| GUGCC
CCAAUC
Deletion
CCAAU
Missing link
CCAAU
Correlated substitution
Conventional alignment:
Seq1: CACGACCAATCTCGTG
Seq2: CACGGCCAATC-CGTG
Correct alignment:
Seq1: CACGACCAATCTCGTG
Seq2: CACGGCCAAT-CCGTG
Hickson et al., 2000; Kjer, 1995; Notredame et al., 1997
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14. Multiple Alignment: Guide Tree
ATTCCAAG...
ATTTCCAAG...
ATTCCCAAG...
ATCGGAAG...
ATCCGAAG...
ATCCAAAG...
AATTCCAAG...
AATTTCCAAG...
AATTCCCAAG...
AAGTCCAAG...
AAGTCAAG...
ATT-CC-AAG...
ATTTCC-AAG...
ATTCCC-AAG...
AT--CGGAAG...
AT-CCG-AAG...
AT-CCA-AAG...
AATTCC-AAG...
AATTTCCAAG...
AATTCCCAAG...
AAGTCC-AAG...
AAGTC--AAG...
Seq1
Seq2
Seq3
Seq4
Seq5
Seq6
Seq7
Seq8
Seq9
Seq10
Seq11
Seq12
Seq13
Seq14
Seq15
Seq16
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15. Aligned Sequences
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16. CLUSTAL * : . Symbols used?
CLUSTAL W (1.81) Multiple Sequence Alignments
Sequence 1: ArabidopsisAAG aa
Sequence 2: ArabidopsisAAC aa
Sequence 3: yeast aa
ArabAAG FIVDEADLLLDLGFRRDVEKIIDCLPRQR QSLLFSATIPKEVRRVS-QLVLKR 539
ArabAAC FIVDEADLLLDLGFKRDVEKIIDCLPRQR QSLLFSATIPKEVRRVS-QLVLKR 586
yeast VLDEADRLLEIGFRDDLETISGILNEKNSKSADNIKTLLFSATLDDKVQKLANNIMNKK 323
::**** **::**: *:*.* . * .: ::******: .:*:::: ::: *: : .
Symbols used? *
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17. Binomial distribution
Toss a fair coin once. What is the probability of having a head (H)?
Toss a fair coin twice. What is the probability of having HH, HT or TT (T for tail)? ( )2
Toss a fair coin 10 times and record the outcome, e.g., HTHHTHHTTT. What is the expected number of HH occurring in the string? E = n  p = (10 – 2 +1)0.52
What is the probability of 0, 1, 2, ..., 9 matches? (p + q)n = ( )9
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18. Basic stats in string matching
Given PA, PC, PG, PT in a target (database) sequence, the probability of a query sequence, say, ATTGCC, having a perfect match of the target sequence is: prob = PA (PC)2 PG (PT)2
Let M be the target sequence length and N be the query sequence length, the “matching operation” can be performed (M – N +1) times, e.g., Query: ATG Target CGATTGCCCG
The probability distribution of the number of matches follows a binomial distribution with p = prob and n = (M – N +1)
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19. Basic stats in string matching
Computation involving a binomial distribution requires taking the factorial of n. When n is large (e.g., > 1000), this becomes impractical or impossible for today’s computers.
Approximation is therefore necessary.
When np > 50, the binomial distribution can be approximated by the normal distribution with the mean = np and variance = npq
When np < 1 and n is very large (which implies that p is very small given np < 1), binomial distribution can be approximated by the Poisson distribution with mean and variance equal to np (i.e.,  = 2 = np).
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20. From Binomial to Poisson
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21. Matching two sequences without gap
Assuming equal nucleotide frequencies, the probability of a nucleotide site in the query sequence matching a site in the target sequence is p = 0.25.
The probability of finding an exact match of L letters is a = pL = 0.25L = 2-2L = 2-S, where S is called the bit score in BLAST.
M: query length; N: target length
The query can start at (M – L +1) positions and the target can start at (N – L +1) positions. These two values are called effective lengths of the two sequences and designated m and n, respectively. They are shorter than M and N, respectively.
The expected number of matches with length L is mn2-S, which is called e-value in ungapped BLAST.
S is calculated differently in the gapped BLAST
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22. Expected number of matches: No gap
T: GGTTACACGAGTGCTG |||||||||||||||| Q:CTGAGGTTACACGAGTGCTGCTGA
M = 24, L = 16 m = M – L + 1 = = 9 E = m2-S = 92-216 = E-09
T:AACCGGTTACACGAGTGCTGAATGC |||||||||||||||| Q:CTGAGGTTACACGAGTGCTGCTGA
M = 25, N = 24, L = 16 m = M – L + 1 = = 10 n = N – L + 1 = = 9
E = mn2-S = 1092-216 = E-08
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23. Gapped BLAST Adapted from Crane & Raymer 2003
Input sequence: AILVPTVIGCTVPT
Algorithm:
Break the query sequence into words: AILV, ILVP, LVPT, VPTV, PTVI, TVIG, VIGC, IGCT, GCTV, CTVP, TVPT
Discard common words (i.e., words made entirely of common amino acids) or sequence of low complexity
Search for matches against database sequences, assess significance and decide whether to discard to continue with extension using dynamic programming: AILVPTVIGCTVPT MVQGWALYDFLKCRAILVPTVIACTCVAMLALYDFLKC
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24. Blast Output (Nuc. Seq.) BLASTN 2.2.4 [Aug-26-2002] ... Query= Seq1 38
Database: MgCDS
480 sequences; 526,317 total letters
Score E
Sequences producing significant alignments: (bits) Value
MG bases e-004
Score = 34.2 bits (17), Expect = 7e-004
Identities = 35/40 (87%), Gaps = 2/40 (5%)
Query: 1 atgaataacg--attatttccaacgacaaaacaaaaccac 38
|||||||||| ||||||||||| |||||| ||||||||
Sbjct: 1 atgaataacgttattatttccaataacaaaataaaaccac 40
Lambda K H
Matrix: blastn matrix:1 -3
Gap Penalties: Existence: 5, Extension: 2 …
effective length of query: 26
effective length of database: 520,557
Matches: 35*1 = 35
Mismatches: 3*(-3) = -9
Gap Open: 1*5 = 5
Gap extension: 2*2 =4
R = = 17
S = [λR – ln(K)]/ln(2) =[1.37*17-ln(0.711)]/ln(2) = 34
E = mn2-S = 26 * * 2-34 = 7.878E-04
x p(x)
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25. (which is not homologous to #1)
Why is “sequence complexity” important when judging whether two sequences are homologous?
… or whether their similarity is by chance
Human DNA
Chimp DNA
Pu-rich region #1
Pu-rich region #2
(which is not homologous to #1)
AAGAGGAG
Region of unbiased
base composition
where G=C=A=T
How frequently is such an 8-nt seq (AAGAGGAG) expected to occur by chance in a DNA sequence?
If within unbiased region?
1 / 48
... once every 65.5 kb on average
If within Pu-rich region?
1 / 28
... once every 256 bp on average
If both sequences are purine rich, then high % identity (or a small e-value) may not reflect shared evolutionary origin

26. E-Value in BLAST
The e-value is the expected number of random matches that is equally good or better than the reported match. It can be a number near zero or much larger than 1.
It is NOT the probability of finding the reported match.
Only when the e-value is extremely small can it be interpreted as the probability of finding 1 match that is as good as the reported one (see next slide).
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27. E-value and P(1)
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28. Problem with BLAST
Q: GGC GCG CCC AAG CUG UGC T: GGT GCA CCT AAA CUA UGT
Alternatives:
FASTA
AA sequence
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