Sequence Alignment II

1
Sequence Alignment II

• K-tuple methodsStatistics of alignments

2
Database searches

• What is the problem?
• Large number of sequences to search your query
  sequence against.
• Various indexing schemes and heuristics are used,
  one of which is BLAST.
• heuristic is a technique to solve a problem that
  ignores whether the solution can be proven to be
  correct, but usually produces a good solution,
  are intended to gain computational performance or
  conceptual simplicity potentially at the cost of
  accuracy or precision.

http//en.wikipedia.org/wiki/HeuristicsComputer_s
cience
3
K-tuple methods
http//creativecommons.org/licenses/by-sa/2.0/
4
Concepts of Sequence Similarity Searching

• The premise
• The sequence itself is not informative it must
  be analyzed by comparative methods against
  existing databases to develop hypothesis
  concerning relatives and function.

5
Important Terms for Sequence Similarity Searching
with very different meanings

• Similarity
• The extent to which nucleotide or protein
  sequences are related. In BLAST similarity refers
  to a positive matrix score.
• Identity
• The extent to which two (nucleotide or amino
  acid) sequences are invariant.
• Homology
• Similarity attributed to descent from a common
  ancestor.

6
Sequence Similarity Searching The Approach

• Sequence similarity searching involves the use of
  a set of algorithms (such as the BLAST programs)
  to compare a query sequence to all the sequences
  in a specified database.
• Comparisons are made in a pairwise fashion. Each
  comparison is given a score reflecting the degree
  of similarity between the query and the sequence
  being compared.

7
Blast
QUERY sequence(s)
BLAST results
BLAST program
BLAST database
8
Topics
BLAST program

• There are different blast programs
• Understanding the BLAST algorithm
• Word size
• HSPs (High Scoring Pairs)
• Understanding BLAST statistics
• The alignment score (S)
• Scoring Matrices
• Dealing with gaps in an alignment
• The expectation value (E)

9
The BLAST algorithm

• The BLAST programs (Basic Local Alignment Search
  Tools) are a set of sequence comparison
  algorithms introduced in 1990 for optimal local
  alignments to a query.
• Altschul SF, Gish W, Miller W, Myers EW, Lipman
  DJ (1990) Basic local alignment search tool. J.
  Mol. Biol. 215403-410.
• Altschul SF, Madden TL, Schaeffer AA, Zhang J,
  Zhang Z, Miller W, Lipman DJ (1997) Gapped BLAST
  and PSI-BLAST a new generation of protein
  database search programs. NAR 253389-3402.

10
http//www.ncbi.nlm.nih.gov/BLAST
blastn
11
Other BLAST programs

• BLAST 2 Sequences (bl2seq)
• Aligns two sequences of your choice
• Gives dot-plot like output

12
More BLAST programs

• BLAST against genomes
• Many available
• BLAST parameters pre-optimized
• Handy for mapping query to genome
• Search for short exact matches
• BLAST parameters pre-optimized
• Great for checking probes and primers

13
How Does BLAST Work?

• The BLAST programs improved the overall speed of
  searches while retaining good sensitivity
  (important as databases continue to grow) by
  breaking the query and database sequences into
  fragments ("words"), and initially seeking
  matches between fragments.
• Word hits are then extended in either direction
  in an attempt to generate an alignment with a
  score exceeding the threshold of T".

14
Picture used with permission from Chapter 11 of
Bioinformatics A Practical Guide to the
Analysis of Genes and Proteins
15
Each BLAST hit generates an alignment that can
contain one or more high scoring pairs (HSPs)
16
Each BLAST hit generates an alignment that can
contain one or more high scoring pairs (HSPs)
17
Where does the score (S) come from?

• The quality of each pair-wise alignment is
  represented as a score and the scores are ranked.
  
• Scoring matrices are used to calculate the score
  of the alignment base by base (DNA) or amino acid
  by amino acid (protein).
• The alignment score will be the sum of the scores
  for each position.

18
Whats a scoring matrix?

• Substitution matrices are used for amino acid
  alignments. These are matrices in which each
  possible residue substitution is given a score
  reflecting the probability that it is related to
  the corresponding residue in the query.

19
PAM vs. BLOSUM scoring matrices

• BLOSUM 62 is the default matrix in BLAST 2.0.
  Though it is tailored for comparisons of
  moderately distant proteins, it performs well in
  detecting closer relationships. A search for
  distant relatives may be more sensitive with a
  different matrix.

20
PAM vs BLOSUM scoring matrices

• The PAM Family
• PAM matrices are based on global alignments of
  closely related proteins.
• The PAM1 is the matrix calculated from
  comparisons of sequences with no more than 1
  divergence.
• Other PAM matrices are extrapolated from PAM1.

• The BLOSUM family
• BLOSUM matrices are based on local alignments.
• BLOSUM 62 is a matrix calculated from comparisons
  of sequences with no less than 62 divergence.
• All BLOSUM matrices are based on observed
  alignments they are not extrapolated from
  comparisons of closely related proteins.

21
What happens if you have a gap in the alignment?

• A gap is a position in the alignment at which a
  letter is paired with a null
• Gap scores are negative. Since a single
  mutational event may cause the insertion or
  deletion of more than one residue, the presence
  of a gap is frequently ascribed more significance
  than the length of the gap.
• Hence the gap is penalized heavily, whereas a
  lesser penalty is assigned to each subsequent
  residue in the gap.

22
Percent Sequence Identity

• The extent to which two nucleotide or amino acid
  sequences are invariant

A C C T G A G A G A C G T G G C
A G
mismatch
indel
70 identical
23
BLAST algorithm

• Keyword search of all words of length w in the
  query of default length n in database of length m
  with score above threshold
• w 11 for nucleotide queries, 3 for proteins
• Do local alignment extension for each hit of
  keyword search
• Extend result until longest match above threshold
  is achieved and output

24
BLAST algorithm (contd)
keyword
Query KRHRKVLRDNIQGITKPAIRRLARRGGVKRISGLIYEETRGVL
KIFLENVIRD
GVK 18 GAK 16 GIK 16 GGK 14 GLK 13 GNK 12 GRK
11 GEK 11 GDK 11
Neighborhood words
neighborhood score threshold (T 13)
extension
Query 22 VLRDNIQGITKPAIRRLARRGGVKRISGLIYEETRGVLK
60 DN G IR L GK I L E
RGK Sbjct 226 IIKDNGRGFSGKQIRNLNYGIGLKVIADLV-EK
HRGIIK 263
High-scoring Pair (HSP)
25
Local alignment

• Find the best local alignment between two
  strings, over the recurrence

26
Local alignment (contd)

• Input strings v and w and scoring matrix d
• Output substrings of v and w whose global
  alignment as defined by d, is maximal among all
  global alignments of all substrings of v and w

27
Original BLAST

• Dictionary
• All words of length w
• Alignment
• Ungapped extensions until score falls below
  statistical threshold T
• Output
• All local alignments with score gt statistical
  threshold

28
Original BLAST Example
A C G A A G T A A G G T C
C A G T

• w 4, T 4
• Exact keyword match of GGTC
• Extend diagonals with mismatches until score
  falls below a threshold
• Output result
• GTAAGGTCC
• GTTAGGTCC

C T G A T C C T G G A T T
G C G A
From lectures by Serafim Batzoglou (Stanford)
29
Gapped BLAST Example
A C G A A G T A A G G T C
C A G T

• Original BLAST exact keyword search, THEN
• Extend with gaps in a zone around ends of exact
  match
• Output result
• GTAAGGTCCAGT
• GTTAGGTC-AGT

C T G A T C C T G G A T T
G C G A
From lectures by Serafim Batzoglou (Stanford)
30
Gapped BLAST Example (contd)
A C G A A G T A A G G T C
C A G T

• Original BLAST exact keyword search, THEN
• Extend with gaps around ends of exact match until
  score ltT, then merge nearby alignments
• Output result
• GTAAGGTCCAGT
• GTTAGGTC-AGT

C T G A T C C T G G A T T
G C G A
From lectures by Serafim Batzoglou (Stanford)
31
Topics
BLAST databases

• The different blast databases provided by the
  NCBI
• Protein databases
• Nucleotide databases
• Genomic databases
• Considerations for choosing a BLAST database
• Custom databases for BLAST

32
BLAST protein databases available at through
blastp web interface _at_ NCBI
33
Considerations for choosing a BLAST database

• First consider your research question
• Are you looking for an ortholog in a particular
  species?
• BLAST against the genome of that species.
• Are you looking for additional members of a
  protein family across all species?
• BLAST against nr, if you cant find hits check
  wgs, htgs, and the trace archives.
• Are you looking to annotate genes in your species
  of interest?
• BLAST against known genes (RefSeq) and/or ESTs
  from a closely related species.

34
When choosing a database for BLAST

• It is important to know your reagents.
• Changing your choice of database is changing your
  search space completely
• Database size affects the BLAST statistics
• record BLAST parameters, database choice,
  database size in your bioinformatics lab book,
  just as you would for your wet-bench experiments.
• Databases change rapidly and are updated
  frequently
• It may be necessary to repeat your analyses

35
Topics
BLAST results

• Choosing the right BLAST program
• Running a blastp search
• BLAST parameters and options to consider
• Viewing BLAST results
• Look at your alignments
• Using the BLAST taxonomy report

36
BLAST parameters and options to consider
conserved domains
Entrez query
E-value cutoff
Word size
37
More BLAST parameters and options to consider
filtering
gap penalities
matrix
38
Run your BLAST search
BLAST
39
The BLAST Queue
click for more info
Note your RID
40
Formatting and Retrieving your BLAST results
Results
options
41
A graphical view of your BLAST results
42
The BLAST hit list
Score
E-Value
GenBank
alignment
EntrezGene
43
The BLAST pairwise alignments
Identity
Similarity
44
Sample BLAST output

• Blast of human beta globin protein against zebra
  fish

• Score E
• Sequences producing significant alignments
  (bits) Value
• gi18858329refNP_571095.1 ba1 globin Danio
  rerio gtgi147757... 171 3e-44
• gi18858331refNP_571096.1 ba2 globin
  SIdZ118J2.3 Danio rer... 170 7e-44
• gi37606100embCAE48992.1 SIbY187G17.6 (novel
  beta globin) D... 170 7e-44
• gi31419195gbAAH53176.1 Ba1 protein Danio
  rerio 168 3e-43
• ALIGNMENTS
• gtgi18858329refNP_571095.1 ba1 globin Danio
  rerio
• Length 148
• Score 171 bits (434), Expect 3e-44
• Identities 76/148 (51), Positives 106/148
  (71), Gaps 1/148 (0)
• Query 1 MVHLTPEEKSAVTALWGKVNVDEVGGEALGRLLVVYPWT
  QRFFESFGDLSTPDAVMGNPK 60
• MV T EA LWGKNDEG AL R
  LVYPWTQRF FGLSP AMGNPK
• Sbjct 1 MVEWTDAERTAILGLWGKLNIDEIGPQALSRCLIVYPWT
  QRYFATFGNLSSPAAIMGNPK 60

45
Sample BLAST output (contd)

• Blast of human beta globin DNA against human DNA

• Score E
• Sequences producing significant alignments
  (bits) Value
• gi19849266gbAF487523.1 Homo sapiens gamma A
  hemoglobin (HBG1... 289 1e-75
• gi183868gbM11427.1HUMHBG3E Human gamma-globin
  mRNA, 3' end 289 1e-75
• gi44887617gbAY534688.1 Homo sapiens A-gamma
  globin (HBG1) ge... 280 1e-72
• gi31726embV00512.1HSGGL1 Human messenger RNA
  for gamma-globin 260 1e-66
• gi38683401refNR_001589.1 Homo sapiens
  hemoglobin, beta pseud... 151 7e-34
• gi18462073gbAF339400.1 Homo sapiens haplotype
  PB26 beta-glob... 149 3e-33
• ALIGNMENTS
• gtgi28380636refNG_000007.3 Homo sapiens beta
  globin region (HBB_at_) on chromosome 11
• Length 81706
• Score 149 bits (75), Expect 3e-33
• Identities 183/219 (83)
• Strand Plus / Plus
• 
  
• Query 267 ttgggagatgccacaaagcacctggatgatctcaagg
  gcacctttgcccagctgagtgaa 326
• 
  

46
What do the Score and the e-value really mean?

• The quality of the alignment is represented by
  the Score.
• Score (S)
• The score of an alignment is calculated as the
  sum of substitution and gap scores. Substitution
  scores are given by a look-up table (PAM, BLOSUM)
  whereas gap scores are assigned empirically .
• The significance of each alignment is computed as
  an E value.
• E value (E)
• Expectation value. The number of different
  alignments with scores equivalent to or better
  than S that are expected to occur in a database
  search by chance. The lower the E value, the more
  significant the score.

47
E value

• E value (E)
• Expectation value. The number of different
  alignments with scores equivalent to or better
  than S expected to occur in a database search by
  chance. The lower the E value, the more
  significant the score.

48
Assessing sequence homology

• Need to know how strong an alignment can be
  expected from chance alone
• Chance is the comparison of
• Real but non-homologous sequences
• Real sequences that are shuffled to preserve
  compositional properties
• Sequences that are generated randomly based upon
  a DNA or protein sequence model (favored)

49
High Scoring Pairs (HSPs)

• All segment pairs whose scores can not be
  improved by extension or trimming
• Need to model a random sequence to analyze how
  high the score is in relation to chance

50
Expected number of HSPs

• Expected number of HSPs with score gt S
• E-value E for the score S
• E Kmne-lS
• Given
• Two sequences, length n and m
• The statistics of HSP scores are characterized by
  two parameters K and ?
• K scale for the search space size
• ? scale for the scoring system

51
BLAST statistics to record in your bioinformatics
labbook
Record the statistics that are found at bottom of
your BLAST results page
52
Scoring matrices

• Amino acid substitution matrices
• PAM
• BLOSUM

53
Bit Scores

• Normalized score to be able to compare sequences
• Bit score
• S lS ln(K) ln(2)
• E-value of bit score
• E mn2-S

54
Assessing the significance of an alignment

• How to assess the significance of an alignment
  between the comparison of a protein of length m
  to a database containing many different proteins,
  of varying lengths?
• Calculate a "database search" E-value. Multiply
  the pairwise-comparison E-value by the number of
  sequences in the database N divided by the length
  of the sequence in the database n

55
Homology Some Guidelines

• Similarity can be indicative of homology
• Generally, if two sequences are significantly
  similar over entire length they are likely
  homologous
• Low complexity regions can be highly similar
  without being homologous
• Homologous sequences not always highly similar

56
Homology Some Guidelines

• Suggested BLAST Cutoffs
• (source Chapter 11 Bioinformatics A Practical
  Guide to the Analysis of Genes and Proteins)
• For nucleotide based searches, one should look
  for hits with E-values of 10-6 or less and
  sequence identity of 70 or more
• For protein based searches, one should look for
  hits with E-values of 10-3 or less and sequence
  identity of 25 or more

57
Contributors

• Special thanks to David Wishart, Andy Baxevanis,
  Stephanie Minnema, Sohrab Shah, and Francis
  Ouellette for their contributions to these
  materials

http//creativecommons.org/licenses/by-sa/2.0/
58
FASTA

• A FASTA search begins by breaking the search
  sequence into words.
• For genomic sequences, a word size of 4 or 6
  nucleotides is used 1 or 2 for polypeptide
  sequences.

59
FASTA

• Next a table is constructed for the query
  sequence (word size is 1)
• E.g. FAMLGFIKYLPGCM

A C D E F G H I K L M N P Q R S T V W Y
2

60
FASTA

• Next a table is constructed for the query
  sequence
• E.g. FAMLGFIKYLPGCM

A C D E F G H I K L M N P Q R S T V W Y
2 13

61
FASTA

• Next a table is constructed for the query
  sequence
• E.g. FAMLGFIKYLPGCM

A C D E F G H I K L M N P Q R S T V W Y
2 13 1
6
62
FASTA

• Next a table is constructed for the query
  sequence
• E.g. FAMLGFIKYLPGCM

A C D E F G H I K L M N P Q R S T V W Y
2 13 1 5
6 12
63
FASTA

• Next a table is constructed for the query
  sequence
• E.g. FAMLGFIKYLPGCM

A C D E F G H I K L M N P Q R S T V W Y
2 13 1 5 7
6 12
64
FASTA

• The table for the query sequence is complete
• E.g. FAMLGFIKYLPGCM

A C D E F G H I K L M N P Q R S T V W Y
2 13 1 5 7 8 4 3 11 9
6 12 10 14
65
FASTA

• Compare the query sequence table with the target
  sequence
• Query FAMLGFIKYLPGCM
• Index of Gs are 5 and 12
• Target TGFIKYLPGACT
• Index of Gs are 2 and 9
• Subtract 2 from 5 and 12 producing 3 and 10
• Subtract 9 from 5 and 12 producing -4 and 3

1 2 3 4 5 6 7 8 9 10 11 12
T G F I K Y L P G A C T
3 -4
10 3
66
FASTA

• Compare the query sequence table with the target
  sequence
• Query FAMLGFIKYLPGCM
• Index of Fs are 1 and 6
• Target TGFIKYLPGACT
• Index of F is 3
• Subtract 3 from 1 and 6 producing -2 and 3

1 2 3 4 5 6 7 8 9 10 11 12
T G F I K Y L P G A C T
3 -2 -4
10 3 3
67
FASTA

• Compare the query sequence table with the target
  sequence
• Query FAMLGFIKYLPGCM
• Index of Fs are 1 and 6
• Target TGFIKYLPGACT
• Index of F is 3
• Subtract 3 from 1 and 6 producing -2 and 3

1 2 3 4 5 6 7 8 9 10 11 12
T G F I K Y L P G A C T
3 -2 3 3 3 -3 3 -4 -8 2
10 3 3 3
68
FASTA

• FAMLGFIKYLPGCM
• TGFIKYLPGACT
• Offset by 3

1 2 3 4 5 6 7 8 9 10 11 12
T G F I K Y L P G A C T
3 -2 3 3 3 -3 3 -4 -8 2
10 3 3 3
69
Fasta (word size 2)
70
Database searches
71
Odds score in sequence alignment

• The chance of an aligned amino acid pair being
  found in alignments of related sequences compared
  to the chance of that pair being found in random
  alignments of unrelated sequences.

72
Statistical significance of an alignment

• The probability that random or unrelated
  sequences could be aligned to produce the same
  score.
• Smaller the probability is the better.

73
Probability

• What is the probability that a coin toss will
  yield a head?
• What is the probability that the next pair of
  nucleotides will be a match or mismatch?

74
Bernoulli trials

• A series of n number of independent trials with
  the same outcome probabilities and number of
  choices (e.g., head or tail or match (m) or
  mismatch (mi)).
• P(hhhhh)
• P(mmmmm)

75
Head or Tail..Longest run of heads or tails

• Longest run of heads one would get in a random
  series of coin tosses?
• Fair coin, p 0.5 1/p 1/0.5 2
• Erdös and Rènyi longest run log1/p(n)
• If n 100 longest run 6.65

76
Alignment analogy

• You have two sequences a and b of equal length
• a1a2a3a4
• b1b2b3b4
• if an bn then it is head (match)
• If an does not equal to bn then it is tail
  (mismatch)

77
Alignment Statistics

• For two sequences of length n and m, n times m
  comparisons are being made thus the longest
  length of the predicted match would be log1/p(mn).

78
Alignment Statistics

• Expectation value or the mean longest match would
  be
• E(M) log1/p(Kmn), where K is a constant that
  depends on amino acid or base composition and p
  is the probability of a match.
• This is only true for ungapped local alignments.

79
Distribution of alignment scores

• resembles Gumbel extreme value distribution.

80
Extreme Value Distribution
81
Extreme Value Distribution

• In this distribution, the probability of a score
  being higher than x is given by

• m and n are the lengths of the sequences compared
  
• K and ?   can be calculated from the data in the
  matrix used and from the relative frequencies of
  the amino acids (or nucleotides)

82
Alignment Statistics

• For two sequences of length n and m, n times m
  comparisons are being made thus the longest
  length of the predicted match would be
  log1/p(mn).
• For a pair of random DNA sequences of length 100
  and p 0.25 (equal A,T,C,G), the longest
  expected run of matches would be
• 2 x log1/p (n) 2 x log4 100 6.65

83
Alignment Statistics

• E(M)log1/p(Kmn) means that match length gets
  bigger as the log of the product of sequence
  lengths. Amino acid substitution matrices will
  turn match lengths into alignment scores (S).
• More commonly ? ln(1/p) is used.
• Number of longest run HSP will be estimated
• E Kmne-?S
• How good a sequence score is evaluated based on
  how many HSPs (i.e. E value) one would expect for
  that score.

84
Alignment Statistics

• Two ways to get K and ?
• For 10000 random amino acid sequences with
  various gap penalties, K and lambda parameters
  have been tabulated.
• Calculation of the distribution for two sequences
  being aligned by keeping one of them fixed and
  scrambling the other, thus preserving both the
  sequence length and amino acid composition.

85
Generate random sequences

• You may use the function randperm
• gtgt help randperm
• RANDPERM(n) is a random permutation of the
  integers from 1 to n.
• For example, RANDPERM(6) might be
• 2 4 5 6 1 3.

86
Align a sequence with its randomly permuted state

• gtgt x 'atagacagacca'
• gtgt l length (x)
• l
• 12
• gtgt ind randperm(12)
• ans
• Columns 1 through 9
• 9 4 5 7 3 11 2 8 6
• Columns 10 through 12
• 10 1 12
• gtgt y x(ind)
• y
• agaaactgccaa
• gtgt align1
• atagacagacca
• agaaactgccaa

87
Alignment Statistics
88
Alignment Statistics
89
Alignment Statistics
90
Alignment Statistics
91
Probability Distributions Binomial Distribution

• The number of an event (x) in n trials is given
  by binomial distribution

Binomial coefficient
probability
Probability of event 1
Probability of event 1
n, p, and q are constant x varies n and x are
discrete pq 1
92
Binomial Distribution

• Only two outcomes are possible on each of n
  trials.
• The probability of success for each trial is
  constant (p, and q does not change).
• All trials are independent of each other.

93
Matlab binopdf function

• Y binopdf(x,n,p)
• Where x equals the number of successes (outcome),
  n is the total possible number of trials, P is
  the probability of one type of outcome.

94
Matlab binopdf function

• gtgt x 010 from 0, 1,2, ...,10 number of
  trials
• gtgt y binopdf(x,10,0.5) calculate pdf
• gtgt plot(x,y,'') plot n over y using sign

95
Binomial probability density function
96
Applications

• Calculate the probability of a couples (mother
  AA and father AB genotype) 2 of 10 children
  having AB blood type?
• n 10 total number of children
• x 2 number of children with AB blood
• p 0.5 probability of having AB genotype
• q 0.5 probability of having AA genotype

97
Matlab

• gtgt p 0.5
• gtgt q 1-q
• gtgt n 10
• gtgt x 2
• gtgt fn factorial(n)
• gtgt fx factorial(x)
• gtgt fnminusx factorial(n-x)
• gtgt binocoef fn./(fx.fnminusx)
• gtgt Pr binocoefpnq(N-n)

98
Use parentheses in order to determine order in
calculations

• gtgt p 0.5
• gtgt q 1-q
• gtgt n 10
• gtgt x 2
• gtgt fn factorial(n)
• gtgt fx factorial(x)
• gtgt fnminusx factorial(n-x)
• gtgt binocoef fn./fx.fnminusx
• gtgt Pr binocoefpnq(N-n)

99
Try this!

• gtgt n 1100
• gtgt y binopdf(n,100,0.5)
• gtgt plot(n,y,'')

100
Binomial distribution
101
Binomial Cumulative Distribution Function

• Adds the probability value of the previous case
  to the next.
• gtgt x 010
• gtgt n 10
• gtgt p 0.5
• gtgt y binocdf(x,n,p)
• gtgt plot(x,y,'r')

102
Cumulative distribution
103
Expected value mean value

• The mean or expected value of an outcome (e.g.,
  getting an H from a coin toss) for n trials would
  be
• E(H) np
• p E(H)/n
• ?2 np(1-p)

104
Null hypothesis in statistics

• States equality (or in cases greater than or less
  than) between observed and an expected value
• To test a null hypothesis
• perform a statistical test
• calculate a p value
• reject or do not reject the null hypothesis
  using a threshold.

105
Example

• If a baseball team plays 162 games in a season
  and has a 50-50 chance of winning any game (p
  winning 0.5 q losing 0.5), then the
  probability of that team winning more than 100
  games in a season is
• gtgt 1 - binocdf(100,162,0.5)
• The result is 0.001 (i.e., 1-0.999).
• If a team wins 100 or more games in a season,
  this result suggests that it is likely that the
  team's true probability of winning any game is
  greater than 0.5.

106
Example

• In a population of Drosophila, the frequency of
  AA genotype is p (0.5) and the frequency of AB
  genotype is q (0.5).
• If you sample from this population the number of
  AA or AB individuals in the sampled population
  will be a function of their relative frequencies
  and the sample size (n).
• If n individuals are selected and x number of AB
  individuals are found, is this number greater or
  less than what could be obtained by chance alone?
• gtgt binopdf(7,10,0.5)
• ans
• 0.1172
• gtgt binopdf(70,100,0.5)
• ans
• 2.3171e-005

107
Normal Distribution

• A standard normal distribution will have a mean
  of 0 and variance of 1.

108
Normal Probability Distribution

• gtgt x -50.055
• gtgt y normpdf(x)
• gtgtplot(x,y)

109
Plot(x,y)
110
Normal cumulative distribution

• What is the probability that an observation from
  a standard normal distribution will fall on the
  interval -1 1?
• gtgtp normcdf(-1 1)
• gtgtp(2) - p(1)
• ans
• 0.6827

111
PAM-2
112
PAM-250
113
PAM-250
114
PAM-250
115
PAM-250
116
PAM-250
117
PAM-250
118
Multiple Sequence Alignment
119
Multiple Sequence Alignment
120
MegaBLAST

• megaBLAST
• For aligning sequences which differ slightly due
  to sequencing errors etc.
• Very efficient for long query sequences
• Uses big word (k-tuple) sizes to start search
• Very fast
• Accepts batch submissions of ESTs
• Can upload files of sequences as queries
• More detailed info see megaBLAST pages

121
P-values

• The probability of finding b HSPs with a score
  gtS is given by
• (e-EEb)/b!
• For b 0, that chance is
• e-E
• Thus the probability of finding at least one such
  HSP is
• P 1 e-E

122
Alignment Statistics
123
Alignment Statistics