screen

Alignments
BLAST, BLAT

Genome
vs.
gene
Genome Gene
Built of... DNA DNA
Describes Organism Protein
Single molecule, or
Stored as... Part of genome
a few of them
Both (depending on
Circular/ linear Linear
the species)
“Life cycle” DNA-DNA-DNA-... DNA-RNA-protein
Amount per
cell
Information
content
Size 0.5Mb 100b ... 100000b
*) ... 3500Mb
1 500 .. 50000
2% ... 100% ~30%

The amount of genetic
information in organisms
Name
Mycoplasma
Genome
size (Mb) # genes
genitalium
0.5 470
Escherichia coli
Saccharomyces
4.5 4400
cerevisiae
Drosophila
12 5500
melanogaster
Caenorhabtitis
120 18000
elegans
97 22000
Homo sapiens 3000 23457
Zea mays 2500 50000

The amount of genetic
information in organisms
http://www.cbs.dtu.dk/staff/dave/roanoke/genetics980313.html
Largest genome: amoeba Chaos chaos
(200x human genome) http://www.lawrence.edu/dept/biology/animal/

Sequence searching -
challenges
Exponential growth of
databases

Sequence searching –
definition
Task:
– Query: short, new sequence (~1000
letters)
– Database (searching space): very
many sequences
– Goal: find seqs homologous to the
query

Sequence searching –
definition
We want:
– fast tool
– primarily a filter: most sequences will
be unrelated to the query
– fine-tune the alignment later

Database Search Algorithms:
Sensitivity, Selectivity
• True Positive (TP) – a homology detected (positive)
correctly (true)
Signal Detected Name
Yes Yes True Positive
No No True Negative
Yes No False Negative
No Yes False Positive

Database Search Algorithms:
Sensitivity, Selectivity
• Sensitivity =TP/(TP+FN)
• Selectivity =TN/(TN+FP)
–
Selectivity
Courtesy of Gary Benson (ISSCB 2003)
Sensitivity

What is BLAST
Basic Local Alignment Search Tool
Bad news: it is only a heuristics
– Heuristics: A rule of thumb that often helps in solving
a certain class of problems, but makes no guarantees.
Perkins, DN (1981) The Mind's Best Work
Basic idea:
– High scoring segments have well
conserved (almost identical) part
– As well conserved part are identified,
extend it to the real alignment
-
s
e
q
-
s
e
q
u
e

What means well conserved
for BLAST?
BLAST works with k-words (words of length
k)
– k is a parameter
– different for DNA (>10) and proteins
(2..4)
word w 1 is T-similar to w 2 if the sum of pair
scores is at least T (e.g. T=12)
Similar 3-words
W 1 : R K P
W 2 : R R P
Score: 9 –1 7 ∑ = 15

BLAST algorithm
3 basic steps
1)Preprocess the query: extract all
the k-words
2)Scan for T-similar matches in
database
3)Extend them to alignments
1)Preprocess
2)Scan
3)Extend

BLAST, Step 1:
Preprocess the query
Take the query (e.g. LVNRKPVVP)
Chop it into overlapping k-words (k=3 in this
case) Query: LVNRKPVVP
Word1: LVN
Word2: VNR
Word3: NRK
…
For each word find all similar words (scoring at least
T)
E.g. for RKP the following 3-words are similar:
QKP KKP RQP REP RRP RKP
1)Preprocess
2)Scan
3)Extend

Finite state machine
abstract machine
constant amount of memory
(states)
used in computation and languages
recognizes regular expressions
– cp dmt*.pdf /home/john
1)Preprocess
2)Scan
3)Extend
AC*T|GGC

BLAST, Step 2:
Find ¨exact¨ matches
with scanning
Use all the T-similar k-words to build the Finite
State Machine
Scan for exact matches
1)Preprocess
2)Scan
3)Extend
QKP
KKP
RQP movement
REP
RRP
RKP
...
...VLQKPLKKPPLVKRQPCCEVVRKPLVKVIRCLA...

BLAST, Step 3:
Extending ¨exact¨ matches
Having the list of exact matches we extend
alignment in both directions
Query: L V N R K P V V P
T-similar: R R P
1)Preprocess
2)Scan
3)Extend
Subject: G V C R R P L K C
Score: -3 4 -3 5 2 7 1 -2 -3
…till the sum of scores drops below some
level X (e.g. X=-100) from the best known
- what with gaps?

Gapped BLAST
(now standard)
gapped local alignments are computed:
much, much, much slower
therefore: modified “Hit criteria”
1)Preprocess
2)Scan
3)Extend

Hit criteria
Extends the alignment only if there are
close two hits on the same diagonal
– sensitivity would drop without lowering T
– reduces extensions (90% time is spend
on extensions)
Gapped local alignments are computed
query
pos
– increased sensitivity allows us raise T
– raising T speeds up the search
close hit, same diag
dbpos
1)Preprocess
2)Scan
3)Extend

Gapped BLAST v BLAST
We end up with
– same speed
– gapped alignments!
– much higher sensitivity

BLAST flavours
blastp: protein query, protein db
blastn: DNA query, DNA db
blastx: DNA query, protein db
– in all reading frames. Used to find potential
translation products of an unknown nucleotide
sequence.
tblastn: protein query, DNA db
– database dynamically translated in all reading
frames.
tblastx: DNA query, DNA db
– all translations of query against all translations of
db

PSI-BLAST
Position-Specific Iterated BLAST
A profile is derived from the result
of the first search
Database is searched against the
profile (instead of a sequence)
Up to 3 iterations

Profile
Profile is generalized form of
sequence
probabilities instead of a letter
A
C
D
.
.
.
W
Y
0.5
0
0
.
.
.
0
0.5
0.3
0.1
0
.
.
.
0.3
0.3
0.2
0.0
0.1
.
.
.
0.4
0.3
Score of the profile
...
...
...
...
...
...
...
...
0
0.5
0.2
.
.
.
0.1
0.2
scorep,i , A=∑ B p[i ,B]score blosum62 A ,B
profile position letter

Constructing a profile
Take significant BLAST results
Make an alignment
Assign weights to sequences
Construct the profile
A
C
D
.
.
.
W
Y
0.5
0
0
.
.
.
0
0.5
0.3
0.1
0
.
.
.
0.3
0.3
0.2
0.0
0.1
.
.
.
0.4
0.3
...
...
...
...
...
...
...
...
0
0.5
0.2
.
.
.
0.1
0.2

BLAT
The Blast-Like Alignment Tool
Large-scale genome comparison:
– query can be large
Preprocessing phase:
– BLAST: query
– BLAT: db

BLAT, Step 1:
Preprocess the
database
Index the database with k-words
– k=8..16 for nucleotides
– k=3..5 for proteins
For each k-word store in which
sequences it appears
k-word: RKP
1)Preprocess
2)Scan
3)Extend
Hashed DB:
QKP: HUgn0151194, Gene14, IG0, ...
KKP: haemoglobin, Gene134, IG_30, ...
RQP: HSPHOSR1, GeneA22...
RKP: galactosyltransferase, IG_1...
REP: haemoglobin, Gene134, IG_30, ...
RRP: Z17368, Creatine kinase, ...
...

Hashing – associative
arrays
Indexing with the object
Hash function:
hash:
possible objects - large
– Objects should be “well spread”
x
1)Preprocess
2)Scan
3)Extend
small
(fits in memory)

Hashing - examples
T9 Predictive Text in mobile phones
– “hello” in Multitap:
4, 4, 3, 3, 5, 5, 5,
(pause) 5, 5, 5, 6, 6, 6
– “hello” in T9:
4, 3, 5, 5, 6
– Collisions: 4, 6:
“in”, “go”
1)Preprocess
2)Scan
3)Extend

BLAT, Step 1:
Index to find exact matches
with hashing
The database is preprocessed only
once! (independent from the
query)
k-word: RKP
1)Preprocess
2)Scan
3)Extend
Hashed DB:
QKP: HUgn0151194, Gene14, IG0, ...
KKP: haemoglobin, Gene134, IG_30, ...
RQP: HSPHOSR1, GeneA22...
RKP: galactosyltransferase, IG_1...
REP: haemoglobin, Gene134, IG_30, ...
RRP: Z17368, Creatine kinase, ...
...

BLAT, Step 2:
Hit criteria
1)Preprocess
2)Scan
3)Extend
In a constant time we can get the
sequences with a certain k-word
relaxing hit definition -> improve
sensitivity
– allow imperfect hits
• costly, huge hash grows a few times!
➔ shorten k (would lead to FP), but
expect two hits (see BLAST)

BLAT, Step 3:
Identifying homologous
regions
Exclude common k-words
For all k-words from query
– find out the position in db
For results (qpos, dbpos):
– split into buckets (64kbp)
1)Preprocess
2)Scan
3)Extend
– sort on the diagonal (diag=qposdbpos)

BLAT, Step 3:
Identifying homologous
regions
continued...
1)Preprocess
2)Scan
3)Extend
– from diagonally close hits (gap
limit) create “pre-clusters”
– sort each “pre-cluster” on dbpos
– create clusters from close hits
– run Local Alignment for each
cluster

Seeds – improving sensitivity
More general form of k-word is a
seed
The seed
CT.GT.AT.
gives “hits” with both sequences
...CTCGTTATA...
...CTAGTAATG...

How to detect homology?
Take the score of an maximal local
alignment
can it be obtained by chance?
– any score can be obtained from
comparing (long enough) random
sequences

What is a “chance”?
Extracting local alignments from
random sequences
P-value (e.g. =0.01)
– The probability of obtaining the result
by pure chance
– An alignment giving lower P-value
than set by user is considered a hit.

Best Local Alignments
by chance
Create random seqs, each 1000aa long
Find the max local align
Repeat
# Alignments
7000
6000
5000
4000
3000
2000
1000
0
25 30 35 40 45 50 55 60 65 70 75
Score

The Statistics of local
alignment
http://www.ncbi.nlm.nih.gov/BLAST/tutorial/Altschul-1.html
Subst matrix must guarantee
• E(score(a,b)) < 0 for random a, b
Analytical solution
– sum of i.i.d. variables -> normal
distribution
– max of i.i.d. -> extreme value
distribution (EVD)

Expected number of aligns
E-value: the expected number of
alignments scoring >= S
E=K m n e −S
2x size of seq -> 2x number aligns
2x S -> E drops exponentially

E-value depends on n, m
Example
– For comparing seqA with seqB: S=88
-> E = 0.001
– For comparing seqA with 1000 seqs:
score 88 -> E=1
Important for db searching:
– n – size of query, m - size of db
E=K m n e −S

Deriving K, L
The above eq is theoretical result
for gapless (g=inf) alignment
– K, L can be derived from the subst
table
For gapped case
E=Kmne −S
– it seems that the equation holds
– we can derive K, L from “experiments”
# Alignments
7000
6000
5000
4000
3000
2000
1000
0
25 30 35 40 45 50 55 60 65 70 75
Score

Bit score S'
Score S depends on the substitution
table
What if we want table-independent
score?
E=mn2 −S' where S'=
E=Kmne −S
S−ln K
ln 2

Why does the BLAST work?
Relevant riddle
Are there at least 2 people in
Amsterdam with the same
number of hairs?
– At most 500 000 hairs on
each head
– 700 000 people living in
Amsterdam

Why does the BLAST work?
Pigeons
pigeonhole principle: having 9 boxes and 10
pigeons, there is at least one box with more than 1 pigeon
– n=9, k=7 case:
http://en.wikipedia.org/wiki/Pigeonhole_principle

Why does the BLAST work?
Average case
pigeonhole principle describes the worst
case!
On average we'll expect two pigeons in
the same box much earlier
Birthday paradox: among 23 people,
probability that they have the same
birthday is > 0.5
– note: 365 boxes and only 23 pigeons!

Birthday paradox

Why does the BLA[S]T work?
Forget the T-similar words, now use only identities
2 sequences, 100 nucleotides each:
– What's the minimal sequence identity for which
there's a string of 3 consecutive identities?
0 identities, 100 mismatches:
67 identities, 33 mismatches:
but if seqs are 50% id, we'll detect it with prob. 99%
28% id -> we'll detect it with prob. 50%
– how is it calculated?
68st
?

Expected sensitivity
We assume that letters are
independent
I – identity between seqs, for
human-mouse
– 86% for DNA,
– 89% for proteins
p word id =I k

Expected sensitivity
Q - query size
number of non-overlapping words
R= Q
k
prob. of a “hit”
p detect =1−1−p wordid R

Expected specificity
How many matches by chance (C)?
G – genome size
C=Q−k1∗ G
k
For h-m, to get 99% sensitivity we
have to set k=7, and for Q=1000
C ~= 25,000,000
∗ 1
4 k
– 7h assuming 1/1000 per alignment