Indexing DNA Sequences Using q-Grams

Adriano Galati & Bram Raats

Indexing DNA Sequences Using q-Grams Method for indexing the DNA sequences efficiently

based on q-grams to facilitate similarity search in a DNA database

To sidestep the linear scan of the entire database Proposed:

Hash table C-trees

based on the q-grams These data structures allow quick detection of

sequences

Introduction

Two sequences share a certain number of q-grams if ed is a certain threshold

Since there are 4 letters combinations

Two level index to prune data sequences

4q

Introduction(2)Two level index

Two level index to prune data sequences:1. First level

Clusters of similar q-grams in DNA are generated A typical Hash table is built in the segments with respect to

the qClusters 2. Second level

The segments are transformed into the c-signature based on their q-grams

A new index called the c-signature trees is proposed to organize the c-signatures of all segments of a DNA sequence for search efficiency

Edit distance

To process approximate matching, one common and simple approximation metric is called edit distance

Definition: The edit distance between two sequences is defined

as the minimum number of edit operations (i.e. insertions, deletions and substitutions) of single characters needed to transform the first string into the second

Preliminaries

Intuition:Two sequences would have a large number of

q-grams in common when the ed between them is within a certain number

Given a sequence S, its q-grams are obtained by sliding a window of length q over the characters of S

|S| - q + 1 q-grams for a sequence S

Question (Bogdan) 1. I have noticed that the segments of the database text

that are considered in this method are disjoint (see page 4, Introduction). I understand that for each segment all the consecutive, non-disjoint, q-grams are taken into consideration when computing the q-cluster and the c-signature of the segment. However, I am a bit puzzled that at the border between two adjacent segments nothing is done, which means that (q-1) q-grams are disregarded at each border. Since each segment contains w-q+1 q-grams, it means that overall a ratio of approximately (q-1)/(w-q+1) of all q-grams are disregarded (if we ignore the difference of 1 between the nr. of segments and the nr. of borders between adjacent segments). For common values of q=3 and w=30, this means about 7% of the q-grams. Do you see a solution for overcoming this problem?

Answer (Bogdan)

Effort to improve the efficiency discarding the regions (filtering) with low sequence similarity

Approximate sequence matching is preferred to exact matching in genomic database due to evolutionary mutation in the genomic sequences and the presence of noise data in a real sequence database

q-gram Signature kinds of q-grams All the possible q-grams are denoted as

The q-gram signature is a bitmap with 4q bits where i-th bit corresponds to the presence or absence of ri .

For a sequence S, the i-th bit is set as ‘ 1’ if occurs at least once in sequence S, else ‘ 0’

ir

},...,,{ 1410 qrrr

qq 4},,,{ TGCA

c-signature

q-gram signature where

where and

when

),...,,()( 1101

naaaSsig

),...,,()( 110 kc uuuSsig cnk /

1)1( ci

icj ji au

ckjn 0ja

qn 4

Example c-signature

P=“ACGGTACT”

q-gram signature is (01 00 00 11 00 11 10 00) with 42 dimensions when q=2

)10020210()(2 Psig c

Hash table Any DNA segment s can be encoded into a λ-bit

(bitmap ) by the coding function:

Hash table with size 2λ respect to qClusters

),...,,( 21 eeee

},...,,{ 21 qClusterqClusterqClusterqClusters

01

)(

i

i

i

eelseethen

qClusterramgqsramgqif

112)(

i ii escoding

Question (Jacob)

I can't get my hands on the c-Trees (mentioned first on page 9). Could you please explain how such a tree is built up, because I can't figure it out.

c-Trees

Group of rooted dynamic trees built for indexing c-signature

Height l set by user Given trees Each path from the root to a leaf in Ti

corresponds to the c-signature string

internal node there are children

lkuuuSsig kc /),...,,()( 110 10 ,..., TT

),...,,()( 1)1(1 liililci vvvssig

1cT

Example c-Trees Consider the five DNA segments:

If we get trees

""""""""""

43

210

GACGTsTAAGCsACGTTsCTTAGsACGGTs

)11001001()(

)10101100()(

)01011001()(

)00110101()(

)02001001()(22

42

32

22

12

02

ssig

ssig

ssig

ssig

ssigcq

4l 24

cl

q

Example c-Trees(2)

Query Processing

HT and c-T are built on the DNA segments Query sequence Q is also partitioned in

sliding query patterns Two level filtering

FLF: Hash Table Based Similarity Search SLF: c-Trees Based Similarity Search

1 wQ

11,..., wQqq

Hash Table Based Similarity Search

Query pattern qi encoded to a hash key hi (λ bit) ngbr of hi are enumerated ngbr are encoded in λ bit from the segments

which are within a ed from qi

Once is enumerated, the segments in the bucket will be retrieved as candidates and stored into

ingbr qe ][ ngbreHT

htC

c-Trees Based Similarity Search

Candidates will be further verified by c-trees c-signature of query q is divided into

c-signature strings The algorithm retrieves the segment s which

satisfies the range constraint During query processing, for each leaf in the tree

T1 are computed

htC)(qsig c

iqsig ci 0),(

),( sqed

Space and Time complexity

Space complexity HT is for the table head for the bucket of the table Thus the total space complexity for the Hash

structure is Time complexity for query Space complexity of each tree is

)2( O

)/2( wDO

)/( wD

)( qO))/(4( cO q

Question (Bogdan) I have trouble understanding the graphic in Fig.

2(a). My intuition would tell me that the more common q-grams exist in the 2 sequences, the higher the probability of finding a high score alignment between them. However, the figure seems to show the opposite: as the nr. of q-grams increases, the probability decreases. I've obviously got something mixed up here, but I can't figure out what it is. Could you please explain?

The Sensitivity vs The Number of Common q-grams

Answer (Bogdan)

Sensitivity can be measured by the probability that a high score alignment is found by the algorithm

The graph starts with probability almost 1 when we have only 1 common q-gram and if we increase the number of q-grams, the probability (sensitivity) of matching the alignment will surely decrease