1. Indexing DNA Sequences Using q-Grams
Adriano Galati & Bram Raats

2. 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

3. 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

4. Introduction(2) Two level index
Two level index to prune data sequences:
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
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

5. 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

6. 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

7. 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?

8. 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

9. 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’

10. c-signature
q-gram signature where
where and
when

11. Example c-signature P=“ACGGTACT”
q-gram signature is ( ) with 42 dimensions when q=2

12. 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

13. 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.

14. 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

15. Example c-Trees
Consider the five DNA segments:
If we get trees

16. Example c-Trees(2)

17. 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

18. 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

19. 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

20. 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

21. 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?

22. The Sensitivity vs The Number of Common q-grams

23. 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