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

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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

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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

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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

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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

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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

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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?

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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

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q-gram Signature kinds of q-grams All the possible q-grams are denoted as The q-gram signature is a bitmap with 4 q bits where i-th bit corresponds to the presence or absence of r i. For a sequence S, the i-th bit is set as ‘ 1’ if occurs at least once in sequence S, else ‘ 0’

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c-signature q-gram signature where where and when

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Example c-signature P=“ACGGTACT” q-gram signature is (01 00 00 11 00 11 10 00) with 4 2 dimensions when q=2

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Hash table Any DNA segment s can be encoded into a λ-bit (bitmap ) by the coding function: Hash table with size 2 λ respect to qClusters

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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.

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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 T i corresponds to the c-signature string internal node there are children

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

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Example c-Trees(2)

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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

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Hash Table Based Similarity Search Query pattern q i encoded to a hash key h i (λ bit) ngbr of h i are enumerated ngbr are encoded in λ bit from the segments which are within a ed from q i Once is enumerated, the segments in the bucket will be retrieved as candidates and stored into

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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 T 1 are computed

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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

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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?

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The Sensitivity vs The Number of Common q-grams

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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

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