A Measure for Sequence Similarity Based on Dual Nucleotides and Information Discrepancy

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1 The Fourth Internationa Conference on Computationa Systems Bioogy (ISB2010) Suzhou, China, September 9 11, 2010 Copyright 2010 ORSC & APORC, pp A Measure for Sequence Simiarity Based on Dua Nuceotides and Information Discrepancy Zhen Wang 1,, Jia-Wei Luo 1, Han-Qi Zhou 1, Fang Liu 1 1 Schoo of Computer and Communication Hunan University, Changsha, Hunan Province, Abstract The Function of Degree of Disagreement (FDOD) is a measurement of discrete information among mutipe information sources, which has been successfuy appied to phyogenetic anaysis, structura cassification of proteins, anaysis of SARS virus, etc. According to the chemica property of the dua nuceotides, a measurement of sequence simiarity based on the frequencies of the dua nuceotides is brought up. The phyogenetic reationships of the first exon of β-gobin gene of 11 species and the 11 types of SARS coronavirus isoate genome sequence iustrate the utiity of our approach. Keywords anaysis of simiarity; FDOD; compete information set; dua nuceotides 1 Introduction The main purpose of the sequence simiarity anaysis is to carify the homoogy reationship between the sequences and forecast the structure and function of the new sequence from the known sequences. The compexity of mutipe aignments is exponentia with the growth of the number or ength of the sequences. So for the whoe-genome data, the aignment is hard to achieve [1]. Sequence aignment methods require the users to set parameters, penaty, insert the space to equa the sequence ength. The some subjective factors ead to that different users may get the different resuts [2]. Response to the above inadequacies and imitations, some researchers advance a number of methods which can cacuate the sequence simiarity between different species without mutipe aignments. With the deveopment of information theory, information theory methods gained more attention. Professor Fang advanced a method of the Function of Degree of Disagreement (FDOD) [3][4]. The main character is using the sequence information to descript their reationship without any subjective information. FDOD has been successfuy appied to phyogenetic anaysis [5], structura cassification of proteins [6][7], anaysis of SARS virus [8], etc. However, in FDOD the compete information set of the sequence is represented by the probabiity distribution of _subsequence ( 1). The dimension of the _subsequence increases exponentiay with the increase of. For a subsequence with the ength is, the dimension is 4 (DNA sequence), 20 (protein sequence). The Emai: ance4@qq.com

2 A Measure for Sequence Simiarity 73 dimension wi be very arge whie is arger. In this paper, we advance a new compete information set of sequence which can be representative of the information and features of DNA sequence. Compete information set of DNA sequence is composed of frequencies of the dua nuceotides in different intervas. For DNA sequence, there are ony sixteen kinds of neighboring two bases, so the dimensions of the probabiity distributions of the neighboring two bases in different intervas are 16. This method can reduce the space compexity. 2 Simiarity Anaysis 2.1 FDOD The Function of Degree of Disagreement (FDOD) is a measurement of discrete information based on information theory by Fang [9]. = {a 1,a 2,,a m } is an aphabet of m symbos. S = {S 1,S 2,,S S } is a sequence set formed from the symbo set. We denote the set of a different sequences formed from with ength by Θ, so the number m() of a sequences of Θ equas m. For a sequence S k S, Let the ength of S k be L k and n ik mean the number of the consecutive subsequence segments in S k that match the ith sequence of Θ with ength. Obviousy, the number of the subsequences with ength in S k is: Letting p ik nik L 1 U ( p, p,..., p ), where T k 1k 2 k m( ) k k m () nik Lk 1 (1) i1, so we can obtain a distribution of a sequence m () pik 1,1 Lk i1 For a given set of sequences S = {S1,S2,,SS}, we can get the distribution of a set of subsequences: T U ( p, p,..., p ) Where m () i m ( )1 U ( p, p,..., p )... pik 1, k 1,2,..., S T m ( )2 U ( p, p,..., p ) The FDOD function is defined as foows: T s 1s 2 s m( ) s S m () ik 1 S ik S k1 i1 pij j1 B( U,..., U ) p og Where 0 og0=0, 0 og(0/0)=0. In a DNA primary sequence, = {A, G, C, T} and m =4. Suppose there are two DNA sequences X and Y, we can obtain discrepancies based on FDOD function: p / S (2) (3)

3 74 The 4th Internationa Conference on Computationa Systems Bioogy Y m () p ij D( X, Y) pij og (4) 1 ( jx i pix piy ) / 2 D(X, Y) means discrepancies of two species. The arger D(X, Y) is, the ower the simiarity of the two sequences is. Using FDOD function to cacuate discrepancies of DNA sequences, they ony depend on the origina information about sequences, no other subjective factors are invoved [10]. 2.2 A measure of sequence simiarity based on dua nuceotides and information discrepancy According to chemica properties of the adjacent nuceotide diad, we propose the measure of sequence simiarity based on the frequency of dua nuceotides upon the FDOD function. In a DNA primary sequence, the four DNA bases A, C, G and T can be divided into three casses by their chemica properties: purine R = {A, G}/pyrimidine Y = {C,T}, amino M = {A, C}/ketone K = {G, T}, and weak hydrogen bond W = {A, T}/strong hydrogen bond S = {C, G}. By considering neighboring two bases and the base order, we can get sixteen combinations: AG, GA, CT, TC, AC, CA, GT, TG, AT, TA, CG, GC, AA, CC, GG and TT. According to the three cassifications of the four DNA bases, the dua nuceotides can be divided into four casses: purine dua nuceotides {AG, GA}/pyrimidine dua nuceotides {CT, TC}, amino dua nuceotides {AC, CA}/ketone dua nuceotides {TG, GT}, weak hydrogen bond dua nuceotides {AT, TA}/strong hydrogen bond dua nuceotides {CG, GC}, and repeat dua nuceotides {AA, CC, GG, TT}. In each cass, the frequencies of dua nuceotides in interva are defined as foowing: AG 1 AG% AG GA CT TC n1 n1 GA GA% AG GA CT TC n1 n1 CT 3 CT % AG GA CT TC 6 7 n1 n1 TC TC% AG GA CT TC n1 n1 AC n1 AC% AC n1ca n1gt n1 TG n1 CA CA% AC CA GT TG n1 n1 GT GT % AC CA GT TG n1 n1 TG 8 TG% AC CA GT TG n1 n1 AT 9 AT % AT TA GC CG n1 n 1 n 1 n 1 TA TA% AT TA GC CG n1 n1 GC GC% AT TA GC CG n1 n1 CG CG% AT TA GC CG AA% AA n1 n1 AA n1 n1 GG n1cc n1tt n1 GG GG% AA GG CC TT n1 n1 CC CC% AA GG CC TT n1 n1 TT TT % AA GG CC TT n1 n1 where AG n-1, GA n-1, CT n-1, TC n-1... and TT n-1 respectivey are the cumuative occurrence numbers of AG, GA, CT, TC,... and TT from the first to the (n-1)-th base in DNA sequence whie the interva is. The ength of the sequence is n. For the sixteen kinds of order dua base pairs in DNA sequence, the probabiity distribution dimensions of different intervas are the same. The nove compete (5)

4 A Measure for Sequence Simiarity 75 information set of the DNA sequence can be defined by: 1 2 L L (6) L 1 2 L L where the ength of the DNA sequence is L. Suppose that there are two DNA sequences X and Y, the corresponding information sets are X and Y with ength X 1 X 1X 1Y 1 Y 1Y X 2 X 2 X 2Y 2Y 2Y X (7) Y X 16 X X 16 Y 16 Y 16Y According to FDOD the information divergence of X and Y is defined by: Y 16 k k ij (8) D( X, Y ) ij og Y jx i1 k1 k ( ) / 2 Where 0 og0=0, 0 og(0/0)=0. Obviousy, the smaer D ( X, Y ) is, the more simiar the DNA sequences are. The compete information set is expressed by the probabiity distributions of -subsequence in FDOD. The dimension of -subsequence is the exponentia growth. For DNA sequence the dimension is 4. In this paper, we propose the method of sequence simiarity based on dua nuceotides and information dispersion. The space compexity is O(16*). So, the space compexity becomes ower by this measure on the work of sequence simiarity. 3 Data sets and Resuts 3.1 Data sets In this paper, we wi use two sets of data as our test data. The first set is the first exon of β-gobin gene of 11 species, which are isted in Tabe 1. These sequences are very conservative and short. As the cassic testing data sampe, it have been used in the comparison and anaysis of DNA sequence in many iteratures. The second set is the whoe genome shotgun sequences of 11 SARS corona virus isoates, whose ength are about 29700bp respectivey. The detaied information is shown in Tabe 2. Tabe 1 The coding sequences of the first exon of β-gobin gene of 11 different species Human Goat Opossum Gaus Lemur tx ATGGTGCACCTGACTCCTGAGGAGAAGTCTGCCGTTACTGCCCTGTGGGG CAAGGTGAACGTGGATTAAGTTGGTGGTGAGGCCCTGGGCAG ATGCTGACTGCTGAGGAGAAGGCTGCCGTCACCGGCTTCTGGGGCAAGGT GAAAGTGGATGAAGTTGGTGCTGAGGCCCTGGGCAG ATGGTGCACTTGACTTCTGAGGAGAAGAACTGCATCACTACCATCTGGTCT AAGGTGCAGGTTGACCAGACTGGTGGTGAGGCCCTTGGCAG ATGGTGCACTGGACTGCTGAGGAGAAGCAGCTCATCACCGGCCTCTGGGG CAAGGTCAATGTGGCCGAATGTGGGGCCGAAGCCCTGGCCAG ATGACTTTGCTGAGTGCTGAGGAGAATGCTCATGTCACCTCTCTGTGGGGC AAGGTGGATGTAGAGAAAGTTGGTGGCGAGGCCTTGGGCAG it

5 76 The 4th Internationa Conference on Computationa Systems Bioogy Mouse Rabbit Rat Goria Bovine Chimpanzee ATGGTTGCACCTGACTGATGCTGAGAAGTCTGCTGTCTCTTGCCTGTGGGC AAAGGTGAACCCCGATGAAGTTGGTGGTGAGGCCCTGGGCAGG ATGGTGCATCTGTCCAGTGAGGAGAAGTCTGCGGTCACTGCCCTGTGGGG CAAGGTGAATGTGGAAGAAGTTGGTGGTGAGGCCCTGGGC ATGGTGCACCTAACTGATGCTGAGAAGGCTACTGTTAGTGGCCTGTGGGG AAAGGTGAACCCTGATAATGTTGGCGCTGAGGCCCTGGGCAG ATGGTGCACCTGACTCCTGAGGAGAAGTCTGCCGTTACTGCCCTGTGGGG CAAGGTGAACGTGGATGAAGTTGGTGGTGAGGCCCTGGGCAGG ATGCTGACTGCTGAGGAGAAGGCTGCCGTCACCGCCTTTTGGGGCAAGGT GAAAGTGGATGAAGTTGGTGGTGAGGCCCTGGGCAG ATGGTGCACCTGACTCCTGAGGAGAAGTCTGCCGTTACTGCCCTGTGGGG CAAGGTGAACGTGGATGAAGTTGGTGGTGAGGCCCTGGGCAGGTTGGTATCA AGG Tabe 2 The species, accessions, engths and origins of the 11 types of SARS coronavirus isoate genome sequence No. Species Accession Length(bp) From 1 CUHK-Su10 AY Hong Kong 2 HKU AY Hong Kong 3 CUHK-W1 AY Hong Kong 4 Sin2500 AY Singapore 5 Sin2677 AY Singapore 6 Sin2679 AY Singapore 7 Sin2748 AY Singapore 8 Sin2774 AY Singapore 9 TOR2 AY Canada Toronto 10 TW1 AY Taiwan 11 Urbani AY American 3.2 Resuts and Discussion We use the measure of sequence simiarity based on doubing nuceotides and information dispersion to buid the information divergence matrix for the first exon of β-gobin gene of 11 different species in Tabe 3 (L=10). Based on the information divergence matrix, using the Neighbor program in the PHYLIP package ( we can obtain the phyogenetic tree beonging to eeven different species isted in Fig. 1. We buid the information divergence matrix for the SARS coronavirus data in Tabe 4 (L=100) and obtain the phyogenetic tree in Fig. 2. Tabe 3 Simiarity/Dissimiarity Matrix for the Coding Sequences of Tabe 1 based on the information divergence (L=10) Name. Human Goat Opossum Gaus Lemur Mouse Rabbit Rat Goria Bovine Chim. Human Goat Opossum Gaus Lemur Mouse Rabbit Rat Goria Bovine Chim Tabe 4 Simiarity/Dissimiarity Matrix the for Coding Sequences of Tabe 2 (L=100) No

6 Goria A Measure for Sequence Simiarity 77 Bovine Chim Tabe 4 Simiarity/Dissimiarity Tabe 4Simiarity/Dissimiarity Matrix for Matrix the Coding for Sequences of Tabe 2 (L=100) No TOR2 TOR2 HKU HKU TW1 TW1 CUHK-Su CUHK-Su Rat Rat Gaus Gaus Urbani Urbani CUHK-W CUHK-W Mouse Mouse Opossum m Group3 Group2 Group2 Group1 Group1 Chimpanzee Human Human Goria Rabbit Goria Rabbit Bovine Goat Lemur Bovine Goat Lemur Fig. 1Phyogenetic tree constructed Fig. by 1 Phyogenetic neighbor joining tree constructed method by neighbor joining method Sin27 Sin27 Sin277 Sin267 Sin277 Sin267 Sin250 Sin250 Sin267 Sin267 Fig. 2Phyogenetic tree constructed by Fig. neighbor 2 Phyogenetic joining tree method constructed for SARS coronavirus by neighbor joining method for SARS coronavirus From Tabe 3, we can see Gaus is farthest away from the other 10 species (the distances were a more than , and the highest vaue reached ), foowed by Opossum. Gaus is non-mammas whie other species are mammas and Opossum has the furthest genetic reationship of a mammas. The simiarity resuts are basicay consistent with the facts. We find that the smaer entries in Tabe 2 are associated with the pairs Human and Goria(0.0102), Goria and Chimpanzee(0.0324), Goat and Bovine(0.0342), Human and Chimpanzee(0.0366). Chimpanzee(0.0324), Goat and Bovine( ), Human and Chimpanzee(0.0366). The The discrepancy indices of these pairs are the smaest ones in the tabe, which means they are simiar to each other in each pairs. It is more in ine with the facts. to each other in each pairs. It is more in ine with the facts. Then we give the anaysis of the genetic reationship for the 11 SARS corona virus isoates. From Fig.2 we can see that group 1 (CUHK-Su10 and CUHK-W1) has a cose genetic reationship, group 2 (Sin2748, Sin2677, Sin2500, Sin2679 and From Tabe 3, we can see Gaus is farthest away from the other 10 species (the distances were a more than , and the highest vaue reached ), foowed by Opossum. Gaus From Tabe 3, we can see Gaus is farthest away from the other 10 species (the distances were non-mammas whie other species are mammas and Opossum has the furthest genetic reationship a more than , and the highest vaue reached ), foowed by Opossum. Gaus is of a mammas. The simiarity resuts are basicay consistent with the facts. We find that the non-mammas whie other species are mammas and Opossum has the furthest genetic reationship smaer entries in Tabe 2 are associated with the pairs Human and Goria(0.0102), Goria and of a mammas. The simiarity resuts are basicay consistent with the facts. We find that the smaer entries in Tabe 2 are associated with the pairs Human and Goria(0.0102), Goria and discrepancy indices of these pairs are the smaest ones in the tabe, which means they are simiar Then we give the anaysis of the genetic reationship or the f11 SARS corona virus isoates. From Fig.2 we can see that group 1 (CUHK-Su10 and CUHK-W1) has a cose genetic reationship, group 2 (Sin2748, Sin2677, Sin2500, Sin2679 and Sin2774) has cose affinity, group 3 (TOR2, TW1, HKU and Urbani) has cose affinity from Fig.2. Referring to Tabe 2 it is distinct the types of group 1 come from Hong Kong, with the types of group 2 come from Singapore, whie the group 3 can be attributed to goba broadcasters. So, the genetic reationship for the 11 SARS corona virus isoates can be proved by their geography reationship.

7 78 The 4th Internationa Conference on Computationa Systems Bioogy Sin2774) has cose affinity, group 3 (TOR2, TW1, HKU and Urbani) has cose affinity from Fig.2. Referring to Tabe 2 it is distinct the types of group 1 come from Hong Kong, with the types of group 2 come from Singapore, whie the group 3 can be attributed to goba broadcasters. So, the genetic reationship for the 11 SARS corona virus isoates can be proved by their geography reationship Goat Opossum Gaus Lemur Mouse Rabbit Rat Goria Bovine Chimpanzee Fig. 3 The track changes of the distance vaues of Human and other 10 kinds of sequences with L HKU CUHK-W1 Sin2500 Sin2677 Sin2679 Sin2748 Sin2774 TOR2 TW1 Urbani Fig. 4 The track changes of the distance vaues of CUHK-Su10 and other 10 kinds of viruses with L

8 A Measure for Sequence Simiarity Fig. 5 The track changes of bodong(l) of Human with L Fig. 6 The track changes of bodong(l) of CUHK-Su10 with L Now we wi study the reationship of the parameter L with the distance vaues between DNA sequences. Given an information set P, the distance matrix based on P is denoted by dis(l). When P changes to P +1, we define bodong(l) as the sum of the absoute vaue of difference between the corresponding eements of two distance matrices, i.e., bodong (L) = dis (L+1) dis (L) (9) Fig 3 shows that distance vaues of Human and other 10 kinds of sequences are changed with L whie Fig 5 shows that the vaues of bodong(l) of Human are changed with L. Fig 4 shows that distance vaues of CUHK-Su10 and other 10 kinds of viruses are changed with L whie Fig 6 shows that the vaues of bodong(l) of CUHK-Su10 are changed with L. From Fig 3 and Fig 5, we can see the distance vaues between species are not monotonicay increasing or decreasing as the vaue of L increases. Whie L is very sma, the information set incude ess information, so the distance vaues changed greaty. They tend to sowy change when L increases. Fig 4 and Fig 6 aso proved this viewpoint. The resuts shown from Fig 3 to Fig 5 aso indicate that we can set the proper vaue for parameter L ony considering the variation of the distance vaue between DNA sequences without anayzing the compete information set P which coud contend more information as the L increases.

9 80 The 4th Internationa Conference on Computationa Systems Bioogy 4 Concusion In this paper, we consider the properties of the neighboring dua nuceotides to construct the nove compete information set of the DNA sequence based on the frequencies of the dua nuceotides in different intervas. According to information dispersion, we get an approach to make simiarity anaysis of DNA sequence. The advantage of our method is that can refect the reationship between bioogica sequences objectivey and computationa compexity can be inear growth with the growth of sequence ength. So, it is easy to process arge scae data. Acknowedgment This work is supported in part by the Nationa Nature Science Foundation of Hunan province (Grant No. 07JJ5086) and Hunan University Students innovative piot scheme. References [1] Xu Cai, Weiwu Fang, Wen Zhang. Comparison of aignment-free methods based on mitochondrion compete genome. Computers and Appied Chemistry, 2005, 22(10): [2] Wen Zhang, Huanwen Tang, Weiwu Fang, Zhiong Xiu. Appication of a new measure of information discrepancy to the anaysis of SARS corona virus. Computers and Appied Chemistry, 2003, 20(6): [3] Wei-Wu Fang, FS Roberts, Zhengrong Ma. A measure of discrepancy of mutipe sequences. Information Science, 2001, 137: [4] Wei-Wu Fang. The characterization of a measure of information discrepancy. Information Science, 2000, 125: [5] Wen Zhang, Huanwen Tang, Weiwu FANG, Xu Cai, Weiwei Zhang. Construction of phyogenetic tree of whoe proteome microbia organisms as inferred from a new measure of information discrepancy. Journa of Daian University of Technoogy, 2005, 45(6): [6] Li-Zhen Zhang, Huanwen Tang. A method of protein structure cass prediction based on subsequence distribution. Computers and Appied Chemistry, 2003, 23(3):1-6. [7] Jie Song, Huanwen Tang. Cassification of Homo-oigomeric Proteins by a New Measure of Information Discrepancy. Mathematics in Practice and Theory, 2007, 37(8): [8] Zhen Qi, Runsheng Chen. Phyogenetic anaysis of SARS coronavirus based on whoe-genome comparison. Chinese Science Buetin, 2003, 48(12): [9] WW Fang. The disagreement degree of muti-person judgments in additive structure. Mathematica Socia Sciences, 1994, 28(2): [10] Min Zhang. Research on Mutipe sequence Aignment Agorithms in Bioinformatics. Daian University of Technoogy [11] Ruan Y J, Wei C L, Ee L A, et a. Comparative fu-ength genome sequence anaysis of 14 SARS coronavirus Isoates and common mutations associated with putative origins of infection. The Lancet, 2003, 361 (9371):