Identifying DNA motifs based on match and mismatch alignment information

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1 J Math Che (2) 5: DOI.7/ ORIGINAL PAPER Identifying DNA otif baed on atch and iatch alignent inforation Jian-Jun Shu Kian Yan Yong Received: 22 October 22 / Accepted: 2 March 2 / Publihed online: 2 April 2 Springer Science+Buine Media New York 2 Abtract The conventional way of identifying DNA otif, olely baed on atch alignent inforation, i uceptible to a high nuber of puriou ite. A novel coring yte ha been introduced by taking both atch and iatch alignent inforation into account. The iatch alignent inforation i ueful to reove puriou ite encountered in DNA otif earching. A an eaple, a correct TATA bo ite in Hoo apien H 4/g gene ha uccefully been identified baed on atch and iatch alignent inforation. Keyword DNA coding Scoring atri Sequence analyi Introduction The identification of DNA binding ite for trancription factor (otif) i iportant for a coplete undertanding of co-regulation of gene epreion, but till reain to be quite challenging to achieve. Two approache doinate otif-finding algorith []: () the word-baed way [2 4] that relie on ehautive enueration or counting frequencie and (2) the probabilitic way [5 7] that relie on optiizing a calarbaed coring atri [8,9], which i viualized conveniently by a equence logo []. However, both way uffer fro the proble of producing a high nuber of puriou ite, due to the ole conideration of atch alignent inforation. In thi paper, a novel coring yte i introduced by incorporating the vectorbaed repreentation of DNA equence into the coring atri. In the vector-baed repreentation of DNA equence, the four nucleotide bae are placed at an equal J.-J. Shu (B) K. Y. Yong School of Mechanical and Aeropace Engineering, Nanyang Technological Univerity, 5 Nanyang Avenue, Singapore 69798, Singapore e-ail: jjhu@ntu.edu.g 2

2 J Math Che (2) 5: ditance fro each other in a three-dienional pace. Thi i poible by placing each point on the verte of a tetrahedron. Any point within the tetrahedron repreent the different cobination of each nucleotide bae type. Therefore the weight ditribution for each poition can be replaced a a point in the tetrahedron in pace uing the threedienional coordinate. Thi point i unique for the different weight ditribution of DNA four nucleotide bae. The advantage of thi approach i twofold: firt, the nuber of indice ued for repreenting the weight ditribution at each poition can be reduced fro four to three in ter of the three-dienional coordinate; Second, the ue of atheatical operator, naely the dot and cro product, can be adopted to decribe the weight ditribution in the three-dienional coordinate and erved a the bai of eauring the quantity of atch and iatch alignent inforation for each poition. A cae tudy how that, by uing iatch alignent inforation, a correct TATA bo ite in Hoo apien H4/g gene ha uccefully been identified. 2 Method 2. Scalar-baed repreentation of DNA nucleotide bae code In calar-baed coring chee, each DNA four nucleotide bae (A, T, G and C) wa repreented by a et of nuber, uch a,2, and 4. The proble with thi repreentation i that of unequal weightage aigned to each nucleotide bae []. In order to aign the ae weightage for each nucleotide bae, a binary encoding chee wa propoed [2]. However, the binary encoding chee i unable to accoodate the DNA four nucleotide fully. The cople, quaternion and hypercople nueral yte have been introduced into the encoding chee by taking advantage of utilizing iaginary doain [,4]. 2.2 Vector-baed repreentation of DNA nucleotide bae code In vector-baed coring chee, the coordinate yte that i elected for vector-baed repreentation i hown in Fig. : The DNA four nucleotide bae are repreented by the vertice A, T, G and C with O being the origin, which i elected inide the tetrahedron uch that it ditance fro each of the vertice i equal to unity, OA = OT = OG = OC =. It i well known that the center of gravity for a regular tetrahedron i three-quarter height below the highet point of the tetrahedron. Thi point i placed at the origin and the vertical height OA i taken to be one unit, a hown in Fig. 2. Therefore the reaining vertical ditance OP i one-third unit. Fro there, angle POC can be found by taking an invere tangent that work out to be 7.5. Uing thi inforation, the angle AOC i found to be 9.5. By oe atheatical anipulation, the ditance between any two nucleotide bae i the ae and found to be.6. Thi enure an equal aignent of weightage for DNA four nucleotide bae. By thi aignent, the ditance between two point i range fro for a perfect atch to.6 for a coplete iatch. 2

3 722 J Math Che (2) 5: A ( ).5 z -.5 C y -.5 O ( ) G T 6.5 Fig. A tetrahedron with aigned nucleotide bae in, y and z-ae Fig. 2 The tetrahedron A G.6 O T / P 7.5 o C 2. Vector-baed repreentation of DNA otif The conventional calar-baed coring atri [8,9] can be converted to a vectorbaed coring atri a the following: For the given weightage of p b [, ] of the nucleotide bae type b {A, T, G, C}, the vector-baed coring atri i repreented by a point at the coordinate (, y, z) 2 = (p A A ) 2 + (p C C ) 2 + (p G G ) 2 + (p T T ) 2 (a) (pa ) 2 ( ) 2 ( ) 2 ( ) 2 y = A y + pc C y + pg G y + pt T y (b) z = (p A A z ) 2 + (p C C z ) 2 + (p G G z ) 2 + (p T T z ) 2 (c)

4 J Math Che (2) 5: where b = ( b, b y, b z ) denote the, y and z-coordinate of the nucleotide bae type b {A, T, G, C}, repectively. 2.4 Scalar-baed coring: atch alignent inforation The ditance between two point in the vector-baed coring atri repreent the degree of the iilarity between the. The nearer are two point, the better i the atch. Thi can be coputed by uing the dot product. For the given coordinate (n, y n, z n ) of a DNA ubtring and ( n, y n, z n ) of a otif at poition n of the ae length N, the atch alignent inforation i the value of the dot product of their coordinate a follow: Score of atch alignent inforation = n, yn, ) ( z n n, yn, )] z n. (2) The reultant dot product give a calar. The larger the nuber, the greater the iilarity between the DNA ubtring and the otif. n= 2.5 Vector-baed coring: iatch alignent inforation In thi paper, a novel approach i propoed to analyze the type of iatche baed on iatch alignent inforation. It can be ued to decide whether one ite ha a greater chance of containing otif over the other although they ay have the ae atch alignent inforation. In noral double-tranded DNA, two-ring purine bae A and G are bigger in ize a copared with one-ring pyriidine bae T and C. One bigger two-ring nucleotide bae pair up with one aller one-ring nucleotide bae in a anner of A to T and G to C. DNA iatche can generally be claified into three type: tranitional, copleentary and tranveral iatche.. Tranition (tranitional iatch) occur when one nucleotide bae i replaced by another of the ae ize, i.e., interchange between two-ring purine bae (A G) or between one-ring pyriidine bae (T C). Becaue the replaceent involve nucleotide bae of the ae ize, tranitional iatch i le likely to reult in aino acid ubtitution due to wobble, and i therefore ore likely to perit a ilent ubtitution in population a ingle nucleotide polyorphi. Hence, tranitional iatch i conidered relatively acceptable. 2. Copleent (copleentary iatch) occur when one nucleotide bae i replaced by it copleentary nucleotide bae of a different ize, i.e., interchange between copleentary nucleotide bae (A T) or (G C).. Tranverion (tranveral iatch) occur when one nucleotide bae i replaced by it non-copleentary nucleotide bae of a different ize, i.e., interchange between non-copleentary nucleotide bae (A C) or (T G). Aong three type of iatche, tranveral iatch i conidered the ot ignificant. An alignent with a high nuber of tranveral iatche generally doe not contain any otif. 2

5 724 J Math Che (2) 5: Table Miatch vector Type Pair Coordinate y z Tranition A G 6 2 C T Copleent A T 2 2 G C Tranverion A C 6 2 T G For the given coordinate ( n, y n, z n ) of a DNA ubtring and ( n, y n, z n ) of a otif at poition n of the ae length N, the iatch alignent inforation i calculated by taking the cro product of their coordinate a follow: Score of iatch alignent inforation = n, yn, ) ( z n n, yn, )] z n. n= () The reultant cro product give a vector whoe three coponent contain the following inforation: Score of tranitional iatch alignent inforation = n, yn, ) ( z n n, yn, )] ( ) z n A G + C T ; (4a) n= Score of copleentary iatch alignent inforation = n, yn, ) ( z n n, yn, )] ( ) z n A T + G C ; (4b) n= Score of tranveral iatch alignent inforation = n, yn, ) ( z n n, yn, )] ( ) z n A C + T G (4c) n= Here the repective iatch vector are hown in Table. 2

6 J Math Che (2) 5: Table 2 TATA bo vector-baed coring atri A T G C p A p T p G p C y.482 z..... Reult and dicuion. Cae tudy of TATA bo in Hoo apien H4/g gene A TATA bo i a egent of DNA equence found in the prooter region of ot gene in eukaryote. It i involved in the proce of trancription by RNA polyerae, acting a the binding ite of either trancription factor or hitone [5]. Hitone act a a pool around which DNA wind and there are five ajor failie, naely H, H2A, H2B, H and H4. H i known a the linker hitone, while H2A, H2B, H and H4 are known a the core hitone. They are involved in the different tage of DNA packing. In thi cae tudy, it i intereting to identify TATA bo in Hoo apien H4/g gene [6]. The H 4/g gene i reponible for producing H4 hitone. By identifying the TATA bo, it i poible to tudy the regulation of H4 hitone production during DNA packing. A an eaple, a TATA bo vector-baed coring atri generated fro RNA polyerae II prooter region [7], a hown in the upper part of Table 2,iuedto identify the poible ite containing the otif within H 4/g gene. The correponding weightage p b [, ] of the nucleotide bae type b {A, T, G, C} and vector-baed coring atri in ter of coordinate (, y, z) in Eq. () are hown in the iddle and lower part of Table 2, repectively. The vector-baed coring atri i aligned with H4/g gene equence bae by bae until the lat nucleotide bae. For each alignent, the atch alignent inforation i calculated by uing Eq. (2) and plotted in Fig...2 Reult and dicuion The plot copoed of peak and trough. Each peak repreent a local high iilarity between the TATA bo vector-baed coring atri and the region within H 4/g gene, and vice vera for trough. There are two highly poible ite (poition 85 and 8) at which the TATA bo could be ituated. However, it i not clear which i the real 2

7 726 J Math Che (2) 5: Match alignent Inforation Score Fig. Match alignent inforation of Hoo apien H4/g gene TATA bo baed on the atch alignent inforation alone, ince both have the ae core. In order to ditinguih thee two ite, the iatch alignent inforation hould be ued. The iatch alignent inforation a dicued i claified into three categorie: tranition, copleent and tranverion. Aong thee three type of iatche, the tranitional iatch i conidered the ot acceptable. If the nucleotide bae type A i replaced by G or vice vera, it i deeed to have le effect on the proce of trancription [8]. Thi i becaue both nucleotide bae type have the ae ize. However, if the different ize nucleotide bae type C replace the nucleotide bae type A in tranveral iatch, the degree of iatch i greater than that of tranitional one [8], becaue of having a ignificant effect on the trancription proce. Standing in between i the copleentary iatch, although the nucleotide bae A and T ay have a different ize, they are copleent a they bind to each other in a DNA chain. Given thee three clae of iatch alignent inforation, the ot acceptable i the tranitional iatch. Thi i followed by the copleentary iatch and the leat acceptable tranveral iatch. By uing Eq. () and (4), a coparion of the tranitional iatch alignent inforation how that the core are the ae for both poition. It i till not poible to differentiate the diiilarity between thee two ite. Hence the copleentary iatch alignent inforation hould be conidered. Figure 4 how that poition 85 ha the higher copleentary iatch alignent inforation a copared with poition 8. Thi iplie that the nucleotide bae A i replaced by the nucleotide bae T, a well a G by C ore often at poition 85. Hence the relatively-acceptable iatch, the copleentary iatch, occur at poition 85. Since the TATA bo conit of a tring of A and T bae, the copleentary iatch between A and T 2

8 J Math Che (2) 5: Copleentary iatch alignent inforation Score Fig. 4 Copleentary iatch alignent inforation of Hoo apien H4/g gene i unlikely to affect the function of the TATA bo a a ignal for trancription proce. Therefore by uing the copleentary iatch alignent inforation, poition 85 i ore likely to be the ite for the TATA bo in H4/g gene. 4 Concluion A calar-baed coring atri i the ueful way of repreenting an alignent and alo ued a a coring ean to predict otif ite. However by uing the atch alignent inforation alone, there ay be a high nuber of falely predicted ite, epecially for le conerved otif. In order to reove puriou ite, the iatch alignent coponent hould be conidered. The vector-baed coring atri can be ued to elaborate atch and iatch alignent inforation; atch degree fro the dot product and iatch degree fro the cro product. Uing the iatch alignent inforation, puriou ite can be reoved and the efficiency in identifying real otif can be iproved [9]. Reference. M.K. Da, H.-K. Dai, A urvey of DNA otif finding algorith. BMC Bioinfor. 8(7), S2 (27) 2. M. Topa, in Proceeding of the Seventh International Conference on Intelligent Syte for, Molecular Biology. An eact ethod for finding hort otif in equence, with application to the ribooe binding ite proble (999), pp J.-J. Shu, Y. Li, A tatitical fat-tail tet of predicting regulatory region in the Droophila genoe. Coput. Biol. Med. 42(9), (22) 2

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