Disulfide Bonding Pattern Prediction Using Support Vector Machine with Parameters Tuned by Multiple Trajectory Search

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1 Proceedngs of the 9th WSEAS Internatonal Conference on APPLIED IFORMAICS AD COMMUICAIOS (AIC '9) Dsulfde Bondng Pattern Predcton Usng Support Vector Machne wth Parameters uned by Multple rajectory Search HSUA-HUG LI 1,, LI-YU SEG 3,4 1 Department of Appled Mathematcs, atonal Chung Hsng Unversty, achung, awan 4, ROC Department of Management Informaton Systems, Central awan Unversty of Scence and echnology, achung 461, awan, R.O.C 3 Insttute of etworkng and Multmeda, atonal Chung Hsng Unversty, achung, awan 4, ROC 4 Department of Computer Scence and Engneerng, atonal Chung Hsng Unversty, achung, awan 4, ROC shln@ctust.edu.tw, lytseng@cs.nchu.edu.tw Abstract: - he predcton of the locaton of dsulfde brdges helps towards the soluton of proten foldng problem. Most of prevous works on dsulfde connectvty pattern predcton use the pror knowledge of the bondng state of cystenes. In ths study an effectve method s proposed to predct dsulfde connectvty pattern wthout the pror knowledge of cystens bondng state. In prevous research works reported n the lterature, to the best of our knowledge, wthout the pror knowledge of the bondng state of cystenes, the best accuracy rate for the predcton of the overall dsulfde connectvty pattern (Qp) and that of dsulfde brdge predcton(qc) are 48% and 51% respectvely for the dataset SPX. hs study uses the cysten poston dfference, the cysten ndex dfference, the predcted secondary structure of proten and the PSSM score as the features. he support vector machne (SVM) s traned to compute the connectvty probabltes of cystene pars. An evolutonary algorthm called the multple trajectory search (MS) s ntegrated wth the SVM tranng to tune the parameters for the SVM and the wndow szes for the predcted secondary structure and the PSSM. he maxmum weght perfect matchng algorthm s then used to fnd the dsulfde connectvty pattern. estng our method on the same dataset SPX, the accuracy rates are 5.8% and 58.1% for dsulfde connectvty pattern predcton and dsulfde brdge predcton when the bondng state of cystenes s not known n advance. Key-Words: - dsulfde bondng pattern, dsulfde bondng state, SVM, multple trajectory search, metaheurstcs 1 Introducton Dsulfde bonds play an mport structural role n stablzng proten conformatons. he predcton of dsulfde bondng pattern helps to a certan degree the predcton of the three-dmensonal proten structure and hence ts functon because dsulfde bonds mpose geometrcal constrants on the proten backbones. Some recent research works do have shown the close relaton between the dsulfde bondng patterns and the proten structures [1,]. In the realm of the dsulfde bond predcton, two problems are addressed. he frst s the predcton of the dsulfde bondng states and the second s the predcton of the dsulfde bondng pattern. Recently, sgnfcant progress has been made n the predcton of the dsulfde bondng states. Several methods based on statstcal analyss [3], neural networks [4,5], or support vector machnes [6] had been proposed. hey are qute effectve n predctng the bondng state of cystenes wth the accuracy rates around 81%-9%. Recently, several methods were proposed for the predcton of the dsulfde bondng pattern. he frst method was presented by Farsell and Casado [7]. hey reduced dsulfde connectvty to the graph matchng problem n whch vertces are oxdzed cystenes and edges are labeled by the strength of nteracton (contact potental) n the assocated par of cystenes. he Monte Carlo smulated annealng method s used to fnd the optmal values of contact potentals and fnally the dsulfde brdges are located by fndng the maxmum weght perfect matchng. Farsell et al. [8] mproved ther prevous ISS: ISB:

2 Proceedngs of the 9th WSEAS Internatonal Conference on APPLIED IFORMAICS AD COMMUICAIOS (AIC '9) results by usng neural networks to predct the cystene parwse nteractons. Vullo and Frascon [9] developed an ad-hoc recursve neural network for scorng labeled undrected graphs that represent the connectvty pattern and they mproved the accuracy rate of bondng pattern predcton sgnfcantly from 34% to 44%. Cheng et al. [1] mproved the predcton accuracy by usng two-dmensonal recursve neural networks to predct connectvty probabltes between cystene pars. Ferrè and Clote [11] desgned the dresdue neural network to predct connectvty probabltes between cystene pars. hey also used secondary structure nformaton and dresdue frequences n ther tranng. sa et al. [1] used the support vector machne to predct connectvty probabltes between cystene pars. he features used n tranng the support vector machne are local sequence profles and the lnear dstance of cystenes. All above mentoned methods are based on the reducton of the connectvty pattern predcton to the maxmum weght perfect matchng problem. he followng four methods are not based on ths reducton. Chen and Hwang [13] used the support vector machne to predct the bondng pattern drectly. he features they used n tranng the support vector machne are the couplng between the local sequence envronments of cystene pars, the cystene separatons, and the amno acd content. Zhao et al. [14] used a smple feature called cystene separatons profles (CSP) to predct the connectvty patterns. Chen et al. [15] proposed a two-level model. Lu et al. [16] obtaned the accuracy of 73.9% by usng GA to optmze feature selecton for the SVM. Song et al. [17] obtaned the accuracy of 74.4% by usng multple sequence vectors and secondary structure. hs accuracy rate s the best one found n the lterature. Rubnsten et al. [18] analyzes the correlated mutaton patterns n multple sequence algnments to predct the dsulfde bond connectvty. All these methods except Cheng et al. [1] and Ferrè et al. [11] assume that the bondng states are known. he method proposed by Cheng et al. [1] and Ferrè et al. [11] can be appled whether the bondng states are known or not. 1.1 Support vector machne he goal of support vector machne (SVM) s to separate multple clusters by constructng a set of separatng hyperplanes wth greatest margn to the boundary of each cluster. For a two-class classfcaton example, let us vew the nput data as n n-dmensonal space. SVM wll construct the hyperplane (Eq. 1) n the space to separate two classes that leaves the maxmum margns from both classes. [19,] g( x ) w x w (1) he dstance of a pont from a hyperplane s gven by g( ) z x () w he values of w and w n Eq. (1) are scaled so that the values of g(x) at the nearest ponts n class 1 and class equal to 1 and -1 respectvely. herefore, fndng the hyperplane becomes a nonlnear quadratc optmzaton problem, whch can be formulated as: w Mnmze J ( w) Subject to y ( w x w ) 1, 1,,..., (3) he above mnmzer must satsfy Karush- Kuhn-ucker (KK) condton, and t can be solved by consderng Lagrangan dualty. he problem can be stated equvalently by ts Wolfe dual representaton form: Maxmze Subject to w w L( w, w, λ) w y x, 1 where L(w, w, λ) s the Lagrangan functon and λs the vector of Lagrangan multplers. By comparng Eqs. (3) and (4), t s noted that the frst two constrants n Eq. (4) become equalty constrants and ths makes the problem easer to be solved. After a lttle bt algebra manpulaton, Eq. (4) becomes 1 max ( ) 1 j y y jx x j λ, j (5) Subject to y wth λ 1 As soon as the Lagrangan multplers are obtaned by maxmzng the above equaton, the optmal hyperplane can be obtaned from w y 1 x n Eq. (4). Once the optmal hyperplane s obtaned, classfcaton of a sample s performed based on the sgn of the followng equaton: g( x) w x w y x x w (6) 1 s 1 [ y ( w 1 y, where s s the number of support vectors. For a vector x R l n the orgnal feature space, assume that there exsts a mappng from x R l to y = (x) and λ x w ) -1] (4) ISS: ISB:

3 Proceedngs of the 9th WSEAS Internatonal Conference on APPLIED IFORMAICS AD COMMUICAIOS (AIC '9) R k, where k s usually much hgher than l. hen t s always true that r ( x) r ( K ( x, (7) r where r (x) s the r th component of the mappng and the kernel functon K(x, s a symmetrc functon satsfyng the followng condton K( x, g( dxdz, and g( x) dx (8) For a nonlnear classfer, varous kernels, ncludng polynomal, radal bass functon, and hyperbolc tangent, as shown n Eq. (9) can be used for mappng the orgnal sample space nto a new Eucldan space n whch Mercer s condtons are satsfed. he lnear classfer can then be desgned for classfcaton. q K( x, ( x z 1), q (9a) K ( x, exp( x z K ( x, tanh( x z ) / ) (9b) (9c) n-fold cross-valdaton of the SVM model s acheved by dvdng the dataset nto n folds. When some fold s reserved for testng, the other n-1 folds are used for tranng the model. Materals and Methods.1 Dataset In order to compare the predcton accuracy rates wth prevously reported method by Cheng et al. [1], the same dataset SPX used by them was employed n the experment. In SPX, all protens were extracted from the PDB on May 17, 4 that contan at least one ntrachan dsulfde bond and all protens that contan less than 1 amno acds were removed. Furthermore, to reduce overrepresentaton of partcular proten famles, Cheng et al. used the UnqueProt, a proten redundancy reducton tool based on the HSSP dstance [1], to choose 118 protens by settng the HSSP cut-off dstance to 1. In SPX, the proten sequences were randomly dvded nto 1 subsets wth roughly equal sze for 1-fold cross-valdaton experment.. Methodology Cheng et al. [1] predcted the bondng state of cystenes frst, and then they predcted the dsulfde bond pattern for the predcted oxdzed cystenes. Our method, nstead of predctng bondng state frst, drectly predcts the bondng probablty of all pars of cystenes. Our method uses the cysten poston dfference, the cysten ndex dfference, the predcted secondary structure of the proten and the PSSM score as features. he SVM s traned to compute the connectvty probabltes of all the cystene pars. he MS [] s used to evolve the parameters C and γfor SVM and wndow szes for the predcted secondary structure and the PSSM. he maxmum weght perfect matchng algorthm s then used to fnd the dsulfde connectvty pattern wthout the pror knowledge of the bondng state of cystenes..3 Features (1) CPD (ormalzed cystene poston dfference): Let {c 1,c,,c n } be the postons of the cystenes n ascendng order. he normalzed cysten poston dfference between c and c j s defned as c -c j /(c n -c 1 ). () CID (ormalzed cystene ndex dfference): Let {c 1,c,,c n } be the postons of the cystenes n ascendng order. he normalzed cysten orderng ndex between c and c j s defned as -j /n. (3) PSSM: PSI-BLAS [3] s used to obtan the local sequence profles. he output fle contans four parts. he frst part s the poston-specfc scorng matrx (PSSM). he PSSM score s used as one of features. (4) PSS (Predcted secondary structure): he predcted secondary structure obtaned by applyng Jones predcton method [4] s used as a feature. In practce, the PSIPRED program s used to predct the secondary structure nformaton..4 Constructon of Predcton Model Based on SVM It s noted that SVM s superor to tradtonal statstcal and neural network classfers n many applcatons. However, t s crtcal to determne proper combnaton of SVM parameters (C and γ) n order to acheve good classfcaton performance. he SVM mplementaton used n ths work s LIBSVM [5]. Snce the predcton rate s hghly nfluenced by the value of the parameters C and γ, the multple trajectory search [] s used for fndng good settngs of parameter value for the SVM and wndow szes for the PSS and the PSSM..5 Multple trajectory search for selectng SVM parameters and wndow szes ISS: ISB:

4 Proceedngs of the 9th WSEAS Internatonal Conference on APPLIED IFORMAICS AD COMMUICAIOS (AIC '9) Multple trajectory search can fnd optmal or nearoptmal soluton wthn an acceptable tme, and s faster than the dynamc programmng or the branchand-bound strategy. Prevously, some research works appled the evolutonary algorthms to select features n the frst phase and then used the selected features to tran the SVM n the second phase. In ths study, the MS and the SVM tranng are tghtly ntegrated. Snce the values of parameters C and γfor the SVM are crtcal to classfcaton accuracy of the SVM, selectng proper values of C and γbecomes an mportant task. radtonally, the regular grd search strategy was used to perform the parameter value selecton. However, t s very tmeconsumng. In ths work, the MS s ntegrated wth the SVM tranng to select not only the value of parameters C and γbut also the wndow szes of the PSS and the PSSM. A chromosome s coded as S =(C, γ, S 1, S ) where C and γ are the log values of the parameters C and γ,and S 1, S are the wndow szes for the PSS and the PSSM respectvely. he ftness functon s defned as the accuracy of the SVM on dsulfde connectvty predcton. he flowchart of the ntegraton of the MS and SVM tranng s shown n Fg. 1. Fg. 1. Flowchart of the proposed method..6 Maxmum weght perfect matchng When a test proten s gven, the connectvty probablty of each cystene par wll be computed by the traned SVM. A complete graph s then constructed wth all cystenes as nodes and the weght assocated wth each edge s the dsulfde connectvty probablty of the par of cystenes that are ncdent to ths edge. he Gabow s algorthm [6] s then appled to fnd the maxmum weght perfect matchng. Because the Gabow s algorthm can only be appled wth nteger edge labels, the dsulfde connectvty probablty of the par of cystenes s multpled by 1 and then truncated nto an nteger to represent the weght assocated wth the edge. hs matchng represents the predcton result of the dsulfde connectvty pattern. We set a probablty threshold, when the dsulfde connectvty probablty of two cystenes s greater than the probablty threshold, then there s a bond between the two cystenes, otherwse there s no bond between the two cystenes. For dataset SPX wth 1-fold cross-valdaton, the results of parameter value selecton by the proposed method are as follows: log C = 6. and log γ= -5.6 for SVM, the wndow szes are 3 and 3 for the PSS and the PSSM. Moreover, the probablty threshold s set to. for a bond to be exsted between two cystens. hs value s determned emprcally. 3 Experment Results In order to evaluate the performance of the predcton, two accuracy ndces Q P and Q C are used: Q C and Q C P P P C C C where C P s the number of protens whose bondng patterns are correctly predcted; P s the total number of protens n the test set; C C s number of dsulfde brdges that are correctly predcted and C s the total number of dsulfde brdges n test protens. ables 1 and show the results for brdge classfcaton and the predcton of the dsulfde bondng pattern of the dataset SPX. For brdge classfcaton, Cheng et al. [1] lsted senstvty and specfcty nstead of accuracy. From the defnton of senstvty and specfcty, n general the value of accuracy les between them. From able1, t s noted that the overall senstvty s 5% for Cheng s method and the predcton accuracy (Qc) s 58.1% for our method. here s an ncrease of predcton accuracy from 5% to 58%. As for the dsulfde connectvty predcton, Cheng s method wth true secondary structure (SS) ISS: ISB:

5 Proceedngs of the 9th WSEAS Internatonal Conference on APPLIED IFORMAICS AD COMMUICAIOS (AIC '9) and solvent accessblty (SA) nformaton n the nputs has the accuracy rate 51%. And Cheng s method wth predcted secondary structure (PSS) and predcted solvent accessblty (PSA) nformaton n the nputs has the predcton accuracy 48% only. In ths study, usng predcted secondary structure n the nputs, the predcton accuracy s 5.8%. here s an ncrease of predcton accuracy from 48% to 5.8%. able 1. Brdge classfcaton result for dataset SPX wthout the pror knowledge of the bondng state of cystenes. # of Cheng et al. (6) hs work bonds Senstvty Specfcty Accuracy(Q c ) 1 71% 48% 73.1% 59% 6% 74.6% 3 55% 61% 6.7% 4 44% 48% 54.8% 5 3% 35% 38.4% 6 3% 36% 33.3% 7 9% 3% 31.4% 8 % % 5.% 9 44% 5% 33.3% 1 33% 36% 33.3% 1 38% 39% 83.3% 14 79% 85% 1.% 16 13% 13% 18.8% 17 53% 6% 58.8% 5 3% 53% 16.% 6 31% 51% 46.% All 5% 51% 58.1% able. Dsulfde connectvty predcton result for dataset SPX wthout the pror knowledge of the bondng state of cystenes. # of bonds Cheng et al. (6) Q p wth SS and SA Q p wth PSS and PSA hs work Accuracy(Q p) 1 59% 59% 59.5% 59% 56% 68.7% 3 5% 47% 5.1% 4 34% % 33.% 5~6 % 13% 11.8% All 51% 48% 5.8% 4 Concluson Recently, the progress n the predcton of the oxdaton states of cystenes n proten sequence s sgnfcant. But for the predcton of the bondng pattern of cystenes, much research effort s stll needed to mprove the predcton accuracy. o these authors knowledge, all prevous approaches except those presented by Ferrè et al. [11] and Cheng et al. [1] assume that the oxdaton states of cystenes were known n advance. o practcally solve the predcton of the bondng pattern of cystenes, ths assumpton eventually should be removed. In ths work, wthout the pror knowledge of the oxdaton states of cystenes, by ntegratng the MS and the SVM tranng to tune parameters of SVM and the wndow szes of the PSS and the PSSM, the proposed method acheves the accuracy of 5.8% on the bondng pattern predcton, whch mproves the accuracy of 51% obtaned by Cheng et al. [1]. References. [1] C. C. Chuang, C. Y. Chen, J. M. Yang, P. C. Lyu, J. K. Hwang, Relatonshp between proten structures and dsulfde-bondng patterns, Protens, Vol. 55, 3, pp.1 5. [] H. W.. van Vljmen, A. Gupta, L. S. arasmhan, J. Sngh, A novel database of dsulfde patterns and ts applcaton to the dscovery of dstantly related homologs, J. Mol. Bol., Vol. 335, 4, pp [3] A. Fser, I. Smon, Predctng the oxdaton state of cystenes by multple sequence algnment, Bonformatcs, Vol. 16,, pp [4] P. Farsell, P. Rccobell, R. Casado, Role of evolutonary nformaton n predctng the dsulfde-bondng state of cystene n protens, Protens, Vol. 36, 1999, pp [5] P. L. Martell, P. Farsell, L. Malagut, R. Casado, Predcton of the dsulfde-bondng state of cystenes n protens wth hdden neural networks, Proten Engneerng, Vol. 15,, pp [6] Y. C. Chen, Y. S. Ln, C. J. Ln, J. K. Hwang, Predcton of the bondng states of cystenes usng the support vector machnes based on multple feature vectors and cystene state sequences, Protens, Vol.55, 4, pp [7] P. Farsell, R. Casado, Predcton of dsulfde connectvty n protens, Bonformatcs, Vol. 17, 1, pp [8] P. Farsell, P. L. Martell, R. Casado, A neural network base method for predctng the dsulfde connectvty n protens, In Daman,E. ISS: ISB:

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