Prediction of Disulfide Bonding Pattern Based on Support Vector Machine with Parameters Tuned by Multiple Trajectory Search

Transcription

1 Hsuan-Hung Ln, Ln-Yu seng Predcton of Dsulfde Bondng Pattern Based on Support Vector Machne wth Parameters uned by Multple rajectory Search HSUAN-HUNG LIN 1,, LIN-YU SENG 3,4 1 Department of Appled Mathematcs, Natonal 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 Networkng and Multmeda, Natonal Chung Hsng Unversty, achung, awan 4, ROC 4 Department of Computer Scence and Engneerng, Natonal 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 solvng the 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. o the best of our knowledge, wthout the pror knowledge of the bondng state of cystenes, the best accuracy rate reported n the lterature 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. In ths study, the cysten poston dfference, the cysten ndex dfference, the predcted secondary structure of proten and the PSSM score are used as 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 54.5% and 6% 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, SVM, multple trajectory search 1 Introducton Dsulfde bonds play an mportant 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, ]. As shown n Fg. 1, the structures of (a) the tck antcoagulant peptde (1AP), a protease nhbtor, and (b) the bovne pancreatc trypsn nhbtor (1QLQ), a serne protease nhbtor. her sequence dentty s only 18.%, the absence of sgnfcant sequence dentty between 1AP and 1QLQ was noted by Antuch et al. [3] and PSI-BLAS searches n the SwssProt/rEMBL and NR database were unsuccessful n dentfyng the smlarty between these two protens. In dsulfde-bondng base classfcaton, these two protens have the same dsulfde-bondng connectvty pattern (1-6, -3, 4-5), and all of whch are classfed n the BPI-lke superfamly n SCOP [4]. 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 [5], neural networks [6, 7], or support vector machnes [8] had been proposed. hey are qute effectve n predctng the bondng state of cystenes wth the accuracy rates around 81%-9%. ISSN: Issue 9, Volume 8, September 9

2 Hsuan-Hung Ln, Ln-Yu seng (a) (b) Fg. 1 he structures of (a) the tck antcoagulant peptde (1AP), a protease nhbtor, and (b) the bovne pancreatc trypsn nhbtor (1QLQ), a serne protease nhbtor. Recently, several methods were proposed for the predcton of the dsulfde bondng pattern. he frst method was presented by Farsell and Casado [9]. 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. [1] mproved ther prevous results by usng neural networks to predct the cystene parwse nteractons. Vullo and Frascon [11] 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 twodmensonal recursve neural networks to predct connectvty probabltes between cystene pars. Ferrè and Clote [13] 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. [14] 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 [15] 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. [16] used a smple feature called cystene separatons profles (CSP) to predct the connectvty patterns. Chen et al. [17] proposed a two-level model. Lu et al. [18] obtaned the accuracy of 73.9% by usng GA to optmze feature selecton for the SVM. Song et al. [19] 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. [] 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. [13] assume that the bondng states are known. he method proposed by Cheng et al. [1] and Ferrè et al. [13] can be appled whether the bondng states are known or not. 1.1 Support vector machne Support vector machne (SVM) s a supervsed learnng method used for classfcaton [1]. It s beleved to be superor to tradtonal statstcal and neural network classfers. However, t s crtcal to determne sutable combnaton of SVM parameters regardng classfcaton performance. A specal property of SVM s that t can smultaneously mnmze the emprcal classfcaton error and maxmze the geometrc margn. It s a useful technque for data classfcaton and regresson and has become an mportant tool for machne learnng and data mnng. It s a powerful methodology for ISSN: Issue 9, Volume 8, September 9

3 Hsuan-Hung Ln, Ln-Yu seng solvng problems n nonlnear classfcaton, functon estmaton and densty estmaton whch has also led to many applcatons, such as the mage nterpretaton, data mnng and other botechnologcal felds [-4]. SVM s generally used for data whch can be classfed nto two clusters, however, classfcaton of multple clusters can also be easly expanded [5]. In general, SVM has better performance when competed wth exstng methods, such as neural networks and decson trees [6-8]. Recently, applcaton of SVM n medcne has grown rapdly. For examples, t has been appled n predcton of RNA-bndng stes n protens [9], proten secondary structure predcton [3]. SVM has also been appled to bologcal problems [31, 3], electrcal energy consumpton forecastng [33], remote sensng mage classfcaton [34], and pattern recognton and data classfcaton [35]. 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. [36, 37] g( x ) w x w (1) he dstance of a pont from a hyperplane s gven by g( ) z x w () As shown n Fg., the 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,,..., N (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 N 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 N 1 max ( ) 1 j y y jx x j λ, j (5) N 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 N y 1 x n Eq. (4). N N 1 [ y ( w 1 y, x w ) -1] and λ (4) Once the optmal hyperplane s obtaned, classfcaton of a sample s performed based on the sgn of the followng equaton: Fg.. he hyperplane wth greatest margn. Note that the margn of drecton s larger than the margn of drecton 1 Ns g( x) w x w y x x w (6) 1 where Ns 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) R k, where k s usually much hgher than l. hen t s always true that r ( x) ( K ( x, (7) r 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 ISSN: Issue 9, Volume 8, September 9

4 Hsuan-Hung Ln, Ln-Yu seng 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 K ( x, exp( x z K ( x, tanh( x z ) / ) (9a) (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. 1. Multple rajectory Search he multple trajectory search (MS) had been presented for large scale global optmzaton [38]. he MS had also been used to solve the multobjectve optmzaton problems and obtaned satsfactory results [39]. It uses multple agents to search the soluton space concurrently. Each agent does an terated local search usng one of three canddate local search methods. By choosng a local search method that best fts the landscape of a soluton s neghborhood, an agent may fnd ts way to a local optmum or the global optmum Orthogonal Array and Smulated Orthogonal Array he concept of orthogonal arrays whch are used n expermental desgn methods s brefly ntroduced. Suppose n an experment, there are k factors and each factor has q levels. In order to fnd the best setng of each factor s level, qkexperments must be done. Very often, t s not possble or cost effectve to test all qk combnatons. It s desrable to sample a small but representatve sample of combnatons for testng. he orthogonal arrays were developed for ths purpose. In an experment that has k factors and each factor has q levels, an orthogonal array OA(n,k,q,t) s an array wth n rows and k columns whch s a representatve sample of n testng experments that satsfes the followng three condtons. (1) For the factor n any column, every level occurs the same number of tmes. () For the t factors n any t columns, every combnaton of q levels occurs the same number of tmes. (3) he selected combnatons are unformly dstrbuted over the whole space of all the possble combnatons. In the notaton OA(n,k,q,t), n s the number of experments, k s the number of factors, q s the number of levels of each factor and t s called the strength. he orthogonal arrays exst for only some specfcn s andk s. So t s not approprate to use the OA n some applcatons. seng et al. [38] proposed the smulated OA (SOA). he SOA satsfes only the frst of the above mentoned three condtons, but t s easy to construct an SOA of almost any sze. Suppose there are k factors and each factor has q levels, an m k smulated orthogonal array SOA m k wth m beng a multple of q can be generated as follows. For each column of SOA m k, a random permutaton of,1,, q-1 s generated and denoted as sequence C. hen the elements n C are pcked one by one sequentally and flled n a randomly chosen empty entry of the column. If all elements n C were pcked, the process pcks elements agan from the begnnng of C. So n every column of SOA m k, each of q elements wll appear the same number of tmes (condton 1). 1.. he Multple rajectory Search he MS generates M ntal solutons by utlzng the smulated orthogonal array SOA M N, where the number of factors corresponds to the dmenson N and the number of levels of each factor s taken to be M. So eachof, 1,, M-1 wll appear once n every column. Usng SOA tends to make these M ntal solutons unformly dstrbuted over the feasble soluton space. he ntal search range for local search methods s set to half of the dfference between the upper bound and the lower bound. Afterwards, local search methods wll change the search range. he MS conssts of teratons of local searches untl the maxmum number of functon evaluatons s reached. In the frst teraton, the MS conducts local searches on all of M ntal solutons. But n the followng teratons, only some better solutons are chosen as foreground solutons and the MS conducts local searches on these solutons. hree local search methods are provded for the MS. he MS wll frst test the performance of three local search methods and then choose the one that performs best, that s, the one that best fts the landscape of the neghborhood of the soluton, to do the search. After conductng the search on foreground solutons, the MS apples Local Search 1 to the current best soluton tryng to mprove the current best soluton. Before the end of an teraton, some better solutons are chosen as the foreground ISSN: Issue 9, Volume 8, September 9

5 Hsuan-Hung Ln, Ln-Yu seng solutons for the next teraton. he multple trajectory search algorthm s descrbed n the followng. Multple rajectory Search /*Generate M ntal solutons */ Buld smulated orthogonal array SOA M N For = 1 to M For j = 1 to N X [j] = l + (u -l ) * SOA[, j] / (M-1) Evaluate functon values of X s For = 1 to M Enable[] RUE Improve[] RUE SearchRangeX = (UPPER_BOUND-LOWER_BOUND)/ Whle ( #ofevaluaton predefned_max_evaluaton) For I =1 to M If Enable[] = RUE hen GradeX LS1_estGrade LS_estGrade LS3_estGrade For j = 1 to #oflocalsearchest LS1_estGrade LS1_estGrade+ LocalSearch1(X, SearchRangeX ) LS_estGrade LS_estGrade+ LocalSearch(X, SearchRange X ) LS3_estGrade LS3_estGrade+ LocalSearch3(X, SearchRange X ) Choose the one wth the best estgrade and let t be LocalSearchK /* K may be 1,, or 3 */ For j = 1 to #oflocalsearch GradeX GradeX + LocalSearchK(X, SearchRangeX ) For I = 1 to #oflocalsearchbest LocalSearch1(BestSoluton,SearchRangeBestSoluton) For = 1 to M Enable[] FALSE Choose #offoreground X s whose GradeX are best among the M solutons and set ther correspondng Enable[] to RUE End Whle In the MS, three local search methods are used for searchng dfferent landscape of the neghborhood of a soluton. Local Search 1 searches along one dmenson from the frst dmenson to the last dmenson. Local Search s smlar to Local Search 1 except that t searches along a drecton derved from about one-fourth of dmensons. In both local search methods, the search range (SR) wll be cut to one-half untl t s less than f the prevous local search does not make mprovement. In Local Search 1, on the dmenson concernng the search, the soluton s coordnate of ths dmenson s frst subtracted by SR to see f the objectve functon value s mproved. If t s, the search proceeds to consder the next dmenson. If t s not, the soluton s restored and then the soluton s coordnate of ths dmenson s added by.5*sr, agan to see f the objectve functon value s mproved. If t s, the search proceeds to consder the next dmenson. If t s not, the soluton s restored and the search proceeds to consder the next dmenson. Local Search 1 and Local Search are lsted n the followng. Functon LocalSearch1(X k, SR) If Improve[k]=FALSE hen SR = SR / If SR < 1e-15 hen SR (UPPER_BOUND-LOWER_BOUND) *.4 Improve[k] FALSE For = 1 to N X k[] X k[]- SR If X k s better than current best soluton hen grade grade + BONUS1 Update current best soluton If functon value of X k s the same hen restore X k to ts orgnal value If functon value of X k degenerates hen restore X k to ts orgnal value X k[]_x k[] +.5* SR If X k s better than current best soluton hen grade grade + BONUS1 Update current best soluton If functon value of X k has not been mproved hen restore X k to ts orgnal value grade grade + BONUS Improve[k] RUE grade grade + BONUS Improve[k] RUE return grade ISSN: Issue 9, Volume 8, September 9

6 Hsuan-Hung Ln, Ln-Yu seng Functon LocalSearch(X k, SR) If Improve[k] = FALSE hen SR = SR/ If SR < 1e-15 hen SR (UPPER_BOUND-LOWER_BOUND) *.4 Improve[k] FALSE For l = 1 to N For = 1 to N r[] Random{,1,,3} D[] Random{-1,1} For = 1 to N If r[] = hen X k[] X k[] SR * D[] If X k s better than current best soluton hen grade grade + BONUS1 Update current best soluton If functon value of X k s the same hen restore X k to ts orgnal value If functon value of X k degenerates hen restore X k to ts orgnal value For = to N If r[]= hen X k[]_x k[] +.5 * SR * D[] If X k s better than current best soluton hen grade grade + BONUS1 Update current best soluton If functon value of X k has not been mproved hen restore X k to ts orgnal value grade grade + BONUS Improve[k] RUE grade grade + BONUS Improve[k] RUE return grade Local Search 3 s dfferent from Local Search 1 and Local Search. Local Search 3 consders three small movements along each dmenson and heurstcally determnes the movement of the soluton along each dmenson. In Local Search 3, although the search s along each dmenson from the frst dmenson to the last dmenson, the evaluaton of the objectve functon value s done after searchng all the dmensons, and the soluton wll be moved to the new poston only f the objectve functon has been mproved at ths evaluaton. Local Search 3 s descrbed n the followng. Functon LocalSearch3(X,SR) For = 1 to N X 1 X s th coordnate s ncreased by.1 Y 1 X s th coordnate s decreased by.1 X X s th coordnate s ncreased by. If X 1 s better than current best soluton hen grade grade + BONUS1 Update current best soluton If Y 1 s better than current best soluton hen grade_grade + BONUS1 Update current best soluton If X s better than current best soluton hen grade grade + BONUS1 Update current best soluton D 1 = F(X) - F(X 1) If D 1 > // X 1 s better than X hen grade grade + BONUS D = F(X) - F(Y 1) If D > //Y 1 s better than X hen grade grade + BONUS D 3 = F(X) - F(X ) If D 3 > //X s better than X hen grade grade + BONUS a Random[.4,.5] b Random[.1,.3] c Random[, 1] X[] = X[] + a(d 1 - D ) + b(d 3-D 1) + c If functon value of X has not been mproved hen restore X to ts orgnal value grade grade + BONUS return grade 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 ISSN: Issue 9, Volume 8, September 9

7 Hsuan-Hung Ln, Ln-Yu seng 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 [4], 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 [38] 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) NCPD (Normalzed 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 ). () NCID (Normalzed Cystene Index 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 [41] 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 [43]. Snce the predcton rate s hghly nfluenced by the value of the parameters C andγ, the multple trajectory search [38] s used for fndng good settngs of parameter values for the SVM and the wndow szes for the PSS and the PSSM..5 Multple rajectory Search for Selectng SVM Parameters and Wndow Szes he multple trajectory search can fnd optmal or near-optmal soluton wthn an acceptable tme, and s faster than the dynamc programmng or the branch-and-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 andγbut also the wndow szes of the PSS and the PSSM. As shown n Fg. 3, a chromosome s coded as S =(C, γ, S 1, S ) where C andγ are the log values of the parameters C andγ, 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. 4. log C log γ S 1 S Wndow sze for the PSS SVM Parameters and the PSSM Fg. 3. Chromosome of the proposed method. ISSN: Issue 9, Volume 8, September 9

8 Hsuan-Hung Ln, Ln-Yu seng Fg. 4. 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 [44] 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 = 7.4 and log γ= -4.6 for SVM, the wndow szes are 1 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 Q P C C 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. ISSN: Issue 9, Volume 8, September 9

9 Hsuan-Hung Ln, Ln-Yu seng 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 able 1, t s noted that the overall senstvty s 5% for Cheng s method and the predcton accuracy (Qc) s 6% for our method. here s an ncrease of predcton accuracy from 5% to 6%. As for the dsulfde connectvty predcton, Cheng s method wth true secondary structure (SS) 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 54.5%. here s an ncrease of predcton accuracy from 48% to 54.5%. able 1. Brdge classfcaton result for dataset SPX wthout the pror knowledge of the bondng state of cystenes. # of bonds Cheng et al. (6) hs work Senstvty Specfcty Accuracy(Q c ) 1 71% 48% 7.9% 59% 6% 73.% 3 55% 61% 69.7% 4 44% 48% 59.7% 5 3% 35% 4.% 6 3% 36% 33.3% 7 9% 3% 7.1% 8 % %.5% 9 44% 5% 44.4% 1 33% 36% 3.3% 1 38% 39% 58.3% 14 79% 85% 1.% 16 13% 13% 15.6% 17 53% 6% 55.9% 5 3% 53%.% 6 31% 51% 3.8% All 5% 51% 6.% 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% 6.6% 59% 56% 65.9% 3 5% 47% 59.8% 4 34% % 36.4% 5~6 % 13% 11.8% All 51% 48% 54.5% 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. [13] 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 54.5% 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. Narasmhan, 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] W. Antuch, P. Guntert, M. Blleter,. Hawthorne, H. Grossenbacher, K. Wuthrch, NMR soluton structure of the recombnant tck antcoagulant proten (rap), a factor Xa nhbtor from the tck Ornthodoros moubata, FEBS Letters, Vol. 35, 1994, pp ISSN: Issue 9, Volume 8, September 9

10 Hsuan-Hung Ln, Ln-Yu seng [4] L. C. Loredana, E. B Steven, J. P. H. m, C. Chotha, A. G. Murzn, SCOP database n : refnements accommodate structural genomcs, Nuclec Acds Res. Vol. 3,, pp [5] A. Fser, I. Smon, Predctng the oxdaton state of cystenes by multple sequence algnment, Bonformatcs, Vol. 16,, pp [6] 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 [7] 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 [8] 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 [9] P. Farsell, R. Casado, Predcton of dsulfde connectvty n protens, Bonformatcs, Vol. 17, 1, pp [1] P. Farsell, P. L. Martell, R. Casado, A neural network base method for predctng the dsulfde connectvty n protens, In Daman,E. et al., eds. Knowledge based Intellgent Informaton Engneerng Systems and Alled echnologes KES, IOS Press, Amsterdam, 1, pp [11] A. Vullo, P. Frascon, Dsulfde connectvty predcton usng recursve neural networks and evolutonary nformaton, Bonformatcs, Vol., 4, pp [1] J. Cheng, H. Sago, P. Bald, Large-scale predcton of dsulphde brdges usng kernel methods, two-dmensonal recursve neural networks, and weghted graph matchng, Protens, Vol. 6, 6, pp [13] F. Ferrè, P. Clote, Dsulfde connectvty predcton usng secondary structure nformaton and dresdue frequences, Bonformatcs, Vol. 1, 5, pp [14] C. H. sa, B. J. Chen, H. H. Chan, H. L. Lu, C.Y. Kao, Improvng dsulfde connectvty predcton wth sequental dstance between oxdzed cystenes, Bonformatcs, Vol. 1, 5, pp [15] Y. C. Chen, J. K. Hwang, Predcton of dsulfde connectvty from proten sequences, Protens, Vol. 61, 5, pp [16] E. Zhao, H. L. Lu, C. H. sa, H. K. sa, C. H. Chan, C. Y. Kao, Cystene separatons profles on proten sequences nfer dsulfde connectvty, Bonformatcs, Vol. 1, 5, pp [17] B. J. Chen, C. H. sa, C. H. Chan, C.Y. Kao, Dsulfde connectvty predcton wth 7% accuracy usng two-level models, Protens, Vol. 55(1), 6, pp [18] C. H. Lu, Y. C. Chen, C. S. Yu, J. K. Hwang, Predctng dsulfde connectvty patterns, Protens, Vol. 67, 7, pp [19] J. Song, Z. Yuan, H. an.. Huber. K. Burrage, Predctng dsulfde connectvty from proten sequence usng multple sequence feature vectors and secondary structure, Bonformatcs, Vol. 3, 7, pp [] R. Rubnsten, A. Fser, Predctng dsulfde bond connectvty n protens by correlated mutatons analyss, Bonformatcs, Vol. 4, 8, pp [1] C. C. Chang, C. J. Ln, LIBSVM: a lbrary for support vector machnes, 1, Retreved from [] S. Idcula-homas, A. J. Kulkarn, B. D. Kulkarn, V. K. Jayaraman, P. V. Balaj, A support vector machne-based method for predctng the propensty of a proten to be soluble or to form ncluson body on overexpresson n Eschercha col, Bonformatcs, Vol., 6, pp [3] P. M. Kasson, J. B. Huppa, M. M. Davs, A.. Brunger, A hybrd machne-learnng approach for segmentaton of proten localzaton data, Bonformatcs, Vol. 1, 5, pp [4] M. E. Mavroforaks, H. V. Georgou, N. Dmtropoulos, D. Cavouras, S. heodords, Mammographc masses characterzaton based on localzed texture and dataset fractal analyss usng lnear, neural and support vector machne classfers, Artf Intell Med, Vol. 37, 6, pp [5] C. W. Hsu, C. J. Ln, A comparson of methods for multclass support vector machnes, IEEE rans Neural Network, Vol. 13,, pp [6] M. P. S. Brown, W. N. Grundy, D. Ln, N. Crstann, C. Sugnet,. S. Furey, J. M. Ares, et al., Knowledge-based analyss of mcroarray gene expresson data usng support vector machnes, PNAS, Vol. 97,, pp [7] D. DeCoste, B. Schuolkopf, ranng nvarant support vector machnes, Machne Learnng Vol. 46,, pp ISSN: Issue 9, Volume 8, September 9

11 Hsuan-Hung Ln, Ln-Yu seng [8] Y. Lecun, L. Jackel, L. Bottou, A. Brunot, C. Cortes, J. Denker, et al., Comparson of learnng algorthms for handwrtten dgt recognton, Internatonal Conference on Artfcal Neural Networks, 1995, pp [9] J. ong, P. Jang and Z. Lu, RISP: A webbased server for predcton of RNA-bndng stes n protens, Computer Methods and Programs n Bomedcne, Vol. 9, 8, pp [3] Y. Q, F. LIN, K. K. Wong, A Networked mult-class SVM for proten secondary structure predcton, WSEAS Internatonal Conference on: Mathematcal Bology and Ecology (MABE '5), Udne, Italy, January -, 5. [31] M. Brown, W. Grundy, D. Ln, N. Crstann, C. Sugnet, M. Ares, D. Haussler, Support vector machne classfcaton of mcroarray gene expresson data, echncal Report UCSCCRL-99-9, Unversty of Calforna, Santa Cruz, [3] C. H. Yeang, S. Ramaswamy, P. amayo, S. Mukherjee, R. M. Rfkn, M. Angelo, M. Rech, E. Lander, J. Mesrov,. Golub, Molecular classfcaton of multple tumor types, Bonformatcs, Vol. 17, 1, pp.316s-3s. [33] X. P. Zhang, R. Gu, Electrcal energy consumpton forecastng based on contegraton and a support vector machne n Chna, WSEAS ransactons on Mathematcs, Issue 1, Vol. 6, 7, pp [34] H. Xao, X. Zhang, Comparson studes on classfcaton for remote sensng mage on data mnng method, WSEAS ransactons on Computers, Issue 5, Vol. 7, 8, pp [35] G. Pajares, Support vector machnes for shade dentfcaton n urban areas, WSEAS ransactons on Informaton Scence and Applcatons, Vol., No. 1, 5, pp [36] S. heodords, K. Koutroumbas, Pattern Recognton. nd edn. Academc Press, San Deago, 3. [37] N. Crstann, J. Shawe-aylor, An ntroducton to support vector machnes and other kernel-based methods, Cambrdge Unversty Press, Cambrdge UK.. [38] L. Y. seng, C. Chen, Multple trajectory search for large scale global optmzaton, Proceedngs of the 8 IEEE Congress on Evolutonary Computaton CEC 8, pp [39] L. Y. seng, C. Chen, Multple trajectory search for multobjectve optmzaton, Proceedngs of 7 IEEE Congress on Evol. Comput., 7, pp [4] C. Sander, R. Schneder, Database of homology-derved proten structures and the structural meanng of sequence algnment, Protens, Vol. 9, 1991, pp [41] S. F. Altschul,. L. Madden, A. A. Schäffer, J. Zhang, Z. Zhang, W. Mller, D. J. Lpman, Gapped BLAS and PSI-BLAS: a new generaton of proten database search programs, Nuclec Acds Res., Vol. 5, 1997, pp [4] D.. Jones, Proten secondary structure predcton based on poston-specfc scorng matrces, J. Mol. Bol., Vol. 9, 1999, pp [43] C. C. Chang, C. J. Ln, LIBSVM : a lbrary for support vector machnes, 1. [44] H. N. Gabow, Implementaton of algorthms for maxmum matchng on nonbpartte graphs, Phd hess, Stanford Unversty, CA ISSN: Issue 9, Volume 8, September 9