Predicting Protein Functional Class with the Weighted Segmented Pseudo-Amino Acid Composition Moment Vector

Transcription

1 MATCH Counications in Matheatical and in Coputer Cheistry MATCH Coun. Math. Coput. Che. 66 (2011) ISSN Predicting Protein Functional Class with the Weighted Segented Pseudo-Aino Acid Coposition Moent Vector Xinyuan Zhou 1,Xi Li 2, Man Li 3, Xinguo Lu 2 1 Departent of Coputer Science and Technology, Changsha University Changsha Hunan, , China 2 School of inforation science and technology, Hunan University, Changsha Hunan, , China 3 Departent of Coputer Science, Hunan University of Chinese Medicine, Changsha Hunan, , China (Received Septeber 27, 2010) Abstract Predicting protein function at the proteoic-scale is one of the fundaental goals in cell biology and proteoics. In this paper, we proposed a new ethod for characterizing protein sequences the Weighted Segented Pseudo-aino acid coposition Moent Vector (W-SPsAA-MV). Fro protein sequences, the encoding ethod of W-SPsAA-MV is applied to protein functional class prediction associated with the nearest neighbor algorith (NNA) and covariant discriinant (CD) classifier. The experient results show that our new ethod is efficient to predict functional class of query proteins when protein-protein interaction inforation is liited. Corresponding author. E-ail address: xyzhou@yeah.net (X.Y. Zhou)

2 Introduction The nuber of sequenced nucleotide sequences encoding proteins is growing at an extraordinarily fast rate, but the rate of sequence acquisition far surpasses one of protein function deterination. Protein function prediction becoes an iportant issue in the post-genoe era as the gap between the aount of sequence inforation and functional identification widens. With the accuulation of sequence inforation, attention has been paid to the developent of autoatic and reliable ethods for the prediction of protein function fro sequence. Generally speaking, protein function depends on its structure, which depends on protein sequence. At present, this fact has been widely recognized and has becoe the theoretical basis of protein functional prediction based on protein sequence[1]. Various coputational approaches for the prediction of protein functional classes fro protein sequences and analysis of protein sequences have been developed. Aong the, the sequence siilarity-based approach is the ost faous. It is generally believed that proteins of the high sequences siilarity are hoologous proteins which have the sae or siilar structures and function[2].this ethod is ainly achieved through sequence alignent, such as FASTA [3]and BLAST[4]. However, not all hoologous proteins share analogous function[5]. Therefore, the sequence siilarity-based ethod is not suitable for the prediction of protein functional classification in the case of poor siilarity, especially for orphan sequences. Instead of using the sequence siilarity-based approach, ethods that rely on an alternative representation of proteins were proposed in soe papers[6-12]. These ethods are ainly extract soe characteristics contained in protein sequence and use data ining or achine learning ethods to predict protein function class. Ross[6] used data ining prediction(dmp) ethod to predict protein functional classification fro sequences. DMP also can work when protein function is unknown. Cai was used of soe properties of aino acids[7], including aino acid coposition,

3 -447- hydrophobicity, plarity, charge and other properties to represent the protein sequence as specific feature vector, which contains three parts, the coposition (C), transition(t) and distribution(d).the SVM is used to predict protein functional classes in this ethod. In 2007, Wang proposed EBGW approach and cobined with nearest neighbor algorith to predict protein function[8]. And this ethod has been successfully applied to the study of protein structure prediction[9]. The concept of pseudo aino acid coposition was proposed by Chou to predict protein subcellular location and structural classes and so on[10,11]. In this paper, we adopt the Weighted Segented Pseudo-aino acid coposition Moent Vector (W-SPsAA-MV) to represent the saple of a protein via a discrete odel. We obtain good results using W-SPsAA-MV associate with nearest neighbor algorith (NNA) and covariant discriinant (CD) classifier respectively in our study. 2. Dataset We load down the 1818 proteins fro ftp://ftpips.gsf.de/yeast/ which was used in GOM[13], EBGW[8] and GE[12] ethod. There are 1377 proteins as known proteins aong the. The eighteen functional categories of all proteins were shown in Table 1, including the unclassified proteins. The W-SPsAA-MV coding vector diension ust be less than the nuber of saples of each functional categories subset when we adopt CD classifier. Because the W-SPsAA-MV is 58-diensional vector, we can t assign to the functional category whose saple size saller than 58 for adopting CD classifier. Therefore, for CD classifier, the Nu. 3 and Nu. 17 functional categories in Table 1 will not be considered, because they are only 26 and 5 saples respectively. In this way, there are 1373 proteins with known function for CD classifier.

4 -448- Table 1 The nubers of each functional class in dataset Nu Functional class total 1 Metabolis Energy 95 3 Developent (Systeic) 26 4 Cell Type Differentiation Protein Systhesis 98 6 Interaction with the Environent Cell Fate Biogenesis of Cellular Coponents Transcription Protein Fate(folding, odification, destination) Cell Cyle and DNA Processing Protein with Binding function of Cofactor requireent Cellular Transport,Transport Facilities and Transport routes Regulation of Metabolis and Protein function Cellular Counication/Signal Transduction Mechanis Cell Rescue, Defense and Virulence Transposable eleents, Viral and Plasid proteins 5 18 Unclassified protein Methods 3.1. The Weighted Segented Pseudo-aino acid coposition Moent Vector (W-SPsAA-MV) The feature extraction of protein sequences is that every protein sequence was represented as a specific feature vector. In this paper, the Weighted Segented Pseudo-aino acid coposition Moent Vector (W-SpsAA-MV) is proposed as the characterization of protein sequences. W-SpsAA-MV includes not only the aino acid coposition inforation, but also take into account the physiocheical properties of aino acids, position and local inforation. This encoding vector

5 -449- ainly contains three parts, first part is the conventional aino acid coposition, second part is the segented aino acid coding, these two parts are called Segented Pseudo-aino acid coposition (SpsAA), and the third part is the oent vector of aino acid (MV). Given a protein P, its W-SpsAA-MV can be generally forulated as: P [ p, p, p, p, p, p, p ] T (1) where the first 20 eleents p 1, p 2, p 20 are associated with 20 coponents in the conventional aino acid coposition. The iddle eleents p 20 1, p 20, p 20 1 are the segented aino acid coding. The last 20 eleents are the oent vector of aino acid. Given a protein P with L aino acid residues, R1RRRRRR R L (2) where R 1 represents the first residue in the sequence, R 2 represents second, and so forth. The conventional aino acid coposition of protein P can be forulated as: P AA f1 f 2 f20 (3) where f is the occurrence frequency of aino acid A in the protein P, 1 f2 that of aino acid C, and so forth. Here, without loss of generality, the single codes of 20 native aino acids are used according to their alphabetical order. The second part of W-SpsAA-MV is the segented aino acid coding. At first, based on physiocheical characteristics such as residue s hydrophobic property and charged property and so on, we can classify residues into four different classes according to Dandekra[14]. Neutral or non-polar aino acid: A 1 ={G,A,V,L,I,M,P,F,W}; Neutral or polar aino acid: A 2 ={Q,N,S,T,Y,C}; Acidic aino acid: A 3 ={D,E}; Alkalescent aino acid: A 4 ={H,K,R}. And then we grouped these physiocheical properties with every two classes.

6 -450- Thus, three groups can be obtained as follows: { A 1, A 2 } vs {A 3, A 4 }, {A 1, A 3 } vs {A 2, A 4 } and {A 1, A 4 } vs{a 2, A 3 }.We set three rules as described below: Rule 1: Suppose protein P shown in forula (2), and we transfor protein sequence P into nuerical sequence in this way(zhang, et al,2005,wang,et al.,2007): 1 Ri { A1, A2} H1( Ri ) 0 Ri { A3, A4} 1 Ri { A1, A3} H2( Ri ) 0 Ri { A2, A4} 1 Ri { A1, A4} H3( Ri ) 0 Ri { A2, A3} (4) (5) (6) Hence, protein sequence P can be represented as three binary sequences S i =H i (P)=H i (R 1 ) H i (R 2 ) H i (R L ), (i=1,2,3). We call S 1, S 2, S 3 the 1-eigen sequence, 2-eigen sequence and 3-eigen sequences, respectively. Rule 2: For eigen sequence S with length L, let M a positive integer, we can divided S into M subsequence fragents, and was written as S 1, S 2,, S M (1ML), where M is the nuber of fragents. An exaple of the segentation process can be seen in Figure 1. Figure 1. The segentation of characteristic sequence In the Figure 1, the eigen sequence S with length 40 was segented into 6 eigen subsequence fragents. The length of k-th eigen subsequence was defined as: k L ( k 1) L n k M M (7) where L is the length of eigen sequence S, and M is the nuber of segent. Rule 3: For every eigen sequence S, we defined the segented subsequence coding as the frequency of 1 in every eigen subsequence fragents. In this way, we

7 -451- can obtain a M-diensional vector fro a eigen sequence. We can obtain three eigen sequence fro a protein sequence according to Rule 1, therefore, a 3M-dientional vector can be gained, which was called the segented aino acid coposition. This vector was defined as: P [,,,,,,,, ] T (1) (1) (2) (2) (3) (3) ss 1 M 1 M 1 M (8) where the first M eleents is the frequency of 1 in M segents of 1-eigen sequence, the iddle M eleents that of 2-eigen sequence, and the last M eleents that of 3-eigen sequence. The third part of W-SpsAA-MV is the oent vector of aino acid (MV)[15-17], which was defined as: P MV a a a (1) 1 (1) 2 (1) 20 where 20 eleents in P MV was forulated as: (9) a (1) i l w pij L ( L i (1,2, 20) (10) 1) j1 where pij eans the i-th type aino acid in the protein sequence P located in j-th. And ai is forulated according with the alphabetical order. L is the length of protein sequence P, and w is the weight factor. Supposing w =1, for protein P 1 : AAACCC and protein P 2 : ACACAC, the MV of the according to forula (10) can be represented as: PP1 (0.5,0.5,0,,0,0.5,1.25,0,,0) T (11) PP2 (0.5,0.5,0,,0,0.75,1.0,0,,0) T (12) In suary, the W-SpsAA-MV in Eq (1) can be uniquely derived by noralizing the 40+ eleents in Eqs (3), (8) and (9) according to the following equations:

8 -452- wf 1 u, (1 u 20) pu w2 k, (1k 3 M) 1 wa 3 t, (1 t20) LL ( 1) (13) where w 1, w2 and w 3 are the weight factors which were used to regulate the degree of influence of each feature on the classification syste. For different datasets and conditions, we choose different w 1, w2 and w 3 value to achieve the best result. M is the nuber of segent of eigen sequence, we chose M=6 to achieve the best result for our experiental dataset. Therefore, we can get 58-dientional vector for W-SPsAA-MV Nearest neighbor algorith (NNA) The NNA[18] is well known in pattern recognition counity due ainly to its good result and its siple-to-use feature. The NNA assign to an unclassified saple point the classification of the nearest of a set of classified points. In this section we introduced how the NNA was used to predict protein functional class in ters of W-SPsAA-MV. The classification process of the NNA is as follows. Suppose a set of proteins {P 1,P 2,, P n } that have been classified into categories {C 1, C 2,, C }, fro which an unknown protein P can be classified into those categories using the NNA. First, the nearest neighbor of protein P is given by the following equation: nn( P) Pk (14) where P is the W-SPsAA-MV of protein, And P i is deterined by the following equation: n DPP (, ) in DPP (, ) (15) k i1 i Where n is the nuber of known proteins. And D(P, P i ) is defined as DPP (, ) 1 ( P P)/( P P) (16) where i i i P Pi is the dot product of P and P i.the P and P i ean the odule of P and P i respectively. Obviously, when P P, then DPP (, ) =0. i i

9 -453- According to the rule of NNA, if and only if in[ DPP (, ) ( PC)] in[ DPP (, ) ( PC)] in[ DPP (, ) ( P C )] (17) i i 1 i i 2 i i Here, we use because soe proteins belong to ore than one category Covariant Discriinant (CD) classifier The CD classifier has been applied to protein structural class and subcellular location prediction[19-21], and achieved satisfactory results. In this paper, the CD classifier is used to predict protein functional classification based on W-SPsAA-MV discrete odel. Suppose there are N proteins (P 1,P 2,,P N ) which have been classified into functional categories subset, such as: S S1S2 S3 S (18) where each subset S (=1,2,, ) is coposed of proteins with the sae functional class. There are N proteins in the functional subset S. Since every protein has ore than one function, different functional subsets aybe contain the sae proteins. Obviously, N N1N2 N3 N (19) where N is the total nuber of proteins. N 1 eans the nuber of proteins in functional subset S 1 and N 2 eans the nuber of proteins in functional subset S 2, and so forth. According to Eq (1), we can suppose that the u-th protein in the subset S is forulated by P [ p, p,, p, p,, p, p,, p ] u u u u u u u u T,1,2,20,21,20,21,40 (20) u where p, j(j=1,2,,40+ ) eans the j-th coponent of the u-th protein in subset S. The standard vector for the subset S is represented by P [ p, p,, p, p,, p, p,, p ] T (21) where,1,2,20,21,20,21,40

10 -454- p i, N 1 u pi, (i=1,2,,40+ ) (22) N u 1 where N is the nuber of proteins in the -th functional subset S. P can be considered as the standard protein of the subset S. According to the definition of W-SPsAA-MV, the saple of a query protein P should be given by P [ p, p, p, p, p, p, p ] T (23) The eleent for the query protein P can be derived by Eq (13). In this way, the siilarity between a unknown protein P and CD function. 2 (, ) Mah (, ) P is forulated by Eq (24), which is SPP D PP C =1,2,,M (24) In Eq (24), 2 Mah D ( PP, ) is the squared Mahalanobis distance between the query protein P and P, D ( P, P ) ( PP ) C ( P P ) (25) 2 T 1 Mah where T is the transpose operator, and (40+ )(40+ )-diensional atrix. 1 C is the inverse atrix of C, which is a C c c c 1,1 1,40 c 40,1 40,40 (26) where C is the covariance atrix for the subset S and the i, j c is given by 1 c ( p p )( p p ), (i,j=1,2,,40+ ) (27) N u u i, j, i i,, j, j N 1 u1 In Eq (24), C is the deterinant of atrix C. The saller the value D(P, P ), the greater the siilarity between P and P. A query protein P ay have one or ore functional classes, but we generally can only predict a functional category by calculating the iniu of Eq (24). Therefore, the query protein will be assigned to ( 1) functional categories through the following function:

11 -455- u Min F P P F P P F P P (28) { (, 1), (, 2),, (, )} where u is the functional set which was assigned to the query protein P. Min eans the nearest point between the query protein P and P (=1,2,, ). For our data set, we take =5 and also lists the predict results when =1,2,3,4,5 respectively Evaluation ethod In this paper, to prove the effectiveness of W-SPsAA-MV associated with NNA ethod, we copare the predict results of our approach and GOM, EBGW and GE ethod. We exained the prediction quality by the test which was used in the other four ethods. Here, the yeast proteoe is divided into eight groups according to the nuber of partner protein, and about 40% proteins of each group are separated fro the original dataset as testing test, the reaining proteins as training set. The goal of the ethod is to predict functional classes of the proteins in the test set using that of the reaining proteins. After rando sapling for any ties for every group, we consider the average success rate as the last success rate. For W-SPsAA-MV associated with CD classifier, we adopt self-consistency exaination, Jackknife exaination and 5-fold cross validation exaination to verify its effectiveness. 4. Results and discussion 4.1. The result and discussion for W-SPsAA-MV and NNA All datasets are calculated using our W-SPsAA-MV ethod and the nearest neighbor algrith (NNA), and the results were tested by the evaluation ethod as entioned above. In W-SPsAA-MV, different values w 1, w 2, w 3 and M have a significant ipact on the final results. After repeated test, we find that M=6 is the best choice for the dataset. And the value of w 1, w 2 and w 3 were shown in Table 2 for the different conditions. The coparison result between our ethod and GOM, EBGW and GE ethod is shown in Table 2. The overall accuracy of protein classification is

12 -456- iproved fro GOM, EBGW and GE ethod in soe cases. The K in Table 2 denotes the nuber of interacting partners, and N k is the nuber of proteins, which has k interacting partners function is known Table 2 The coparison results between our ethod and different algoriths K K=1 K=2 K=3 K=4 K=5 K=6 K=7 K>7 n K GOM a (%) EBGW b (%) GE c (%) w w w our ethod(%) a Coes fro[13]. b Coes fro[8]. c Coes fro[12]. Fro Table 2, we can find that the accuracy of our ethod is better than that of GOM ethod when K=2 and 4 with 7% and 1% iproveent, respectively. Especially when K=1, the accuracy of our ethod achieve to about 62.5%, while the GOM approach can t ake prediction. Therefore, the results show that W-SpsAA-MV and NNA can be used to predict protein functional class as a copleent ethod, when the protein-protein interaction inforation is liited. Besides, fro Table 2, we find that the success rate of our ethod is 62.5%, 68%, 78.5%, 80% and 85% when K=1, 2, 5, 6 and 7, respectively, which is better than EBGW ethod. We can see fro Table 2, our ethod s prediction overall accuracy is better than the GE ethod in ost cases. Therefore, the results deonstrate that the perforance of W-SpsAA-MV is superior to EBGW and GE as a whole. During our study, we find that the choice of M, w 1, w 2 and w 3 is very iportant,

13 -457- different value of M, w 1, w 2 and w 3 will have a ajor ipact on the last result. So we need test any ties to selet optial values The result and discussion for W-SPsAA-MV and CD classifier The Table 3, 4 and 5 give the prediction results for W-SpsAA-MV and CD classifier. We take w 1 =5, w 2 =0.1 and w 3 =1 respectively for CD classifier with self-consistency exaination, Jackknife exaination and 5-fold cross validation exaination. Table 3 The self-consistency results using W-SpsAA-MV and CD classifier N N 1 N 2 N 3 N 4 N 5 nuber k=1(%) 70.8 k=2(%) k=3(%) k=4(%) k=5(%) Table 4 The jackknife test results using W-SpsAA-MV and CD classifier N N 1 N 2 N 3 N 4 N 5 nuber k=1(%) 40.1 k=2(%) k=3(%) k=4(%) k=5(%)

14 -458- Table 5 The 5-fold cross-validation results using W-SpsAA-MV and CD classifier N N 1 N 2 N 3 N 4 N 5 k=1(%) 38.3 k=2(%) k=3(%) k=4(%) k=5(%) In Table 3, the nuber denotes the nuber of proteins which have ore than N functional categories. According to different N value, we can find the nuber of protein functional categories is uncertain, soe only have a functional class, and soe have ore than five functional categories. The k denotes the probability of accurately predict k functional classes for query proteins. When k=1 and N 1, we assign a nearest functional category to proteins of test set and reach 70.8% prediction accuracy. When k=2 and N 1, two functional categories was assigned to proteins of test set, the probability of accurately predict one of which is 84.6%. When k=2 and N 2, the probability which this two functional categories were accurately predict is 50.8% for CD classifier. Fro Figure 2, we find every curve gradually rise with the increase of k value, which eans that when N value is unchanged, as the k value increase, the prediction accuracy increase significantly. Especially, when N 1, the overall accuracy has increased fro 70.8% to 97.1%. This is because when the predicted functional categories increase, the probability will undoubtedly increase as long as one of these functional categories is accurate. Fro the vertical axis of Fig.1, we can find when k

15 -459- is constant, the prediction accuracy will less and less with the N value increase, which deonstrate that the ore the nuber of functional categories which was predict correctly with CD classifier, the less the success rate. For exaple, when k=5, the success rate has reduced fro 97.1% to 28.4% with the N value increase. Therefore, it is very difficult to predict accurately all functional categories for a query protein. Figure 2. Curve for self-consistency using CD classifier. Jackknife test also called leave-one-out test, which is considered the ost objective and ost rigorous evaluation ethod. The jackknife test result using CD classifier with W-SPsAA-MV is shown in Table 4. In addition, we adopt 5-fold cross-validation to evaluate our ethod. The Table 5 shows the accuracy using 5-fold cross-validation. Fro Table 4 and Table 5, we can find that the predicted result is siilar by coparing the jackknife test and 5-fold cross-validation. In order to directly copare the predicted result of three evaluation ethods, Figure 3 shows the predicted result curves when N 1. Fro Figure 3, we can find the accuracy of self-consistency is best and that of jackknife test and 5-fold cross-validation are fairly. Self-consistency contains the test saples theselves so that extracted features are ore consistent with the test saples, so the accuracy is better than that of other two assessent ethods. We also find fro Figure 3 the accuracy of jackknife test and 5-fold cross-validation grow faster than that of self-consistency exaination.

16 -460- Figure 3. Accuracy of self-consistency using CD classifier. 5. Conclusion In this paper, a new ethod of characterizing protein sequence naed W-SPsAA-MV is proposed. We adopt the nearest neighbor algorith (NNA) and covariant discriinant (CD) classifier respectively based on W-SPsAA-MV to predict protein functional classes.the experiental result show that the accuracy of W-SPsAA-MV with NNA is better than GOM, SWN-BA, EBGW and GE ethods in soe cases. In addition, by analyzing the experiental results with CD classifier, we can find the effect of predict is not very satisfactory when we assign a sall nuber of functional classes to query proteins. While the predicted effect is significantly iproved obviously with the increase of the nuber of predicted functional categories increase. So, the results deonstrate that W-SPsAA-MV is convenient to calculate and effective on the proble of protein functional class prediction. Furtherore, our approach is applicable in the case of litte and no inforation of protein-protein interaction. Acknowledgeent This work is supported by the National Nature Science Foundation of China (Grant , ) the National Nature Science Foundation of Hunan province (Grant 07JJ5080) and the Planned Science and Technology Project of Hunan Province (Grant 2009FJ3195).

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