FragBag, an accurate representation of protein structure, retrieves structural neighbors from the entire PDB quickly and accurately


 Sharyl Underwood
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1 FrgBg, n ccurte representtion of protein structure, retrieves structurl neighbors from the entire PDB quickly n ccurtely Inbl BuowskiTl, Yuvl Nov b, n Rchel Kolony, Deprtment of Computer Science n b Deprtment of Sttistics, University of Hif, Mount Crmel, Hif 3905, Isrel Communicte by Michel Levitt, Stnfor University School of Meicine, Stnfor, CA, December, 2009 (receive for review November 3, 2009) Fst ientifiction of protein structures tht re similr to specifie query structure in the entire Protein Dt Bnk (PDB) is funmentl in structure n function preiction. We present FrgBg: An ultrfst n ccurte metho for compring protein structures. We escribe protein structure by the collection of its overlpping short contiguous bckbone segments, n iscretize this set using librry of frgments. Then, we succinctly represent the protein s bgsoffrgments vector tht counts the number of occurrences of ech frgment n mesure the similrity between two structures by the similrity between their vectors. Our representtion hs two itionl benefits: (i) it cn be use to construct n inverte inex, for implementing fst structurl serch engine of the entire PDB, n (ii) one cn specify structure s collection of substructures, without combining them into single structure; this is vluble for structure preiction, when there re relible preictions only of prts of the protein. We use receiver operting chrcteristic curve nlysis to quntify the success of FrgBg in ientifying neighbor cnite sets in tset of over 2,900 structures. The gol stnr is the set of neighbors foun by six stte of the rt structurl ligners. Our best FrgBg librry fins more ccurte cnite sets thn the three other filter methos: The SGM, PRIDE, n metho by Zotenko et l. More interestingly, FrgBg performs on pr with the computtionlly expensive, yet highly truste structurl ligners STRUCTAL n CE. evlution of structure serch fst structurl serch of Protein Dt Bnk filter n refine protein bckbone frgments protein structure serch Fining structurl neighbors of protein, i.e., proteins tht shre with it sizble substructure, is n importnt yet persistently ifficult, tsk. Such structurl neighbors my hint t protein s function or evolutionry origin even without etectble sequence similrity, s structure is more conserve thn sequence. Inee, mny methos for protein function (, 2) n structure (3) preiction rely on fining such neighbors. Structurl clssifictions such s SCOP (4) n CATH (5) ientify some neighbors; however, there re mny other neighbors, which lthough clssifie ifferently, re ctully structurlly similr n importnt for function n structure preiction (, 6). Devising fst, ccurte, yet comprehensive, structurl serch tools for the rpily growing Protein Dt Bnk (PDB) remins n importnt chllenge. Structurl lignment quntifies the similrity between two protein structures, by ientifying two eqully size, geometriclly similr substructures. Mny structurl lignment methos hve been propose over the pst twenty yers [e.g., STRUCTAL (7), CE (8), n SSM (9)]. Regrless of the wy they quntify similrity n their serch heuristics, one cn efine common similrity score to ssess the resulting lignments, n crete bestofll metho tht gives the best lignment uner tht score (0). Unfortuntely, ligning two structures is n expensive computtion (0); thus, mny structurl lignment servers consier only representtive subset of the Protein Dt Bnk (PDB) (e.g. FATCAT () n CE). However, by using such sequencenonreunnt representtive sets we risk excluing interesting structurl vribility (2). In ny cse, nively structurlly ligning query ginst the entire PDB, or structurlly ligning ll PDB structures ginst one nother, is prohibitively expensive, s it requires O(n) or Oðn 2 Þ computtionlly intensive comprisons. To serch the entire PDB efficiently, reserchers evise the filter n refine prigm (3). A filter metho quickly sifts through lrge set of structures, n selects smll cnite set to be structurlly ligne by more ccurte, but computtionlly expensive, metho. Filter methos gin their spee by representing structures bstrctly typiclly s vectors n compring these representtions quickly. Such vector representtions llow constructing n inverte inex t structure tht enbles fst retrievl of neighbors, even in huge tsets [e.g. (4)]. PRIDE represents structure by the histogrms of igonls in its internl istnce mtrix, n mesures similrity between two structures by the similrity between their histogrms (5). Choi et l. (6) represent structure by vector of frequencies of locl fetures in its internl istnce mtrix, n mesure similrity between two structures by the istnce between their corresponing vectors. Inspire by knot theory, Rögen n Fin evise the Scle Guss Metric (SGM) metho, which represents structure by vector of 30 globl topologicl mesures of its bckbone (7). Zotenko et l. (8) represent protein structure by vector of the frequencies of ptterns of seconry structure element (SSE) triplets. Severl methos [e.g., (9), (20)] represent structure s n orere string of structurl frgments, n sequencelign these strings to mesure structurl similrity; such representtions re less suitble for constructing n inverte inex. To serch in very lrge tsets, computer scientists often represent objects s bgofwors (BOW) unorere collections of locl fetures. Web serch engines use n inverte inex of the BOW representtion of the web. Ech ocument n query is represente by the number of occurrences of its wors (2). In Computer Vision, texture imges re represente s BOW of locl imge fetures for texture recognition, object clssifiction, n imge n vieo retrievl [e.g., (22 23)]. In protein sequence nlysis, Leslie n coworkers escribe protein sequences s BOW of their kmers for etecting remote homology (24). In FrgBg we represent protein structure s BOW of bckbone frgments, n use this representtion to ientify quickly goo cnite sets of structurl neighbors. Specificlly, we represent structure by vector whose entries count the number of times ech frgment pproximtes segment in the protein bckbone (Fig. ), n mesure similrity between two structures by the similrity between their corresponing vectors. In testing our pproch, we consier 24 librries of vrious sizes n Author contributions: I.B.T., Y.N., n R.K. performe reserch n nlyze t; n Y.N. n R.K. esigne reserch n wrote the pper. The uthors eclre no conflict of interest. To whom corresponence shoul be resse. Emil: This rticle contins supporting informtion online t /DCSupplementl. BIOPHYSICS AND COMPUTATIONAL BIOLOGY PNAS Februry 23, 200 vol. 07 no
2 frgment lengths, n use three BOW similrity mesures (Euclien, Cosine, n Histogrm Intersection). We stuy how well ifferent mesures ientify structurl neighbors, reltive to stringent gol stnr: The structurl neighbors foun by bestofsix structurl lignment metho (0). We lso test sttisticlly whether BOW representtions of structures within CATH ctegories re inee similr to ech other. We then compre the performnce of our mesure with tht of other filter methos SGM, Zotenko et l. (8), n PRIDE, to BLAST sequence lignment (25), n to the structurl lignment methos STRUC TAL, CE, n SSM. Our best filter metho outperforms other filter methos n BLAST. More importntly, it performs on pr with the computtionlly expensive structurl ligners STRUCTAL n CE. In our tests, the rnking of the methos is insensitive to the threshol vlue efining structurl neighbors. Compring FrgBg vectors is orers of mgnitues fster thn structurl lignment; it lso is well suite for using in inverte inices. Thus, our metho cn be use to quickly ientify goo cnite sets of structurl neighbors in the entire PDB. Results In FrgBg, the bgoffrgments tht represents protein structure is succinctly escribe by vector of length N, the size of the frgment librry. Fig. illustrtes how this vector is clculte from the αcrbon coorintes of protein. For ech contiguous (n overlpping) kresiue segment long the protein bckbone, we ientify the librry frgment of length k tht fits it best in terms of rms fter optiml superposition. Then, we count the number of times ech librry frgment ws use, n escribe the protein by vector of these counts. Compring Filter Methos vi Receiver Operting Chrcteristic (ROC) Curve Anlysis. We mesure the ccurcy of structurl retrievl methos by how well they ientify cnite sets of structurl neighbors in tbse, given query structure. We consier tbse of 2,928 sequencenonreunnt structures, n query it by ech of its structures. The golstnr nswer inclues neighbors foun by bestofsix structurl ligner (using SSAP (26), STRUCTAL, DALI (27), LSQMAN (28), CE, n SSM); this expensive computtion ws one previously (0). Structurl neighbors of the query re ones ligne to it with structurl lignment score [SAS; see Methos for efinition (7)] below threshol T (for T ¼ 2 Å, 3.5 Å, n 5 Å). We use the re uner the curve (AUC) of the ROC curves to mesure how well ech metho ientifies the structurl neighbors of query, n verge the AUCs over ll 2,928 queries. A higher AUC is better: A perfect imittor of the gol stnr, which rnks the structurl neighbors before ll other proteins, will hve n AUC of, wheres rnom mesure will hve n AUC of 0.5. Fig. 2 (Left) shows the verge AUCs with respect to the three gol stnrs efine bove (corresponing to the three vlues of T) for 24 librries (with frgments of length 5 2 I b c e Librry of Frgments f II f e III f f f e IV Number of Occurnces b c e f Frgment ID Fig.. FrgBg representtion of protein structure. (A) For illustrtion, we consier librry of 6 frgments. (B) Ech (overlpping) contiguous segment in the bckbone is ssocite with its most similr librry frgment. (C) All frgments re collecte to n unorere bg. (D) The structure is represente by vector v, whose entries count the number of times ech librry frgment ppere in the bg. In this exmple, v ¼ð4; 0; 0; 5; ; 3Þ, implying frgment orer (, b, c,, e, f). resiues). We consier three BOW similrity mesures: Cosine, Histogrm Intersection, n Euclien istnces. For comprison, the right pnel shows the verge AUCs of other methos: (i) sequencebse metho using BLAST s Evlue (25), (ii) the filter methos PRIDE, SGM, n tht of Zotenko et l. (8), n (iii) the structure ligners STRUCTAL, CE, n SSM. We sort the lignments by their SAS scores, n for STRUCTAL n Averge AUC of ROC Curve Averge AUC of ROC Curve Averge AUC of ROC Curve Frgment length (number of resiues) Frgment length (number of resiues) Frgment length (number of resiues) SAS Threshol = 5A cosine istnce histogrm Intersection istnce Eucliin istnce histogrm Intersection istnce cosine istnce histogrm Intersection istnce SAS Threshol = 3.5A cosine istnce Eucliin istnce SAS Threshol = 2A Eucliin istnce Librry Size SSM STRUCTAL FrgBg CE SGM Zutenko et l. PRIDE sequence lignment SSM STRUCTAL CE (N) STRUCTAL (N) FrgBg CE SGM Zutenko et l. sequence lignment PRIDE SSM CE(N), STRUCTAL FrgBg STRUCTAL (N) SGM CE Zutenko et l. sequence lignment PRIDE Fig. 2. The verge AUC of ROC curves of ientifying structurl neighbors. The AUC mesures how well rnking of structures imittes the rnking ccoring to gol stnr; lrger vlues correspon to more successful imittors, rnging from 0.5 ( rnom rnker) to ( perfect imittor). We consier three efinitions of structurl neighbors, using SAS threshols of 2 Å, 3.5 Å, n 5 Å. The left pnels show the performnce of librries with frgments of 6 2 resiues, n ifferent number of frgments (vlue long the xxis), n using the cosine (plus sign), Euclien (circles), n Histogrm Intersection (imons) istnces. On the right we compre the best FrgBg result (400() librry n the cosine istnce) to other methos: Sequencebse similrity mesure in finely she blck, filter methos in she blck, n structure lignment methos in soli blck. We see tht the FrgBg performs similrly to CE n STRUCTAL two computtionlly expensive n welltruste structurl ligners BuowskiTl et l.
3 CE, lso by their ntive scores. The verge AUCs plotte in Fig. 2 re lso vilble s supplementry mteril (Tble S). The rnking of the performnce of ifferent methos is generlly inepenent of T, the threshol efining structurl neighbors. Uner the strictest efinition, the neighbors of protein re only structures tht were ligne with n SAS score <2 Å; uner the most lx efinition, the neighbors re the structures tht were ligne with n SAS score <5 Å. As expecte, ll methos perform better (i.e., chieve higher verge AUCs) when the efinition of structurl neighbors is more strict, n less well when the efinition inclues more istnt structures. Becuse structures with SAS score <5 Å re often the most meningful neighbors, which re ifficult to etect ccurtely, we re most intereste in ientifying methos tht excel uner this stringent test (see Discussion). FrgBg s best result is with the 400() librry (400 frgments of length ) n the cosine istnce; the verge AUCs re 0.89 (T ¼ 2 Å), 0.77 (T ¼ 3.5 Å), n 0.75 (T ¼ 5 Å). The cosine istnce performs best. When using cosine istnce or the histogrm intersection istnce, lrger librries (which escribe locl structure vribility in higher etil), typiclly perform better. From compring librries of fixe size (00, 200, or 400 frgments), we lern tht when using cosine istnce, librries of longer frgments perform better; when using the histogrm intersection or the Euclien istnces, the length of the frgment oes not influence the results. The rnking of the filter methos from most to lest successful is (i) FrgBg (using the 400() librry n cosine istnce), (ii) SGM, (iii) Zotenko et l. s metho (8), n (iv) PRIDE, which performs similrly to the sequencebse metho. Among the structurl ligners, the most successful is SSM, followe by STRUCTAL n CE. Fig. 2 n Tble show tht the best filter metho, i.e., the FrgBg representtion mentione bove, performs on pr with CE n STRUCTAL, two computtionlly expensive n highly truste structurl ligners. For exmple, using the T ¼ 5 Å threshol, FrgBg hs n verge AUC of 0.75, which is similr to CE s 0.74 using the ntive score, n 0.75 using SAS score; it is lower thn STRUCTAL s verge AUC of 0.83 using the ntive score n 0.84 using SAS score. Using the T ¼ 3.5 Å threshol, FrgBg hs n verge AUC of 0.77, which is similr to STRUC TAL s 0.77 using its ntive score n to CE s 0.72 using SAS score. SSM outperforms FrgBg t ll three threshols. Ctegories of CATH Proteins hve BOW Descriptions tht Are Different from Ech Other In Sttisticlly Significnt Wy. Next, we test sttisticlly whether FrgBg grees with the CATH clssifiction, t the Clss Architecture (CA) n the Clss, Architecture, n Topology (CAT) levels. In bro strokes, we expect FrgBg Tble. AUCs of ROC Curves Using BestofSix Gol Stnr representtions of proteins in the sme ctegory to be more similr thn those of proteins in ifferent ctegories, n wish to verify tht such similrity, if foun, is not ue to mere chnce. When running mny sttisticl tests, s we o here (one for ech pir of ctegories), the chnces of getting t lest one significnt result is much higher thn the chnces of getting significnt result in single test, even when there is no true unerlying ifference (the multiple comprisons problem ). We control for this problem through the Bonferroni correction (29), n the flse iscovery rte (FDR) pproch (30). When using the Bonferroni correction, we just the require significnce level of ech test, so tht the probbility of flsely eclring t lest one test s significnt is the stnr α ¼ Tble 2 summrizes the results uner the Bonferroni correction, cross the 24 librries. For exmple, there re 2 minlyα CATH ctegories t the CAT level, n thus 2 2 ¼ 66 ctegory pirs; out of the 66 corresponing tests, 6 were significnt t the juste significnce level cross ll 24 librries, hence the frction 6 66 t the tble s first cell in the secon row. The prenthesize figures in the tble re the frction of significnt tests for the 400() librry. The iniviul test results re vilble in Dtsets S n S2. Using the FDR pproch, we fin which tests cn be eclre significnt, while controlling the verge frction of the wrongly eclre tests t some prechosen level; for etils, see ref. 30. Tble 2 lists the frction of tests eclre significnt, verge cross the 24 librries n uner n FDR of 0.05; the prenthesize figures re the frction of the tests eclre significnt for the 400() librry. The frctions reporte in Tble 2, ll being very close to, strongly support the conclusion tht the FrgBg representtion grees with the CATH clssifiction, both t the CA n the CAT level. Comprison of FrgBg Similrity Mesure to rms on Dtset of Structure Pirs Within Nucler Mgnetic Resonnce (NMR) Ensembles. Next, we stuy how well FrgBg ientifies similrity between structures tht re only loclly similr, i.e., hve highly similr substructures tht re connecte ifferently. The bility to ientify such locl similrity my help in etecting similrity to prtilly chrcterize structure, s neee in structure preiction. We consier pirs of structures within n NMR ensemble collection of structures tht re consistent with the experimentl constrints; these typiclly iffer only t severl flexible points long the bckbone, n re thus loclly similr. Our similrity criterion is efine by the threshol 0.35 the verge FrgBg cosine istnce between structures with the sme CAT clssifiction (see Tble 3). We use throughout this section the 400() librry. SAS Similrity Threshol (Å) Metho Averge vlue Rnk Spee * SSM using SAS score [2] Structl using SAS score [2] Structl using ntive score [2] CE using ntive score [2] FrgBg Cos istnce (400,) Fst CE using SAS score [2] FrgBg histogrm intersection (600,) Fst SGM Fst FrgBg Euclien istnce (40,6) Fst Zotenko et l. (8) Fst Sequence mtching by BLAST evlue Fst PRIDE Fst *Averge CPU minutes per query. Essentilly instntneous fter preprocessing (<0. s). BIOPHYSICS AND COMPUTATIONAL BIOLOGY BuowskiTl et l. PNAS Februry 23, 200 vol. 07 no
4 Tble 2. Sttisticl nlysis summry Anlysis using Bonferroni correction *, Anlysis using FDR, Minly α Minly β Mixe α þ β Minly α Minly β Mixe α þ β CA 6 6 (6 6) 3 36 (35 36) 2 2 (2 2) 6 6 (6 6) (36 36) 2 2 (2 2) CAT 6 66 (65 66) (78 78) (225 23) (65 66) (78 78) (23 23) *Nonprenthesize vlues re the number of ctegory pirs foun ifferent (t the Bonferronijuste significnt level) in ll 24 librries, ivie by the totl number of pirs; prenthesize vlues re the frction of significnt comprisons for the librry of 400 frgments of length. In ll cses, vlues close to re esirble. Nonprenthesize vlues re the frction of comprisons eclre significnt in the FDR nlysis, verge cross the 24 librries; prenthesize figures re the frction of the comprisons eclre significnt for the librry of 400 frgments of length. We use the tset of 230 NMR ensembles tht ws constructe in the PRIDE stuy (5). The set inclues 54,465 pirs, 43,246 of which hve rms 4 Å (bqv, bmy, e0, n lx were replce by their newer versions). Fig. 3 shows the FrgBg cosine istnce vs. rms, n the mrginl istributions of the two istnces. The vst mjority of pirs re ientifie s very similr by FrgBg: 9% hve cosine istnce below 0.35, showing tht FrgBg inee ientifies similrity between loclly similr structures. We see similr results using Histogrm intersection n Euclien istnce (Fig. S). For comprison, Tble 3 lists the mens n stnr evitions of the FrgBg istnces between structure pirs t ifferent levels of structurl similrity. The most similr pirs re those within NMR ensembles: We consier ll pirs n only those with rms 4 Å. We lso consier pirs in the set of 2,928 CATH omins tht hve the sme CATH, CAT, CA, n C clssifiction, s well s ll pirs. As expecte, the verge istnce grows s the sets become more structurlly iverse, uner ll three istnces. Discussion A Fst Filter tht Performs On Pr with Structurl Alignment Methos. FrgBg cn quickly ientify structurl neighbor cnites for structure query, n performs s well s some highly truste, computtionlly expensive structurl lignment methos. Our results with FrgBg s 400() librry re s ccurte s CE s, n lmost s ccurte s STRUCTAL s. This is impressive, s CE n STRUCTAL re mong the most ccurte structurl lignment methos (0). As expecte, structurl neighbors re generlly ientifie best by structurl ligners, less well by filters, n lest well by sequence lignment. Our results re robust we see similr rnking of methos using ifferent efinitions for structurl neighbors of protein. An ttrctive feture of bstrct representtions of protein structure such s FrgBg (n other filter methos) is tht one cn store the vectors representing ll PDB proteins in n inverte inex t structure esigne for fst retrievl of neighbors. Evlution Protocol. Retrieving structurl neighbors of query protein from the entire PDB is chllenge. We cnnot euce the structurl neighbors solely from SCOP or CATH, becuse crossfol similrities proteins tht re geometriclly similr, yet clssifie ifferently re very common (0, 3). Kihr n Skolnick (3) note tht crossfol similrities mong smll proteins (<00 resiues), re bunnt even t CATH s C level. Crossfol similrities re prticulrly importnt to ientify, when preicting structure n function (, 6). Recent Criticl Assessment of Techniques for Protein Structure Preiction (CASP) experiments show tht the most successful structure preiction methos construct their preictions from substructures tht re not, in generl, from proteins clssifie in the sme fol [e.g. (3, 32, 33)]. Frieberg n Gozik (34) showe tht crossfol similrities correlte well with the functionl similrity of proteins populting the fols, n Petrey n Honig (6) showe exmples of functionl similrity mong ifferently clssifie proteins. Nevertheless, proteins clssifie in the sme CATH ctegory (t the CA or CAT levels) re truly similr, n we expect their FrgBg representtions to be similr s well. Becuse there re mny CA n CAT ctegories, ech populte with mny proteins, we use sttisticl theory to test n confirm this. Any gol stnr must meet the chllenge: Becuse filter metho nees to ientify structurl neighbors of query, the gol stnr must be ll ientifie neighbors. Here, we fin these neighbors using the expensive computtion of bestofsix structurl ligner. Nmely, we ientify structure s neighbor if ny of the six methos fins in both sizble substructure tht cn be superimpose with low rms. Such neighbor is selecte regrless of its CATH clssifiction, n coul well belong to ctegory other thn tht of the query protein. H we relie on clssifiction, similr structures woul hve been mrke s nonneighbors, n the ROC curve nlysis woul hve effectively penlize filter methos tht correctly ientify them. Becuse structurl similrity tht is ue to sequence similrity is esy to ientify, we use tsets of nonreunnt sequences. This ensures tht we hve eliminte trivil pirs in our evlution protocol. Note tht when the structurl neighbors re efine with the T ¼ 2 Å, 3.5 Å threshols, sequence lignment oes better thn rnom (AUC > 0.5); inee, when there re only few structurl neighbors (e.g., only the query), even trivil sequence lignment metho will perform well, becuse it rnks the query s most similr to itself. This phenomenon will hve greter impct on the verge AUC when the number of structurl neighbors is smll (lower T). Thus, the verge AUC of the Tble 3. Averge FrgBg istnces in tsets of vrying structurl similrity Dtset Histogrm intersection istnce* Euclien (L 2 norm) istnce* Cosine istnce* Within NMR ensemble (rms 4 Å) Within NMR ensemble Sme CATH clssifiction Sme CAT clssifiction Sme CA clssifiction Sme C clssifiction Different C clssifiction *Using the librry of 400 frgments of length BuowskiTl et l.
5 in protein structure spce. Finlly, this inex my be use to nswer prtilly chrcterize queries, to the benefit of the structure preiction community. Methos We consier 24 librries with frgments of 5 2 resiues, constructe in previous stuy (35). There, we clustere the frgments of the Cα trces of 200 ccurtely etermine structures, n forme librry by tking representtive from ech cluster. Fig. 3. Cosine intersection istnce vs. rms in structure pirs within NMR ensembles. The tset hs 230 NMR ensembles with 43,246 pirs hving rms 4 Å (5). FrgBg ientifies the vst mjority (9%) of the pirs in this set s very similr (cosine istnce below 0.35 the verge istnce in pirs of the sme CAT clssifiction, mrke in she pink). sequence lignment metho cts s lower boun, inicting the ifficulty of the tsk. Although not the min focus of this stuy, our results provie nother evlution of the performnce of STRUCTAL, CE, n SSM, n show tht SSM is the top performer. SSM compres structures in two stges. (i) A fst estimtion of structurl similrity by mtching the SSE grphs of the structures. This step clcultes two estimtes of the percent SSE mtch, n the user cn specify their llowe mximl vlues; the SSM server oes not provie combine vlue of these estimtes tht cn be use to rnk structure pirs. (ii) An expensive n ccurte lignment of the Cαs of the two structures. Here, we use the SAS of the lignments foun by SSM fter the secon stge. Serching with Prtilly Define Queries for Protein Structure Preiction. Importntly, FrgBg cn serch the entire PDB for neighbors of query structure tht is only prtilly chrcterize. Such serch is useful for structure preiction, s preiction methos often preict only the structure of prts of protein, n fining composition of these prts in the PDB my hint t how these prts shoul be combine into complete structure. In FrgBg, the missing informtion hs minor impct. The union of the bgsoffrgments of the prts iffers from the true bgoffrgments only by the few frgments in the connecting regions. Similrly, two structures tht re flexible vrints (i.e., iffer only t hinge point) will hve similr FrgBg representtions. Future Directions. We hope to improve FrgBg using similrity mesure tht weights the frgments ifferently, n possibly ignores some; BOWs weighting schemes were successfully use in other res of Computer Science. Currently, ech representtion is bse on one librry, n ll its frgments re weighte eqully. Once we hve weighting scheme, we cn combine librries n trust the weights to select ll significnt frgments. We lso pln to construct FrgBgbse inverte inex for the entire PDB; s note bove, this inex will llow quickly ientifying smll cnite sets of structurl neighbors of protein. The cnite sets will lso inclue structures tht re flexible vrints of the query, potentilly reveling new connections ROC Curve Anlysis with Structurl Alignments Gol Stnr. We use set of 2,928 sequenceiverse CATH v.2.4 omins n their llginstll structurl lignments; the set ws constructe for previous comprison stuy of structurl ligners (0). Two 7resiue long structures (pspa, pspb) were remove becuse they re shorter thn some frgments. All structures were structurlly ligne to ll others by six lignment methos (SSAP, STRUCTAL, DALI, LSQMAN, CE, n SSM) n their SAS scores were recore, where SAS ¼ 00 rms ðlignment lengthþ. Our gol stnr is bse on the best lignment foun by these six methos in terms of the SAS score. The sequences of every pir of structures in this set iffer significntly (FASTA Evlue >0 4 ). A FrgBg escription of protein is row vector; its length, N, isthe size of the librry use. The vector escribing the ith protein is b i ¼ðb i ðþ; b i ð2þ; ;b i ðnþþ, where b i ðjþ is the number of times frgment j is the best locl pproximtion of segment in the ith protein. We consier three istnce metrics between two vectors, b i n b k : (i) cosine istnce, b T i b k b i b k,(ii) histogrm intersection istnce, N j¼ minfb iðjþ;b k ðjþg minfs i ;s k g, where s i ¼ N j¼ b iðjþ, n (iii) Euclien (L 2 ) istnce, b i b k. Sttisticl Anlysis. We now escribe wht t were use in the sttisticl nlysis, how these t re summrize in mtrix form, n the etils of the sttisticl nlysis. Rw Dt. We use the 8,87 omins in the S35 fmily level in CATH Becuse the clssifiction t the C level is bse on seconry structure, we focus on the CA n CAT levels, n run the tests seprtely on ifferent C clsses. To improve the sttisticl power of the tests, we use only ctegories with t lest 30 structures. When prtitioning the tset to ctegories t the CA level, there re 4 ctegories (with t lest 30 structures) in the minlyα clss (totling 2,077 structures out of 2,078); 9 in the minlyβ clss (,968 out of 2,062); n 7 in the mixe α þ β clss (4,507 out of 4,558). There ws only one ctegory in the fewseconrystructure clss, so this clss ws omitte. When prtitioning t the CAT level, there re 2 ctegories in the minlyα clss (totling,03 structures); 3 in the minlyβ clss (,396 structures); n 22 in the mixe α þ β clss (2,68 structures). Dt in Mtrix Form. Consier librry of N frgments, n, sy, the CAlevel clssifiction of the M ¼ 968 minlyβ proteins into Q ¼ 9 ctegories. The FrgBg representtions of thesem proteins is initilly summrize in n M N mtrix B, whose ði;jþth entry is b i ðjþ. The mtrix B is prtitione rowwise into Q blocks corresponing to the Q ctegories, n we enote by M q the number of rows of the qth block. When consiering CATH s CAT level, minlyα proteins, or mixe α þ β proteins, M, Q, n B, s well s the prtition of B, chnge ccoringly. Omnibus Test. Following the usul sttisticl prctice, we first run single omnibus test (29) to check whether there is t lest one pir of ctegories whose proteins FrgBg representtions re ifferent from ech other in sttisticlly significnt wy; only fter such ifference is foun, we compre ll possible pirs of ctegories (post hoc nlysis). The t is multivrite, s ech FrgBg vector consists of N observtions, yet it certinly cnnot be ssume to be normlly istribute. Thus, we use nonprmetric permuttion test, pte from (36). We now construct sttistic w tht cptures the overll issimilrity between vectors belonging to ifferent ctegories; lrge vlues of w support rejecting the null hypothesis, ccoring to which the prtition into blocks crries no informtion with respect to the clssifiction. We first stnrize B s columns by iviing ech column by its stnr evition (36). Let B q be the M q N submtrix of (the stnrize) B, constituting the qth block, n let B q be the Nvector whose entries re the mens of the columns of B q.for two istinct blocks, q n r, we efine Δ qr ¼ mx j B q B r j, where the mximum is tken over the N ifferences (in bsolute vlues) between the entries of the two vectors. The omnibus test sttistic is w ¼ mx q r Δ qr. BIOPHYSICS AND COMPUTATIONAL BIOLOGY BuowskiTl et l. PNAS Februry 23, 200 vol. 07 no
6 Being permuttion test, the omnibus test s pvlue is PðW wþ, where W is similrly compute score uner rnom permuttion of B s rows. Becuse the number of permuttions is too lrge to enumerte, we resort to estimting the pvlue in Monte Crlo fshion, by rwing 000 rnom permuttions of B s rows, n observing the proportion of the permuttions chieving sttistic higher thn w. The omnibus test results were ll significnt, for comprisons both t the CA n CAT levels, for ll 24 librries, n for ech of the three CATH clsses (p < 0.00 in ll cses). Post Hoc Anlysis, Bonferroni Correction, n FDR. Once the omnibus test results were foun significnt, we test the t for more stringent lterntive hypothesis, ccoring to which ny two blocks re ifferent from ech other (rther thn testing for the existence of t lest one pir of ifferent blocks, s the omnibus test oes). To o so, we run the bove test seprtely for ech of the K ¼ QðQ Þ 2 pirs of blocks. When compring blocks q n r, the mtrix B is of imension ðm q þ M r Þ N, n s only two blocks re consiere, this comprison s sttistic reuces to w ¼ Δ qr. The result is collection of Kpvlues, corresponing to the K pirwise comprisons. When using the Bonferroni correction, we eclre s significnt only the comprisons in which the pvlue is below 0.05 K. When using the FDR pproch, we follow (30). ACKNOWLEDGMENTS. We thnk our nonymous reviewers for their helpful comments. This reserch ws supporte by the Mrie Curie IRG Grnt Kolony R, Petrey D, Honig B (2006) Protein structure comprison: Implictions for the nture of fol spce, n structure n function preiction. Curr Opin Struct Biol 6(3): Wtson JD, Lskowski RA, Thornton JM (2005) Preicting protein function from sequence n structurl t. Curr Opin Struct Biol 5(3): Zhng Y (2008) Progress n chllenges in protein structure preiction. Curr Opin Struct Biol 8(3): Murzin AG, Brenner SE, Hubbr T, Chothi C (995) SCOP: A structurl clssifiction of proteins tbse for the investigtion of sequences n structures. J Mol Biol 247(4): Perl FM, et l. (2003) The CATH tbse: An extene protein fmily resource for structurl n functionl genomics. Nucleic Acis Res 3(): Petrey D, Honig B (2009) Is protein clssifiction necessry? Towr lterntive pproches to function nnottion. Curr Opin Struct Biol 9(3): Subbih S, Lurents DV, Levitt M (993) Structurl similrity of DNAbining omins of bcteriophge repressors n the globin core. Curr Biol 3(3): Shinylov IN, Bourne PE (998) Protein structure lignment by incrementl combintoril extension (CE) of the optiml pth. Protein Eng (9): Krissinel E, Henrick K (2004) Seconrystructure mtching (SSM), new tool for fst protein structure lignment in three imensions. Act Crystllogr D 60: Kolony R, Koehl P, Levitt M (2005) Comprehensive Evlution of Protein Structure Alignment Methos: Scoring by Geometric Mesures. J Mol Biol 346(4): Li Z, Ye Y, Gozik A (2006) Flexible structurl neighborhoo tbse of protein structurl similrities n lignments. Nucleic Acis Res 34:D277 D Kosloff M, Kolony R (2008) Sequencesimilr, structureissimilr protein pirs in the PDB. Proteins 7(2): Aung Z, Tn KL (2007) Rpi retrievl of protein structures from tbses. Drug Discov Toy 2(7 8): Aung Z, Tn KL (2004) Rpi 3D protein structure tbse serching using informtion retrievl techniques. Bioinformtics 20(7): Crugo O, Pongor S (2002) Protein fol similrity estimte by probbilistic pproch bse on C(lph)C(lph) istnce comprison. J Mol Biol 35(4): Choi IG, Kwon J, Kim SH (2004) Locl feture frequency profile: A metho to mesure structurl similrity in proteins. Proc Ntl Ac Sci USA 0(): Rögen P, Fin B (2003) Automtic clssifiction of protein structure by using Guss integrls. Proc Ntl Ac Sci USA 00(): Zotenko E, O Lery DP, Przytyck TM (2006) Seconry structure sptil conformtion footprint: A novel metho for fst protein structure comprison n clssifiction. BMC Struct Biol 6:2. 9. Frieberg I, et l. (2007) Using n lignment of frgment strings for compring protein structures. Bioinformtics 23(2):e Tung CH, Hung JW, Yng JM (2007) Kpplph plot erive structurl lphbet n BLOSUMlike substitution mtrix for rpi serch of protein structure tbse. Genome Biol 8(3):R3. 2. Mnning CD, Rghvn P, Schütze H (2008) Introuction to Informtion Retrievl (Cmbrige Univ Press, Cmbrige). 22. Puzich J, Buhmnn JM, Rubner Y, Tomsi C (999) Empiricl evlution of issimilrity mesures for color n texture. The Proceeings of the Seventh IEEE Interntionl Conference on Computer Vision, 999 p FeiFei L, Pietro P (2005) A Byesin Hierrchicl Moel for Lerning Nturl Scene Ctegories. Proceeings of the 2005 IEEE Computer Society Conference on Computer Vision n Pttern Recognition (CVPR 05)  Volume 2  Volume 02 (IEEE Computer Society). 24. Melvin I, et l. (2007) SVMFol: A tool for iscrimintive multiclss protein fol n superfmily recognition. BMC Bioinformtics 8(Suppl 4):S Ttusov TA, Men TL (999) BLAST 2 Sequences, new tool for compring protein n nucleotie sequences. FEMS Microbiol Lett 74(2): Tylor WR, Orengo CA (989) Protein structure lignment. J Mol Biol 208(): Holm L, Sner C (993) Protein structure comprison by lignment of istnce mtrices. J Mol Biol 233(): Kleywegt GJ (996) Use of noncrystllogrphic symmetry in protein structure refinement. Act Crystllogr., Sect. D: Biol. Crystllogr. 52: Miller RGJ (98) Simultneous Sttisticl Inference (Springer, New York), 2n eition. 30. Benjmini Y, Hochberg Y (995) Controlling the flse iscovery rte: A prcticl n powerful pproch to multiple testing. J R Sttist Soc B 57(): Kihr D, Skolnick J (2003) The PDB is Covering Set of Smll Protein Structures. J Mol Biol 334(4): Moult J, et l. (2007) Criticl ssessment of methos of protein structure preiction Roun VII. Proteins 69(Suppl 8): Zhng Y, Arkki AK, Skolnick J (2005) TASSER: An utomte metho for the preiction of protein tertiry structures in CASP6. Proteins: Structure, Function, n Bioinformtics 9999(9999):NA. 34. Frieberg I, Gozik A (2005) Frgnostic: Wlking through protein structure spce. Nucleic Acis Res 33(suppl 2):W Kolony R, Koehl P, Guibs L, Levitt M (2002) Smll librries of protein frgments moel ntive protein structures ccurtely. J Mol Biol 323(2): Goo P (2000) Permuttion Tests (Springer, New York), 2n e BuowskiTl et l.
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