Accuracy of Sequence Alignment and Fold Assessment Using Reduced Amino Acid Alphabets

Transcription

1 63: (2006) Accuracy of Sequece Aligmet ad Fold Assessmet Usig Reduced Amio Acid Alphabets Fracisco Melo 1 * ad Marc A. Marti-Reom 2 1 Departameto de Geética Molecular y Microbiología, Facultad de Ciecias Biológicas, Potificia Uiversidad Católica de Chile, Satiago, Chile 2 Departmets of Biopharmaceutical Scieces ad Pharmaceutical Chemistry, ad Califoria Istitute for Quatitative Biomedical Research, Missio Bay, Uiversity of Califoria, Sa Fracisco, Califoria ABSTRACT Reduced or simplified amio acid alphabets group the 20 aturally occurrig amio acids ito a smaller umber of represetative protei residues. To date, several reduced amio acid alphabets have bee proposed, which have bee derived ad optimized by a variety of methods. The resultig reduced amio acid alphabets have bee applied to patter recogitio, geeratio of cosesus sequeces from multiple aligmets, protei foldig, ad protei structure predictio. I this work, amio acid substitutio matrices ad statistical potetials were derived based o several reduced amio acid alphabets ad their performace assessed i a large bechmark for the tasks of sequece aligmet ad fold assessmet of protei structure models, usig as a referece frame the stadard alphabet of 20 amio acids. The results showed that a large reductio i the total umber of residue types does ot ecessarily traslate ito a sigificat loss of discrimiative power for sequece aligmet ad fold assessmet. Therefore, some defiitios of a few residue types are able to ecode most of the relevat sequece/structure iformatio that is preset i the 20 stadard amio acids. Based o these results, we suggest that the use of reduced amio acid alphabets may allow to icreasig the accuracy of curret substitutio matrices ad statistical potetials for the predictio of protei structure of remote homologs. Proteis 2006; 63: Wiley-Liss, Ic. Key words: statistical potetials; sequece aligmet; fold recogitio; reduced amio acid alphabets INTRODUCTION The cofiguratio of a protei chai is determied by its primary sequece, which is a liear ad asymmetric polymer made of combiatios of the 20 aturally occurrig amio acids. Protei structure ad fuctio are determied by their sequeces ad the surroudig eviromet. Therefore, the complex sequece of amio acids of a protei ecodes for its diversity ad specificity. Because differet amio acid types share similar physicochemical properties ad ca be aturally substituted betwee protei sequeces of the same family, 1 there have bee several attempts to reduce the aturally occurrig amio acid alphabet. 2 9 The problem lies o fidig the proper groupig of amio acids that retais most of the iformatio ecessary for the itegrity of the structure ad fuctio of proteis. Durig the past years, several theoretical works have suggested that the miimum umber of amio acid types eeded to ecode for ative proteis is less tha 20. 2,4,10 12 I additio to this, some experimetal works have demostrated that egieered proteis with a reduced alphabet are able to preserve their fold ad fuctio. The Baker group, determied a stable ad properly folded protei domai usig a sigificatly reduced amio acid alphabet. 4 I this work, Baker ad coworkers demostrated that the SH3 fold could be preserved despite of the substatial reductio from 20 to 5 amio acid types for most of residues of the protei sequece. I a similar work, Stroud ad coworkers desiged a four-helix budle protei of 108 residues log with a reduced alphabet of seve amio acid types. 2 The most simplistic reductio of the amio acid alphabet described to date cosists o the defiitio of two residue types, which is kow as the hydrophobic-polar or HP model. 13,14 Other reductios have bee proposed, by usig a variety of differet approaches to derive reduced amio acid alphabet represetatios. These approaches icluded geetic code mutatios ad optimizatio of hydrophobicity scales, 3 clusterig of amio acids based o the pairwise similarity of distace-depedet eergy terms from statistical potetials 5 ad from amio acid substitutio matrices, 6 miimizatio of mismatches betwee stadard ad reduced amio acid substitutio matrices, 7 maximizatio of secodary structure predictio ability, 8 ad local backboe coformatio clusterig of amio acids. 9 Grat sposor: FONDECYT; Grat umber: ; Grat Sposor: Fudació Ades; Grat umber: 13600/4; Grat sposor: DI- PUC; Grat Number: 2004/01PF. *Correspodece to: Fracisco Melo, Departameto de Geética Molecular y Microbiología, Facultad de Ciecias Biológicas, Potificia Uiversidad Católica de Chile, Alameda 340, Satiago, Chile. fmelo@bio.puc.cl Received 12 April 2005; Revised 22 July 2005; Accepted 29 September 2005 Published olie 27 February 2006 i Wiley IterSciece ( DOI: /prot WILEY-LISS, INC.

2 ID REDUCED AMINO ACID ALPHABETS 987 TABLE I. Amio Acid Alphabets Alphabet descriptio Number of types Referece JO20 A-C-D-E-F-G-H-I-K-L-M-N-P-Q-R-S-T-V-W-Y WW5 AHT-CFILMVWY-DE-GP-KNQRS 5 7 SR5 AEHKQRST-CFILMVWY-DN-G-P 5 9 MU4 AGPST-CILMV-DEHKNQR-FYW 4 6 MM5 AG-C-DEKNPQRST-FILMVWY-H 5 This work RD5 100 radomly reduced alphabets 5 This work a Each amio acid alphabet is described splittig the differet amio acid types by a dash character. For clarity, ad to simplify compariso, amio acid type clusters are sorted alphabetically based o the 20-letter code of the stadard amio acid alphabet. a Due to space restrictios, the 100 radom alphabets are available as supplemetal material. Most of the reduced amio acid represetatios have bee derived based o commo physicochemical properties shared by differet amio acids. These properties iclude hydrophobicity scale, size, flexibility, ad commo chemical groups preset at the residue side chais. 1 Although these observatios have a solid groud, the threedimesioal cotext where the residues are observed withi a protei structure caot be eglected. This is particularly true if the reduced amio acid alphabet is goig to be applied to protei structure predictio. A first objective i this work was to derive a ew optimal ad simplified amio acid alphabet based oly o structural iformatio. A secod objective of this work was to compare the overall performace of several reduced amio acid alphabets (agaist the stadard alphabet) i the areas that costitute a major compoet of curret protei structure predictio methods: sequece aligmet ad fold assessmet. To that ed, based o several reduced protei amio acid alphabets of four ad five residue types, we derived similarity matrices for sequece aligmet ad statistical potetials for fold assessmet. The performace of the reduced amio acid alphabets were idepedetly evaluated ad compared to the full stadard amio acid alphabet usig a large set of kow protei structures. I the Methods sectio, we begi by describig the reduced amio acid alphabets used i this work; ext, we describe the procedure used to geerate a ew optimally reduced amio acid alphabet of five residues; the bechmarkig criteria ad the referece sets used i the bechmark. I the Results, we assess the accuracy of the reduced alphabets i sequece aligmet as well as fold assessmet of protei structure models. Fially, we coclude by discussig the varyig performace of the reduced amio acid alphabets for sequece aligmets ad fold assessmet. METHODS Amio Acid Alphabets I additio to the stadard amio acid alphabet of 20 residue types 15 (JO20), several reduced alphabets were also used i this work (Table I). These alphabets ca be categorized i three differet groups: (1) optimally reduced alphabets previously geerated by others ad available i the literature, (2) a optimally reduced alphabet geerated i this work by a geetic algorithm-based optimizatio, ad (3) a set of radomly reduced alphabets to be used as a low-boud referece assessmet frame. The sigle criterio adopted to select reduced alphabets from the literature was that they should have four or five residue types, because experimetal work idicates that optimally reduced alphabets of about five residue types ecode a large fractio of the origial iformatio that is preset i the stadard alphabet. 4 Three previously described reduced amio acid alphabets of about five residue types were cosidered i this work. These icluded two amio acid alphabets of five residue types by Wag ad Wag 7 (WW5) ad by Solis ad Rackovsky 9 (SR5), ad a four amio acid alphabet by Murphy ad coworkers 6 (MU4). The WW5 alphabet was optimized from the kowledge-based cotact potetial of Miyazawa ad Jeriga 16 by miimizig the mismatches occurrig betwee reduced matrices ad the origial Miyazawa ad Jeriga matrix. 7 The SR5 alphabet was geerated by miimizig the structural iformatio loss (or maximizig the iformatio gai) of collapsed alphabets i a large set of 4-mer peptides extracted from kow protei sequeces. 9 The MU4 alphabet was derived by maximizig the correlatio betwee pairs of amio acids, based o the values of the BLOSUM50 17 similarity matrix. 6 I additio to these existig alphabets, a ew optimal alphabet of five residue types was geerated ad tested (MM5). This alphabet was derived by optimizatio with a geetic algorithm usig structural iformatio from remote homolog proteis (below). Fially, 100 radomly reduced alphabets of five residue types (RD5) were geerated as a lower boud referece frame. A detailed descriptio of these radom alphabets is available as supplemetal material ( puc.cl/protei-alphabets.html). Geeratio of a Reduced Alphabet by Optimizatio with Geetic Algorithms A geetic algorithm (GA) is a search techique to solve optimizatio problems. I a GA, abstract represetatios of cadidate solutios (called idividuals) ecoded i

3 988 F. MELO AND M.A. MARTI-RENOM artificial chromosomes (strigs of umbers i a computer), evolve toward optimal solutios i a give umber of iteratios (geeratios). At each iteratio of the algorithm, a fitess that measures how well the idividual solves the particular problem is calculated. Chromosomes evolve by usig several types of operators of atural evolutio, which iclude iheritace, mutatio, selectio, ad recombiatio. The iitial populatio cosists of radom idividuals that evolve to the ext geeratio by applyig the GA operators ad by biasig the selectio of idividuals by their calculated fitess. After a ew geeratio is created, the fitess of all the populatio is evaluated ad a set of its fittest idividuals will cotribute to the ext geeratio/ iteratio of the algorithm. 18 As a traiig set for the GA optimizatio, a total of 180 structural pairwise aligmets were selected from the SCOP database 19,20 based o the followig criteria: the pairwise sequece idetity betwee the structurally aliged sequeces was below 20% ad the two aliged structures had more tha 100 aliged residues with a global RMSD withi 2.5 Å after optimal superpositio. We the removed all gaps (i.e., isertios ad deletios) from the aligmets ad cocateated them ito a sigle pairwise aligmet that resulted i a total of 25,140 pairs of structurally aliged residues. This log pairwise aligmet costituted the traiig aligmet for the geetic algorithm optimizer. Additioally, the residues i the traiig aligmet were shuffled, geeratig radom aligmets of the same compositio as the traiig aligmet. A geetic algorithm with chromosomes ecodig for reduced amio acid alphabets was traied to maximize the differece betwee the pairwise sequece idetities occurrig i the traiig ad the radom aligmets. The geetic algorithm had a costat populatio of 1000 chromosomes. Each chromosome was costituted of 20 gees arbitrarily represetig a stadard amio acid residue. Give a chromosome, the traiig ad radom aligmets were traslated from the stadard 20 amio acid alphabet to the reduced alphabet that it ecoded. The, the sequece idetity i the traiig ad radom aligmets was calculated ad its differece used as a fitess fuctio of the chromosome adaptatio. The geetic algorithm used elitism i each cycle, the evaluatio was carried out usig liear ormalizatio, ad the Roulette wheel paret selectio method was adopted for the paret selectio process previous to each reproductive step. 18 The reproductio process was carried out usig double poit crossig over ad a rate of 1% chace per chromosome for the occurrece of mutatio evets after reproductio. This optimizatio protocol led to a five-residue amio acid alphabet with a fitess score of 23.8% (58.1% sequece idetity i the traiig aligmet mius a 34.3% sequece idetity i the radom aligmet) after 100,000 iteratios. The algorithm was executed for 100 idepedet rus, covergig to the same fial groupig of amio acids i the optimal chromosome for most of the cases. A list cotaiig the alterative ear-optimal alphabets alog with their fitess scores is available as supplemetal material ( protei.bio.puc.cl/protei-alphabets.html). Calculatio of Reduced Amio Acid Substitutio Matrices A series of amio acid substitutio matrices based o each of the reduced amio acid alphabets were built to evaluate their accuracy i sequece aligmet. The mathematical derivatio of the reduced amio acid substitutio matrices was carried out from the Johso ad Overigto (JO) frequecy matrix 15 as follows: first, let i ad j be the idexes of two stadard amio acids ragig from 1 to 20. Let i ad j be the idexes of a reduced amio acid alphabet ragig from 1 to R, where R is the total umber of amio acid types i the reduced alphabet. Thus, ay amio acid type idex i ad j will be costituted by a set of oe or more idexes from the stadard alphabet, such that the uio of the i or j sets will geerate the total set of idexes i or j, respectively. For each reduced alphabet, the frequecy matrix F was calculated as follows: Fi,j JOi,j i,j i, j i1 j1 where JO(i,j) represets the observed frequecy i the JO substitutio matrix for the amio acid pair ij. Secod, the frequecy matrix was coverted ito a probability matrix P by: Pi,j R j1 Fi,j Fi,j where R is the total umber of residue types. Third, the probability matrix P was coverted to the odds matrix O by: Oi,j Pi,j R Fi,j i1 R i1 R j1 Fi,j Fourth, a scaled log-odds matrix L was calculated: Li,j 100 log 10 Oi,j Fifth, the scaled log-odds matrix was coverted to a similarity matrix S by the followig procedure: the miimum value of the matrix was selected, the sig of it chaged, ad added to each elemet of the matrix. Thus, the matrix values were coverted to the rage [0...N], where N is a positive value. Fially, the reduced similarity matrix S was coverted back to the stadard residue similarity matrix S by applyig a iverse procedure as the oe described above i the first step of the matrix calculatio process: Si,j Si,j i,j i,j

4 REDUCED AMINO ACID ALPHABETS 989 TABLE II. Optimal Gap Pealties for the Amio Acid Substitutio Matrices ID Iitiatio gap pealty Extesio gap pealty JO WW SR MU MM RD a I the case of radomly reduced alphabets (RD5), the most observed iitiatio ad extesio gap pealties are show. The exact pealty values for each radom alphabet are available as supplemetal material. We also geerated a scaled ad coverted stadard amio acid substitutio matrix from the JO origial frequecy matrix. Sequece Aligmet The ALIGN commad i the MODELLER program 21 was used to alig two sequeces by global dyamic programmig algorithm. 22 All default parameters were used, ad oly the substitutio matrix ad the optimal gap pealties were chaged for each ru. The optimal gap iitiatio ad extesio pealties for each substitutio matrix were empirically calculated by maximizig the average structural overlap for the traiig set of 118 pairwise structure aligmets (below). The optimizatio was carried out i a grid of values spaig from 400 to 0 i steps of 20, ad from 100 to 0 i steps of 5 for the iitiatio ad extesio gap pealties, respectively. The optimal gap pealties for each amio acid substitutio matrix based o the reduced alphabets, icludig the most observed values for the 100 matrices based o the radomly reduced alphabets, are listed i Table II. Idividual optimal gap pealties for each of the 100 radom matrices are available as supplemetal material at: bio.puc.cl/protei-alphabets.html. Statistical Potetials for Fold Assessmet Distace-depedet statistical potetials based o each amio acid alphabet were calculated to evaluate their accuracy i the assessmet of comparative protei structure models. A total of 532 oredudat protei chais from the Protei Data Bak (PDB) 23 were used to derive the statistical potetials. This set excluded ay protei structure with duplicated or missig atoms. All proteis i the set shared 25% or less sequece idetity amog them ad had a resolutio higher tha 3.0 Å. 24 The statistical potetials were calculated as previously described by Sippl, 25 but usig the optimal parameters obtaied i our recet work. 24 The followig expressio was used to calculate the potetials: E ij l RT l1 M ij RT l1 M ij fij f l xx where M ij is the umber of observatios for the atomic pair ij ad correspods to: M ij fi,j,l l1 where is the weight give to each observatio. We have used 1/50 as proposed by Sippl, 25 such that o 50 observatios f ij (l) ad f xx (l) have the same weight for the calculatio of E ij (l). The term f ij (l) is the relative frequecy of occurrece of the atomic pair ij i the class of distace l ad correspods to: f ij l fi,j,l M ij where f xx (l) is the relative frequecy of occurrece of all the atomic pairs i the class of distace l, ad ca be expressed as: f xx l i1 i1 fi,j,l j1 j1 fi,j,l l1 The temperature was set to 293 K, so that RT is equivalet to kcal/mol. Based o the eergy obtaied by the potetials described above, a eergy Z-score of a model from the bechmark set of models was calculated for each of the ewly derived statistical potetials. The eergy Z-scores were calculated for the statistical potetial eergy of a model, usig the mea ad stadard deviatio of the statistical potetial eergy of 200 radom sequeces with the same compositio ad structure of the model as previously described. 24 Bechmarkig Criteria The accuracy of a aligmet was measured by relyig o the aliged ative structures extracted from the PDB. 23 First, the root-mea-square deviatio (RMSD) betwee the correspodig C atoms i the two structures was calculated upo rigid-body least-squares superpositio, as implemeted i the SUPERPOSE commad of MOD- ELLER. 21 Secod, the percetage of structurally equivalet positios was calculated as the umber of the C atoms withi a certai cutoff (i.e., 1, 2, 3, 4, ad 5 Å, ad their average) ormalized by the legth of the shorter of the two structures ( structure overlap ). Uless idicated otherwise, the structure overlap quoted is the average over all cutoffs. A statistical aalysis of the differeces betwee aligmet accuracies of various methods was also performed. For this aalysis, the aligmet accuracy of a method was measured idepedetly by the RMSD ad the structural overlap after superimpositio, both calculated as average accuracy for the 220 pairwise aligmets i the testig set. The sigificace of the differeces was computed usig the Studet s t-test statistics. 26

5 990 F. MELO AND M.A. MARTI-RENOM ID TABLE III. Aligmet Accuracy All testig set (220) 40% Sequece Idetity (55) RMSD (Å) Structure overlap (%) RMSD (Å) Structure overlap (%) JO WW SR MU MM RD Average ad stadard deviatio of the structure-based accuracy criteria are show for the testig set of 220 aligmets ad for 55 aligmets with sequece idetity lower tha 40%. Structure overlap represets the fractio of C carbos that are foud at less tha 3.5 Å after optimal superpositio of two structures based o the pairwise sequece aligmet geerated. RD5 represets the average performace of 100 radomly reduced alphabets of five amio acid types each. The performace of classifiers based o the statistical potetial Z-scores as a sigle feature was assessed by meas of receiver operatig characteristic (ROC) curves as previously described. 24 A ROC curve is obtaied by plottig the false egatives fractio agaist the correspodig false positives fractio for all cutoffs o the eergy Z-score. The area uder the ROC curve represets the probability of icorrect classificatio over the whole rage of cutoffs. This area is usually take to be a importat idex because it provides a sigle measure of overall accuracy that is ot depedet upo a particular feature threshold. The optimal classificatio threshold was also obtaied for each statistical potetial eergy Z-score as the value where the highest positive predictio rate was observed. Traiig ad Testig Sequece Aligmet Sets Because our aim was to assess the accuracy of reduced amio acid alphabet matrices for aligig two sequeces, the referece aligmets were pairwise structure-based aligmets. They were obtaied from our comprehesive database of pairwise structure-based aligmets, DBAli. 27 The aligmets i DBAli were calculated by superposig all pairs of proteis of kow structure i the PDB 23 with the program MAMMOTH. 28 The 38,579 chais i the PDB database (as of May, 2003) were clustered to remove redudacy. The fial set of 6993 oredudat chais did ot superimpose to each other with a global RMSD smaller tha 2 Å, had less tha 80% of their C atoms withi 4 Å ad a differece i legth larger tha 30 residues. We radomly selected 400 pairwise structure-based aligmets from the oredudat set of aligmets, which uiformly covered most of the spectra of sequece similarity (from 20 to 100% sequece idetity). To avoid errors i the calculatios of the accuracy of the aligmets, all pairwise structural aligmets with a chai that correspoded to a obsolete or icomplete PDB coordiates file were removed from the list of 400 pairwise aligmets. The fial pairwise aligmets did ot iclude regios of the chais that were ot structurally superimposable. They icluded oly those positios that were superimposed, plus isertios ad deletios, removig additioal parts of the chais such as log N- or C-termial regios or additioal domais. Fially, the list was radomly divided ito two sets of aligmets that maitaied the uiformity of the sequece idetity distributio. This resulted i a traiig set of 118 pairwise aligmets that was used to optimize the gap pealties for each of the substitutio matrices ad a set of 220 pairwise aligmets that was used i the bechmark preseted here. The PDB chai idetifiers, chai legths, percetage sequece idetities, RMSD for the aliged C atoms, average percetage of the aliged C atoms, ad percetage of structurally equivalet residues are listed separately for the traiig ad testig aligmets i Supplemetary Table I ( protei.bio.puc.cl/protei-alphabets.html). Testig Set of Comparative Models To bechmark the accuracy of the reduced amio acid alphabets i protei structure fold assessmet, we used a set cosistig i 800 3D models divided i 400 correct ad 400 icorrect models. 24,29 All correct models had a proper fold assigmet ad were built based o a relatively accurate sequece/structure aligmet. Icorrect models either were built usig a wrog fold or built based o the correct fold, but cotaiig a large fractio of misaligmets. RESULTS I a attempt to obtai optimally reduced represetatios of the stadard amio acid alphabet that were exclusively based o structural iformatio, we developed a ew geetic algorithm (see Methods). The optimal solutio evolved by the geetic algorithm cosisted of a reduced alphabet of five types of amio acids. This ew reduced alphabet, alog with three other reduced alphabets published elsewhere, the stadard alphabet of 20 residues ad 100 radomly reduced alphabets were cosidered ad assessed (Table I). First, we proceeded with testig the accuracy of the aligmets produced whe usig the amio acid substitutio matrices based o the differet reduced alphabets. The testig was carried out with a bechmark set of 220 pairwise structural aligmets. The bechmarkig set covered the whole rage of sequece idetity where pairwise aligmets above 40% sequece idetity may have

6 REDUCED AMINO ACID ALPHABETS 991 bee trivial to reproduce. To assess the accuracy of the matrices with more difficult aligmet pairs, we also calculated the average RMSD for 55 aligmets i the testig set with sequece idetities below 40%. The aligmets obtaied with the substitutio matrix based o the stadard alphabet (JO20) resulted i a average 1.4 Å RMSD after rigid superimpositio of the two structures (2.4 Å RMSD for the difficult aligmets). Similar average results were obtaied with the other four oradom reduced alphabet matrices. I particular, the SR5 matrix produced the best aligmets with 1.3 ad 1.9 Å RMSD averages for all ad difficult aligmets, respectively (Table III). However, the differeces observed betwee the JO20 ad the reduced matrices for the RMSD accuracy measure were ot statistically sigificat at a 95% cofidece level i the Studet s t-test [Fig. 1(A)]. The JO20 ad the reduced alphabets matrices overperformed the radom matrices (RD5) with statistical sigificace as demostrated by the Studet s t-test aalysis [Fig. 1(A)]. The JO20 stadard matrix outperformed with statistical sigificace all the reduced matrices (except matrix SR5) by 1% for the structural overlap measure. All other matrices are statistically more accurate tha the radom matrix but caot be distiguished amog them [Fig. 1(B)]. The differece betwee MM5 ad JO20 is oly 0.95% structural overlap. However, the fact that the differeces are favorable to the JO20 for most of the 220 pairwise aligmets (171 of the aligmets have equal or higher structural overlap ad oly 49 of them have a lower structural overlap) makes the differece i structural overlap statistically sigificat. The discrimiative power of statistical potetials based o reduced amio acid alphabets was also tested. I this bechmark, we assessed how much three-dimesioal iformatio of ative folds is retaied whe the umber of amio acids is reduced to five or four residue types. The bechmark cosisted i the evaluatio of fold assessmet accuracy usig a represetative set of correct ad icorrect comparative protei structure models spaig a large rage of sequece legth. The statistical potetial eergy Z-score was the measure used to separate correct from icorrect protei models. The statistical potetial based o the stadard alphabet (JO20) shows the best classificatio performace, irrespective of model size (Table IV). The performace was evaluated as the total positive predictive rate (percetage of correctly predicted cases) usig the optimal threshold for classificatio i a large set of correct ad icorrect protei models (800 models i total). The complete set was separated ito four subsets based o the sizes of the protei models, which are show i terms of total umber of amio acids. Each subset cotais a total of 100 correct ad 100 icorrect models. The positive predictio rate of reduced potetials for the large models is oly betwee 1 to 3.5% poits lower tha the predictio accuracy of the JO20 potetial. The major differeces i assessmet performace are observed for the very small models. It must be oted that, i geeral, those reduced alphabets derived from structural features Fig. 1. Sequece aligmet accuracies. Statistical sigificace of the differeces i the aligmet accuracies of the tested matrices. Upper diagoal: gray ad white squares idicate pairs of matrices whose performace are ad are ot sigificatly differet at a cofidece level of 95%, respectively. Lower diagoal: the itesity of gray idicates the degree of the average differece betwee the correspodig matrices. (A) The accuracy of a matrix is measured as the average RMSD after rigid superimpositio. (B) The accuracy of a matrix is measured as the average structural overlap after rigid superimpositio. RD5 represets the average performace of 100 radomly reduced alphabets of five amio acid types each. of proteis (i.e., SR5 ad MM5) lead to statistical potetials with better performaces tha other reduced alphabets. O the other had, the potetials based o radom alphabets exhibit a poor performace, approximatig what would be expected from a radom classificatio process. Whe the performace of the statistical potetials was assessed over the whole rage of possible classificatio thresholds (i.e., by meas of receiver operatig characteristic or ROC curves), a clearer picture emerges (Fig. 2). The JO20 potetial had the highest specificity ad sesitivity amog all potetials. I other words, it was the best classifier irrespective of the chose threshold. The MM5 statistical potetial is the secod best classifier for ay

7 992 F. MELO AND M.A. MARTI-RENOM ID Very small (0 50 AAs) TABLE IV. Fold Assessmet Accuracy Small ( AAs) Medium ( AAs) Large (200 AAs) JO WW SR MU MM RD The accuracy of fold assessmet of statistical potetials based o the reduced amio acid alphabets was evaluated as the total positive predictive rate (percetage of correctly predicted cases) usig the optimal threshold for classificatio i a large set of correct ad icorrect protei models. The complete set was separated i four subsets based o the sizes of protei models. RD5 represets the average performace ad stadard deviatio of 100 radomly reduced alphabets of five amio acid types each. All Fig. 2. Statistical potetials accuracies. ROC curves are used to assess the discrimiative power of biary classifiers based o statistical potetials derived by usig differet amio acid types. (A) The statistical potetial usig 20 residue types (solid squares) is compared agaist statistical potetials based o optimally reduced alphabet defiitios. The symbol correspodeces are as follows: MM5 (ope squares), SR5 (solid circles), WW5 (solid diamods), ad MU4 (ope circles). (B) The statistical potetial usig 20 residue types from pael A (dashed lie) is compared agaist 100 statistical potetials based o radomly reduced alphabet defiitios (solid lies). combied rates of false positives ad false egatives. I third place, SR5 ad WW5 exhibit a similar performace. The MU4 potetial is the worst classifier for fold assessmet, amog the potetials based o reduced alphabets that were tested i this work. Fially, the reduced alphabets based o a radom clusterig of residues show a poor performace, comparable to that of a radom classifier. DISCUSSION Several reduced amio acid alphabets have bee described for may applicatios. The simplest is the twoletter amio acid alphabet, also kow as the HP model. 30 This reduced alphabet clusters hydrophobic ad polar residues ito differet groups ad has bee widely used to study protei foldig i simplified 2D ad 3D lattice models. 13,31 Despite its extreme simplicity, this alphabet probably describes the most importat force that stabilizes a ative protei structure: the partitio of polar ad hydrophobic residues that takes place i presece of water. Moreover, it allows complete eumeratio of the sequece ad structure spaces, a desirable property of a model to study ad simulate the kietics ad thermodyamics of protei foldig. However, i real-world applicatios, the HP alphabet is ot accurate eough to properly describe the complex ative protei structures. We have already demostrated that the performace of statistical potetials is highly compromised whe usig the HP alphabet istead of the stadard alphabet of 20 amio acids. 24 Although some argumets have bee give that support the idea that statistical potetials performace is just a cosequece of the partitio propesity of residues i water, 32 this sigle argumet does ot accout for the large differeces i accuracy that are observed betwee the stadard ad the HP statistical potetials for fold assessmet of real protei structures. 24 Therefore, substatial reductios o the amio acid alphabet, which are ot as extreme as the HP model, could still be useful approximatios. I this work, we have assessed the performace

8 REDUCED AMINO ACID ALPHABETS 993 for sequece aligmet ad fold assessmet of some reduced amio acid alphabets ad carried out a compariso agaist the stadard alphabet. These two bechmarks were chose because they costitute essetial core elemets of ay protei structure predictio method ad are also ivolved i other importat applicatios such as fuctioal geome aotatio. Reduced amio acid alphabets ca aid protei structure predictio methods. O the sequece space, a 20-letter code ca geerate a vast umber of possible sequeces, eve for very short proteis. O the structural space, addig several coformatios to each residue, the possible protei structure coformatios are eve larger. I the simplest case (i.e., a system described i a pairwise fashio), the accurate uderstadig of the eergy forces goverig the occurrig iteractios begis with the descriptio of 400 (20 20) or 210 (20 21/2) eergy fuctios for asymmetric ad symmetric iteractios, respectively. Each eergy fuctio, i tur, will require additioal variables or parameters to be properly described. To icrease the accuracy of the eergy fuctios, a further dimesioal growth of the matrix that represets the system is required. Therefore, ay statistical approach based o kow experimetal data will eed to fill i most of the matrix bis to properly describe the system. Ufortuately, because the experimetal data is fiite, i practical terms there is a eed to simplify the matrix used to describe the system. Thus, reducig the amio acid alphabet would allow a more detailed exploratio of other properties i protei structures that could become relevat but have ot bee yet explored due to the outlied limitatios. I this sceario, a importat questio arises: what reductio of the amio acid alphabet will allow us to describe with high accuracy the eergy forces that gover protei structure stability? The aswer to this questio is ambitious, ad it has ot bee yet fully addressed i the literature. Here we tried to address this questio by studyig the accuracy of sequece aligmet ad fold assessmet methods usig optimally reduced amio acid alphabets. We first focused o the use of amio acid substitutio matrices derived from reduced alphabets to alig two sequeces. Our itetio was to assess how the reductio of the amio acid alphabet affected the accuracy of the aligmets produced. The results of this work showed that a small drop i accuracy is observed for sequece aligmets geerated with substitutio matrices derived from reduced amio acid alphabets. The reduced matrices still ecode eough iformatio to outperform radomly geerated matrices. The reduced similarity matrices could be used as a startig poit for icorporatig additioal iformatio ito the aligmet process. For example, iformatio derived from the 3D structure of oe of the aliged sequeces, such as the eviromet-depedet substitutio matrices 33 is likely to further improve the utility of sequece-structure aligmet i comparative modelig applicatios. This additioal iformatio could ow be icluded ad be computatioally treatable over a reduced umber of amio acid types from 20 to just 5, which traslates ito a overall reductio of matrix bis from 210 to 15, respectively. Secod, we focused o the use of statistical potetials derived from reduced amio acid alphabets to assess the accuracy of protei structure models. Oe of the major problems i derivig statistical potetials is the limited size of the database of kow protei structures ad the large umber of parameters required to properly defie a iteractio of two or more bodies i three-dimesioal space. This limitatio could be overcome by reducig the size of the amio acid alphabet. Thus, a more detailed descriptio of the iteractios describig ative protei structures could be achieved. The fact that the statistical potetial based o the JO20 alphabet oly clearly outperforms other potetials based o reduced alphabets for the very small models, may suggests that a large umber of iteractios is required to properly assess a protei model whe a potetial based o a reduced amio acid alphabet is used. This is i agreemet with our previous observatios, where the icrease of the distace rage of a pairwise potetial substatially improved its performace whe assessig very small models (i.e., the total umber of iteractios is icreased ad more cofidece is gaied i the total observed eergy of the model). 24 As it should have bee expected before had, the JO20 potetial exhibited the best performace i model assessmet, irrespective of the sesitivity/specificity balace at ay give classificatio threshold. The potetial based o the ovel MM5 alphabet was the secod best classifier for fold assessmet. The, the SR5 ad WW5 potetials exhibited a overall similar performace, although that for high specificities the SR5 potetial was more accurate. Fially, the MU4 potetial showed the worst performace i fold assessmet amog all the reduced potetials tested. However, it has bee previously demostrated that the iformatio cotet of amio acid alphabets decreases whe the total umber of clusters or residue types are reduced from five to four types. 9,34 This may explai the differeces i accuracy observed for the potetial based o the MU4 alphabet compared to the other optimally reduced alphabets. Therefore, it is early impossible to fairly compare reduced alphabets of differet sizes. The potetials derived from the JO20, MM5, ad SR5 alphabets show similar behavior ad capabilities required for high specificity (i.e., i automated ad large-scale protei structure fold assessmet that requires a good detectio of false positives). This fidig suggests that potetials based o optimally reduced alphabets with additioal three-dimesioal features may exhibit a eve higher specificity for automated protei fold assessmet, compared to the assessed potetial based o the stadard alphabet. The differeces for clusterig amio acids ito differet groups may explai the varyig accuracy of potetials based o differet optimally reduced alphabets. For example, the SR5 ad MM5 alphabets cluster ito differet groups two structurally importat amio acids such as glycie ad prolie. The SR5 alphabet creates two separate groups cotaiig these residues as their uique

9 994 F. MELO AND M.A. MARTI-RENOM members. I cotrast, for the MM5 alphabet, glycie clusters ito a group with alaie, the secod smallest amio acid, ad prolie clusters withi a large group costituted of polar amio acids. It is somehow surprisig that WW5 ad MU4 alphabets have glycie ad prolie defied withi the same cluster. I the case of WW5, these two residues are clustered as uique members of their group. The cysteie amio acid, also a structurally importat residue i proteis, is differetially clustered by the optimally reduced alphabets. The MM5 alphabet clusters this amio as the uique member of its group. The other reduced alphabets cluster the cysteie amio acid i groups cotaiig hydrophobic residues. Most of the polar ad hydrophobic amio acids are clustered ito differet groups, with the exceptio of the MU4 alphabet, which clusters the hydrophobic residues ito two differet groups. Therefore, most of the differeces betwee the optimally reduced alphabets arise from the partitioig of glycie, prolie, cysteie, ad polar residues. Those differeces may partially explai the varyig accuracy of reduced alphabets for fold assessmet. Some radom alphabets successfully clustered glycie, prolie, ad cysteie ito differet groups, but oe of them properly separated hydrophobic ad polar residues (supplemetal material). A sigificat reductio of the stadard amio acid alphabet to five or four differet types did ot result i a substatial reductio of performace for sequece aligmet ad model assessmet. Although varyig performaces were observed, this is true for most of the optimally reduced amio acid alphabets tested i this work. This fidig opes the possibility of expadig the descriptio of the system to derive ew amio acid substitutio matrices ad statistical potetials. To metio some: structural features such as secodary structure prefereces could be added to the substitutio matrices; statistical potetials would ot be blid to the orietatio betwee residues i three-dimesioal space; distacedepedece ad secodary structure or local backboe coformatio could be cosidered simultaeously; three body iteractios could be better described by havig several observatios of each particular state; etc. We will certaily cotiue the exploratio of some of these ew variables to seek for better methods that may prove useful for protei structure predictio. CONCLUSIONS We have assessed the performace of reduced amio acid alphabets for the tasks of sequece aligmet of remote homologs ad fold assessmet of protei structure models. Residue residue substitutio matrices ad statistical potetials based o several optimally reduced alphabets were calculated ad tested usig a large bechmark of protei sequeces ad structures. Based o the results obtaied, we draw the followig coclusios: 1. residue residue substitutio matrices ad statistical potetials calculated o the basis of optimally reduced alphabets exhibit a similar performace as those based o the stadard alphabet i the tasks of sequece aligmet of remote homologs ad fold assessmet of protei structure models. 2. The little loss of performace or accuracy of substitutio matrices ad statistical potetials based o optimally reduced alphabets is clearly compesated by the sigificat reductio of matrix bis that is achieved (i.e., a reduced alphabet of five residue types leads to a 14 or 16 times reductio of the total umber of matrix bis, for symmetric ad asymmetric matrices respectively). ACKNOWLEDGMENTS We are grateful to Prof. Adrej Sali for all his support, ecouragemet, ad access to his CPU Liux cluster. We would like to thak Dr. M.S. Madhusuda for his suggestios. We ackowledge the helpful commets ad suggestios made by the two aoymous reviewers of this mauscript. REFERENCES 1. Creighto TE. Protei foldig. 2d ed. New York: W.H. Freema Compay; Schafmeister CE, LaPorte SL, Miercke LJ, Stroud RM. A desiged four helix budle protei with ative-like structure. Nat Struct Biol 1997;4: Triquier G, Saejouad Y. Which effective property of amio acids is best preserved by the geetic code? Protei Eg 1998;11: Riddle DS, Satiago JV, Bray-Hall ST, Doshi N, Gratcharova VP, Yi Q, Baker D. Fuctioal rapidly foldig proteis from simplified amio acid sequeces. Nat Struct Biol 1997;4: Kuzetsov IB, Rackovsky S. Discrimiative ability with repect to amio acid types: assessig the performace of kowledge-based potetials without threadig. Proteis 2002;49: Murphy LR, Wallqvist A, Levy RM. Simplified amio acid alphabets for protei fold recogitio ad implicatios for foldig. Protei Eg 2000;13: Wag J, Wag W. A computatioal approach to simplifyig the protei foldig alphabet. Nat Struct Biol 1999;6: Aderse CAF, Bruak S. Represetatio of protei-sequece iformatio by amio acid subalphabets. AI Magazie 2004;25: Solis AD, Rackovsky S. Optimized represetatios ad maximal iformatio i proteis. Proteis 2000;38: Esteve JG, Falceto F. A geeral clusterig approach with applicatio to the Miyazawa-Jeriga potetials for amio acids. Proteis 2004;55: Li T, Fa K, Wag J, Wag W. Reductio of protei sequece complexity by residue groupig. Protei Eg 2003;16: Fa K, Wag W. What is the miimum umber of letters required to fold a protei? J Mol Biol 2003;328: Dill KA, Cha HS. From Levithal to pathways to fuels. Nat Struct Biol 1997;4: Wolyes PG. As simple as ca be? Nat Struct Biol 1997;4: Johso MS, Overigto JP. A structural basis for sequece comparisos. A evaluatio of scorig methodologies. J Mol Biol 1993;233: Miyazawa S, Jeriga RL. Residue-residue potetials with a favorable cotact pair term ad a ufavorable high packig desity term, for simulatio ad threadig. J Mol Biol 1996;256: Heikoff S, Heikoff JG. Amio acid substitutio matrices from protei blocks. Proc Natl Acad Sci USA 1992;89: Goldberg DE. Geetic algorithms i search, optimizatio, ad machie learig. Readig, MA: Addiso-Wesley; Murzi AG, Breer SE, Hubbard T, Chothia C. SCOP: a structural classificatio of proteis database for the ivestigatio of sequeces ad structures. J Mol Biol 1995;247: Adreeva A, Howorth D, Breer SE, Hubbard TJ, Chothia C, Murzi AG. SCOP database i 2004: refiemets itegrate structure ad sequece family data. Nucleic Acids Res 2004;32:

10 REDUCED AMINO ACID ALPHABETS Sali A, Bludell TL. Comparative protei modellig by satisfactio of spatial restraits. J Mol Biol 1993;234: Needlema SB, Wusch CD. A geeral method applicable to the search for similarities i the amio acid sequece of two proteis. J Mol Biol 1970;48: Berma HM, Battistuz T, Bhat TN, Bluhm WF, Boure PE, Burkhardt K, Feg Z, Gillilad GL, Iype L, Jai S, Faga P, Marvi J, Padilla D, Ravichadra V, Scheider B, Thaki N, Weissig H, Westbrook JD, Zardecki C. The Protei Data Bak. Acta Crystallogr D 2002;58: Melo F, Sachez R, Sali A. Statistical potetials for fold assessmet. Protei Sci 2002;11: Sippl MJ. Calculatio of coformatioal esembles from potetials of mea force. A approach to the kowledge-based predictio of local structures i globular proteis. J Mol Biol 1990;213: Marti-Reom MA, Madhusudha MS, Fiser A, Rost B, Sali A. Reliability of assessmet of protei structure predictio methods. Structure 2002;10: Marti-Reom MA, Ilyi VA, Sali A. DBAli: A database of protei structure aligmets. Bioiformatics 2001;17: Ortiz AR, Strauss CE, Olmea O. MAMMOTH (matchig molecular models obtaied from theory): a automated method for model compariso. Protei Sci 2002;11: Sachez R, Sali A. Large-scale protei structure modelig of the Saccharomyces cerevisiae geome. Proc Natl Acad Sci USA 1998; 95: Yue K, Fiebig KM, Thomas PD, Cha HS, Shakhovich EI, Dill KA. A test of lattice protei foldig algorithms. Proc Natl Acad Sci USA 1995;92: Cha HS, Dill KA. Comparig foldig codes for proteis ad polymers. Proteis 1996;24: Thomas PD, Dill KA. Statistical potetials extracted from protei structures: how accurate are they? J Mol Biol 1996;257: Overigto J, Doelly D, Johso MS, Sali A, Bludell TL. Eviromet-specific amio acid substitutio tables: tertiary templates ad predictio of protei folds. Protei Sci 1992;1: Solis AD, Rackovsky S. Optimally iformative backboe structural propesities i proteis. Proteis 2002;48: