Improving the Efficiency of MECoMaP: A Protein Residue-Residue Contact Predictor

Imp o ing he Efficiency o MECoMaP: A P o ein Residue-Residue Con ac P edic o Al onso E. M´a quez-Chamo o1, Fede ico Di ina1,Jes´us S. Aguila -Ruiz1, and Cosme E. San ies eban-Toca2 1School o Enginee ing, Pablo de Ola ide Uni e si y o Se illa, Spain {ama cha, di ina,aguila }@upo.es 2Cen o de Bioplan as, Uni e si y o Ciego de A ila, Cuba [email p o ec ed] Abs ac . This wo k p oposes an imp o emen o he mul i-objec i e e olu iona y me hod o he p o ein esidue- esidue con ac p edic ion called MECoMaP. This me hod bases i s p edic ion on physico- chemical p ope ies o amino acids, s uc u al ea u es and e olu iona y in o ma ion o he p o eins. The e olu iona y algo i hm p oduces a se o decision ules ha iden ifies con ac s be ween amino acids. These decision ules gene a ed by he algo i hm ep esen a se o condi ions o p edic esidue- esidue con ac s. A new encoding used, a as e alua ion o he examples om he aining da a se and a ea men o unbalanced classes o da a we e conside ed o imp o e he he efficiency o he algo i hm. Keywo ds: p o ein s uc u e p edic ion, esidue- esidue con ac , mul i- objec i e op imiza ion, e olu iona y compu a ion. 1 In oduc ion One o he cen al goals o bioin o ma ics is he p edic ion o p o ein unc ion and e ia y s uc u e om he linea sequence o amino acids (p ima y s uc u e). De e mining he h ee dimensional s uc u e o p o eins is necessa y o unde s and he unc ions o molecula p o ein le el. On he o he hand, mis olding p o eins can be he p incipal cause o some diseases. Since p o ein unc ion is de e mined by i s s uc u e, a mis old implies ha a p o ein can no ulfill i s unc ion co ec ly. Alzheime ’s disease, cys ic fib osis, bo ine spongi o m encephalopa hy (mad cow disease) and i s human a ian a e now all a ibu ed o p o ein mis olding. The knowledge o he mis olding ac o s and unde s anding he p o ein olding p ocess, would help in de eloping cu es o hese diseases. The p ima y s uc u e, o amino acid sequence, o a p o ein is much easie o de e mine han i s e ia y s uc u e. Mo eo e , he gap be ween he numbe o p o eins wi h known sequence and he numbe o p o eins wi h known e ia y s uc u e is apidly inc easing. In o de o educe his gap, he e ha e been many esea ches ocused on de e mining he e ia y s uc u e o a p o ein om i s sequence [1,2]. The high numbe o p o ein sequences whose h ee- dimensional s uc u es mus be de e mined, make compu a ional me hods o p o ein s uc u e p edic ion (PSP) an essen ial ool. We belie e ha EAs well sui ed o sol ing he PSP p oblem, since PSP can be seen as a sea ch p oblem h ough he space de e mined by all he possible p o ein oldings. Mo eo e , PSP p oblem can be conside ed as a op imiza ion p oblem wi h se e al objec i es [3]. The ask o finding one o mo e subop imal solu ions is called Mul i-objec i e op imiza ion. Ou algo i hm is based on hese app oaches. An use ul, and commonly used, ep esen a ion o p o ein 3D s uc u e is he p o ein con ac map, which ep esen s bina y p oximi ies (con ac o non- con ac ) be ween each pai o amino acids o a p o ein. Ou app oach is included in his ca ego y. The aim o his wo k consis s o imp o ing ou p oposal MECoMaP (Mul i- objec i e E olu iona y Con ac Map P edic o ) [4] in o de o inc ease he efficiency o he p o ein con ac map p edic ion. The p edic ion is based on h ee physico-chemical p ope ies: hyd ophobici y (H), pola i y (P) and cha ge (C), s uc u al ea u es: sol en accessibili y (SA) and seconda y s uc u e (SS) and e olu iona y in o ma ion in o m o Posi ion Specific Sco ing Ma ix (PSSM). I is known ha amino acid p ope ies play an impo an ole in he PSP p oblem [5]. Se e al PSP me hods ely on amino acids p ope ies, e.g.,HPmodels.On he o he hand, a as majo i y o PSP algo i hms used SS, SA and PSSM as p edic i e ea u es. The emainde o his pape is o ganized as ollows. Ou mul i-objec i e e olu iona y app oach is desc ibed in sec ion 2. Sec ion 3 p esen s he expe imen a ion and ob ained esul s. Finally, sec ion 4, includes some conclusions and possible u u e wo ks. 2 Me hodology MECoMaP is based on he S eng h Pa e o E olu iona y Algo i hm (SPEA). Each indi idual o he popula ion ep esen s a decision ule. In pa icula , ules a e based on he p e iously men ioned amino acid p ope ies. Basically ules speci y a se o condi ions on each p ope y, ha , i sa isfied, p edic a con ac be ween wo amino acids. In he ollowing he p epa a ion o da a, a ibu e selec ion, he encoding, he fi ness unc ion and he gene ic ope a o s used by he EA will be p esen ed. 2.1 P epa a ion o Da a We selec ed om PDB a p o ein da a se (DS1) ha consis s o 173 non- edundan p o eins wi h sequence iden i y less han 25%, and was ob ained om [6]. The minimum and maximum leng hs o p o eins a e 31 and 753 amino acids, espec i ely. DS1 con ains 240501 posi i e examples (con ac s) and 5034050 nega i e examples (non-con ac s). The second da a se (DS2), wi h 53 non- edundan and non-homologous globulin p o eins, is de ailed in [7]. The sequence iden i y o DS2 da ase is also lowe han 25%. DS2 is o med by a o al o 30546 con ac s and 356528 non-con ac s. As we can see, he posi i e and nega i e classes (con ac and non-con ac s) a e no ably unbalanced. We ha e pe o med a esampling o da a using 1:1 and 2:1 con ac /non-con ac s a ios. Using 1:1 a io we ob ain a highe a e o p edic ed con ac s, howe e he a e o alse posi i es o he p edic o is inc eased. Specifically, he accu acy esul s o bo h a ios on DS1 and DS2 a e shown in Table 1. As seen in he able, he 2:1 a io p esen ed be e pe o mance. This is also he case o DS2 da a se . The op imiza ion o his pa ame e also implies a lowe compu a ional cos o he algo i hm. Based on he esul s o he able, we decided o pe o m a e-sampling using he 2:1 a io. Table 1. A e age accu acy esul s ob ained o diffe en con ac /non-con ac s a ios o he DS1 and DS2 p o ein da a se Ra io Da a Se Accu acyμ 1:1 DS1 0.21±0.10 2:1 DS1 0.23±0.08 1:1 DS2 0.16±0.13 2:1 DS2 0.20±0.11 2.2 Fea u e Selec ion As s a ed be o e, he p edic ion is based on a se o amino acid p ope ies which a e e y impo an in he olding p ocess. The eason o basing he p edic ion on such p ope ies, is ha i has been shown ha amino acids ha a e in con ac , a e cha ac e ized by simila p ope ies [8]. We selec ed Ky e-Dooli le hyd opa hy p ofile [9], he G an ham p ofile [10] o pola i y and he Klein scale o ne cha ge [11]. Hyd ophobic amino acids a e gene ally ound in he inne o p o eins p o ec ed om di ec con ac wi h wa e . In e sely, he hyd ophilic amino acids a e gene ally ound on he ou side o p o eins as well as in he ac i e cen e s o enzyma ically ac i e p o eins. The ne cha ge akes in o accoun he cha ged g oups p esen in any amino acid, pep ide o p o ein nd he pH o i s en i onmen . In addi ion o hese p ope ies, we also use wo s uc u al ea u es o p o eins (SS and SA) and e olu iona y in o ma ion, in o m o PSSM. Seconda y s uc u e p edic ion consis s o p edic ing he loca ion o α-helices, β-shee s and u ns om a sequence o amino acids. The loca ion o hese mo i s could be used by app oxima ion algo i hms o ob ain he e ia y s uc u e o he p o ein. We ob ain SS p edic ions using PSIPRED. SA e e s o he deg ee o which a esidue in e ac s wi h he sol en molecules. The p edic ion o SA alue is pe o med using ICOS Se e o he p edic ion o s uc u al aspec s o p o ein esidues h p://c unche .cs.no .ac.uk/psp/p edic ion. A PSSM de e mines he subs i u ion sco es be ween amino acids acco ding o hei posi ions in he alignmen . Each cell o he ma ix ep esen s he obse ed subs i u ion equency a a gi en posi ion di ided by he expec ed subs i u ion equency a ha posi ion. PSSM is ob ained using PSI-BLAST. H, P and PSSM alues we e no malized be ween -1 and 1. C alues a e ep esen ed wi h -1, 0 and 1 o nega i e, neu al and posi i e cha ges. SS alues a e iden ified wi h 1, 2 and 0 o alpha-helices, be a-shee s and andom coils, espec i ely. SA alues a e anging om 0 o 4 acco ding o he exposu e le el. The p ocedu e scheme o p ep occessing o he da a is ep esen ed in Figu e 1. We ha e ob ained fi e diffe en files wi h he in o ma ion o he p ope ies. They cons i u e he aining da a o he algo i hm. Fig. 1. P ep ocessing p ocedu e scheme 2.3 Encoding An indi idual is cons i u ed by six blocks which ep esen he diffe en p ope ies o amino acids. Each block indica es he alues o a espec i e p ope y in all he posi ions o he esidues in he window. We use wo windows o ±3 esidues cen e ed a ound he wo a ge amino acids iand j. The e o e, one window is ela i e o amino acids i−3,i−2,i−1,i,i+1,i+2,i+ 3 and he o he one is ela i e o amino acids j−3,j−2,j−1,j,j+1,j+2,j+3. We define each indi idual as a decision ule Ri,j o amino acids iand j: Rij ={{Hmin,H max}1..n,{Pmin,P max}1..n, C1..n,SS1..n,SA 1..n,{PSSMminij ,PSSMmaxij }1..20}(1) whe e nindica es he o al numbe o amino acids (in his case n= 14). Each elemen o Rij mus ulfill he ollowing equi emen s: −1≤Hmin <H max ≤1 −1≤Pmin <P max ≤1 C∈{−1,0,1} SS ∈{−1,0,1,2} SA ∈{−1,0,1,2,3,4} −1≤PSSM1..20 min < PSSM1..20 max ≤1(2) This decision ule de e mines whe he wo amino acids iand ja e in con ac , whe e 1 ≤i<j≤L,beingL he sequence leng h. Ou ep esen a ion consis s in 14×2 a ibu es o H, 14×2 o P, 14 o C, 14 o SS, 14 o SS and 2×2×20 o PSSM, 178 a ibu es in o al. 2.4 Fi ness Func ion As s a ed in [4], we conside wo objec i es o be op imized: co e age and accu acy. Co e age ep esen s he numbe o p edic ed con ac s and accu acy e alua es he eal p edic ed con ac s a e. The e o e, Co e age =C/C and Accu acy =C/Cp,whe eCis he numbe o co ec ly p edic ed con ac s o a p o ein, C is he o al numbe o con ac s o he p o ein and Cpis he numbe o p edic ed con ac s. We aim a finding he bes comp omise be ween hese wo measu es. The fi ness o an indi idual xis gi en by he numbe o indi iduals ha xdomina es. 2.5 Gene ic Ope a o s A 2-poin c osso e ope a ion was employed wi h a bina y ou namen selec ion and a 0.5 p obabili y. In each ou namen , we selec he indi idual which is loca ed in he be e Pa e o on . A fi s mu a ion ope a o ollows a Gaussian dis ibu ion o a andomly selec ed indi idual. This ope a o inc eases o dec eases a gene alue wi h a p obabili y o 0.5 andomly in e al. A second mu a ion ope a o andomly selec s a gene ha is ela ed o a gi en p ope y, wi h a 0.1 p obabili y, and mo es he bounds o he maximum o minimum o he domain, making he p ope y i ele an in his ule. Fo example, i he p ope y is he pola i y, we change he ange o -1, 1 so he ule does no ake in o accoun his p ope y in his case. A e he mu a ion, we es i he ob ained alues a e in he adequa e anges o he co esponding p ope y. The popula ion size is se o 100, and he ini ial popula ion is andomly ini ialized wi h a 0.6 p obabili y. The maximum numbe o gene a ions ha can be pe o med is se o 100. Howe e , i he fi ness o he bes indi idual does no inc ease o e wen y gene a ions, he algo i hm is s opped and a solu ion is p o ided. A he end o he execu ion, epea ed o edundan ules a e disca ded om he solu ion se . 2.6 Efficien E alua ion S uc u e In o de o educe he compu a ional ime o ou me hod, we ha e implemen ed an AVL ee [12] o o de and classi y he aining examples acco ding o hei p ope y alues. This ee o ganizes he in o ma ion in such a way ha i is no necessa y o p ocess all he examples o e alua e indi iduals (candida e decision ules) om he gene ic popula ion gene a ed by MECoMaP. The ime o he ope a ions on an AVL ee is O(log n) a e age, whe e n is he numbe o elemen s. Each node de e mines a condi ion o a p ope y and each lea ep esen s a lis wi h he aining examples ha ulfills all he condi ions impose in he p edeceso nodes. Each le el o he ee ep esen s a de e mined p ope y o a de e mined posi ion o an amino acid. We conside a ee example in figu e 2. Le el 1 ep esen s he hyd ophobici y o amino acid iand le el 2 indica es he pola i y o amino acid j. As example, lea node N1 s o es all he aining examples whose amino acid in posi ion ihas a hyd ophobici y alue lowe han 0 and a pola i y alue in posi ion jis also lowe han 0. We achie e a educ ion o he compu a ional cos abou 50% by means o a as e alua ion o examples om he da ase . Fig. 2. Example o efficien e alua ion s uc u e (AVL ee) 3 Expe imen s and Resul s We ha e buil a file in a ff o ma wi h all he aining da a in o ma ion. This file is cons i u ed by all he p o ein subsequences o wo windows o se en amino acids encoded wi h he alues o he ci ed a ibu es. The posi i e class (con ac ) is ep esen ed wi h 1 and he nega i e class (non-con ac ) is ep esen ed wi h 0. The a io be ween he posi i e and nega i e classes was se o 2:1 o DS1 and DS2 da a se s. The aining da a used con ained all he possible subsequences wi h a minimum sepa a ion be ween con ac esidues o 7 amino acids o DS1 and a sepa a ion 6 amino acids o DS2. We ha e pe o med se e al expe imen s wi h h ee Weka classifie s [13]: N¨ai e Bayes (NB), C4.5 classifie ee (J48) and Nea es Neighbo app oach wi h k= 1 (IB1). The ob ained esul s can be seen in Table 2 o a 3- old c oss- alida ion. We app ecia e low co e age and accu acy alues in all he cases. This expe imen was pe o med wi h he aim o alida ing ou ep esen a ion and confi ms ha he new encoding p o ides enough in o ma ion o a good pe o mance o a lea ning classifie . Mo eo e , we can also no ice ha MECoMaP achie ed he bes esul s o his expe imen and imp o e he esul s o DS1 and DS2 da a se shown in [4]. Table 2. A e age esul s ob ained o MECoMaP and diffe en classifica ion Weka algo i hms o he DS1 and DS2 p o ein da a se Algo i hm Da a Se Co e ageμ±σAccu acyμ±σ J48 DS1 0.04±0.07 0.19±0.08 IB1 DS1 0.08±0.05 0.07±0.05 NB DS1 0.15±0.03 0.08±0.02 MECoMaP DS1 0.18±0.13 0.26±0.32 MECoMaP 2.0 DS1 0.20±0.15 0.29±0.11 J48 DS2 0.10±0.02 0.10±0.05 IB1 DS2 0.07±0.10 0.07±0.05 NB DS2 0.10±0.10 0.18±0.10 MECoMaP DS2 0.12±0.01 0.38±0.09 MECoMaP 2.0 DS2 0.18±0.08 0.39±0.07 4 Conclusions and Fu u e Wo k In his wo k, we p esen ed some imp o emen s o a mul i-objec i e op imiza ion algo i hm o he esidue- esidue con ac p edic ion. Two o hese imp o emen s enhance he efficiency o he algo i hm: he in oduc ion o new ea u es based on e olu iona y in o ma ion (PSSM) o he encoding and a ea men o he unbalanced classes. An efficien e alua ion s uc u e o a as e alua ion o he aining da a is also included o educe he ime complexi y o he EA. 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