Integrating biological knowledge based on functional annotations for biclustering of gene expression data

c o m p u e m e h o d s a n d p o g a m s i n b i o m e d i c i n e 1 1 9 ( 2 0 1 5 ) 163–180 jo u nal ho me p ag e: www.in l.else ie heal h.com/jou nals/cmpb In eg a ing biological knowledge based on unc ional anno a ions o biclus e ing o gene exp ession da a Juan A. Nepomucenoa,∗, Alicia T oncosob, Isabel A. Nepomuceno-Chamo oa, Jesús S. Aguila -Ruizb aDepa amen o de Lenguajes y Sis emas In o má icos, Uni e sidad de Se illa, A d. Reina Me cedes s/n, 41012 Se ille, Spain bDepa men o Compu e Enginee ing, Pablo de Ola ide Uni e si y, C a. U e a km. 1, 41013 Se ille, Spain a i c l e i n o A icle his o y: Recei ed 22 July 2014 Recei ed in e ised o m 17 Feb ua y 2015 Accep ed 27 Feb ua y 2015 Keywo ds: Biclus e ing o gene exp ession da a In eg a ion o biological knowledge Sca e sea ch a b s a c Gene exp ession da a analysis is based on he assump ion ha co-exp essed genes imply co- egula ed genes. This assump ion is being e o mula ed because he co-exp ession o a g oup o genes may be he esul o an independen ac i a ion wi h espec o he same expe imen al condi ion and no due o he same egula o y egime. Fo his eason, adi- ional echniques a e ecen ly being imp o ed wi h he use o p io biological knowledge om open-access eposi o ies oge he wi h gene exp ession da a. Biclus e ing is an unsupe ised machine lea ning echnique ha sea ches pa e ns in gene exp ession da a ma ices. A sca e sea ch-based biclus e ing algo i hm ha in eg a es biological in o ma ion is p oposed in his pape . In addi ion o he gene exp ession da a ma ix, he inpu o he algo i hm is only a di ec anno a ion file ha ela es each gene o a se o e ms om a biological eposi o y whe e genes a e anno a ed. Two di e en biolog- ical measu es, F acGO and SimNTO, a e p oposed o in eg a e his in o ma ion by means o i s addi ion o-be-op imized fi ness unc ion in he sca e sea ch scheme. The measu e F acGO is based on he biological en ichmen and SimNTO is based on he o e lapping among GO anno a ions o pai s o genes. Expe imen al esul s e alua e he p oposed algo- i hm o wo da ase s and show he algo i hm pe o ms be e when biological knowledge is in eg a ed. Mo eo e , he analysis and compa ison be ween he wo di e en biological measu es is p esen ed and i is concluded ha he di e ences depend on bo h he da a sou ce and how he anno a ion file has been buil in he case GO is used. I is also shown ha he p oposed algo i hm ob ains a g ea e numbe o en iched biclus e s han o he classical biclus e ing algo i hms ypically used as benchma k and an analysis o he o e - lapping among biclus e s e eals ha he biclus e s ob ained p esen a low o e lapping. The p oposed me hodology is a gene al-pu pose algo i hm which allows he in eg a ion o biological in o ma ion om se e al sou ces and can be ex ended o o he biclus e ing algo i hms based on he op imiza ion o a me i unc ion. © 2015 Else ie I eland L d. All igh s ese ed. ∗Co esponding au ho . Tel.: +34 954559769. E-mail add ess: [email p o ec ed] (J.A. Nepomuceno). h p://dx.doi.o g/10.1016/j.cmpb.2015.02.010 0169-2607/© 2015 Else ie I eland L d. All igh s ese ed. 164 c o m p u e m e h o d s a n d p o g a m s i n b i o m e d i c i n e 1 1 9 ( 2 0 1 5 ) 163–180 1. In oduc ion Gene exp ession da a ma ices show he exp ession p ofile o housands o genes along dozens o samples, which a e s ud- ied in di e en mic oa ay expe imen s. Each alue in hese ma ices is a nume ical alue ha ep esen s he exp ession alue o a gene in a specific sample. I is assumed ha g oups o genes ha sha e a simila exp ession p ofile also sha e he same egula o y egime and hence he same unc ionali ies. This assump ion is called he guil -by-associa ion heu is ic [1]. I is la ely being e o mula ed because o he co-exp ession o a g oup o genes may be he esul o an independen ac i a- ion wi h espec o he same expe imen al condi ion and no due o he same egula o y egime is cap u ed. Biclus e ing o gene exp ession da a is an unsupe ised machine lea n- ing echnique ha sea ches g oups o genes wi h a simila exp ession p ofile unde a subse o condi ions. Recen ly, in e- g a ion me hods based on he combina ion o mul iple sou ces om open-access da a ha e been p oposed in o he fields as clus e ing o classifica ion. These app oaches can ou pe o m he adi ional algo i hms and inc ease he possibili ies o co - ec ing he spu ious in o ma ion exis ing in high- h oughpu echnology da a as gene exp ession da a o o he “omic” da a. The mos impo an di e ence o biclus e ing wi h espec o adi ional clus e ing is ha biclus e ing aims o clus e simul aneously genes as well as condi ions, a he han ocus- ing solely on ei he one. Clus e ing echniques spli he da a ma ix in o g oups o co-exp essed genes along all samples in he ma ix such ha he union o all he clus e s cons i u es he comple e ma ix and all o hem a e disjoin . Howe e , biclus e ing finds co-exp essed genes only unde a subse o samples. The e o e, he o e lapping among esul s is consid- e ed and he mo i a ion is o disco e hidden pa e ns mo e han o desc ibe he gene exp ession ma ix. No e ha some ecen ly published adi ional clus e ing algo i hms allow he o e lapping be ween clus e s [2,3]. The goal o biclus e ing is o sea ch g oups o locally co-exp essed genes mo e han o desc ibe he gene exp ession ma ix. The mo i a ion is o find hidden pa e ns o disco e po en ial bioma ke s o o mu- la e new hypo hesis. Al hough biclus e ing was s udied fi s ly in he 1960s [4] when i was p o ed o be a NP-ha d p oblem, in he con ex o gene exp ession da a i was fi s ly in oduced by Cheng and Chu ch [5]. In he con ex o biclus e ing, public da abases and eposi- o ies such as he Gene On ology p ojec (GO) o Kyo o Encyclopedia o Genes and Genomes (KEGG) ha e been commonly used o alida e he quali y o biclus e s om a biological poin o iew. Conc e ely, he en ichmen analysis o a se o genes in he con ex o GO is usually used as a s anda d amewo k o compa ison among biclus e ing algo i hms [6]. The esul s a e compa ed acco ding o a anking based on he cha ac e - iza ion o each g oup o genes belonging o a biclus e wi h espec he in o ma ion s o ed in GO. GO is an on ology wi h a hie a chical s uc u e wi h h ee oo s o domains: molecu- la unc ion, biological p ocess and cellula componen . Each gene is ela ed o a se o GO anno a ions wi h di e en le - els o specifici y. These anno a ions a e e ms in he on ology which a e linked wi h g oups o genes. These genes a e anno- a ed in he e m. Low-le el e ms in he ee s uc u e epo mo e de ailed in o ma ion han high-le el e ms which a e mo e gene al. Func ional anno a ion files a e buil such ha each gene is associa ed wi h he se o e ms whe e i is anno- a ed. These open-access biological da a a e commonly used in biclus e ing li e a u e o alida e esul s and hei use is a common ac o in mos o he pape s. Many biclus e - ing algo i hms ha e been p oposed using di e en heu is ic s a egies o sea ch c i e ia o find biclus e s [7–9]. Se e al algo i hms such as Cheng and Chu ch’s algo i hm (CC) [5], I e a i e Signa u e Algo i hm (ISA) [10], O de -p ese ing Sub- ma ix Algo i hm (OPSM) [11] o xMo i s [12] a e usually used as benchma k algo i hms in o de o es ablish a compa ison among biclus e ing algo i hms. CC was he ounda ional algo- i hm and i is based on a de e minis ic g eedy i e a i e sea ch me hod. This me hod finds biclus e s wi h a esidue less o equal han a h eshold ha is gi en as an inpu pa ame e . Al hough he esidue is a measu e usually used in biclus e - ing [5], i canno cap u e cohe en e olu ion pa e ns [13]. The ISA algo i hm uses a nonde e minis ic g eedy algo i hm ha finds up- and down- egula ed pa e ns. The inpu ma ix is eo de ed o find blocks o cohe en alues wi h espec o ows and columns ha a e epo ed as biclus e s. The OPSM algo i hm sea ches o biclus e s acco ding o a model based on linea o de ing among ows. This algo i hm sequen ially finds each biclus e and al hough cohe en e olu ion pa e ns a e cap u ed, i canno find in e se cohe en e olu ion pa - e ns. The xMo i s algo i hm i e a i ely sea ches he la ges biclus e acco ding o some cons ain s by emo ing samples. Di ec and in e se cohe en e olu ion pa e ns a e cap u ed by his algo i hm and a huge numbe o biclus e s a e usu- ally epo ed. Mo eo e , i is impo an o highligh he amily o biclus e ing algo i hms based on e olu iona y compu a ion and me aheu is ics ha op imize a ce ain quali y measu e [14–17]. Likewise, algo i hms o his amily ha use measu es based on co ela ions among genes as a mechanism o find co- exp essed genes ha e been ecen ly published in li e a u es [18–26]. All he abo e-men ioned algo i hms sea ch biclus e s com- posed o co-exp essed genes and he biological knowledge is only used as a pos e io i c i e ion o de e mine he ele ance o he biclus e s ound. Howe e , he au ho in [27] conside ed ha he s udies based on gene exp ession da a had some lim- i a ions. In pa icula , he co-exp ession o a g oup o genes may be he esul o a pa allel and independen ac i a ion wi h espec o he same expe imen al condi ion and no due o cap u e he same biological unc ionali y. The e o e, he assump ion ha co-exp ession means co- egula ion should be ein e p e ed. Fo his eason, he biological knowledge has been inco po a ed du ing he sea ch p ocess o a oid g oups o co-exp essed genes ha do no show biologically ep esen- a i e connec ions. Fo example in he field o clus e ing, he algo i hm p esen ed in [28] uses he K-means algo i hm and in eg a es gene anno a ion files ex ac ed om GO wi h a con- cep o dis ance based on he co-exp ession and unc ional simila i y. A GO-based measu e has been also applied as pa o he wo kflow o a p edic i e algo i hm o classi y genes in [29]. Namely, he a e age o he Pea son co ela ion, which e alua es simila i ies among gene exp ession p ofiles, and a GO-based measu e a e used o define a dis ance. This dis ance c o m p u e m e h o d s a n d p o g a m s i n b i o m e d i c i n e 1 1 9 ( 2 0 1 5 ) 163–180 165 is used o clus e genes and o elabo a e a anking o candida e genes. A gene ea u e selec ion me hod is p esen ed in [30] which in eg a es in o ma ion om KEGG ins ead o om GO. This algo i hm is a KEGG-imp o ed e olu iona y s a egy ha shows a be e pe o mance o selec ing genes han classical algo i hms. Func ional simila i y measu es based on GO in ol e a concep o dis ance be ween wo genes. The e a e se e al seman ic simila i y measu es o compa e GO e ms o which genes a e anno a ed [31]. They can be basically classified in wo g oups: edge-based measu es and in o ma ion con en (IC)-based measu es. The fi s g oup o measu es assumes ha he specifici y o a e m can be di ec ly in e ed om i s dep h in he GO g aph and he second g oup is based on he equency o a e m in he GO g aph. Howe e , a gene is usually anno a ed in se e al e ms and no in only one, and hence, i is be e o use simila i y measu es ha compa e se s o e ms a he han single e ms. A compa ison among his kind o measu es is p esen ed in [31] whe e he simGIC measu e shows he bes pe o mance. This measu e compu es he simila i y be ween wo genes using he IC associa ed o each e m in he genes. No e ha he GO g aph s uc u e is needed o compu e he IC in addi ion o he gene anno a ion file. Also he e a e o he measu es based on a p ep ocessed bina y ma ix ins ead o he ee s uc u e o GO. This ma ix is composed o genes as ows and GO e ms as columns and he elemen s a e 1 o 0 depending on i he gene is o is no anno a ed in he GO e m, espec i ely. These measu es a e based on he Vec o Space Model (VSM) o iginally de eloped in he con ex o in o ma ion e ie al. The measu e p esen ed in [32] can be also classified as a seman ic simila i y measu e bu nei he a p ep ocessed ma ix no he GO g aph s uc u e a e necessa y. This measu e is based on he o e lapping among gene anno a ions om fla GO anno a ion files whe e he ee s uc u e o GO is cap u ed. In pa icula , he anno a ions o each gene a e p opaga ed o uppe le els in he on ology and all he associa ed pa en e ms a e conside ed. I can be s ayed ha he in eg a ion o biological in o ma- ion om di e en sou ces is ac ually one o he challenges and esea ch di ec ions in Bioin o ma ics [33]. The e a e many wo ks ha use o he da a sou ces, no only in o ma ion om GO o KEGG. Fo example, se e al da a sou ces can be me ged o in eg a e biological knowledge as p o ein–p o ein in e ac- ion ne wo ks, genome-wide binding da a and in o ma ion om he li e a u e and no only in o ma ion om GO [34]. The COALESCE algo i hm [35] uses he gene exp ession da a oge he wi h DNA sequence da a as inpu da a and o he suppo ing da a as addi ional in o ma ion du ing he p o- cess in o de o disco e egula o y modules. This algo i hm finds biclus e s ha a e used as a guide o disco e hese modules. The p oposed algo i hm in [36] uses p o ein–p o ein in e ac ion ne wo ks and gene exp ession da a o disco e cance bioma ke s, which a e ound h ough he disco e ing o g oups o genes in biclus e s ha a e also highly connec ed in he ne wo k. Recen ly, a biclus e ing algo i hm [37], which wo ks wi h mic oRNA and a ge genes da a, uses GO in o - ma ion o do a anking o he esul s. F om he bes o ou knowledge, he biological in o ma- ion in eg a ion in biclus e ing o gene exp ession da a has no been s ill in es iga ed. The aim o his pape is o in oduce his idea in he biclus e ing field by means o unc ional anno- a ion files. These files a e fla files whe e each gene is linked wi h i s co esponding e ms in he biological eposi o y. The p oposed algo i hm is a sca e sea ch-based me aheu is ic ha op imizes a fi ness unc ion which defines a c i e ion o e alua e he quali y o he biclus e s. This algo i hm is based on he algo i hm p esen ed in [25] and al hough se - e al p ocedu es di e , he mos ele an con ibu ion is he fi ness unc ion defini ion o in eg a e he biological in o - ma ion. This unc ion consis s o h ee pa s: he fi s one is a e m o con ol he size o he biclus e s; he second one is he co ela ion among genes o cap u e co-exp essed genes; finally, he hi d e m is an addi ional e m o in eg a e he biological in o ma ion. The goal is o es ablish an equi- lib ium in he fi ness unc ion o find biclus e s composed o co-exp essed genes ha cap u e simila biological unc- ionali ies. Addi ionally, wo di e en biological in eg a ion possibili ies a e expe imen ally s udied: fi s ly, he biological in o ma ion is included wi h a measu e p oposed he e based on an en ichmen s udy o a se o genes, and secondly, wi h a GO-based measu e ha compu es he o e lapping among he anno a ed e ms o a g oup o genes. Bo h measu es only use as inpu da a o in eg a e he unc ional in o ma ion an anno- a ion file ha ela es genes and biological e ms. The e o e, he inpu da a o he algo i hm a e only he gene exp es- sion ma ix and a unc ional anno a ion file. The p oposed me hodology is a gene al-pu pose algo i hm which allows he in eg a ion o biological in o ma ion om se e al sou ces such as GO, pa hways KEGG o any biological in o ma ion p o- ided by fla anno a ion files and can be ex ended o o he biclus e ing algo i hms based on he op imiza ion o a me i unc ion. The emainde o his pape is o ganized as ollows. Sec- ion 2 p esen s he algo i hm whe e fi s ly he fi ness unc ion is defined and secondly he sea ch p ocedu e is desc ibed. In he fi ness unc ion sec ion, wo di e en biological in e- g a ion measu es a e also defined. Expe imen s a e desc ibed and discussed in Sec ion 3. Namely, he expe imen al esul s a e analyzed om h ee poin s o iew: he in eg a ion o biological in o ma ion imp o es he algo i hm pe o mance; he pe o mance o ou app oach is be e han ha ob ained by se e al benchma k algo i hms; and he esul s om he wo di e en biological in eg a ion measu es a e dis- cussed. Finally, Sec ion 4 is de o ed o conclusions and u u e wo k. 2. Me hodology The p oposed me hodology is di ided in o wo phases clea ly di e en ia ed. In a fi s s ep, a fi ness unc ion in eg a ing bio- logical knowledge om unc ional anno a ion files is designed o measu e he quali y o biclus e s in Sec ion 2.2. A sea ch p ocess based on a sca e sea ch algo i hm is applied by minimizing he measu e p o ided by his fi ness unc ion in Sec ion 2.3. In a sense, he me hodology sepa a es he sea ch- ing and he cha ac e iza ion o he biclus e s o be ound. Tha is, he sea ch p ocess is independen o he es ablished c i e- ion, which is defined by he fi ness unc ion, o find biclus e s. 166 c o m p u e m e h o d s a n d p o g a m s i n b i o m e d i c i n e 1 1 9 ( 2 0 1 5 ) 163–180 2.1. Inpu da a The inpu da a o he algo i hm a e basically he gene exp es- sion ma ix and a di ec anno a ion file. The gene exp ession ma ix is composed o gene exp ession p ofiles and samples ha a e ep esen ed in ows and columns, espec i ely. Each elemen in he ma ix ep esen s he le el o exp ession o a gene unde a pa icula sample o expe imen al condi ion. Di ec anno a ion files a e fla files whe e each line is cons i- u ed by a gene wi h a se o e ms om a biological eposi o y. These e ms a e labels o a de e mined biological unc ion- ali y whe e he gene is in ol ed. Fo example, his sen ence TVP15 GO:0006810,GO:0016192 is a line in a di ec anno a ion file ex ac ed om GO, whe e TVP15 is he gene name and GO:0006810 and GO:0016192 a e wo GO e ms whe e his gene is anno a ed. No e ha di ec anno a ion files may be down- loaded om eposi o ies in se e al ways. Ne e heless, he p oposed me hodology is a gene al-pu pose algo i hm which allows he in eg a ion o biological in o ma ion om se e al sou ces o in o ma ion. Addi ionally, he numbe o biclus e s o ob ain is also p o ided as an inpu pa ame e . 2.2. Fi ness unc ion The main goal is o define a fi ness unc ion ha in eg a es biological knowledge o find biologically ele an biclus e s, in addi ion o o he measu es such as he co ela ion o find biclus e s wi h enclosed in e es ing pa e ns and he olume o find non- i ial biclus e s. The gene exp ession ma ix can be seen as a nume ical ma ix D whe e an elemen (i, j) is he exp ession le el o gene i unde he sample o condi ion j. A biclus e B is a subma ix o D wi h N genes and M condi ions, ha is, B = {(gi, cj)}i,j whe e i ∈ {1, . . ., N} and j ∈ {1, . . ., M}. The p oposed fi ness unc ion o e alua e B is defined as ollows: (B) = M1· 1(B) + M2· 2(B) + M3· 3(B) (1) whe e 1measu es he olume o he biclus e , 2 he pa e ns ound in he biclus e and 3 he quali y o he biclus e om a biological iew poin , and M1, M2and M3a e pa ame e s o weigh he ele ance o he measu es 1, 2and 3, espec i ely. The measu e 1is used o con ol he olume o biclus e . I is defined as 1(B) =1 N · Q(2) whe e N is he numbe o genes and Q he numbe o condi- ions in he biclus e B. This e m is impo an o deal wi h he size o biclus e s du ing he sea ch p ocess and o a oid i ele an in o ma ion [38]. I is used o a oid finding i ial biclus e s wi h only a e y low numbe o genes o condi ions, as o example a biclus e wi h only wo condi ions. The measu e 2is based on he a e age co ela ion among he genes o he biclus e . No e ha only he condi ions in he biclus e a e conside ed and no all condi ions in he gene exp ession ma ix. This e m is conside ed in o de o cap u e mos o he ele an pa e ns in biclus e s such as shi ing and scaling pa e ns [13] o ac i a ion-inhibi ion pa e ns [22]. The co ela ion has been p e iously used as me i unc ion o de e mine co-exp essed genes and i e alua es he g ade o dependence among genes [25]. I is defined as ollows: co (B) =1 N 2 N−1  i=1 N  j=i+1 |ij| (3) whe e ij is he Pea son co ela ion coe ficien be ween he genes giand gj. No e ha only N 2elemen s ha e been con- empla ed due o he symme y o he co ela ion coe ficien . The absolu e alue is conside ed o a oid ha g oups o genes wi h high posi i e co ela ion alues could elimina e he e ec o g oups o genes wi h high nega i e co ela ion alues. I is no ewo hy o men ion, he a e age co ela ion e alua es a biclus e conside ing bo h genes and condi ions, ha is, wo biclus e s wi h he same se o genes bu a di e en se o condi ions p o ide di e en alues o he co ela ion. As he sca e sea ch is applied o minimize he fi ness unc ion , he unc ion 2can be defined as 2(B) = 1 − co (B) (4) The measu e 3is based on a di ec anno a ion file om a biological knowledge eposi o y, and hence, i de e mines how he biological in o ma ion is in eg a ed in he p ocess. No e ha he e m 3(B) e alua es he se o genes o he biclus e B bu no he condi ions, ha is, 3has he same alue o wo biclus e s wi h he same se o genes and di e en se s o condi ions. The e o e, 3e alua es he biological ele ance o a biclus e bu i canno find in e es ing pa e ns in a biclus- e and i canno di e en ia e biclus e s wi h he same se o genes. Two di e en unc ions, which use only as biological da a sou ce a di ec anno a ion file wi h he in o ma ion o he genes in he gene exp ession ma ix, a e p oposed o he measu e 3in he ollowing Sec ions 2.2.1 and 2.2.2. 2.2.1. F ac ional Gene On ology measu e A measu e based on he analysis o he en ichmen o a biclus- e [39] is p oposed in his pape o measu e he biological ele ance o a biclus e . The measu e is he p opo ion o ac- ion o genes in a biclus e associa ed o en iched GO e ms, he eina e F acGO. The e ms wi h an adjus ed p- alue unde a gi en h eshold a e said o be en iched o o e ep esen ed. This h eshold is known as significance le el and is usually se o 0.05. The adjus ed p- alue o each anno a ed e m in he anno a ion file is compu ed wi h espec o he g oup o genes ha belong o he biclus e . The uni e se o genes is he comple e se o genes in he gene exp ession ma ix. Fishe ’s exac es has been used o de e mine s a is ically o e ep e- sen ed e ms and Bon e oni es has been used o co ec he adjus ed p- alues o mul iple compa isons as he numbe o c o m p u e m e h o d s a n d p o g a m s i n b i o m e d i c i n e 1 1 9 ( 2 0 1 5 ) 163–180 167 hypo heses es ed is he numbe o e ms in he anno a ion file. Thus, F acGO is defined as ollows: F acGO(B) =⎧ ⎪ ⎨ ⎪ ⎩ 0 i J = 0 1 J · N J  i=1 xii J ≥ 1(5) whe e J is he numbe o en iched GO e ms, namely he num- be o GO e ms wi h an adjus ed p- alue less han 0.05, N is he numbe o genes in he biclus e and xiis he numbe o genes o he biclus e ha p esen s he GO e m i in he anno- a ion file. No e ha F acGO is equal o 1 i all he genes o he biclus e a e associa ed wi h all en iched GO e ms (xi= N, ∀i = {1, . . ., J}) and 0 when he e is no an en iched GO e m. I can be concluded ha F acGO has a alue o 1 o biologically ele an biclus e s and 0 o he wise. In his case, he p oposed unc ion 3can be di ec ly defined as 3(B) = 1 − F acGO(B) (6) I can be no ed ha he biclus e B is conside ed a high- quali y biclus e i 3is equal o 0 and a bad biclus e i i s alue is se o 1. 2.2.2. No malize e m o e lap measu e Se e al gene pai wise GO-based measu es ha e been p oposed in he li e a u e. These measu es compu e he simila i y be ween wo genes based on hei GO anno a ions. The sim- NTO measu e, which is based on he e m o e lap defined in [32], only uses anno a ion files as inpu . This measu e is as e and simple han o he measu es based on in o ma ion con- en (IC). These IC-based measu es use he GO ee s uc u e as addi ional in o ma ion along wi h he anno a ion file. Sim- NTO cap u es he GO hie a chical s uc u e i he anno a ion files a e buil by con aining all pa en e ms o each e m. A measu e based on he unc ional simila i y o a biclus e using simNTO measu e is p oposed as a measu e o e alua e he biological ele ance o a biclus e in his wo k. This mea- su e is defined by means o he a e age o e lapping be ween he pai s o genes o a biclus e acco ding o he in o ma ion om he GO anno a ion file. Tha is, SimNTO(B) =1 N 2 N−1  i=1 N  j=i+1 simNTO(gi, gj) (7) whe e N is he numbe o genes in he biclus e B and sim- NTO is he no malized e m o e lap measu e p oposed in [32]. In pa icula , simNTO measu es he o e lapping be ween wo genes g1and g2wi h espec o GO e ms and is defined as simNTO(g1, g2) =|anno g1∩ anno g2| min(|anno g1|, |anno g2|)(8) whe e anno giis he se o GO e ms associa ed o he gene gi and | · | is he numbe o elemen s o a se . I is impo an o men ion ha he di ec anno a ion file mus be buil by p op- aga ing he e ms owa d he uppe le els in he on ology o compu e his measu e. The e o e, anno giis defined by consid- e ing he se o all di ec anno a ions o he gene giand he associa ed pa en e ms in he on ology, excluding he oo o he hie a chy. Acco dingly, he anno a ion file mus cap u e he GO ee s uc u e. No e ha he simNTO measu e anges om 0 o 1. Two genes sha e he same anno a ions and a e e y simila in he on ology i simNTO has a alue o 1, and 0 o he wise. Mo eo e , i one gene g is no con empla ed in he anno a ion file because he e is no any in o ma ion in GO, anno gis he emp y se , and in his case, he simNTO measu e is di ec ly se o 0. In his case, he p oposed unc ion 3is defined as ollows: 3(B) = 1 − SimNTO(B) (9) I can be app ecia ed ha 3(B) = 0 when B is composed o a g oup o genes ha sha e simila biological unc ionali ies in GO, and he e o e, B is a ele an biclus e acco ding o GO. 2.3. Desc ip ion o he algo i hm An algo i hm based on a me aheu is ic scheme has been con- side ed due o he compu a ional na u e o biclus e ing. The sea ch scheme de i es om he algo i hm p esen ed in [25] whe e a sca e sea ch was also applied in biclus e ing o gene exp ession da a. The p oposed algo i hm is a sequen ial co e - ing algo i hm, namely, each biclus e is ob ained by applying an independen sca e sea ch p ocedu e. This i e a i e p o- cess, join ly wi h he bias in oduced in he sea ch h ough he fi ness unc ion defini ion, con ols he non-de e minis ic na u e o he p ocess. The sca e sea ch is a popula ion-based e olu iona y me aheu is ic whe e a popula ion o solu ions e ol es un il an op imal solu ion is eached. The basic idea in he sca e sea ch is o pe o m he op imiza ion wi h a small se o solu ions, called he e e ence se , ins ead o a comple e popula ion o solu ions as in o he popula ion-based me aheu is ics [40]. The e e ence se is composed o he bes solu ions acco ding o in ensifica ion and di e si y s a egies. Fig. 1 shows he basic idea behind he p oposed algo i hm. All he s eps composing his algo i hm a e going o be b iefly desc ibed in Sec ions 2.3.1 and 2.3.2. 2.3.1. Sca e sea ch A solu ion ep esen s a biclus e , which is codified by wo bina y s ings whe e he bi s indica e i he gene o condi ion is p esen o no in he biclus e . Fi s ly, an ini ial popula- ion is gene a ed by he di e sifica ion gene a ion me hod and is composed o solu ions as sca e as possible, which a e hen imp o ed by a local sea ch p ocedu e ha will be desc ibed in Sec ion 2.3.2. Con a y o he gene ic algo i hms he ini- ial popula ion is buil ollowing a mechanism o achie e di e sifica ion and no a gene al andomiza ion p ocess. The di e sifica ion gene a ion me hod gene a es a collec ion o solu- ions om a seed solu ion. I x is a bina y s ing used as seed, a new s ing xis gene a ed o each alue o an in ege h = 1, 2, 3, . . ., hmax as ollows: x 1+kh = 1 − x1+kh o k = 0, 1, 2, 3, . . ., n/h(10) 168 c o m p u e m e h o d s a n d p o g a m s i n b i o m e d i c i n e 1 1 9 ( 2 0 1 5 ) 163–180 Fig. 1 – The p oposed sca e sea ch o biclus e ing. whe e x = (x1, . . ., xn), n is he numbe o bi s, k akes al- ues om 0 o he la ges in ege sa is ying k ≤ n/h. Due o he bina y s ing size and o he sca e sea ch li e a u e ecom- menda ions [40], he maximum alue o h is hmax = n/5. All he emaining bi s o xa e equal o hose o x. A e gene a ing all he possible solu ions wi h ha seed, i mo e solu ions we e needed in he ini ial popula ion, he ule will be applied again using he las solu ion as a new seed. This me hod is he s an- da d p ocedu e usually used in sca e sea ch algo i hms wi h bina y codifica ion [40]. The idea o sca e be ween wo solu- ions is in oduced by he Hamming dis ance. The Hamming dis ance be ween wo bina y s ings is defined as he num- be o posi ions a which he co esponding 0’s and 1’s a e di e en . Once he ini ial popula ion is gene a ed, he e e ence se is buil by he build e e ence se me hod. This me hod consis s in selec ing he fi e bes solu ions and he fi e mos sca e ed solu ions wi h espec o he emaining o exis ing solu ions in he se om he ini ial popula ion. The e o e, he e e ence se con ains he mos ep esen a i e solu ions om he ini- ial popula ion acco ding o quali y and di e si y c i e ia. The sca e solu ions p o ide di e si y in he sea ch p ocess o a oid local op ima. This di e si y s a egy plays a simila ole o he mu a ion ope a o s in gene ic algo i hms, o example. On he o he hand, he quali y solu ions a e conside ed as mechanism o define an in ensifica ion s a egy in he sea ch. I is impo an o upda e he ini ial popula ion by emo ing he solu ions selec ed by his me hod. The e e ence se e ol es by using he subse gene a ion me hod, he solu ion combina ion me hod and he e e ence se upda e me hod un il he e e ence se is s able. Once he e - e ence se does no change, he e e ence se is ebuil wi h he fi e bes solu ions om he p e ious e e ence se and he fi e mos sca e ed solu ions wi h espec o he emaining solu ions in he se om he ini ial popula ion. The subse gen- e a ion me hod gene a es subse s o pai s o solu ions om he e e ence se o be combined by he solu ion combina ion me hod wi h he pu pose o c ea ing new solu ions. Once he new solu- ions a e ob ained, he local sea ch p ocedu e is again applied o imp o e hem. The solu ion combina ion me hod is based on he uni o m c osso e ope a o commonly used in e olu ion- a y compu a ion. The e e ence se upda e me hod consis s in choosing he 10 bes solu ions, acco ding o he fi ness unc- ion, om he joining o he solu ions o he e e ence se and he new solu ions ob ained by he solu ion combina ion me hod. The ou pu is he bes biclus e in he las e e ence se . The whole p ocess is epea ed as many imes as numbe o biclus e s o be ob ained, which is an inpu pa ame e o he algo i hm. No mechanism o edundancy con ol among esul s has been conside ed and i could be hough ha he same biclus e is always ound. Se e al wo ks based on me a- heu is ics include mechanisms o edundancy con ol bu hese algo i hms usually use only an ini ial popula ion in he comple e p ocess. Conc e ely, he algo i hm published in [41] p esen s an addi ional e m in he fi ness unc ion o con ol he edundancy in o de o a oid simila i ies among biclus e s and o find epea edly he same biclus e . Howe e , i a di e - en ini ial popula ion is buil o each biclus e ob ained by he p oposed algo i hm, his addi ional e m can be emo ed and i is enough fil e ing hose highly edundan biclus e s. Mo eo e , i is in e es ing o ob ain biclus e s sha ing g oups o genes om a biological poin o iew [2,3]. Consequen ly, he p oposed algo i hm does no con empla e an addi ional e m in he fi ness unc ion and builds an ini ial popula ion c o m p u e m e h o d s a n d p o g a m s i n b i o m e d i c i n e 1 1 9 ( 2 0 1 5 ) 163–180 169 o each ound biclus e . An o e lapping h eshold o 30% is chosen and he biclus e s wi h an o e lapping g ea e han his h eshold a e emo ed. The pa ame e s o he algo i hm ha e been chosen acco d- ing o ecommenda ions o he li e a u e o sca e sea ch [40] and p e ious wo ks [25]. In pa icula , 200 o he size o he ini ial popula ion, 10 o he size o he e e ence se and 20 o he numbe o i e a ions o he e olu iona y p ocess ( he inne loop in Fig. 1). 2.3.2. Imp o emen me hod The imp o emen me hod is a local sea ch p ocedu e designed o imp o e he quali y o solu ions acco ding o he fi ness unc ion. Namely, gi en a biclus e his me hod gene - a es a new biclus e wi h a be e alue o i s fi ness unc ion. In gene al, he imp o emen me hod in a sca e sea ch is specifically designed o each p oblem as i depends on he na u e o he fi ness unc ion [25]. Al hough an imp o emen me hod guided by a heu is ic is be e han a blind imp o e- men me hod, he heu is ic o imp o e he quali y o biclus e s is ela ed o he fi ness unc ion o he p oblem. In his wo k, se e al di e en fi ness unc ions a e analyzed, namely one o each measu e p oposed o in eg a e biological knowledge, and he e o e, he same heu is ic is no good o all he fi - ness unc ions. Fo his eason, a blind imp o emen me hod is p oposed wi h he pu pose o being used wi h all hem. This independence o he imp o emen me hod ega ding he fi - ness unc ion mo i a es a blind sea ch among solu ions close o he o iginal solu ion. Some imes his sea ch does no find a be e solu ion, and he e o e, in hese cases he o iginal solu- ion is no imp o ed. This me hod plays an impo an ole o speed up he con e gence o he sea ch. The imp o emen me hod aims a selec ing he bes biclus- e om a ce ain numbe o new biclus e s gene a ed by he combina ion o di e en bina y s ings. These new solu ions a e gene a ed by means o pe mu a ions (see Fig. 2) in o de o be close (in he sense o he hamming dis ance) o he o iginal biclus e /solu ion. No e ha he new solu ions mus imp o e he o iginal solu ion bu in he same “neighbo hood”. I new biclus e s do no imp o e he sea ch, he ou pu is he o iginal biclus e . Fig. 2 shows how bina y s ings a e combined. These bina y s ings ha e been ob ained om he bina y s ings o he o iginal biclus e o be imp o ed. In pa icula , each bi o he bina y s ing o he o iginal biclus e is analyzed and i he bi is se o 0 hen he bi o he new bina y s ing is also se o 0 and i he bi is 1, hen he ollowing ou cases a e conside ed: • Case 1: The nex bi is changed o 1 and he cu en bi does no change i s alue. • Case 2: The nex bi is changed o 1 and he cu en bi is changed o 0. • Case 3: The p e ious bi is changed o 1 and he cu en bi does no change i s alue. • Case 4: The p e ious bi is changed o 1 and he cu en bi is changed o 0. Twel e new biclus e s ha e been gene a ed by applying his me hod. I he new biclus e s do no imp o e he alue o he fi ness unc ion o he o iginal biclus e , he ou pu o he imp o emen me hod is he o iginal biclus e . 3. Expe imen s The goal o he expe imen s is o analyze how he in eg a ion o biological in o ma ion has a ele an influence on he pe - o mance o he p oposed algo i hm. In pa icula , he esul s ob ained om F acGO and SimNTO measu es p oposed he e in o de o in eg a e he biological knowledge a e compa ed. Finally, he esul s ob ained by he p oposed algo i hm a e compa ed wi h hose o he classical biclus e ing algo i hms such as ChCh [5], ISA [10], OPSM [11] and xMo i s [12] ypically used as benchma k in he li e a u e. The s anda d compa ison me hodology among biclus e ing algo i hms is usually based on he gene en ichmen in he ob ained biclus e s [6]. In his wo k, a biclus e is said o be en iched i a leas one en iched GO e m is associa ed o i . This sec ion p esen s he expe imen s ca ied ou o assess he pe o mance o he p oposed algo i hm on he da ase s desc ibed in Sec ion 3.1. The esul s a e ga he ed in Sec ion 3.2 and a discussion can be ound in Sec ion 3.3. 3.1. Da a se s Two yeas da ase s wi h accession numbe s GDS1116 and GDS2914 om he GEO eposi o y [42] ha e been used in he expe imen a ion. The fi s one is composed o 7085 exp ession p ofiles and 131 samples and ecollec s he gene ic a ia ion in he gene exp ession be ween pa en s and p ogenies om a c oss o wo di e en kinds o yeas s ains. The second one has 15,488 exp ession p ofiles and 36 samples and is a ime cou se expe imen in which yeas cells deal wi h a low dose o ca eine a e analyzed. The aw da a ha e been p o- cessed wi h he Babelomics web ool [43]. Fo bo h da ase s, he exp ession p ofiles wi h mo e han a 30% o missing al- ues ha e been fil e ed and he emaining missing alues ha e been eplaced wi h he mean o he alues in he p ofile. The p ofiles, which appea se e al imes bu ep esen ing he same gene, ha e been summed up by means o he median o he alues. A e p ocessing he aw da a, GDS1116 exp ession ma ix is a ma ix composed o 882 genes and 131 samples o expe imen al condi ions and GDS2914 a ma ix o 975 genes and 36 condi ions. Biological in o ma ion is p o ided by a di ec anno a ion file om biological p ocess domain (BP) o Gene On ology (GO). This file shows he GO e ms associa ed wi h each gene o he da a se . No e ha his in o ma ion could be downloaded om GO in di e en ways. In his wo k, he ee s uc u e o GO is conside ed and he anno a ion file has been ob ained by p op- aga ing he anno a ions o he uppe le els in he on ology. Tha is, each gene is also ela ed o GO e ms co esponding o all pa en nodes un il he oo node. The anno a ion files o bo h da ase s ha e been gene a ed by he Babelomics ool wi h de aul op ions. Fo GDS1116 da a se , 632 genes a e anno a ed in he file om he 882 genes o he exp ession ma ix. This file con ains 245 di e en GO e ms and he a e age numbe o GO e ms pe gene is equal o 10.6. Fo GDS2914 da a se , 658 genes a e anno a ed om a o al numbe o 975 genes, he file 170 c o m p u e m e h o d s a n d p o g a m s i n b i o m e d i c i n e 1 1 9 ( 2 0 1 5 ) 163–180 Fig. 2 – The p oposed imp o emen me hod: a es example. con ains 256 GO e ms and he a e age numbe o GO e ms pe gene is 10.1. 3.2. Resul s In his sec ion he esul s a e ga he ed wi h he pu pose o e alua ing he impo ance o in eg a ing biological knowledge o find high-quali y biclus e s. The esul s ob ained om he p oposed algo i hm o di e en configu a ions o he fi - ness unc ion a e p esen ed and compa ed wi h espec o se e al ypical a iables such as he size o biclus e s, o e - lapping among biclus e s and en ichmen o biclus e s. Also, he esul s ob ained om di e en eposi o ies such as GO, KEGG pa hways and In e P o a e p esen ed. Each un o he algo i hm ob ains 100 biclus e s. This numbe has been cho- sen because o ob ain a high numbe o biclus e s is desi able due o he compa ison among biclus e ing algo i hms is usu- ally es ablished in e ms o pe cen ages o en iched biclus e s. No e ha he algo i hm ob ains each biclus e h ough an independen non-de e minis ic p ocedu e. Table 1 p esen s he pe cen age o en iched biclus e s ob ained by he p o- posed algo i hm o di e en numbe s o biclus e s (namely, 10, 50 and 100). I can be obse ed ha he pe cen age does no depend on he numbe o biclus e s conside ed as inpu pa ame e . The fi ness unc ion pa ame e se ing is expe i- men al s udied o analyze he pe o mance o he biological in eg a ion measu es. Table 2 summa izes he quali y o biclus e s ob ained by he p oposed algo i hm o GDS1116 and GDS2914 da ase s when di e en configu a ions o he fi ness unc ion ha e been conside ed. Specifically, he column Measu e, indica es i he fi ness unc ion akes in o accoun biological in o ma- ion by means o he measu es SimNTO (Eq. (7)) o F acGO (Eq. (6)) o no ( 3= 0 in Eq. (1)). The column Pa ame e s ep esen s he weigh co esponding o each e m o he fi ness unc ion. I is impo an o highligh ha all e ms i a y be ween 0 and 1. Gi en he impo ance o a oiding i ial biclus e s wi h a low numbe o genes o condi ions, o example only wo genes o condi ions, he pa ame e M1associa ed o he ol- ume o he biclus e always has been se o 2 [25]. Namely, he ollowing h ee configu a ions ha e been analyzed when he biological knowledge is in eg a ed in he fi ness unc ion: o find biclus e s wi h unde lying co ela ed pa e ns and o find biological high-quali y biclus e s a e equally impo an (M2= 1, M3= 1), o find biclus e s wi h co ela ed pa e ns is mo e impo an han o find biological high-quali y biclus- e s (M2= 2, M3= 1) o ice- e sa (M2= 1, M3= 2); when he algo i hm sea ches o biclus e s wi hou a p io i biological knowledge (M3= 0), wo configu a ions ha e been analyzed depending on he ele ance o finding biclus e s wi h enclosed pa e ns (M2= 1 o M2= 2). No e ha M1canno be equal o ze o o a oid i ial biclus e s [25]. On he o he hand, i M2= 0 he numbe o condi ions is no co ec ly con olled by he fi ness unc ion, and he e o e, he algo i hm is no a biclus- e ing algo i hm because can clus e genes bu no condi ions. Finally, M3= 0 is conside ed when biological in o ma ion is no conside ed. The nex columns in Table 2, size, en iched biclus e s (%), GO e ms pe biclus e and ime, show he a e age numbe o genes and condi ions o 100 biclus e s ob ained by he p oposed algo i hm, he pe cen age o en iched biclus e s, he a e age numbe o en iched GO e ms pe biclus e and he compu a ion ime o he algo i hm o ob ain a biclus e , espec i ely. Al hough he en ichmen o biological signifi- cance o GO e ms is usually s udied ega ding he biological p ocess (BP) domain o GO, in his wo k he biological signifi- cance has been also s udied o molecula unc ion (MF) and cellula componen (CC) domains. No e ha he pe cen age o en iched biclus e s is he s anda d biological e alua ion c i- e ion commonly used in biclus e ing [6,44]. I should also c o m p u e m e h o d s a n d p o g a m s i n b i o m e d i c i n e 1 1 9 ( 2 0 1 5 ) 163–180 171 Table 1 – Pe cen age o en iched biclus e s ob ained by he p oposed algo i hm o di e en numbe s o biclus e s. Fi ness unc ion configu a ion Numbe o biclus e s (M1, M2, M3) En iched biclus e s (%) BP MF CC 1-SimNTO 10 (2,1,1) 100 100 100 1-SimNTO 50 (2,1,1) 100 98 100 1-SimNTO 100 (2,1,1) 99 97 97 1-F acGO 10 (2,1,1) 100 70 50 1-F acGO 50 (2,1,1) 100 72 64 1-F acGO 100 (2,1,1) 100 73 67 0 10 (2,1,0) 85 82 88 0 50 (2,1,0) 82 72 84 0 100 (2,1,0) 85 82 88 Table 2 – Resul s ob ained by di e en fi ness unc ion configu a ions o bo h da ase s. Each ow shows a un ha ob ains 100 biclus e s. Da ase Fi ness unc ion Size En iched biclus e s (%) GO e ms pe biclus. (BP) Time (s) Measu e 3Pa ame e s (M1, M2, M3) BP MF CC (2, 1, 1) (11.6 × 15.6) 99 97 97 5.74 28.65 1-SimNTO (2, 1, 2) (8.7 × 15.2) 87 75 84 3.67 15.78 (2, 2, 1) (10.1 × 5.1) 95 83 89 4.5 24.03 GDS1116 (2, 1, 1) (181.6 × 19.4) 100 73 67 1 5410.98 1-F acGO (2, 1, 2) (193.9 × 19.3) 100 79 79 1 5546.12 (2, 2, 1) (109.2 × 3) 100 47 52 1 5682.65 (2, 1, 0) (23.5 × 14.7) 85 82 88 2.16 38.29 0 (2, 2, 0) (46.8 × 3.2) 25 17 21 0.4 11.51 (2, 1, 1) (10.9 × 10.9) 87 33 33 5.45 27.76 1-SimNTO (2, 1, 2) (8.0 × 10.2) 65 24 33 2.94 15.67 (2, 2, 1) (9.5 × 3.3) 87 25 30 5.39 22.18 GDS2914 (2, 1, 1) (180.6 × 15.1) 100 97 94 1.01 5420.84 1-F acGO (2, 1, 2) (193.2 × 15.8) 100 98 94 1 5920.09 (2, 2, 1) (102.8 × 3) 100 72 67 1 6311.43 (2, 1, 0) (24.1 × 9.0) 2 5 6 0.02 13.14 0 (2, 2, 0) (37.1 × 3.1) 13 15 17 0.19 7.16 Fig. 3 – Pe cen age o en iched biclus e s o GDS1116 om Tables 2 and 3. 178 c o m p u e m e h o d s a n d p o g a m s i n b i o m e d i c i n e 1 1 9 ( 2 0 1 5 ) 163–180 Fig. 11 – GO e m clus e s epo ed by Re igo om biclus e 1 o he F acGO measu e and 211 configu a ion. Only wo gene al GO e ms a e epo ed: p o ein-ubiqui ina ion and me abolism. measu e cap u es biclus e s whe e genes a e oge he in a same GO e m, and as a consequence, hei genes a e anno- a ed in he uppe le els o he GO hie a chy. No e ha he anno a ion files used as inpu pa ame e a e gene a ed cap- u ing all he associa ed pa en e ms o each gene. Gene Te m Linke [48] and Re igo [49] ools ha e been used o con- fi m ha he biclus e s based on he F acGO measu e show e y gene al GO in o ma ion. Fi s ly, he fi s ool fil e s i ele- an GO in o ma ion by iden i ying me ag oups o genes wi h cohe en biological significance. Secondly, Re igo summa izes a lis o hese GO e ms by finding ep esen a i e subse s o e ms using a clus e ing p ocedu e ha emo es edundan e ms. Fig. 11 shows he significan en iched GO e m in he fi s biclus e ob ained by he F acGO measu e and 211 con- figu a ion. All en iched GO e ms ha e been clus e ed in wo e y gene al e ms in GO: me abolism and p o ein ubiqui- a ion. A e ha ing applied his pipeline analysis, Gene Te m Linke and Re igo, all epo ed en iched GO e ms a e clus- e ed in gene al GO e ms. The e o e, he assump ion ha F acGO-based biclus e s a e composed o genes anno a ed in he uppe le els o he GO hie a chy is confi med. The F acGO measu e finds biclus e s wi h a gene al in o ma ion in GO, and hence, hese biclus e s a e composed o genes ha a e no ela ed as g oup wi h any pa hway. The comple e in o ma ion o all figu es can be ead as Supplemen a y in o ma ion. 4. Conclusions A sca e sea ch-based biclus e ing algo i hm ha in eg a es biological in o ma ion has been p oposed in his pape . The da a inpu o he p oposed algo i hm a e he gene exp es- sion ma ix and a di ec anno a ion file linking genes wi h se s o biological e ms ex ac ed om a biological eposi o y o da abase. The Gene On ology, KEGG pa hways and In e P o da abases ha e been used as sou ce o gene a ing hese files in his wo k. Two di e en biological measu es, F acGO and SimNTO, ha e been p oposed o in eg a e his in o ma ion by means o i s addi ion o he fi ness unc ion o be op imized o e alua e he quali y o he biclus e s in he sca e sea ch. The measu e F acGO is based on he biological en ichmen and SimNTO is based on he o e lapping among GO anno a ions o pai s o genes. Expe imen al esul s om he applica ion o he p oposed algo i hm o wo da ase s ha e been epo ed and discussed showing a be e pe o mance when biological knowledge is in eg a ed and be e biclus e s han ha o he classical biclus e ing algo i hms. The main mo i a ion has been o use a s anda d biolog- ical alida ion c i e ion in biclus e ing [6,44] as mechanism o in eg a e biological knowledge. This c i e ion is based on he pe cen age o en iched biclus e s ha is calcula ed using di ec anno a ion files. I hese files a e GO files which ha e been gene a ed by p opaga ing anno a ions o uppe le els in he GO hie a chy, he expe imen al esul s show ha F acGO- based biclus e s only sha e gene al GO e ms and hey do no cap u e ele an biological in o ma ion. In his case, he Sim- NTO measu e, which is based on he e m o e lap defined in [32] and uses anno a ion files as inpu , is as e and simple han o he GO seman ic measu es and sol es his p oblem. Se e al expe imen s show ha SimNTO-based biclus e s cap u e el- e an biological in o ma ion ha p esen pa hways mapping in Reac ome, o example. I is impo an o no e ha SimNTO cap u es he GO hie a chical s uc u e i he anno a ion files con ain all pa en e ms o each e m. As a summa y, he di - e ences be ween he F acGO and SimNTO measu es depend on he da a sou ce and how he anno a ion file has been buil in he case GO is used. Fu u e wo k will be ocused on he s udy o o he biolog- ical measu es o handle mic oRNA/mRNA da a and how o in eg a e in o ma ion om di e en biological sou ces. Some imp o emen s in he sea ch p ocedu e o he p oposed algo- i hm will be also analyzed such as he se ing configu a ion o inne pa ame e s. Conflic s o in e es We decla e ha we ha e no any ac ual o po en ial compe ing financial in e es s. Acknowledgmen s We would like o hank Spanish Minis y o Science and Inno- a ion, Jun a de Andalucía and Uni e si y Pablo de Ola ide o he financial suppo unde p ojec s TIN2011-28956-C02-02, P12-TIC-1728 and APPB813097, espec i ely. Appendix A. Supplemen a y da a Supplemen a y da a associa ed wi h his a icle can be ound, in he online e sion, a h p://dx.doi.o g/10.1016/j. cmpb.2015.02.010. e e e n c e s [1] F. Ma kowe z, R. Spang, In e ing cellula ne wo ks – a e iew, BMC Bioin o m. 8 (2007) S5. c o m p u e m e h o d s a n d p o g a m s i n b i o m e d i c i n e 1 1 9 ( 2 0 1 5 ) 163–180 179 [2] K. Rh isso ak ai, K. Gunsalus, Mine: module iden ifica ion in ne wo ks, BMC Bioin o m. 12 (2011) 192. [3] T. Nepusz, H. Yu, A. Paccana o, De ec ing o e lapping p o ein complexes in p o ein–p o ein in e ac ion ne wo ks, Na . Me hods 9 (2012) 471. [4] J. Mo gan, J. Sonquis z, P oblems in he analysis o su ey da a, and a p oposal, J. Am. S a . Assoc. 58 (1963) 415–434. [5] Y. Cheng, G. Chu ch, Biclus e ing o exp ession da a, in: P oceedings o he 8 h In e na ional Con e ence on In elligen Sys ems o Molecula Biology, ol. 8, 2000, pp. 93–103. [6] A. P elic, S. Bleule , P. Zimme mann, A. Wille, P. Buhlmann, W. G uissem, L. Hennig, L. Thiele, E. Zi zle , A sys ema ic compa ison and e alua ion o biclus e ing me hods o gene exp ession da a, Bioin o ma ics 22 (2006) 1122–1129. [7] S. Madei a, A. Oli ei a, Biclus e ing algo i hms o biological da a analysis: a su ey, IEEE T ans. Compu . Biol. Bioin o m. 1 (2004) 24–45. [8] A. Tanay, R. Sha an, R. Shami , Biclus e ing algo i hms: a su ey Handbook o Compu a ional Molecula Biology, ol. 9, Edi ed by: Alu u S. Chapman & Hall/CRC Compu e and In o ma ion Science Se ies, 2005, pp. 26–31. [9] S. Busygin, O. P okopye , P. Pa dalos, Biclus e ing in da a mining, Compu . Ope . Res. 35 (2008) 2964–2987. [10] S. Be gmann, J. Ihmels, N. Ba kai, I e a i e signa u e algo i hm o he analysis o la ge-scale gene exp ession da a, Phys. Re . E 67 (2003) 1–18. [11] A. Ben-Do , B. Cho , R. Ka p, Z. Yakhini, Disco e ing local s uc u e in gene exp ession da a: he o de -p ese ing subma ix p oblem, J. Compu . Biol. 10 (2003) 373–384. [12] T. Mu ali, S. Kasi , Ex ac ing conse ed gene exp ession mo i s om gene exp ession da a, in: P oceedings o Pacific Symposium on Biocompu ing, 2003, pp. 77–88. [13] J. Aguila -Ruiz, Shi ing and scaling pa e ns om gene exp ession da a, Bioin o ma ics 21 (2005) 3840–3845. [14] H. Banka, S. Mi a, E olu iona y biclus e ing o gene exp essions, Ubiqui y 7 (2006) 1–12. [15] F. Di ina, J. Aguila -Ruiz, A mul i-objec i e app oach o disco e biclus e s in mic oa ay da a, in: P oceedings o he 9 h Annual Con e ence on Gene ic and E olu iona y Compu a ion, ACM P ess, New Yo k, USA, 2007, pp. 385–392. [16] J. Liu, Z. Li, X. Hu, Y. Chen, Biclus e ing o mic oa ay da a wi h MOSPO based on c owding dis ance, BMC Bioin o m. 10 (2009) S9. [17] C.A. Gallo, J.A. Ca ballido, I. Ponzoni, Mic oa ay biclus e ing: a no el meme ic app oach based on he PISA pla o m, in: P oceedings o he 7 h Eu opean Con e ence on E olu iona y Compu a ion, Machine Lea ning and Da a Mining – E oBIO 2009, 2009, pp. 44–55. [18] W. Ayadi, M. Elloumi, J.-K. Hao, A biclus e ing algo i hm based on a biclus e enume a ion ee: applica ion o DNA mic oa ay da a, BioDa a Min. 2 (2009) 9. [19] W.-H. Yang, H. Yan, D.-Q. Dai, Finding co ela ed biclus e s om gene exp ession da a, IEEE T ans. Knowl. Da a Eng. (2010) 568–584. [20] G. Li, Q. Ma, H. Tang, A.H. Pa e son, Y. Xu, Qubic: a quali a i e biclus e ing algo i hm o analyses o gene exp ession da a, Nucleic Acids Res. 37 (2009) e101. [21] A. Bha acha ya, R.K. De, Bi-co ela ion clus e ing algo i hm o de e mining a se o co- egula ed genes, Bioin o ma ics 25 (2009) 2795–2801. [22] A. Bha acha ya, R.K. De, Bi-co ela ion clus e ing algo i hm o de e mining a se o co- egula ed genes, Bioin o ma ics 25 (2009) 2795–2801. [23] T. Yun, G.-S. Yi, Biclus e ing o he comp ehensi e sea ch o co ela ed gene exp ession pa e ns using clus e ed seed expansion, BMC Genomics 14 (2013) 144. [24] T. Zeng, J. Li, Maximiza ion o nega i e co ela ions in ime-cou se gene exp ession da a o enhancing unde s anding o molecula pa hways, Nucleic Acids Res. 38 (2010) e1. [25] J.A. Nepomuceno, A. T oncoso, J. Aguila -Ruiz, Biclus e ing o gene exp ession da a by co ela ion-based sca e sea ch, BioDa a Min. 4 (2011) 3. [26] J.L. Flo es, I. Inza, P. La a ˜ naga, B. Cal o, A new measu e o gene exp ession biclus e ing based on non-pa ame ic co ela ion, Compu . Me hods P og ams Biomed. 112 (2013) 367–397. [27] J. B yan, P oblems in gene clus e ing based on gene exp ession da a, J. Mul i a . Anal. 90 (2004) 44–66. [28] M. Ve banck, S. Le, J. Pages, A new unsupe ised gene clus e ing algo i hm based on he in eg a ion o biological knowledge in o exp ession da a, BMC Bioin o m. 14 (2013) 42. [29] F. Azuaje, H. Wang, H. Zheng, F. Leona d, M. Rolland-Tu ne , L. Zhang, Y. De aux, D. Wagne , P edic i e in eg a ion o gene unc ional simila i y and co-exp ession defines ea men esponse o endo helial p ogeni o cells, BMC Sys . Biol. 5 (2011) 46. [30] R. Luque-Baena, D. U da, M.G. Cla os, L. F anco, J. Je ez, Robus gene signa u es om mic oa ay da a using gene ic algo i hms en iched wi h biological pa hway keywo ds, J. Biomed. In o m. 49 (2014) 32–44. [31] C. Pesqui a, D. Fa ia, H. Bas os, A. Fe ei a, A. Falcao, F. Cou o, Me ics o go based p o ein seman ic simila i y: a sys ema ic e alua ion, BMC Bioin o m. 9 (2008) S4. [32] M. Mis y, P. Pa lidis, Gene on ology e m o e lap as a measu e o gene unc ional simila i y, BMC Bioin o m. 9 (2008) 327. [33] F. Azuaje, Bioin o ma ics and Bioma ke Disco e y: Omic Da a Analysis o Pe sonalized Medicine, Wiley-Blackwell, 2010. [34] K. Lo, A. Ra e y, K. Dombek, J. Zhu, E. Schad , R. Bumga ne , K. Yeung, In eg a ing ex e nal biological knowledge in he cons uc ion o egula o y ne wo ks om ime-se ies exp ession da a, BMC Sys . Biol. 6 (2012) 101. [35] C. Hu enhowe , K.T. Mu ungu, N. Indik, W. Yang, M. Sch oede , J.J. Fo man, O.G. T oyanskaya, H.A. Colle , De ailing egula o y ne wo ks h ough la ge scale da a in eg a ion, Bioin o ma ics 25 (2009) 3267–3274. [36] P.E.A. Dao, In e ing cance subne wo k ma ke s using densi y-cons ained biclus e ing, Bioin o ma ics 26 (2010) 625–631. [37] G. Pio, M. Ceci, D. D’Elia, C. Loglisci, D. Male ba, A no el biclus e ing algo i hm o he disco e y o meaning ul biological co ela ions be ween mic o nas and hei a ge genes, BMC Bioin o m. 14 (2013) S8. [38] J.A. Nepomuceno, A. T oncoso, J.S. Aguila -Ruiz, E olu iona y me aheu is ic o biclus e ing based on linea co ela ions among genes, in: SAC 2010: P oceedings o he 2010 ACM Symposium on Applied Compu ing (SAC), Sie e, Swi ze land, Ma ch 22–26, 2010, 2010, pp. 1143–1147. [39] G.F. Be iz, O.D. King, B. B yan , C. Sande , F.P. Ro h, Cha ac e izing gene se s wi h FuncAssocia e, Bioin o ma ics 19 (2003) 2502–2504. [40] R. Ma i, M. Laguna, Sca e Sea ch. Me hodology and Implemen a ion in C, Kluwe Academic Publishe s, Bos on, 2003. [41] J.A. Nepomuceno, A.T. Lo a, J.S. Aguila -Ruiz, An o e lapping con ol-biclus e ing algo i hm om gene exp ession da a, in: Nin h In e na ional Con e ence on In elligen Sys ems 180 c o m p u e m e h o d s a n d p o g a m s i n b i o m e d i c i n e 1 1 9 ( 2 0 1 5 ) 163–180 Design and Applica ions, ISDA 2009, Pisa, I aly, No embe 30–Decembe 2, 2009, 2009, pp. 1239–1244. [42] R. Edga , M. Dom ache , A.E. Lash, Gene exp ession omnibus: NCBI gene exp ession and hyb idiza ion a ay da a eposi o y, Nucleic Acids Res. 30 (2002) 207–210. [43] I. Medina, J. Ca bonell, L. Pulido, S.C. Madei a, S. Goe z, A. Conesa, J. Tá aga, A. Pascual-Mon ano, R. Nogales-Cadenas, J. San oyo, F. Ga cía, M. Ma bà, D. Mon ane , J. Dopazo, Babelomics: an in eg a i e pla o m o he analysis o ansc ip omics, p o eomics and genomic da a wi h ad anced unc ional p ofiling, Nucleic Acids Res. 38 (2010) W210–W213. [44] K. E en, M. De eci, O. Kucuk unc, U.V. Ca alyu ek, A compa a i e analysis o biclus e ing algo i hms o gene exp ession da a, B ie . Bioin o m. 14 (2013) 279–292. [45] S. Ba kow, S. Bleule , A. P elic, P. Zimme mann, E. Zi zle , Bica : a biclus e ing analysis oolbox, Bioin o ma ics 22 (2006) 1282–1283. [46] H. Caniza, A.E. Rome o, S. He on, H. Yang, A. De o o, M. F asca, M. Mesi i, G. Valen ini, A. Paccana o, Goss o: a s and-alone applica ion and a web ool o calcula ing seman ic simila i ies on he gene on ology, Bioin o ma ics 30 (2014) 2235–2236. [47] R. Haw, H. He mjakob, P. D’Eus achio, L. S ein, Reac ome pa hway analysis o en ich biological disco e y in p o eomics da a se s, P o eomics 11 (2011) 3598–3613. [48] C. Fon anillo, R. Nogales-Cadenas, A. Pascual-Mon ano, J. De Las Ri as, Func ional analysis beyond en ichmen : non- edundan ecip ocal linkage o genes and biological e ms, PLoS ONE 6 (2011) e24289. [49] F. Supek, M. Bosnjak, N. Skunca, T. Smuc, Re igo summa izes and isualizes long lis s o gene on ology e ms, PLoS ONE 6 (2011) e21800.