Full design automation of multi-state RNA devices to program gene expression using energy-based optimization

Full Design Au oma ion o Mul i-S a e RNA De ices o P og am Gene Exp ession Using Ene gy-Based Op imiza ion Guille mo Rod igo 1. , Thomas E. Land ain 1. , Esz e Maje 2 , Jose ´-An onio Da o `s 2 , Al onso Ja amillo 1 * 1Ins i u e o Sys ems and Syn he ic Biology, CNRS UPS 3509 – Uni e si e ´d’E ´ y Val d’Essonne – Genopole, E ´ y, F ance, 2Ins i u o de Biologı ´a Molecula y Cellula de Plan as, CSIC – Uni e sidad Poli e ´cnica de Valencia, Valencia, Spain Abs ac Small RNAs (sRNAs) can ope a e as egula o y agen s o con ol p o ein exp ession by in e ac ion wi h he 59un ansla ed egion o he mRNA. We ha e de eloped a physicochemical amewo k, elying on base pai in e ac ion ene gies, o design mul i-s a e sRNA de ices by sol ing an op imiza ion p oblem wi h an objec i e unc ion accoun ing o he s abili y o he ansi ion and inal in e molecula s a es. Con a y o he analysis o he eac ion kine ics o an ensemble o sRNAs, we sol e he in e se p oblem o inding sequences sa is ying a ge ed eac ions. We show he e ha ou objec i e unc ion co ela es well wi h measu ed ibo egula o y ac i i y o a se o mu an s. This has enabled he applica ion o he me hodology o an ex ended design o RNA de ices wi h speci ied beha io , assuming di e en molecula in e ac ion models based on Wa son-C ick in e ac ion. We designed se e al YES, NOT, AND, and OR logic ga es, including he design o combina o ial ibo egula o s. In sum, ou de no o app oach p o ides a new pa adigm in syn he ic biology o design molecula in e ac ion mechanisms acili a ing u u e high- h oughpu unc ional sRNA design. Ci a ion: Rod igo G, Land ain TE, Maje E, Da o `s J-A, Ja amillo A (2013) Full Design Au oma ion o Mul i-S a e RNA De ices o P og am Gene Exp ession Using Ene gy-Based Op imiza ion. PLoS Compu Biol 9(8): e1003172. doi:10.1371/jou nal.pcbi.1003172 Edi o : Adam P. A kin, Law ence Be keley Na ional Labo a o y, Uni ed S a es o Ame ica Recei ed No embe 3, 2012; Accep ed June 21, 2013; Published Augus 1, 2013 Copy igh : ß2013 Rod igo e al. This is an open-access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License, which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal au ho and sou ce a e c edi ed. Funding: Wo k suppo ed by he g an s FP7-ICT-043338 (BACTOCOM) o AJ, and BIO2011-26741 (Minis e io de Economı ´a y Compe i i idad, Spain) o JAD. GR is suppo ed by an EMBO long- e m ellowship co- unded by Ma ie Cu ie ac ions (ALTF-1177-2011), and TEL by a PhD ellowship om he AXA Resea ch Fund. The unde s had no ole in s udy design, da a collec ion and analysis, decision o publish, o p epa a ion o he manusc ip . Compe ing In e es s: The au ho s ha e decla ed ha no compe ing in e es s exis . * E-mail: al onso.ja [email protected]. .These au ho s con ibu ed equally o his wo k. In oduc ion Small non-coding RNA (sRNA) has aised a big in e es because o he p edic abili y and modula i y o i s binding wi h a la ge a ie y o molecules and mac omolecules [1]. Gi en his unc ional po en ial, he use o sRNAs o con ol p o ein exp ession has igge ed a new way o enginee in eg a ed egula o y ne wo ks [2]. Al hough a ional echniques ha e been success ully applied o edesign na u al sys ems [3,4], enginee syn he ic ones [2,5–7] and assemble modula s uc u es [8–10], de no o sequence design s ill emains di icul because o he size and complexi y o mul i-s a e sys ems. To o e come his, we p opose an e olu iona y compu- a ion design s a egy [11], whe e all design speci ica ions a e au oma ically assembled o yield an op imal solu ion. In his wo k, we demons a e a ull design au oma ion o RNA sequences ha implemen di e se ibo egula o y mechanisms, able o p oduce se e al sRNA-based logic ga es ha a e unc ional in li ing cells. We gene alize ou p e ious wo k [11] on he design o ibo egula o s o ac i a ing p o ein exp ession, which could be conside ed as YES ga es, o de i e objec i e unc ions o design ibo egula o s implemen ing se e al logic ga es. Fu he mo e, we expe imen ally alida e ou objec i e unc ion by conside ing mu an s o na u al and syn he ic ibo egula o s [11,4], and his allows assessing he gene ali y o he me hodology. By gene alizing he posi i e ibo egula ion pa adigm, whe e an sRNA in e ac s h ough Wa son-C ick pai ing wi h a a ge mRNA o igge a con o ma ional change enabling ibosome docking, we can ex end he me hodology o design a bi a y logic ga es, accoun ing o new egula o y mechanisms, such as an i- e mina ion, and implemen ing cons ained design s a egies (Fig. 1). Fo ha , we exploi an isense and allos e ic RNA [12,13], wo conse ed mechanisms based on p ecise seconda y s uc u es, and whose majo ole has been epo ed o e he las yea s in bac e ia [14], bu also in humans [15] and plan s [16]. Ou me hod s a s om andom sequences o p oceed wi h successi e ounds o a mu a ion ope a o , ollowed by selec ion using an objec i e unc ion ha accoun s o he ee ene gies o all possible eac ions and he seconda y s uc u es o all species. P e ious wo k on ull design au oma ion o nucleic acids was ocused on in i o annealing o small DNAs [17–20], hamme head ibozymes [21], o ibosome binding si es (RBSs) [22]. In he ollowing, we will s a by o mula ing he RNA design p oblem as an in e se p oblem o p og am gene exp ession. This is basedonanop imiza ionme hod ha minimizesanab ini io objec i e unc ion, which con as s wi h o he app oaches [4]. We will e alua e such an objec i e unc ion by enginee ing and cha ac e izing ou own mu an lib a y o syn he ic ibo egula o s ac i a ing gene exp ession. A e wa ds, we will show and exempli y how o design sRNA-based logic ga es, including complex ga es in ol ing syne gis ic in e ac ions o di e en sRNAs as inpu s. Finally, we will discuss he esul s s essing he limi a ions o ou me hodology. PLOS Compu a ional Biology | www.ploscompbiol.o g 1 Augus 2013 | Volume 9 | Issue 8 | e1003172 Resul s Fo mula ion o an in e se p oblem Ribo egula ion is based on con o ma ional changes, a e in e ac ion, in he s uc u es o RNA molecules, which allow con olling p o ein exp ession. To design such egula o y RNAs, we op imize he po en ial ene gy cu e de ined in he ansi ion s a e heo y [23], minimizing he ee ene gies o he ansi ion and hyb idiza ion s a es. We assume ha he indi idual olding s a e is o med be o e in e molecula RNA-RNA in e ac ion, because i s ime scale is o milliseconds whe eas hyb idiza ion akes seconds o e en minu es [24,25]. The in e ac ion mechanism is guided by means o he seed egion (nuclea ion si e; he i s nucleo ides ha ge pai ed) o o m an in e media e complex a he ansi ion s a e [3,11]. Then, bo h RNAs a e des abilized o o m a complex wi h a new s uc u e and minimal ene gy. He e, we conside he s uc u es o all indi idual species as design speci ica ions. To add ess he compu a ional design, we i s ly ha e o ind sequences olding in o p ede ined s uc u es and, second, ind sequences able o in e ac speci ically among hem o o m complexes displaying he co ec beha io . The s uc u al con- s ain s a e exploi ed o conside ably educe he combina o ial space and accele a e he design o nucleic acid sequences. Ou compu a ional p ocedu e op imizes a he same ime all RNA sequences o he ci cui . Du ing he op imiza ion, we do no impose cons ain s in nucleo ide sequence, such as s ems wi h high GC- con en o loops wi h YUNR mo i s, which ha e been ound in na u al sys ems [12]. Impo an ly, ou designs a e jus based on basic physicochemical p inciples and no on addi ional i ing, allowing he solu ion o he ull design p oblem. Bu , is he p oposed objec i e unc ion p edic i e enough o allow he designabili y o mul i-s a e RNA de ices? To illus a e his ques ion, we cons uc ed he e a lib a y o mu an s o one o ou p e iously designed ci cui s ( he de ice RAJ11 [11], implemen ing a YES logic ga e as shown in Fig. 1B). Then, we ep esen ed he expe imen al alues o he measu ed ac i a ion old agains he objec i e unc ion calcula ed o hose mu an s (Fig. 2A). To gi e u he suppo o ou objec i e unc ion, we e alua ed i o a se o mu a ional a ian s o he IS10 an isense RNA sys em [4], implemen ing a NOT logic ga e (Fig. 1A), and hen we ep esen ed hose alues agains he expe imen al ep ession olds epo ed (Fig. 2B). This na u al sys em cons i u es an independen alida ion. The objec i e unc ion he e (Eq. 13) accoun ed o he ee ene gy o o ma ion and he leng h o he seed in he sRNA-mRNA in e ac ion. Fig. 2 shows a good co ela ion (wi hou any i ing) o ou objec i e unc ion and expe imen al da a, which suppo s he designabili y o hose de ices. Design o simple sRNA-based logic ga es We i s applied ou design me hodology o ob ain sRNA-based ep ession and ac i a ion. Many known ibo egula o s impa a ep essi e ac ion on hei a ge s by p omo ing accele a ed deg ada ion h ough endo ibonucleases, which ini ia e u no e o bo h RNAs [26]. Ins ead, we he e accoun o sRNAs ha bind speci ically o a segmen o i s a ge mRNA in o de o inhibi ansla ion (NOT logic unc ion) [4]. The mos in ui i e mecha- nism consis s in blocking he Shine-Dalga no sequence, which is gene ally loca ed abou eigh base pai s ups eam o he s a codon (AUG), o p e en ing ibosome docking (Fig. 1A). Fo ins ance, in E. coli plasmid F, sRNA FinP di ec ly binds o he 59 un ansla ed egion (UTR) o p o ein T aJ [12]. We cons uc ed he ollowing objec i e unc ions (de ini ions o DG kin and DG s in sec ion Me hods) o sol e he op imiza ion p oblem In Ou min DGs 5’UTR,RBS ee ðÞ DGkin sRNA,5’UTRðÞzDGs sRNA :5’UTR,RBSpai ed  (01: 10 ð1Þ These unc ions a e associa ed o each en y o he u h Table, and hen he solu ion o his p oblem will yield NOT logic ga es. In Fig. 3, we show se e al compu a ional designs o his logic de ice. We applied ou me hodology wi h di e en na u al occu ing s uc u es in ol ing one, wo o h ee hai pins o he ans- ep essing sRNAs. In ou designs, we used he Shine- Dalga no sequence AGGAGA. Al hough he majo i y o sRNA-media ed egula ion in E. coli consis s in ep ession, an sRNA can also ope a e as an ac i a o (YES logic unc ion) [2]. In his case, he sRNA ans-ac i a es a cis- ep essed gene by i s 59UTR. A e in e ac ion, he con o ma- ional change in he 59UTR eleases he Shine-Dalga no sequence and allows ansla ion (Fig. 1B). Fo ins ance, in E. coli, sRNA Ds A is esponsible o ac i a ing he exp ession o sigma ac o RpoS, which modula es he s ess esponse [13]. Hence, we cons uc ed he ollowing objec i e unc ions In Ou min DGs 5’UTR,RBSpai ed  DGkin sRNA,5’UTRðÞzDGs sRNA :5’UTR,RBS ee ðÞ (00 11 :ð2Þ The solu ion o his p oblem will p oduce he in ended unc ion speci ied in he u h Table. This p oblem is much complex ha he p e ious one because he e he wo RNA species ha e s uc u e. In Fig. 4, we show se e al compu a ional designs o YES logic ga es based on con o ma ional changes in he 59UTRs o he a ge genes. We applied ou me hodology wi h di e en s uc u es o he ans-ac i a ing sRNAs, while main aining a common s uc u e o he 59UTR. We also a emp ed he compu a ional design o a syn he ic RNA able o in e ac wi h he RpoS 59UTR, and hen enhance he ansla ion a e. Fig. S2 shows he sequences and s uc u es ob ained. In addi ion, we exploi ed ou me hodology o design NOT logic ga es based on s uc u ed 59UTRs. He e, he ans-ac i a ing sRNA in e ac s wi h he 59UTR o induce a con o ma ional Au ho Summa y Is ou cu en knowledge o in i o RNA-RNA in e ac ions and he modynamics enough o pe o m he unsupe ised compu a ional design o ully syn he ic sequences encod- ing unc ional RNAs in li ing cells? Recen wo k ga e a posi i e answe o he challenging p oblem o designing ac i a ing ibo egula o s. This was done by in eg a ing heo y and compu a ion o de elop a physicochemical amewo k o he design o egula o y RNA sys ems, using Wa son-C ick in e ac ions and op imiza ion algo i hms. S ill, he objec i e unc ion was no di ec ly alida ed, p e en ing using wi h con idence he me hodology o o he sys ems. We he e alida e expe imen ally an objec i e unc ion elying on ee ene gies o RNA complex ac i a ion and o ma ion, which allows ex ending he amewo k o p oduce logic de ices ha can be imple- men ed o p og am gene exp ession. We demons a e ha i is possible o design inc easingly sophis ica ed and modula unc ions, poin ing ou esul s ou ha ene gy- based op imiza ion me hods can pe o m he la ge combina o ial sea ch equi ed o RNA design. ð1Þ ð2Þ Regula o y RNA Design PLOS Compu a ional Biology | www.ploscompbiol.o g 2 Augus 2013 | Volume 9 | Issue 8 | e1003172 change ha blocks he Shine-Dalga no sequence (Fig. 1C). The objec i e unc ions o sol e he co esponding p oblem ead In Ou min DGs 5’UTR,RBS ee ðÞ DGkin sRNA,5’UTR ðÞ zDGs sRNA :5’UTR,RBSpai ed in amol  (01 10 ,ð3Þ whe e he di e ence wi h Eqs. (1) elies on he imposi ion ha he RBS mus be pai ed a he in amolecula le el. Fig. 5A shows a compu a ional design implemen ing his egula o y mechanism. We also designed ibo egula o s wi h ac i a ion ac i i y based on a mechanism o an i- e mina ion [27]. This design elies on a ans- egula ing sRNA able o des abilize he s uc u e o a e mina o , which is he e he cis- egula ing elemen , esul ing in a complex ha allows he p og ession o he RNA polyme ase (Fig. 1D). This mechanism can also en ail kine ic e ec s [3], whe e he in e ac ion has o occu be o e RNA polyme ase eads h ough he e mina o . This may impose a na ow ime window o ope a ion, which we specula e su moun able p o ided a gi en ee ene gy h eshold and a high a io sRNA/mRNA. In his case, he objec i e unc ions we e In Ou min DGs 5’UTR,Hai pin wi h poly(U) ðÞ DGkin sRNA,5’UTRðÞzDGs sRNA :5’UTR, No hai pinðÞ (00 11 ,ð4Þ whe e he 59UTR encodes o a e mina o ha is o med in absence o he sRNA. The solu ion o his p oblem will also sa is y he u h Table o YES. Fig. 5B shows a compu a ional design o a YES logic ga e based on his mechanism. In he inal s uc u e o he complex, he e mina o hai pin is des abilized and he poly(U) ail does no ha e any e ec . Figu e 1. Schemes o di e en sRNA-based mechanisms o con ol p o ein exp ession. Ribo egula ion is based on con o ma ional changes in he seconda y s uc u es o RNA molecules ha allow con olling p o ein exp ession. The annealing mechanism be ween wo sRNAs s a s by he nucleo ides in he seed o o m an in e media e complex and hen ollows o each he s uc u e o minimal ene gy. (A) Scheme o a NOT logic ga e, which consis s in an sRNA able o bind o he RBS sequence o block ansla ion. (B) Scheme o a YES logic ga e, whe e he sRNA is designed o elease he RBS ha is cis- ep essed. (C) Scheme o a u he NOT logic ga e, whe e he sRNA is able o induce cis- ep ession (exploi ing he mechanism shown in B). (D) Scheme o a u he YES logic ga e, whe e he sRNA in e ac s wi h a ansc ip ion e mina o placed ups eam o he RBS, allowing o p e en ing he o ma ion o he mRNA. (E) Scheme o an AND logic ga e, whe e wo sRNAs a e designed o in e ac among hem and o m a complex ha can elease he RBS. doi:10.1371/jou nal.pcbi.1003172.g001 ð3Þ ð4Þ Regula o y RNA Design PLOS Compu a ional Biology | www.ploscompbiol.o g 3 Augus 2013 | Volume 9 | Issue 8 | e1003172 Design o combina o ial sRNA-based logic ga es We hen applied ou me hodology o he design o highe -o de ibo egula o y de ices. Taking he NOT logic ga e shown in Fig. 5A as a e e ence, we pe o med he design o a new 59UTR o cis- ep ession and ha was able o espond o he same ibo egula o , in his case wo king as an ac i a o . The op imiza ion p oblem ead In Ou min DGs 5’UTR,RBSpai ed  DGkin sRNA,5’UTR ðÞ zDGs sRNA :5’UTR,RBS ee ðÞj sRNA cons (00 11 ,ð5Þ whe e he di e ence wi h Eqs. (2) elies on he imposi ion ha he sRNA sequence is cons an . Likewise, he same sRNA will ha e he abili y o bo h ep ess and ac i a e p o ein exp ession (coupled YES/NOT logic ga e). Exploi ing u he his modula i y, we ca ied ou he design o an OR logic ga e using he 59UTR sequence jus designed. We now en o ced he design o a new sRNA ha had also he abili y o eleasing he RBS, main aining cons an he 59UTR sequence. The op imiza ion p oblem had hen only one ins ance, gi en by In Ou min DGkin sRNA,5’UTRðÞzDGs sRNA :5’UTR,RBS ee ðÞD50UTR cons 11 :ð6Þ Thus, he esul ing sys em will in eg a e wo sRNAs capable o ac i a ing he elease o he RBS con ained in a single 59UTR. Subsequen ly, we e i ied he e was no in e e ence be ween he wo sRNAs, al hough his could ha e also been inco po a ed in o he design p ocess. Fig. 6 shows he in eg a i e ci cui (mul i-inpu , mul i-ou pu ) ha we inally ob ained wi h his s a egy based on se ial design o cons ained YES ga es. Mo i a ed by he p e ious esul s, we ca ied ou he design o coope a i e ibo egula ions. The egula o y unc ion o mul iple- sRNA complexes has no been epo ed in p oka yo es (all na u al sys ems o ibo egula ion in ol e wo RNA species, a mos in e ac ing wi h p o eins such as RNA chape ones o endo ibo- nucleases [28]), which u he encou ages he explo a ion by means o compu a ional me hods. To illus a e he powe o ou app oach, we ocused on he design o syne gis ic ac i a ion (AND logic unc ion), whe e wo ans- egula ing sRNAs i s in e ac among hem o o m a complex ha will hen ac i a e ansla ion (Fig. 1E). To sol e he op imiza ion p oblem, we cons uc ed he ollowing objec i e unc ions In1In2Ou min DGs 5’UTR,RBSpai ed  {DGkin sRNA1,5’UTRðÞ {DGkin sRNA2,5’UTRðÞ DGkin sRNA1,sRNA2 ðÞzDGkin sRNA1:sRNA2,5’UTRðÞz DGs sRNA1:sRNA2:5’UTR,RBS ee ðÞ 8 > > > > > > > > < > > > > > > > > : 000 100 010 111 :ð7Þ As in he p e ious cases, hese unc ions a e associa ed o each en y o he u h Table, and hence he solu ion o his p oblem will yield AND logic ga es. In Fig. 7, we show wo di e en designs o his logic, combina o ial de ice. By hemsel es, he ans- egula ing sRNAs canno elease he RBS. Howe e , he dime hey o m has a dis inc s uc u e ha allows in e playing wi h he 59UTR. Discussion In conclusion, we ha e ollowed a bo om-up app oach o design RNA de ices wi h YES, NOT, AND, and OR logic unc ions, based on i s physical p inciples. These logic ga es implemen mul i-s a e sRNA de ices o which he e was no design me hod be o e, and ha can be in e connec ed o c ea e mo e complex logic p og ams. Al hough we could sol e in e molecula in e se olding p oblems [29], i was no possible he sys ema ic design o mul iple RNA species implemen ing a bi a y logic ga es. Fo hei design, each en y o he u h Table imposes a s uc u al speci ica ion. He e, we accoun ed o he ee ene gies o all possible eac ions ( he modynamic po en ial) o sol e his mul i-objec i e in e se p oblem by op imiza ion. Because ou me hodology does no equi e na u al sequences (wi h he Figu e 2. Expe imen al alida ion o he objec i e unc ion. (A) Rep esen a ion o he log o he expe imen al ac i a ion olds o a se o RNA de ices cons uc ed in his wo k (mu a ional a ian s o he RAJ11 sys em [11]) e sus DG kin (Eq. 13). This sys em implemen s a YES logic ga e, which was designed wi h he algo i hm p esen ed he e (see also Table S4). (B) Rep esen a ion o he log o he expe imen al ep ession olds ecen ly epo ed o a se o mu a ional a ian s o he IS10 an isense RNA sys em [4] e sus DG kin . This sys em implemen s a NOT logic ga e, and i se es o es he p edic abili y o he me hod agains independen expe imen al da a (see also Table S2). He e, we do no conside DG s as we a e only analyzing he in e ac ion abili y. The lines co espond o linea eg essions, and he coe icien s R 2 a e shown, assuming a model whe e he old change scales exponen ially wi h he ee ene gy. doi:10.1371/jou nal.pcbi.1003172.g002 ð5Þ ð6Þ ð7Þ Regula o y RNA Design PLOS Compu a ional Biology | www.ploscompbiol.o g 4 Augus 2013 | Volume 9 | Issue 8 | e1003172 excep ion o key mo i s such as he Shine-Dalga no sequence), we ha e sol ed he ull design p oblem o egula o y RNA o implemen ing logic p og ams in li ing cells. Ou app oach has, howe e , some limi a ions, which p ospec u he esea ch in he ield. One o hem is he use o he seconda y s uc u e o model ibo egula ion. This ype o egula ion could in ol e pseudokno in e ac ions and e en non-canonical base pai ing, o which h ee-dimensional models could be e cap u e he in e ac ion ea u es [30]. In addi ion, ou model does no accoun o RNA chape ons (e.g., H q) [31], no co- ac o s such as Mg 2+ o Zn 2+ , no kine ic binding e ec s, which migh ha e an impac on he designs. Ano he es ain o he cu en me hod is he en o cemen o a gi en s uc u e o all single species in he ci cui (al hough no o he complex ones), because his cons ains he sequence space o possible solu ions [11]. By lea ing uncons ained hose s uc u es, we could pe o m addi ions and/o dele ions (no only eplacemen s) o nucleo ides du ing he op imiza ion, and we would need o include in o he unc ion DG s a new e m o he s abili y (e.g., based on ee ene gy). Finally, he con e gence o he algo i hm is highly educed when e ol ing sys ems wi h mul iple species, making necessa y o educe he sequence space by eusing unc ional modules o ob ain mo e sophis ica ed sys ems. Despi e hese limi a ions, we ha e demons a ed he powe o compu a ional design ( h ough heu is ic op imiza ion) o o e come he complexi y in ob aining ully syn he ic ibo egula ion, explo - ing he as combina o ial space o sequences. The p oposed objec i e unc ion was shown p edic i e enough o allow he designabili y o mul i-s a e RNA de ices, as DG kin explained di e ences in expe imen al ep ession old o a se o mu a ional a ian s o he IS10 an isense RNA sys em (Fig. 2) [4]. Mo eo e , we ecen ly alida ed expe imen ally some designs o YES logic ga es in bac e ia, encou aging u he wo k [11]. E en hough, he design p oblem does no equi e a pe ec p edic ion, and simila o e en lowe co ela ions can be su icien o ackle his p oblem, such as in he case o au oma ed RBS design [22]. O cou se, mo e sophis ica ed objec i e unc ions will be de eloped in he coming yea s o imp o e he design o unc ional RNAs. The combina ion o DG kin and DG s , o e e y possible con o ma ional s a e (in a- o in e molecula ) o a gi en geno ype, esul s in an e ec i e ee ene gy ha de ines a i ness landscape. In case o ibo egula ion, he o al sea ch space can be abou 10 40 sequences [11], and ypical op imiza ions ha lead o su icien ly good solu ions consis o 10 6 –10 7 i e a ions. Indeed, he gene al- ized p oblem o inding he nucleo ide sequences o mul i-species ensembles ha will old in o speci ied con o ma ions has an exponen ially la ge numbe o solu ions. I emains howe e a ques ion how o dis inguish se e al op imized sequences (assuming equal ene ge ic ea u es). Fo ins ance, di e ences in in acellula s abili y o he species will a ec he a io sRNA/mRNA, and hen be key o he egula o y ac i i y. Addi ionally, he kine ics o RNA olding, binding, and u no e will ha e signi ican impac on he pe o mance o designed RNA ci cui s [3,10]. All hese c i e ia, ei he om i s p inciples o om expe imen al eedback, will be exploi ed o enhance he design me hodology. Figu e 3. Designs o sRNA-based NOT logic ga es. We show ou designs (A o D) using di e en s uc u es o he ans- ep essing sRNAs (mechanism shown in Fig. 1A). (A.1) De ail o a design, showing he RBS in blue, s a codon in g een, and seed egion in ed. The seconda y s uc u es o he in amolecula and in e molecula olding s a es a e p esen ed. (A.2, B.1, C.1 and D.1) Helical plo o he complex, whe e he RBS is blocked. DG,DG kin and DG s a e in Kcal/mol. Zis he pa i ion unc ion. (A.3, B.2, C.2 and D.2) Base pai ing p obabili y ma ix, enci cling he pai s o in e molecula in e ac ion wi h high p obabili y. RNA sequences shown in Table S1. Seconda y s uc u es imposed o all species shown in Fig. S1. doi:10.1371/jou nal.pcbi.1003172.g003 Regula o y RNA Design PLOS Compu a ional Biology | www.ploscompbiol.o g 5 Augus 2013 | Volume 9 | Issue 8 | e1003172 Ou p esen me hodology is gene al and could be applied o ob ain designs based on u he mechanisms. In addi ion, ins ead o a emp ing ull designs, i pe mi s eusing comple e known sequences (na u al o syn he ic) o cons ain he design o new logic sys ems. This capaci y enables he c ea ion o a la ge a ie y o combina o ial sRNA sys ems, inc easing sophis ica ion a a educed compu a ional cos . Mo eo e , ou app oach can be used o analyze po en ial RNA sequences o a gi en unc ional ci cui as a e e se enginee ing ool. The designed sRNA-based logic ga es can be combined wi h ansc ip ion egula ion o gene a e mo e complex unc ions [32], and also be in eg a ed in o lib a ies o models o he compu a ional design o mo e complex ne wo ks in ol ing ansc ip ion and pos - ansc ip ion egula ion [33]. Ye , ou ull design au oma ion app oach oge he wi h high- h oughpu sc eening echniques will p opel he cons uc ion o modula and o hogonal de ices o syn he ic biology [34]. Me hods The modynamic model We conside ed ibo egula ion (RNA-RNA in e ac ion) in e ms o he modynamics [29,35,36], assuming ha he sys em eaches an equilib ium s a e. We i s applied an in e se olding s a egy o e he s uc u es o all indi idual species. Then, neu al mu a ions in s uc u e we e e alua ed wi h an objec i e unc ion in ended o op imize he in e molecula olding s a es. To ob ain an in e mo- lecula olding sa is ying he elease o blockage o he RBS, in p inciple, we needed o maximize he pa i ion unc ion (Z)o he whole sys em. Using he eac ion coo dina e o he sys em ( ), de ined as he numbe o in e molecula Wa son-C ick in e ac ions (i.e., = 0 ep esen s indi idual olding) [11], Zcan be w i en as Z~X exp {G ðÞ RT  ,ð8Þ whe e G( ) is he e ec i e ee ene gy o he s a e wi h eac ion coo dina e (whe e G(0) ep esen s he ee ene gy o he no- in e ac ion s a e, wi h G=0 o he un olded s a e), R he gas cons an , and T he empe a u e. He e, we a e in e es ed in G( )a he eac ion coo dina es o he ansi ion, G( ans ), and inal in e molec- ula (hyb idiza ion) s a es, G( hyb ), o de ine ou unc ions DG, he ee ene gy o o ma ion, and DG { , he ee ene gy o ac i a ion, by DG~G hyb  {G0ðÞ DGz z~G ans ðÞ{G0ðÞ: ð9Þ To compu e he ee ene gy and seconda y s uc u e o all species (single and complexes) o a sys em, we used he ViennaRNA [37] and Mul iRNAFold [38] (when ha ing mo e han wo RNA species) so wa e. We only conside ed he Figu e 4. Designs o sRNA-based YES logic ga es. We show ou designs (A o D) using di e en s uc u es o he ans-ac i a ing sRNAs (mechanism shown in Fig. 1B). (A.1) De ail o a design, showing he RBS in blue, s a codon in g een, and seed egion in ed. The seconda y s uc u es o he in amolecula and in e molecula olding s a es a e p esen ed. (A.2, B.1, C.1 and D.1) Helical plo o he complex, whe e he RBS is eleased. DG,DG kin and DG s a e in Kcal/mol. Zis he pa i ion unc ion. (A.3, B.2, C.2 and D.2) Base pai ing p obabili y ma ix, enci cling he pai s o in e molecula in e ac ion wi h high p obabili y. RNA sequences shown in Table S1. Seconda y s uc u es imposed o all species shown in Fig. S1. doi:10.1371/jou nal.pcbi.1003172.g004 Regula o y RNA Design PLOS Compu a ional Biology | www.ploscompbiol.o g 6 Augus 2013 | Volume 9 | Issue 8 | e1003172 minimum ee ene gy s a e disca ding he subop imal ones. He e, we did no conside pseudokno s. A e wa ds, he designed sequences we e analyzed wi h he Nupack so wa e [29], which is able o compu e ensemble p ope ies such as Z. In his wo k, we used he M old 3.0 RNA ene gy pa ame e s [39], and always conside ed T=37uC (which gi es RT = 0.61 Kcal/mol). De i ing a gene ic objec i e unc ion o in i o RNA-RNA in e ac ions In an RNA-RNA in e ac ion be ween species Aand B,an in e media e complex a he ansi ion s a e ([A:B] { ) is o med media ed by he seed. Then, a as eac ion inducing a con o ma ional change occu s. Deno ing k on and k o he o wa d and e e se cons an s, espec i ely, o o m [A:B] { , and k hyb he hyb idiza ion cons an o o m he inal complex (A:B), he mass ac ion kine ic model eads dA:B½ z z d ~konAB{ko A:B½ z z{khyb A:B½ z z{d1A:B½ z z dA :B d ~khyb A:B½ z z{d2A:B, ð10Þ whe e d 1 and d 2 a e he deg ada ion cons an s. Assuming ha k o + k hyb is much g ea e han d 1 (sRNA deg ada ion akes se e al minu es [13]), we can ob ain in s eady s a e [A:B] { =AB/K M , whe e K M =(k o +k hyb )/k on is he Michaelis cons an . Hence, A:B (and also he ansla ion a e) will be in s eady s a e p opo ional o k hyb /K M , assuming he e is no sa u a ion. The cons an k on can be ob ained by i ing in i o DNA hyb idiza ion da a, whe e only he leng h o he seed (a), i espec i e o he sequence, de e mines he kine ic cons an ollowing a Bol zmann ac o [25]. Mo eo e , we can say ha he cons an k hyb is de e mined by DG( he ee ene gy o o ma ion be ween A+B and A:B) also wi h a Bol zmann ac o . This allows us o w i e kon!exp { aGp RT  khyb!exp { DG RT  :ð11Þ The e o e, he esul ing model eads khyb KM ~khybkon ko zkhyb !1 ko zkhyb exp { DGzaGp RT  ,ð12Þ whe e G p is a i ed pa ame e o accoun o he a e age ene ge ic con ibu ion o one nucleo ide. G p =21.28 Kcal/mol [25]. Finally, we p oposed DG+aG p as he objec i e unc ion o op imize RNA- RNA in e ac ions. This o mula ion is in pa equi alen o maximize Z, because om he A henius equa ion [23] DG { and ashould ha e a linea ela ionship. Op imiza ion algo i hm Ou e olu iona y algo i hm consis s in a Mon e Ca lo Simula ed Annealing [40], which can be pa allelized o e ol e a Figu e 5. Fu he designs o sRNA-based NOT and YES logic ga es. We show wo designs (A and B) using he mechanisms shown in Figs. 1C and 1D. Fo he NOT ga e, helical plo s showing (A.1) he RBS exposed, and (A.2) he RBS blocked a e sRNA in e ac ion. Fo he YES ga e, helical plo s showing (B.1) a ansc ip ion e mina o , and (B.2) ha he hai pin be o e he poly(U) ail is des abilized a e sRNA in e ac ion. DGis in Kcal/mol. Zis he pa i ion unc ion. (A.3 and B.3) Base pai ing p obabili y ma ix, enci cling he pai s o in e molecula in e ac ion wi h high p obabili y. RNA sequences shown in Table S1. Seconda y s uc u es imposed o all species shown in Fig. S1. doi:10.1371/jou nal.pcbi.1003172.g005 Regula o y RNA Design PLOS Compu a ional Biology | www.ploscompbiol.o g 7 Augus 2013 | Volume 9 | Issue 8 | e1003172 popula ion o sequences. Ou app oach consis s in op imizing an objec i e unc ion accoun ing o he in e ac ion and s uc u e o he RNAs ha lead o he a ge beha io . The design speci ica ions comp ise he seconda y s uc u es o all single RNAs, c i ical subsequences o nucleo ides (e.g., RBS), he eac ion ee ene gies, and he s uc u e o he ou pu complex. The algo i hm s a s om pu e andom sequences sa is ying he s uc u al and subsequence cons ain s, al hough i can also be speci ied an ini ial sequence. I he subsequence cons ain s do no allow sa is ying he s uc u es, he algo i hm s ops. E en ually, we can in oduce a elaxa ion in he s uc u al cons ain s ( h ough an ha monic cons ain ) allowing ha ing species wi h dissimila s uc u es o hei a ge s. Subsequen ly, an i e a i e p ocess o mu a ion and selec ion is implemen ed (see scheme o he algo i hm in Fig. S3). The mu a ion ope a o consis s in ei he andom o di ec ed nucleo ide eplacemen s. We do no conside addi ions o dele ions, so he leng h o he RNAs is main ained cons an . To speed up he con e gence, we gene a ed a mu a ion ope a o ha only c ea ed use ul mu a ions, e.g., mu a ions ha a e always gua an eed o con ibu e o an in e ac ion among RNA species. We do his by aking a wo d (i.e., se o consecu i e nucleo ides) om one sequence, making i s e e se complemen a y, and andomly inse ing i in o ano he sequence. Ini ially, he leng h o his wo d is h ee, and i is educed o one (i.e., single poin mu a ion) du ing he op imiza ion p ocess. Those mu a ions speed up he in silico e olu ion. I a nucleo ide ha has o be mu a ed belongs o a s em, i s pai in he s em is also mu a ed wi h he co esponding nucleo ide wi h he aim o p e en ing he dis up ion o he seconda y s uc u e and imp o ing he con e gence. We a oid sequences ha ing consecu i e epea s o ou o mo e iden ical nucleo ides. The objec i e unc ion is a weigh ed sum o wo e ms o be minimized. The i s e m (DG kin ) accoun s o he eac ion kine ics o he sys em. Fo ha , we compu e he DGand ao all possible eac ions, ha ing be ween species Aand B DGkin A,BðÞ~DGzaGp:ð13Þ No ice ha DG kin is a nega i e- alued a iable. We will minimize o maximize DG kin i he eac ion mus occu o no (in o de o ob ain he speci ied beha io ). Maximizing DG kin is equi alen o minimize 2DG kin . Du ing he op imiza ion we exclude sequences o ming homodime s. In addi ion, we conside ed DG sa =215 K- cal/mol and a sa = 6 as a bi a y sa u a ion le els (i.e., le els om which he e is no need o u he minimiza ion). These alues can be enla ged o ge designs wi h lowe DG kin , al hough a a cos o al e ing he con e gence. The second e m (DG s ) accoun s o he s uc u al change o he ou pu RNA. Fo ha , we use a Hamming dis ance (d) be ween he cu en and a ge s uc u es, being DGs A,S ðÞ~{dA,S ðÞGp:ð14Þ This indica es ha species A(which can be single o complex) is e ol ed o display he a ge s uc u e, o subs uc u e, S (e.g., RBS pai ed, hen ep essing p o ein ansla ion). G p is used o escale he dis ance in e ms o ee ene gy. We no e ha DG s is a posi i e- alued a iable, which we will minimize. Figu e 6. Design o a mul i-inpu , mul i-ou pu sRNA-based logic ci cui . We show a design o a ci cui ha assembles di e en ibo egula o s. He e, sRNA R13 is able o bo h ep ess and ac i a e he exp ession o wo di e en cis- ep essed genes, by cR31 and cR19 espec i ely, esul ing in a coupled YES/NOT logic ga e. In addi ion, sRNA R19 is able o ac i a e cR19, implemen ing oge he wi h R13 an OR logic ga e. RNA sequences shown in Table S1. Seconda y s uc u es imposed o all species shown in Fig. S1. doi:10.1371/jou nal.pcbi.1003172.g006 Regula o y RNA Design PLOS Compu a ional Biology | www.ploscompbiol.o g 8 Augus 2013 | Volume 9 | Issue 8 | e1003172 Expe imen al lib a y o RNA de ices 100 ng o plasmid pRAJ11 coding o he ibo egula o y de ice RAJ11 we e subjec ed o 30 cycles o PCR ampli ica ion wi h di e gen p ime s I (59-CCGCGAAGACCGGCACGGNNNGG- TTGATTGTGTGAGTCTGTC-39, N is A, C, G o T; BpiI ecogni ion and clea age si es unde lined) and II (59-GGCGGAA- GACGCGTGCTCAGTATCTCTATCACTG-39, BpiI ecogni- ion and clea age si es unde lined) in a olume o 20 mL wi h 0.4 U o he high ideli y Phusion DNA polyme ase (The mo Fishe Scien i ic) in he p esence o HF bu e (The mo Fishe Scien i ic), 3% dime hyl sul oxide, 0.2 mM each dNTP and 0.5 mM each p ime . Reac ions consis ed o an ini ial dena u a ion o 30 s a 98uC ollowed by 30 cycles o 10 s a 98uC, 30 s a 55uC and 1:15 min a 72uC, wi h a inal incuba ion o 10 min a 72uC. A e PCR, 10 U o DpnI (The mo Fishe Scien i ic) we e added o each sample o diges he empla e plasmid and incuba ed o 1 h a 37uC. Reac ion p oduc s we e elec opho esed in a 1% aga ose gel in TAE bu e (40 mM T is, 20 mM sodium ace a e, 1 mM EDTA, pH 7.2) and he gel s ained wi h e hidium b omide. The 4460-bp long DNA p oduc co esponding o he ull-leng h plasmid was elu ed om he gel, diges ed wi h BpiI o 1 h a 37uC (The mo Fishe Scien i ic) and inally subjec ed o sel -ci cula i- za ion wi h 5 U o T4 DNA ligase (The mo Fishe Scien i ic) o 1 h a 22uC. Reac ion p oduc s we e pu i ied by ch oma og aphy wi h silica gel spin columns (DNA Clean and Concen a o , Zymo Resea ch) and elec opo a ed in E. coli DH5a. Recombinan bac e ia we e selec ed in pla es wi h 50 mg/mL ampicillin. Plasmids we e pu i ied om liquid cul u es o selec ed clones Figu e 7. Designs o sRNA-based AND logic ga es. We show wo designs (A and B) using di e en s uc u es o he ans-ac i a ing sRNAs (mechanism shown in Fig. 1E). (A.1) De ail o a design, showing he RBS in blue, s a codon in g een, and seed egions in ed and magen a. The seconda y s uc u es o he in amolecula and in e molecula olding s a es a e p esen ed. (A.2 and B.1) Helical plo o he complex, whe e he RBS is eleased. DG,DG kin and DG s a e in Kcal/mol. Zis he pa i ion unc ion. (A.3 and B.2) Base pai ing p obabili y ma ix, enci cling he pai s o in e molecula in e ac ions wi h high p obabili y. RNA sequences shown in Table S1. Seconda y s uc u es imposed o all species shown in Fig. S1. doi:10.1371/jou nal.pcbi.1003172.g007 Regula o y RNA Design PLOS Compu a ional Biology | www.ploscompbiol.o g 9 Augus 2013 | Volume 9 | Issue 8 | e1003172