Targeting Differentially Co-regulated Genes by Multiobjective and Multimodal Optimization

Ta ge ing Di e en ially Co- egula ed Genes by Mul iobjec i e and Mul imodal Op imiza ion Osca Ha a i1, C is ina Rubio-Escude o1, and Igo Zwi 1,2 1 Dep . Compu e Science and A i icial In elligence, Uni e si y o G anada, E-18071, Spain 2 Howa d Hughes Medical Ins i u e, Depa men o Molecula Mic obiology, Washing on Uni e si y School o Medicine, S . Louis, MO 63110-1093, USA [email p o ec ed], [email p o ec ed], [email p o ec ed] Abs ac . A c i ical challenge o he pos genomic e a is o unde s and how genes a e di e en ially egula ed in and be ween gene ic ne wo ks. The ac ha such co- egula ed genes may be di e en ially egula ed sugges s ha sub le di e ences in he sha ed cis-ac ing egula o y elemen s a e likely signi ican , howe e i is unknown which o hese ea u es inc ease o educe exp ession o genes. In p inciple, his exp ession can be measu ed by mic oa ay expe i- men s, hough hey inco po a e sys ema ic e o s, and mo eo e p oduce a lim- i ed classi ica ion (e.g. up/down egula ed genes). In his wo k, we p esen an unsupe ised machine lea ning me hod o ackle he complexi ies go e ning gene exp ession, which conside s gene exp ession da a as one ea u e among many. I analyzes ea u es concu en ly, ecognizes dynamic ela ions and gen- e a es p o iles, which a e g oups o p omo e s sha ing common ea u es. The me hod makes use o mul iobjec i e echniques o e alua e he pe o mance o p o iles, and has a mul imodal app oach o p oduce al e na i e desc ip ions o same exp ession a ge . We apply his me hod o p obe he egula o y ne wo ks go e ned by he PhoP/PhoQ wo-componen sys em in he en e ic bac e ia Es- che ichia coli and Salmonella en e ica. Ou analysis unco e ed p o iles ha we e expe imen ally alida ed, sugges ing co ela ions be ween p omo e egu- la o y ea u es and gene exp ession kine ics measu ed by g een luo escen p o- ein (GFP) assays. 1 In oduc ion Gene ic and genomic app oaches ha e been success ully used o assign genes o dis- inc egula o y ne wo ks. Howe e , li le is known abou he di e en ial exp ession o genes wi hin a egulon. A i s simples , genes wi hin a egulon a e con olled by a common ansc ip ional egula o in esponse o he same inducing signal. Mo eo e i is sugges ed ha sub le di e ences in he sha ed cis-ac ing egula o y elemen s a e p obably signi ican in he genes exp ession. Howe e , i is no known which o hese ea u es, independen ly o collec i ely, can se exp ession pa e ns apa . Indeed, simila exp ession pa e ns can be gene a ed om di e en o a mix u e o mul iple unde lying ea u es, hus, making i mo e di icul o disce n he causes o analogous egula o y e ec s. Please pu chase PDF Spli -Me ge on www. e ypd .com o emo e his wa e ma k. The ma e ial equi ed o analyzing he p omo e ea u es go e ning bac e ial gene exp ession is widely a ailable. I consis s o genome sequences, ansc ip ion da a, and biological da abases con aining examples o p eciously explo ed cases. In p inci- ple, genes could be di e en ia ed by inco po a ing in o he analysis quan i a i e and kine ic measu emen s o gene exp ession [1] and/o conside ing he pa icipa ion o o he ansc ip ion ac o s [2-4]. Howe e , he e a e cons ain s in such analyses due o sys ema ic e o s in mic oa ay expe imen s, he ex a wo k equi ed o ob ain ki- ne ic da a and he missing in o ma ion abou addi ional signals impac ing on gene exp ession. These cons ain s hi he o allow a ela i ely c ude classi ica ion o gene exp ession pa e ns in o a limi ed numbe o classes (e.g., up- and down- egula ed genes [5, 6]), hus concealing dis inc ions among exp ession ea u es, such as hose ha cha ac e ize he empo al o de o genes o hei le els o in ensi y He e we desc ibe an unsupe ised machine lea ning me hod ha disc imina es among co- egula ed p omo e s by simul aneously conside ing bo h cis-ac ing egula- o y ea u es and gene exp ession. By i ue o being an unsupe ised me hod, i is nei he cons ained by a dependen a iable [2, 7], such as exp ession da a, which would es ic he classi ica ion o he dual exp ession classes epo ed by mic oa ay expe imen s; no i equi es p e-exis ing kine ic da a. Ou me hod ea s each o he p omo e ea u es wi h equal weigh , because i is no known be o ehand which ea- u es a e impo an . Thus, i explo es all o he possible agg ega ions o ea u es; and applies mul iobjec i e and mul imodal echniques [8, 9] o iden i y al e na i e op imal solu ions ha desc ibe a ge se s o genes om di e en pe spec i es. We applied ou me hodology o he in es iga ion o genes egula ed by he PhoP p o ein o Esche ichia coli and Salmonella en e ica se o a Typhimu ium. We e- co e ed se e al p o iles ha we e expe imen ally alida ed [10] o es ablish ha PhoP uses di e en con igu a ions o p omo e o egula e genes. We inally co ela ed hese g oups wi h mo e accu a e independen expe imen s ha measu e gene exp es- sion o e ime by using GFP assays. 2 Me hods The pu pose o his me hod is o iden i y all o he possible subs uc u es, he e e med p o iles (i.e., g oups o p omo e s sha ing a common se o ea u es), ha cha ac e ize se s o genes. These common a ibu es can ul ima ely cla i y he key cis- ea u es ha p oduce dis inc kine ic pa e ns, shedding ligh in he ansc ip ional mechanisms ha he cell employs o di e en ially egula e genes belonging o a egulon. The iden i ica ion o he p omo e ea u es ha de e mine he dis inc exp ession beha io o co- egula ed genes is a challenging ask because (i) he di icul y in asce - aining he ole o he di e ences in he sha ed cis-ac ing egula o y elemen s o co- egula ed p omo e s; (ii) de ailed kine ic da a ha would help he classi ica ion o exp ession pa e ns is no always a ailable, o i is a ailable o a limi ed subse o genes; and (iii) he limi ed ex en o genes egula ed by a ansc ip ional ac o . To ci cum en hese cons ains, ou me hod explo es all o he possible cis- ea u e ag- g ega ions, looking o hose ha be e cha ac e ize di e en subse o genes; uses an unsupe ised app oach, whe e p e-exis ing classes a e no equi ed; and allows a Please pu chase PDF Spli -Me ge on www. e ypd .com o emo e his wa e ma k. uzzy inco po a ion o p omo e s o e ined hypo hesis which enables a same ins ance o suppo mo e han one hypo hesis. Ou me hod ep esen s, lea ns and in e s om s uc u al da a by ollowing ou main phases: (1) Da abase con o ma ion; (2) P o ile lea ning; (3) P o ile e alua- ion (4) E alua ion o ex e nal classes. 2.1 Da abase Con o ma ion Biological Model. Mul iple independen and in e ela ed a ibu es o p omo e s, na u ally encoded in o di e se da a ypes, should be conside ed o pe o m an in e- g a ed analysis o p omo e egula o y ea u es. We ocus on ou ypes o ea u es o desc ibing ou se o co- egula ed p omo e s [2, 3, 10, 11]: “submo i s”, ix-leng h DNA mo i s om ansc ip ional egula o binding si es, ep esen ed by posi ion weigh ma ices [12] (Fig 1.a). We used hese ma ices o p o o ype DNA sequences, whe e i s elemen s a e he weigh s used o sco e a es sequence o measu e how close ha sequence wo d ma ches he pa e n desc ibed by he ma ix; “o ien a ion”, which cha ac e izes he binding boxes as ei he in di ec o opposi e o ien a ion ela i e o he open eading ame; “RNA pol si es”, ep esen s he RNA polyme ase: hei loca- ion in he ch omosome is s udied as a dis ibu ion and encoded in o uzzy se s (close, medium, and emo e). I also models he class o sigma 70 p omo e [13]: class I p o- mo e s bind o ups eam loca ions (Fig 1.b). By con as class II p omo e s bind o si es ha o e lap he p omo e egion. [14](Fig 1.c); and “exp ession”, which consid- e s gene exp ession om mul iple expe imen s ep esen ed as ec o pa e ns. See [15] o a de ail desc ip ion o he lea ning p ocess o hese ea u es. -35 - 10 -35 - 10 Polyme ase PhoP box Polyme ase PhoP box PhoP PhoPh b) +1 c) +1 Class I Class II 0 1 2 bi s 5′ 4 T 5 A 6 G T 7 A T 8 C T G 9 T C A 10 11 T C A G 12 13 G T 14 A T C 15 A G T 16 A G 17 A T 18 T 19 G A T 20 A 21 G C A T 22 C G A 23 C A T 0 1 2 bi s 5′ 4 G T C 5 T A G 6 G T 7 A T 8 G T 9 A 10 11 12 G A T 13 C A T 14 15 A G T 16 A G 17 G A T 18 T 19 A T 20 A 21 G T A 22 23 A T a) Fig. 1. Di e en cis- ea u es pa icipa ing in he egula ion scheme. a) PhoP binding box modeled as posi ion weigh ma ices shown as logos: The cha ac e s ep esen ing he sequence a e s acked on op o each o he o each posi ion in he aligned sequences. The heigh o each le e is made p opo ional o i s equency.. b-c)Two ansc ip ion ac o s had binded o a DNA s ain and ec ui ed RNA polyme ase (Class I/II espec i ely). A PhoP box migh be lo- ca ed in he same s ain as he polyme ase (b) o in he opposi e di ec ion (c). Rep esen a ion Model. We use uzzy se s as a common amewo k o ep esen he domain independen ea u es. We clus e p omo e s conside ing each ea u e inde- penden ly by using uzzy C-means clus e ing (FCM) me hod and a alidi y index [16] o es ima e he numbe o clus e s, as an unsupe ised disc e iza ion o he ea u es [9, 17]. Fo example, we ob ained h ee clus e s o he “exp ession” ea u e ( 1 1 E: s ong e idence o up egula ion; 1 2 E: mild e idence o up egula ion; and 1 3 E: e i- dence o down egula ion). As a esul o his p ocess, we ob ain ini ial p o o ypes o p o iles, and a e able o accoun o he a iabili y o he da a by ea ing hese Please pu chase PDF Spli -Me ge on www. e ypd .com o emo e his wa e ma k. ea u es as uzzy (i.e., no p ecisely de ined) ins ead o ca ego ical en i ies. Thus, ou da abase is con o med by he membe ship o each p omo e o each o he clus e o e e y ea u e. 2.2 P o ile Lea ning Ou me hod uses a concep ual clus e ing app oach o inc emen ally ind signi ican cha ac e iza ion o p omo e s (p o iles) while explo ing he ea u es space [18-20]. Ini ial p o iles a e agg ega ed o c ea e compound highe le el p o iles (i.e. o sp ing p o iles) by using he uzzy in e sec ion1. In a hie a chical p ocess, he numbe o ea u es sha ed by a p o ile is inc eased, esul ing in a la ice o p o iles. Le el n p o- iles a e buil by agg ega ing le el n-1 p o iles (Fig. 2). This is because he me hod e-disc e izes he o iginal ea u es: ¦¦ n kjk n k kjk j xV 11 / PP (1) whe e jk μ is he membe ship o he p omo e k o clus e j; and k xis he o iginal aw da a o ea u e . This allows o he p o o ypes o he p o iles o be dynamically adap ed o he p omo e s eco e ed by i . In accoun o hese new p o o ypes, he membe ship o he en i e da abase o p omo e s is e-e alua ed: 1 1/1 2 1)( − − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡⎟ ⎠ ⎞ ⎜ ⎝ ⎛−+= m j ji ij wVxx μ (2) whe e j wis he “bandwi h” o he uzzy se j V [16]. This allows e-assigna ions o obse a ions be ween sibling p o iles [21], which is especially use ul o gain suppo o hypo hesis in p oblems, such as ou s, ha ha e a educed numbe o samples. 2.3 P o ile E alua ion We applied mul iobjec i e and mul imodal echniques o e alua e he pe o mance o he p o iles [8, 9, 22], conside ing he con lic ing c i e ia o he ex en o he p o ile, and he quali y o ma ching among i s membe s and he co esponding ea u es. The ex en o he p o ile is calcula ed by using he hype geome ic dis ibu ion ha gi es he p obabili y o in e sec ion (PI) o an o sp ing p o ile and i s pa en s: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −= ∑=h g qn hq q h VPI p q ji 0 ,1)((3) whe e i Vis an alpha-cu o he o sp ing p o ile, o size h; j Vis an alpha-cu o he un- ion o i s pa en s, o size n; p is he numbe o p omo e s o he in e sec ion; and g is he numbe o candida es. The PI is an adap i e measu e ha is sensi i e o small se s o examples, while i e ains speci ici y wi h la ge da ase s [23]. 1 Fuzzy logic-based ope a ions, such as T-no m/T-cono m, include ope a o s which a e used as basic logic ope a o s, such as AND o OR, [16]. In his wo k we used he MINIMUN and MAXIMUM as T-no m and T-cono m, espec i ely. Please pu chase PDF Spli -Me ge on www. e ypd .com o emo e his wa e ma k. O 1 P 1 O 1 P 2 ... O 2 P 6 P 1 P 2 ... P 6 M 1 M 2 M 3 M 4 O 1 O 2 E 1 E 2 E 3 P 1 E 1 P 1 E 2 ... P 6 E 3 M 1 O 1 P 1 ... M 4 O 2 P 6 M 1 O 1 M 1 O 2 ... M 4 O 2 O 1 P 1 E 1 ... O 2 P 6 E 3 M 1 O 1 P 1 E 1 M 1 O 1 P 1 E 2 ... M 4 O 2 P 6 E 3 1111 11 11 1 111 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 Fig. 2. Schema ic iew o he me hod. The me hod na iga es h ough he ea u e-space la ice gene a ing and e alua ing p o iles. Hie a chically, p o iles o one le el a e combined o gene - a e he p o iles o he ollowing one. Obse a ions can mig a e om pa en al o o sp ing clus- e s (i.e., hie a chical clus e ing), and among sibling clus e s (i.e., op imiza ion clus e ing). The quali y o ma ching be ween p omo e s and ea u es o a p o ile (i.e., simila - i y o in e sec ion (SI)) is calcula ed using he equa ion (4), whe e α Uis an alpha-cu o he p o ile i and α n is i s numbe o elemen s. ( ) {} αμμμ αα α >=−= ∑∈ikik Uk ikiU nVSI :1)( (4) The adeo be ween he opposing objec i es (i.e., PI and SI) is es ima ed by se- lec ing a se o solu ions ha a e non-domina ed, in he sense ha he e is no o he so- lu ion ha is supe io o hem in all objec i es (i.e., Pa e o op imal on ie ) [8, 9]. The dominance ela ionship in a minimiza ion p oblem is de ined by: )()()()( bOajObOaOiii ba jjii <∃≤∀≺(5) whe e he i Oand j Oa e ei he PI o SI. This app oach is less biased han weigh ing he objec i es because i iden i ies he p o iles lying in he Pa e o op imal on ie [8, 9], which is he collec ion o local mul iobjec i e op ima in he sense ha i s membe s a e no wo se han (i.e. domina ed by) he o he p o iles in any o he objec- i es being conside ed. Ano he objec i e indi ec ly conside ed is he p o ile di e si y, which consis s o main aining a dis ibu ed se o solu ions in he Pa e o on ie , and hus, iden i ying clus e s ha desc ibe objec s om al e na i e egula o y scena ios. The e o e, ou app oach applies he non-dominance ela ionship locally, ha is, i iden i ies all non- domina ed op imal p o iles ha ha e no be e solu ion in he local neighbo hood Please pu chase PDF Spli -Me ge on www. e ypd .com o emo e his wa e ma k. [8, 9]. We e alua e niches by applying equa ion (3) o e e y pai o solu ion and es- ablish a small h eshold alue as bounda ies o neighbo hoods. 2.4 E alua ion o Ex e nal Classes This p oposed unsupe ised me hod, in con as o supe ised app oaches, does no need he speci ica ion o ou pu classes. Consequen ly, he disco e ed p o iles can be used o independen ly explain ex e nal classes as a p ocess o en e med labeling [7] Ins ead o choosing a single p o ile o cha ac e ize an ex e nal a ge se , he me hod selec s all o he p o iles ha a e co ela ed enough o he que y se . To ind i s classes o equi alence i applies equa ion (3) o he a ge se and he en i e collec- ion o p o iles p e iously p oduced. In his way, he me hod can eco e all o he al- e na i e p o iles ha ma ch he ex e nal class, including he mos speci ic and gene al solu ions. 3 Resul s We in es iga ed he u ili y o ou app oach by explo ing he egula o y a ge s o he PhoP p o ein in E. coli and S. en e ica, which is a he op o a highly connec ed ne - wo k ha con ols ansc ip ion o dozens o genes media ing i ulence and he adap- a ion o low Mg2+ en i onmen s [24]. As li le is known abou he mechanism by which cis- egula o y ea u es go e n gene exp ession, we sea ched h ough he space o all po en ial hypo heses; e alua ed hem, by conside ing bo h hei ex en and simi- la i y o he eco e ed p omo e s; and ob ained al e na i e desc ip ions o a ge se o genes. Mo eo e , o ackle cons ains o he c ude classi ica ion ob ained by mi- c oa ay expe imen s -which would no ha e allowed inding de ail opologies o p omo e s- in an unsupe ised app oach we modeled gene exp ession as one ea u e among many. We demons a ed ha ou me hod makes p edic ions a wo le els: i de ec s new candida e p omo e o a egula o y p o ein; and i indica es al e na i e possible con- igu a ions by which genes p e iously iden i ied as con olled by a egula o a e di e en ially exp essed. We eco e ed se e al op imally e alua ed p o iles, hus, e- ealing dis inc pu a i e p o iles ha can desc ibe he PhoP egula ion p ocess: One p o ile ( 4 2 4 3 4 2 4 1PMEO : PI=1.57E-4, SI=0.002) co esponds o canonical PhoP- egul ed p omo e s (e.g., hose o he phoP, mg A, s A, slyB, yobG, ybjX, ompX, PagP, pdgL, pipD, and pm D genes) cha ac e ized by a class II RNA polyme ase si es si ua ed close o he PhoP boxes, high exp ession pa e ns and a ypical PhoP box submo i in a di ec o ien a ion. No ably, his p o ile eco e s p omo e s p e iously no known o be di ec ly egula ed by PhoP. The me hod was also able o desc ibe his a ge by using o he p o iles, being he mos gene al ones composed o only wo ea u es (Fig 3.a) Ano he p o ile ( 4 1 4 2 4 1 4 3POME :PI=3.53E-4, SI=0.032) includes p omo e s (e.g., hose o he mg C, mig-14, pagC, pagK, and i K genes o Salmonella) ha sha e PhoP boxes in he opposi e o ien a ion o he canonical PhoP- egula ed p omo e s, as well as class I RNA polyme ase si es si ua ed a medium dis ances om he PhoP Please pu chase PDF Spli -Me ge on www. e ypd .com o emo e his wa e ma k. boxes. As expec ed, he me hod was able o iden i y his a ge se by mo e gene al hypo hesis ha agg ega es again only wo ea u es (Fig 3.b). Finally, ano he p o ile ( 3 4 3 2 3 2POE : PI=6.48E-06, SI=0.070), which is sligh ly di - e en om he o me , includes p omo e s (e.g., hose o he ompT gene o E. coli and he pipD, ug L and ybjX genes o Salmonella) is de ined by a PhoP binding si e in he opposi e o ien a ion, he RNA polyme ase o he canonical PhoP egula ed p o- mo e s and a mild e idence o up egula ion. The me hod was also able o cha ac e - ize his a ge by a speci ic Phop box submo i and he same ype o RNA polyme ase. The abo e p o iles di e in he numbe o ea u es because ou me hod uses a mul- i a ia e en i onmen , whe e ea u e selec ion is locally pe o med o each p o ile, as no e e y ea u e is ele an o all p o iles. The p edic ions made by ou me hod we e expe imen ally alida ed [10] o es ablish ha he PhoP p o ein uses mul iple mechanisms o con ol gene ansc ip ion. Fu he mo e, as hese p o iles can be used o e ec i ely explain he di e en ki- ne ic beha io o co- egula ed genes, we measu ed he p omo e ac i i y and g ow h kine ics o GFP epo e s ains wi h high- empo al esolu ion (Fig. 4); and ob ained independen a ge se s by clus e ing hem by using FCM. We ound ha he clus e ha eco e s hose p omo e s ha exp essed ea lie ise imes and highe le els o ansc ip ion (e.g. mg A, ompX, pagP, phoP, pm D, s A, slyB, ybjX, yobG) is co e- la ed o p o ile 4 2 4 3 4 2 4 1PMEO (p- alue < 0.03) (Fig. 3.a). Ano he a ge se includes hose p omo e s ha exp essed he la es ise ime and lowes le els o ansc ip ion (e.g. mg C, mig-14, pagC, pagK, pipD, ug L, i K, pagD); and i is co ela ed o p o- ile 4 1 4 2 4 1 4 3POME (p- alue < 0.013) (Fig. 3.b). The clus e which con ains he p omo - e s ha showed in e media e alues (e.g., hose o he ompT gene o E. coli and he pipD, ug L and ybjX genes o Salmonella) is co ela ed o p o ile 3 4 3 2 3 2POE (p- alue < 0.025) This de ailed analysis o he gene exp ession beha io would no be possible o be ob ained by applying a supe ised machine lea ning app oach because o he lack o kine ic da a o some p omo e s. 4 Discussion We showed ha ou me hod can make p ecise mechanis ic p edic ions e en wi h in- comple e inpu da ase and high le els o unce ain y; making use o se e al cha ac- e is ics ha con ibu e o i s powe : (i) i conside s c ude gene exp ession as one ea u e among many (unsupe ised app oach), he eby allowing classi ica ion o p o- mo e s e en in i s absence; (ii) i has a mul imodal na u e ha allows al e na i e de- sc ip ions o a sys em by p o iding se e al adequa e solu ions [9] ha cha ac e ize a a ge se o genes; (iii) i allows p omo e s o be membe s o mo e han one p o ile by using uzzy clus e ing hus explici ly ea ing he p o iles as hypo heses, which a e es ed and e ined du ing he analysis; and (i ) i is pa icula ly use ul o knowledge disco e y in en i onmen s wi h educed da ase s and high le els o unce ain y. Please pu chase PDF Spli -Me ge on www. e ypd .com o emo e his wa e ma k. E3M3P3 232 O4E4M4P4 1232 O3E3P3 122 E2P2 22 E2P2 23 O2P2 23 mg A, ompX pg E,phoP s A, slyB, udg, yobG, y bL mg C,nmpC phoP, pm D s A, ybjX yobG 0.0161 0.0220 0.0220 T 1 O3E3M3 123 0.0220 O2E2 12 0.0069 E2M2 23 mg A, ompX phoP, s A slyB,udg y bL mg A, ompX phoP, s A slyB, udg ybjX, y bL 0.0069 0.0220 0.0220 ompX, pg E phoP, s A slyB, ybjX, yobG y bL mg A, ompX phoP, slyB ybjX,y bL 0.0220 phoP, s A ybjX, yobG ompX, pg E phoP, s A slyB, ybjX, yobG, y bL mg A, ompX pg E,phoP s A, slyB, udg ybjX, yobG, y bL a) b) E3M3O3 312E4M4O4P4 3121 M3O3P3 121 E3M3P3 311 O2P2 21 E3O3P3 321 E2O2 32 mg C, mig14 pagC, pagK pdgL, i K mg C, mig14 pagC, pagK pdgL, i K mg C, mig14 pagC, pagK pdgL,ug L i K mg C, mig14 pagC, pagK pdgL, i K mg C, mig14 pagC, pagK pdgL,pipD ug L, i K mg C, mig14 pagC, pagK pdgL, i K ybjX mg C, mig14 pagC, pagK pdgL, i K 0.01259 0.00329 0.01259 0.01259 0.01259 0.03585 0.00070 T2 Fig. 3. Cha o Co ela ed P o iles. Ta ge s a e display a he cen e o each cha , su - ounded by he p o iles ha hi hem. Op imal p o iles a e si ua ed close o he a ge s. Fo each p o ile i is displayed he ea u es ha cha ac e izes i , he p omo e s ha eco e s (bold- ace belonging o he a ge , and i alic no belonging o i ) and he co ela ion o he a ge se . E s ands o “Exp ession”, P o “RNA Pol. Si es”, O o “O ien a ion” and “M” o “Submo- i ”; subsc ip s deno e he clus e and supe sc ip s he e-disc e ized le el. 0 102030405060708090 0 2000 4000 6000 8000 10000 12000 Time dGFP phoP yobG slyB pagC pagK ug L Fig. 4. Rise ime and le els o ansc ip ion. T ansc ip ional ac i i y o wild- ype Salmonella ha bo ing plasmids wi h a ansc ip ional usion be ween a p omo e less g p gene and he Salmo- nella p omo e s. The ac i i y o each p omo e is p opo ional o he numbe o GFP molecules p oduced pe uni ime pe cell [dGi( )/d ]/ODi( )], whe e Gi( ) is GFP luo escence om wild- ype Salmonella s ain 14028s, and ODi( ) is he op ical densi y. The ac i i y signal was smoo hed by a polynomial i (six h o de ). De ails abou gene ic expe imen s can be ound in h p://www.pnas.o g/ and abou GFP assays a ailable unde equi emen s o he au ho s. Please pu chase PDF Spli -Me ge on www. e ypd .com o emo e his wa e ma k. The p edic ions made by ou me hod we e expe imen ally alida ed [10] o es ab- lish ha he PhoP p o ein uses mul iple mechanisms o con ol gene ansc ip ion, and is a cen al elemen in a highly connec ed ne wo k. These p o iles can be used o e - ec i ely explain he di e en kine ic beha io o co- egula ed genes. Acknowledgmen s This wo k was pa ly suppo ed by he Spanish Minis y o Science and Technology unde P ojec BIO2004-0270-E, and I.Z. is also suppo ed by and by Howa d Hughes Medical Ins i u e. 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