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.
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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
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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
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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.
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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
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[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
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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.
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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.
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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. O.H. acknowledges he doc o al MAEC- AECI ellowship.
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Please pu chase PDF Spli -Me ge on www. e ypd .com o emo e his wa e ma k.