as homolog amily membe U / Wn -1 esponsi e Cdc42
homolog (RHOU/WRCH1) : Time beha iou al s udy o 3 d
o de combina ions in WNT3A s imula ed HEK 293 cells
sh ip akash sinha
Independen Resea che ; O cid ID : o cid.o g/0000-0001-7027-5788
Add ess : 104-Madhu isha Heigh s Phase 1, Risali, Bhilai-490006, India
Co esponding au ho email : sinha.sh ip [email protected]
Abs ac
RHOU (o WRCH1) is a small 21 kDa signaling guanine nucleo ide-binding p o ein
(G p o ein), belonging o he class o GTPase (hyd olase enzymes ha bind o he
nucleo ide guanosine iphospha e (GTP) and hyd olyze i o guanosine diphospha e
(GDP)), and is a membe o he Rho amily o GTPases (a sub amily o Ra sa coma
i us o Ras supe amily). Guj al and MacBea h [1] p o ides a quan i a i e, and dy-
namic s udy o WNT3A-media ed s imula ion o HEK 293 cells, whe e hey eco d
ime based exp ession p o iles o se e al esponse genes which co ela ed signi ican ly
wi h p oli e a ion and mig a ion. By moni o ing he dynamics o gene exp ession us-
ing sel -o ganizing maps, hey iden i ied clus e s o genes ha exhibi simila exp es-
sion dynamics and unco e ed p e iously un ecognized posi i e and nega i e eedback
loops. Howe e , hei s udy depic s/uses singula measu emen s o indi idual gene
exp ession a di e en ime snapsho s/poin s o in e he sys em wide analysis o he
pa hway. A any pa icula ime poin , i is o en he case ha genes a e wo king syne -
gis ically in combina ions, e en hough hei exp ession measu emen s a e singula in
na u e. He e, I •enume a e and ank all 2415 RHOU ela ed 3 d o de combina ions in
a o es o 71C3combina ions using ou di e en sensi i i y me hods; •show he con-
se ed ankings o RHOU-X-X combina ions, which poin o exis ence o biological
syne gy o some o hese combina ions ac oss he di e en sensi i i y me hods; and •
s udy he beha iou o some o hese combina ions ela ed o WNT3A esponse genes
ha a e anked by he machine lea ning sea ch engine (Sinha [2]) in ime. Pa e ns o
combina ions eme ge, some o which ha e been es ed in we lab, while o he s equi e
u he we lab analysis.
Keywo ds: Sensi i i y analysis, Suppo ec o anking, Hilbe Schmid
Independence C i e ion indices (HSIC) and Sobol indicies, WNT3A
ITime beha iou al s udy o 3-od RHOU/WRCH1 comb. in WNT3A s imula ed cells
1Aspec s o unpublished wo k we e p esen ed in a pos e session a Cell Symposia: Technology. Biology.
Da a Science, 9-11 Oc obe 2016, Be keley, Cali o nia, USA.
P ep in submi ed o P ep in Ma ch 13, 2025
1. Signi icance
Sinha [2] ecen ly demons a ed he use o machine lea ning based sea ch engine o
ank/ e eal gene combina ions a 2nd o de o he ime se ies da a by Guj al and
MacBea h [1] and showed how i is possible o loca e combina ions o p io i y ha
migh be wo king syne gis ically, using sensi i i y me hods and powe ul suppo ec-
o anking algo i hm. Howe e , he p oblem explodes combina o ially wi h e en a
small se o 71 eco ded genes in he s udy by Guj al and MacBea h [1], when one
s eps o explo e 3 d o de combina ions. Wi h he o al numbe o 71C3(= 57155) com-
bina ions, i becomes nea ly impossible o any biologis o s udy he sys em wide dy-
namics o any pa hway. Also, he amoun o ime usually needed o sea ch o and es
a combina ion is a mo e han he sea ch down by he machine lea ning based sea ch
engine. He e, I ex end he esea ch wo k by Sinha [2] o conduc a beha io al s udy o
3 d o de RHOU ela ed combina ions using indi idual gene exp essions measu ed in
ime, in WNT3A s imula ed HEK 293 cells.
2. In oduc ion
The de ails o he machine lea ning based sea ch engine has been ecen ly published in
Sinha [2] and deployed o explo e he 2nd o de combina ions o genes in he da a se
p o ided by Guj al and MacBea h [1]. Ne e heless, he e, I poin o he undamen als
o he published wo k o comple eness.
2.1. A combina o ial p oblem
Sensi i i y analysis plays a majo ole in compu ing he s eng h o he in luence o
in ol ed ac o s in any phenomena unde in es iga ion. When applied o exp ession
p o iles o a ious in a/ex acellula ac o s ha o m an in eg al pa o a signaling
pa hway, he a iance and densi y based analysis yields a ange o sensi i i y indices
o indi idual as well as a ious combina ions o ac o s. These combina ions deno e
he highe o de in e ac ions among he in ol ed ac o s. Compu a ion o highe o -
de in e ac ions is o en ime consuming bu i gi es a chance o explo e he a ious
combina ions ha migh be o in e es in he wo king mechanism o he pa hway. Fo
example, in a ange o ou h o de combina ions among he a ious ac o s o he Wn
pa hway, i would be easy o assess he in luence o he des uc ion complex o med by
APC, AXIN, CSKI and GSK3 in e ac ion. Bu he e ec o hese combina ions a y
o e ime as measu emen s o old changes and de ia ions in old changes a y. So
i is impe a i e o know how an in e ac ion o a combina ion o he in ol ed ac o s
beha e in ime and Sinha [2] de elops a p ocedu e o ack he beha iou by exploi ing
he in luences o hese in ol ed ac o s.
2
2.2. A possible solu ion
In his wo k, a e es ima ing he indi idual e ec s o ac o s o a highe o de combi-
na ion, he indi idual indices a e conside ed as disc imina i e ea u es. A combina ion,
hen, is a ea u e se in highe o de (≥2 ,i.e mul i a ia e). Wi h an excessi ely la ge
numbe o ac o s in ol ed in he pa hway, i is di icul o sea ch o impo an com-
bina ions in a wide sea ch space o e di e en o de s. Exploi ing he analogy wi h
he issues o p io i izing webpages using anking algo i hms, o a pa icula o de , a
ull se o combina ions o in e ac ions can hen be p io i ized based on hese ea u es
using a powe ul anking algo i hm ia suppo ec o s Joachims [3]. Reco ding he
changing ankings o he combina ions o e ime e eals how highe o de in e ac ions
beha e wi hin he pa hway and when an in e en ion migh be necessa y o in luence
he in e ac ion wi hin he pa hway.
2.3. as homolog amily membe U / Wn -1 esponsi e Cdc42 ho-
molog (RHOU/WRCH1)
RHOU (o WRCH1) is a small 21 kDa signaling guanine nucleo ide-binding p o ein
(G p o ein), belonging o he class o GTPase (hyd olase enzymes ha bind o he
nucleo ide guanosine iphospha e (GTP) and hyd olyze i o guanosine diphospha e
(GDP)), and is a membe o he Rho amily o GTPases (a sub amily o Ra sa coma
i us o Ras supe amily).
The ansi ion o guanine nucleo ide binding p o eins be ween he ’on’ (GTP-bound)
and ’o ’ (GDP-bound) s a es is a pa adigm o molecula swi ching a e a chemical e-
ac ion. S ou en e al. [4] y o p o ide a pic u e o he p ocess o he mechanism by
which he swi ch signal is ansmi ed o he downs eam ecipien s in he in acellu-
la signal pa hway, hough i has been ex ensi ely s udied by biochemical, biophysical
and gene ic me hods. Based on he simila i ies o as-p21 and elonga ion ac o Tu,
hey p oposed a model o he GDP s a e o as-p21 ha was in ag eemen wi h all
ele an expe imen al e idence. Thei model p o ided impo an clues abou : (1) a
possible molecula mechanism o signal ansmission om he si e o GTP hyd olysis
o downs eam e ec o s; (2) a majo con o ma ional change du ing signal gene a ion
and a key esidue in ol ed in his p ocess i.e Ty -64; and (3) egions in as-p21 ha
could be di e en ially ecognized by binding o ex e nal pa ne s in a GTP/GDP s a e
dependen ashion, mos no ably esidues D69, Q70, R73, T74, R102, K104, D105 a
he end o he α-helices 2 and 3.
GTPases o he Rho amily play impo an oles in con e ing and ampli ying ex-
e nal signals in o cellula e ec s. No only do hey con ol he dynamics o he F-ac in
cy oskele on, hey ha e also been implica ed in many basic cellula p ocesses ha in-
luence cell p oli e a ion, di e en ia ion, mo ili y, adhesion, su i al, o sec e ion. To
elucida e he e olu iona y his o y o he Rho amily, Bou eux e al. [5] analyzed o e
20 species co e ing majo euka yo ic clades om unicellula o ganisms o mammals,
and econs uc ed he on ogeny and he ch onology o eme gence o he di e en sub-
amilies. Thei da a es ablished ha he 20 mammalian Rho membe s a e s uc u ed
in o 8 sub amilies, among which Rac is he ounde o he whole amily. Rho, Cdc42,
RhoUV, and RhoBTB sub amilies appea ed be o e Coeloma es and RhoJQ, Cdc42 iso-
3
o ms, RhoDF, and Rnd eme ged in cho da es. Thei analysis o Rho mRNA exp es-
sion pa e ns in mouse issues showed ha sub amilies had issue-speci ic and low-le el
exp ession ha suppo ed hei implica ion only in na ow ime windows o in di e -
en ia ed me abolic unc ions.
The Rho amily o GTPases is a sub amily o he Ra sa coma i us (RAS) su-
pe amily. In he cou se o ou ine passage o Moloney’s leukemogenic i us (MLV),
Ha ey [6] collec ed plasma om a leukemic a (Ches e Bea y Ins i u e ou b ed al-
bino s ain) which had been inocula ed wi h MLV-con aining mouse plasma when new-
bo n. A e s o age a 70◦C o h ee mon hs, hey dilu ed he a plasma 1 in 30 wi h
Hanks’s saline and passed h ough a ’Selas 02’ il e , es ed and ound i impe ious o
Esch. coli. The il a e was injec ed in o 15 new-bo n BALB/c mice, o po ency es
and hey epo ed ha only 6 su i ed o weaning and on he 32nd day, 5 had umou s
a o nea he injec ion si e, and all had g ossly enla ged spleens. This was iden i ied
as he beginning o RAS esea ch. Th ee addi ional e o i uses we e iden i ied, i.e •
Ki s en and Maye [7] passed mouse e y h oblas osis i us (MEV) o newbo n W/Fu
a s. They obse ed ha he a s de eloped gene alized malignan lymphomas a e
6-7 mon hs. Two sepa a e se ial cell- ee passage sedes we e ini ia ed. Ra lymphomas
induced e y h oblas osis in less han 20% o he a s ha died wi hin 4 weeks a e
inocula ion. The su i ing a s emained appa en ly heal hy o mon hs un il hey died
om lymphomas. Inocula ion o newbo n C3H /Gs mice wi h he same il a es caused
only lymphomas in 3550% o he mice a e 38 mon hs. •Pe e s e al. [8] iden i ied
na u ally occu ing sa coma i us o he BALB/cC mouse; and •Rasheed e al. [9]
obse ed ha a Sp ague-Dawley (SD-1) a emb yo cul u e, a low passage le el, e-
leased an endogenous eco opic ype C i us (SD-RaLV) and a e abou 20 u he
passages i unde wen spon aneous ans o ma ion. The SD-RaLV, eleased om he
ans o med cells, did no cause apid ans o ma ion o o he a emb yo cells, bu ,
when he ans o med cells we e epea edly cocul i a ed wi h h ee di e en chemi-
cally ans o med and se ially ansplan ed a umo cell lines (sa coma, ca cinoma,
and hepa oma), apidly ib oblas - ans o ming ”sa coma” i uses (RaSV) we e eco -
e ed a e each a emp . The p oduc i e clones we e ound o be posi i e o a speci ic
p30 an igen and he RaSVs eleased we e se ially ansmi ed o o he a emb yo cells.
RaSV genome was escued om he nonp oduc i e clones by supe in ec ion wi h SD-
RaLV, wild a ype C i us, and se e al he e ologous ype C i uses. Thei indings
poin ed o na u ally occu ing ans o ma ion-speci ic (s c) genes being eco e ed in
i o in he o m o s able ”sa coma” i uses. Malumb es and Ba bacid [10] suma ise
he de elopmen s ela ed o he i s 30 yea s o esea ch ega ding RAS. A su ey o
RAS mu a ions in cance can be ound in P io e al. [11].
Tao e al. [12] epo ed he isola ion and cloning o he WNT-1 esponsi e Cdc42
homolog (WRCH1) cDNA, whose mRNA le el inc eased in esponse o WNT-1 sig-
naling in WNT-1 ans o med cells, WNT-1 ansgene induced mouse mamma y u-
mo s, and WNT-1 e o i us in ec ed cells. To con i m ha WRCH1 was egula ed by
WNT-1 signaling, hey in ec ed C57MG cells wi h ei he an emp y e o i al ec o o
a WNT-1-exp essing e o i us. WRCH1 mRNA was ound o be up- egula ed mo e
han ou old in C57MG/WNT-1 cells e sus C57MG/ ec o cells. Fu he , o e ex-
p ession o WRCH1 phenocopied WNT-1 in mo phological ans o ma ion o mouse
mamma y epi helial cells. To iden i y i WRCH1 was a homolog o he Rho amily
4
o GTPases, hey cloned ull-leng h mouse and human WRCH1 cDNAs, based on he
pa ial sequence o mouse WRCH1 cDNA isola ed om PCR-selec cDNA sub ac-
ion. They obse e d ha he cDNAs o human and mouse WRCH1 encoded p o eins
o 258 and 261 amino acid esidues, espec i ely, which a e 92% iden ical. Thei anal-
ysis o he deduced amino acid sequence o WRCH1 iden i ied i as a homolog o he
Rho amily o GTPases. The human WRCH1 p o ein sha ed 57% iden i y and 70%
simila i y wi h Cdc42, and 30%-55% simila i y wi h o he membe s o he Rho amily.
I was obse ed ha bo h human and mouse WRCH1 con ained GTP and GDP binding
domains, he e ec o domain, and a CAAX lipid modi ica ion signal a hei C e mini,
all o which we e conse ed among mos membe s o he Rho amily, as documen ed
in Ridley [13]. Like Cdc42, hey ound ha WRCH1 could ac i a e PAK-1 and JNK-1,
and induce ilopodium o ma ion and s ess ibe dissolu ion.
I p esen 3 d o de combina ions o RHOU wi h o he genes, ha he machine
lea ning based sea ch engine poin s o, as possible syne gis ic combina ions ha migh
be wo king in ime.
3. Me hods
Please e e o sec ions o Sinha [2] o me hods, design o s udy and analysis o da a
o 2nd o de combina ions. The same me hod and design o s udy is used o gene a e
esul s o 3 d o de combina ions p esen ed in his s udy.
4. Time se ies da a
Guj al and MacBea h [1] p esen a se o 71 WNT- ela ed gene exp ession alues o 6
di e en imes poin s o e a ange o 24-hou pe iod using qPCR. The changes ep e-
sen he old-change in he exp ession le els o genes in 200 ng/mL WNT3A-s imula ed
HEK 293 cells in ime ela i e o hei le els in uns imula ed, se um-s a ed cells a 0-
hou . Guj al and MacBea h [1] s a e ha qPCR da a a e he means o h ee biological
eplica es. Only genes whose mean ansc ip le els changed by mo e han wo- old a
one o mo e ime poin s du ing he 24-hou ime cou se we e conside ed signi ican .
Posi i e (nega i e) numbe s ep esen up (down) - egula ion. We ha e al eady co e ed
he issues ela ed o hese da a se s in de ail in Sinha [14]. Reade s a e eques ed o
go h ough hem in he poin ed e e ence. The ools o s udy which a e used he e ha e
been published in ano he ounda ional wo k in Sinha [14].
5. Design o expe imen
5.1. Pipeline o ime se ies da a
Fo he case o ime se ies da a, in e ac ions among he con ibu ing ac o s a e s udied
by compa ing iple s o old-changes a single ime poin s. The p odecu e begins wi h
he gene a ion o dis ibu ion a ound measu emen s a single ime poin s wi h added
noise is done o es ima e he indices. A dis ibu ion is gene a ed o he old changes
5
a single ime poin s. Then o e e y gene, he e is a ec o o alues ep esen ing old
changes as well as de ia ions in old changes o di e en ime poin s and du a ions
be ween ime poin s, espec i ely. Nex a lis ing o all Cn
kcombina ions o knumbe
o genes om a o al o ngenes is gene a ed. kis ≥2 and ≤(n−1). Each o he com-
bina ion o o de k ep esen s a unique se o in e ac ion be ween he in ol ed gene ic
ac o s. A e his, he da ase s a e combined in a speci ed o ma which go as inpu
as pe he equi emen o a pa icula sensi i i y analysis me hod. Thus o each p h
combina ion in Cn
kcombina ions, he da ase is p epa ed in he equi ed o ma om
he dis ibu ions o wo sepa a e cases which ha e been discussed abo e. (See .R code
in mainSc ip -1-1.R). A e he da a has been ans o med, ec o ized p og amming
is employed o densi y based sensi i i y analysis and looping is employed o a i-
ance based sensi i i y analysis o compu e he equi ed sensi i i y indices o each o
he pcombina ions. This p ocedu e is done o di e en kinds o sensi i i y analysis
me hods.
A e he abo e sensi i i y indices ha e been s o ed o each o he p h combina-
ion, he nex s ep in he design o expe imen is conduc ed. Since he e is only one
eco ding o sensi i i y index pe combina ion, each combina ion o ms a aining ex-
ample which is allo ed a aining index and he sensi i i y indices o he indi idual
gene ic ac o s o m he aining example. Thus he e a e Cn
k aining examples o k h
o de in e ac ion. Using his aining se SVMRank
lea n Joachims [3] is used o gene a e a
model on de aul alue C alue o 20. In he cu en expe imen on oy model C alue
has no been unned. The aining se helps in he gene a ion o he model as he di -
e en gene combina ions a e numbe ed in o de which a e used as ank indices. The
model is hen used o gene a e sco e on he obse a ions in he es ing se using he
SV MRank
classi y Joachims [3]. No e ha due o a ailabili y o only one example pe com-
bina ion, a e he model has been buil , he same aining da a is used as es da a o
gene a es he sco es. This p ocedu e is execu ed o each and e e y sensi i i y analysis
me hod. This is ollowed by so ing o hese sco es along wi h he ank indices (i.e he
aining indices) al eady assigned o he gene combina ions. The end esul is a so ed
o de o he gene combina ions based on he anking sco e lea ned by he SV MRank
algo i hm. Finally, his en i e p ocedu e is compu ed o sensi i i y indices gene a ed
o each and e e y old change a ime poin and de ia ions in old change a di e en
du a ions. Obse ing he changing ank o a pa icula combina ion a di e en imes
and di e en ime pe iods will e eal how a combina ion is beha ing.
No e ha he ollowing is he o de in which he iles should be execu ed in R, in
o de , o ob aining he desi ed esul s (No e ha he code will no be explained he e) - •
use sou ce(”mainSc ip -1-1.R”) wi h a gumen s o Dynamic da a •sou ce(”SVMRank-
Resul s-D.R”), o ank he in e ac ions (again his needs o be done sepa a ely o
di e en kinds o SA me hods), •use sou ce(”Combine-Time- iles.R”), i compu -
ing indices sepa a ely ia p e ious ile, •sou ce(”So -n-Plo -D.R”) o so he in e -
ac ions. No e ha he so ing is chages he in e ac ion anking in ime. Thus •use
sou ce(”In e ac ion-P io i y-In ime.R”) o ind he p io i ized anking o each and e -
e y in e ac ion o e he di e en ime poin s and inally •use sou ce(”P in -Ranking-
AND-In e ac ion-Rank.R”) o p in indi idual anking o he equi ed inpu ac o wi h
o he in e ac ion ac o s.
6
6. Resul s & Discussion
6.1. Time se ies da a by Guj al and MacBea h [1]
NOTE - Ranking was assigned on sco es ha we e so ed in DECREASING alues.
So, 1 was assigned o highes sco e and ice e sa.
Resul s o he 3 d o de in e ac ions a e p esen ed he e. The esul s i s discuss
he beha iou o in e ac ions ac oss he snapsho s o ime using he compu ed sensi-
i i ies on old change measu emen s pe ime snapsho . The analysis was done us-
ing 4 di e en sensi i i y indices. Ou o he 71C3combina ions, I conside /p esen
only hose combina ions ha show a anking wi hin i s 10,000 ou o 57,155. This
choice is libe al and biologis s/oncologis s can ha e a mo e s ic e choice as pe need.
Two obse a ions a e made, • he anking o a pa icula combina ion is conse ed (i.e
wi hin he 10,000 ange) in a pa icula ime poin o in he ea ly phase o la e phase
o WNT3A s imula ion, ac oss he majo i y o he ou sensi i i y me hods, which is a
s ic c i e ia o assessmen o • he anking o a pa icula combina ion is conse ed
ac oss ime poin s/phase (i.e hey a e wi hin he 10,000 ange) and he majo i y o he
ou sensi i i y me hods, which is elaxed c i e ia o assessmen . Applying his il e
helps e eal impo an combina ions o in e es ha migh be wo king syne gis ically
a a highe o de le el in he cell.
Rega ding echnical poin s o implemen a ion, he ankings we e gene a ed wi h-
ou scaling/no malizing he ime se ies da a p o ided by Guj al and MacBea h [1].
Fo es ima ing he sensi i i y indices, a small gaussian dis ibu ion using he unc ion
no m ha gene a es a ec o o no mally dis ibu ed andom a iables gi en a ec o
leng h n (he e 9, he 10 h one is he mean/ eco ded gene egula ion i sel ), a popula ion
mean µand popula ion s anda d de ia ion σ. The syn ax o using no m is as ollows:
no m(n, mean, sd). Fu he , I use he ji e un ion o add a li le bi o noise o he
da a. This helps o see i he gene a ed ankings a e obus o no .
6.2. Enume a ion and anking o 2415 RHOU-X-X combina ions
om Guj al and MacBea h [1]
In he supplemen a y sec ion, I p esen ou iles, each con aining he ankings o 3 d
o de combina ions, ha wa y in ime (shown o 5 ime poin s). Each ile ep esen s
he ankings compu ed using a pa icula sensi i i y me hod. The changing ankings
in ime o a pa icula combina ion ep esen s he impo ance o con ibu ion/ ole ha
combina ion plays in he cell s imula ed wi h WNT3A. The sensi i i y me hods used
a e Hilbe Schmid Independence C i e ion indices (HSIC) indices (wi h b and linea
ke nel in Da Veiga [15]) and Sobol indicies (wi h 2002 implemen a ion in Sal elli [16]
and ma inez implemen a ion in Ma inez [17] and Baudin e al. [18]).
6.3. Conse ed machine lea ning ankings o es ed RHOU-X-X
combina ions
A o al o 2415, 3 d o de combina ions in ol ing RHOU we e ob ained om a ull se
o 71C3= 57155 combina ions. Fu he , om his selec ed se , using he abo e c i e ia
7
o conse ed ankings, I epo / abula e he meaning ul combina ions ha migh be
wo king syne gis ically. Tables 2, 3 and 4 show he ankings o he same combina-
ions as in able 1, bu using b ke nel o HSIC, 2002 implemen a ion o SOBOL
and ma inez implemen a ion o SOBOL, espec i ely. As one allies he ankings o
ac oss hese ables o a pa icula combina ion, one inds ha he ole o he combina-
ion o in e es is conse ed. This conse a ion poin s o he exis ence o he biological
syne gy, whe he he combina ion has been es ed o unexplo ed/un es ed.
6.3.1. Examining he beha iou o WNT-RHOU-X combina ions
We know om he abo e li e a u e ha WNT1 up- egula es WRCH1/RHOU. Look-
ing a he ables abo e, one inds he ollowing combina ions o membe s o WNT
amily along wi h RHOU, o be p ominen a 3 d o de le el - LRP6-RHOU-WNT2B,
FBXW11-RHOU-WNT2B, RHOU-SLC9A3R1-WNT4, LRP6-RHOU-WNT2, EP300-
RHOU-WNT2, RHOU-WNT1-WNT4, LRP6-RHOU-WNT5A, RHOU-SFRP1-WNT4
and GSK3B-RHOU-WNT2. All hese combina ions indica e he exis ence o a possi-
ble syne gy when hey ake a highe ank in he lis o combina ions.
6.3.2. Examining he beha iou o FZD-RHOU-X combina ions
I is also known ha he WNT signaling pa hways a e ac i a ed by he binding o a
WNT-p o ein ligand o a F izzled amily ecep o (FZD), which passes he biological
signal o he Dishe elled (DVL) p o ein inside he cell. Looking a he ables abo e,
one inds he ollowing combina ions o membe s o FZD amily along wi h RHOU,
o be p ominen a 3 d o de le el - FZD5-JUN-RHOU, FZD5-CCND2-RHOU, FZD1-
PORCN-RHOU, FZD2-NKD1-RHOU, APC-FZD6-RHOU, FZD5-GSK3A-RHOU, FZD1-
NKD1-RHOU, FSHB-FZD2-RHOU, CXXC4-FZD2-RHOU, FZD8-GSK3A-RHOU,
FZD1-FZD2-RHOU, FZD8-LRP6-RHOU, FZD7-NKD1-RHOU, CXXC4-FZD7-RHOU,
FRZB-FZD2-RHOU, FZD5-NKD1-RHOU, CTNNBIP1-FZD2-RHOU, FZD7-PORCN-
RHOU, FZD5-LRP6-RHOU, AXIN1-FZD2-RHOU and FZD1-GSK3A-RHOU. All
hese combina ions indica e he exis ence o a possible syne gy when hey ake a highe
ank in he lis o combina ions.
6.3.3. Examining he beha iou o DVL-RHOU-X combina ions
Again, i is also known ha he WNT signaling pa hways a e ac i a ed by he binding
o a WNT-p o ein ligand o a F izzled amily ecep o (FZD), which passes he bio-
logical signal o he Dishe elled (DVL) p o ein inside he cell. Looking a he ables
abo e, one inds he ollowing combina ions o membe s o DVL amily along wi h
RHOU, o be p ominen a 3 d o de le el - AXIN1-DVL1-RHOU, DVL1-FBXW11-
RHOU, DKK1-DVL2-RHOU, DVL2-FGF4-RHOU, DVL1-LRP6-RHOU, CXXC4-
DVL2-RHOU, DVL1-FOXN1-RHOU, DVL1-RHOU-TCF7 and CTNNBIP1-DVL2-
RHOU. All hese combina ions indica e he exis ence o a possible syne gy when hey
ake a highe ank in he lis o combina ions.
8
RANKING @ iUSING HSIC - LINEAR
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
FBXW11-LRP6-RHOU 11 53077 50648 30258 27900 CCND1-FGF4-RHOU 77 55663 35981 27067 10821
FZD5-JUN-RHOU 105 12942 56571 25707 3718 CTNNBIP1-JUN-RHOU 119 11333 54553 37428 52492
CSNK1D-FGF4-RHOU 137 7470 45846 49163 20155 DAAM1-LRP6-RHOU 160 47568 49021 54157 20385
CCND2-LRP6-RHOU 195 23197 17269 56080 2265 DKK1-JUN-RHOU 210 3670 42736 27568 47765
AXIN1-DVL1-RHOU 314 6052 39138 50246 11753 APC-PITX2-RHOU 397 38592 32191 27698 15148
DKK1-LRP6-RHOU 401 7782 55096 29348 20780 FZD8-LRP6-RHOU 468 41362 6887 53473 47929
CTNNB1-FOXN1-RHOU 475 856 5984 14676 48295 CSNK2A1-MYC-RHOU 501 22087 50879 39343 4386
LRP6-RHOU-WNT2B 521 21284 29060 52854 25865 AES-AXIN1-RHOU 524 50360 32314 44626 11228
CXXC4-FGF4-RHOU 583 24551 34633 53319 56248 FBXW2-RHOU-TCF7 658 32560 43438 3752 18218
FZD5-CCND2-RHOU 694 44791 4209 21405 30546 CXXC4-DVL2-RHOU 703 7173 6556 19343 52966
EP300-GSK3B-RHOU 762 29861 9716 10624 2207 FBXW11-RHOU-SENP2 810 39829 54582 1076 13192
FOSL1-PPP2R1A-RHOU 846 41555 5035 55239 46031 CXXC4-JUN-RHOU 881 1789 43156 41625 53423
FBXW11-RHOU-WNT2B 887 56605 51928 47819 44859 GSK3B-RHOU-TLE2 898 47931 45636 21326 13471
FSHB-NKD1-RHOU 974 40540 14067 9128 35039 CCND1-PYGO1-RHOU 1040 56164 34165 35225 53648
GSK3B-LRP6-RHOU 1052 31885 19160 38602 12879 FRAT1-PORCN-RHOU 1077 31453 10861 21530 17749
FZD1-PORCN-RHOU 1095 21176 12741 16941 18130 EP300-RHOU-WNT2 1132 42400 48712 18390 28303
GSK3B-RHOU-TCF7 1149 7136 32592 11483 26116 BCL9-FGF4-RHOU 1153 22570 51717 42895 26298
CTBP1-FGF4-RHOU 1171 15515 48677 31280 24137 RHOU-WNT1-WNT4 1198 602 1780 21941 43967
CTBP2-GSK3B-RHOU 1205 55707 18585 4716 40362 PITX2-PORCN-RHOU 1220 38816 23756 29958 13324
GSK3B-RHOU-SENP2 1230 39467 21376 11806 9365 CXXC4-FOXN1-RHOU 1258 949 4951 19719 52102
BCL9-PORCN-RHOU 1284 46597 6968 29490 21809 CSNK1A1-LRP6-RHOU 1294 10065 15184 54599 10820
CSNK1G1-PORCN-RHOU 1299 27191 33972 15284 20376 FZD7-NKD1-RHOU 1307 26801 3329 51286 46329
FZD2-NKD1-RHOU 1310 19610 4807 33843 1134 AXIN1-EP300-RHOU 1312 1646 32903 47413 5408
FOSL1-PORCN-RHOU 1333 44749 10281 23020 23848 CTNNBIP1-FGF4-RHOU 1375 44903 56902 26308 45676
DVL1-FBXW11-RHOU 1388 30499 7484 11321 46544 DVL1-FOXN1-RHOU 1438 38257 4549 11910 29038
APC-FZD6-RHOU 1482 46230 8189 40700 5636 AXIN1-FOXN1-RHOU 1511 738 4253 15602 21213
FBXW11-RHOU-SFRP4 1516 48741 46254 2195 24642 DKK1-FGF4-RHOU 1553 5607 24412 21107 41674
KREMEN1-RHOU-TCF7 1573 55772 27141 223 46704 CSNK1G1-FOXN1-RHOU 1587 4796 8477 31603 16974
BCL9-JUN-RHOU 1653 6622 56085 44704 6331 FOSL1-FOXN1-RHOU 1660 21880 3384 19296 29104
DKK1-RHOU-SENP2 1744 25698 53164 542 50407 CXXC4-FZD7-RHOU 1774 20795 27044 52150 54907
DIXDC1-NKD1-RHOU 1798 6195 3765 22405 3157 FBXW11-GSK3B-RHOU 1864 39036 24146 19812 16311
DKK1-DVL2-RHOU 1867 1810 33595 42349 53523 FRZB-GSK3B-RHOU 1880 22893 26634 12199 52276
CSNK1G1-JUN-RHOU 1898 1165 55257 34817 23988 FRZB-FZD2-RHOU 1944 892 20805 28505 49730
DAAM1-FOXN1-RHOU 1998 39331 29857 17353 20914 DVL1-RHOU-TCF7 2030 52920 36405 7523 7698
LRP5-PORCN-RHOU 2053 8242 9590 48746 20172 FZD5-NKD1-RHOU 2086 9792 3471 18764 2521
FZD5-GSK3A-RHOU 2110 29982 2718 17049 4051 JUN-PYGO1-RHOU 2122 21105 6824 25993 11386
FZD1-NKD1-RHOU 2176 20088 11316 49737 2429 RHOU-TCF7-TLE2 2188 38946 13808 2888 33725
FSHB-FZD2-RHOU 2193 41442 55751 28895 48790 FRZB-GSK3A-RHOU 2205 2231 3514 26794 25129
CTBP1-GSK3A-RHOU 2252 6219 1718 35013 4228 CXXC4-GSK3A-RHOU 2262 20534 4082 47103 49826
DKK1-PYGO1-RHOU 2300 4971 25047 37502 11114 DKK1-FOXN1-RHOU 2310 27439 38761 12307 33517
CXXC4-FZD2-RHOU 2317 6671 22273 26084 55079 CSNK1G1-NKD1-RHOU 2328 3565 14141 34128 1880
FZD8-GSK3A-RHOU 2345 48981 3671 53392 35952 LRP6-RHOU-WNT5A 2371 52871 42173 56381 27277
DKK1-GSK3A-RHOU 2372 2731 45043 25134 42183 CTNNBIP1-FZD2-RHOU 2379 32067 25451 19277 52045
DVL2-FGF4-RHOU 2435 40706 45840 38213 42586 FZD7-PORCN-RHOU 2438 54301 6262 19661 38352
RHOU-SLC9A3R1-WNT4 2468 14726 19963 23342 24539 DAAM1-GSK3A-RHOU 2493 51743 28750 45637 28520
FRZB-LRP6-RHOU 2562 9229 2215 54525 26580 CTNNBIP1-DVL2-RHOU 2585 40458 19092 23270 50147
FBXW11-FOXN1-RHOU 2589 20834 7791 16907 24143 RHOU-SFRP1-WNT4 2662 39129 39941 42257 16102
DVL1-LRP6-RHOU 2680 50479 18313 55087 36829 FSHB-GSK3A-RHOU 2698 43462 34330 18933 10698
FZD1-FZD2-RHOU 2705 42439 38341 30031 28378 DKK1-PORCN-RHOU 2715 27097 49203 3892 51823
CCND3-PORCN-RHOU 2736 51197 20602 16051 28331 GSK3B-RHOU-WNT2 2741 33291 48297 6678 23276
FRZB-PORCN-RHOU 2754 2260 14728 21581 34283 FBXW2-RHOU-SENP2 2810 46432 53903 6485 38309
CTNNBIP1-LEF1-RHOU 2851 53935 15418 28550 56338 CSNK1D-FOXN1-RHOU 2891 4517 7734 29359 18640
CTNNBIP1-FRAT1-RHOU 2910 38029 54971 19935 51723 CTBP2-LRP6-RHOU 3030 56710 12170 56649 31539
FBXW11-FGF4-RHOU 3056 50852 55649 31582 13375 FZD5-LRP6-RHOU 3179 36603 10552 23856 22468
CSNK1G1-GSK3B-RHOU 3190 3405 4726 1433 8406 CTNNBIP1-NKD1-RHOU 3194 27112 11412 35287 15481
BTRC-RHOU-TCF7 3204 41293 40925 4745 45576 AXIN1-FZD2-RHOU 3216 31244 38793 27939 11583
CSNK1G1-DIXDC1-RHOU 3247 13611 55894 17887 29476 CSNK1G1-GSK3A-RHOU 3261 12094 4223 43874 25027
DAAM1-JUN-RHOU 3292 50276 41716 52344 40041 FBXW2-RHOU-SFRP4 3317 44736 54923 11444 31855
CTNNBIP1-NLK-RHOU 3322 501 7291 43407 48933 DIXDC1-JUN-RHOU 3325 2215 36161 42538 1991
BTRC-RHOU-FBXW4 3368 55758 50831 743 47356 CTNNBIP1-PORCN-RHOU 3494 46942 8439 8140 23879
FRZB-NKD1-RHOU 3499 2171 5014 35449 27330 FZD1-GSK3A-RHOU 3616 49363 7865 50000 3642
LRP6-RHOU-WNT2 3651 45818 48676 55006 6351 APC-GSK3A-RHOU 3658 24361 6768 42843 11981
DAAM1-FGF4-RHOU 3669 42155 55076 53871 14927 DIXDC1-GSK3A-RHOU 3688 25193 1738 30131 17732
Table 1: Rankings o RHOU-X-X. A lis o app oxima ely i s 125 combina ions wi h ankings below
10,000 ou o 57,155. SA - HSIC; Ke nel - linea
9
