po cupine O-acyl ans e ase (PORCN) : 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
104-Madhu isha Heigh s Phase 1, Risali, Bhilai-490006, India
Abs ac
PORCN belongs o he amily o memb ane bound O-acyl ans e ase (MBOAT). MBOAT
membe s con ain mul iple ansmemb ane domains and ca y wo conse ed esidues,
a conse ed his idine (His) embedded in a hyd ophobic s e ch o esidues and an as-
pa agine (Asn) o his idine wi hin a mo e hyd ophilic egion some 30-50 esidues up-
s eam. I can add palmi olea e g oups o WNT p o eins ha is necessa y o WNT lig-
and sec e ion. Guj al and MacBea h [1] p o ides a quan i a i e, and dynamic s udy o
WNT3A-media ed s imula ion o HEK 293 cells, whe e hey eco d ime based exp es-
sion 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 using sel -o ganizing
maps, hey iden i ied clus e s o genes ha exhibi simila exp ession 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 com-
bina 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 PORCN 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 conse ed ank-
ings o PORCN-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 PORCN comb. in WNT3A s imula ed cells
Email add ess: [email p o ec ed] (sh ip akash sinha)
1Aspec s o unpublished wo k we e p esen ed in a pos e session a Cell Symposia: Technology.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 June 14, 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)
combina ions, i becomes nea ly impossible o any biologis o s udy he sys em wide
dynamics 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 PORCN 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. Po cupine (PORCN)
The D osophila segmen pola i y gene p oduc Po cupine (Po c) was i s iden i ied as
being necessa y o p ocessing Wingless (Wg), a D osophila Wn (Wn ) amily mem-
be . Tanaka e al. [4] iden i ied Mouse (Mpo c) and Xenopus (Xpo c) homologs o
po c and ound ha hey encode endoplasmic e iculum (ER) p o eins wi h mul iple
ansmemb ane domains. Fu he , Mpo c mRNA was di e en ially exp essed du ing
emb yogenesis and in a ious adul issues, demons a ing ha he al e na i e splic-
ing is egula ed o syn hesize he speci ic ypes o Mpo c. In ans ec ed mammalian
cells, hey ound all ypes o Mpo c a ec ed he p ocessing o mouse WNT1, WNT3A,
WNT4, WNT6, and WNT7B bu no WNT5A. Las ly, hey also ound ha all ypes o
Mpo c co-immunop ecipi a ed wi h a ious WNT p o eins. Thei esul s sugges ed
ha Mpo c may unc ion as a chape one-like molecule o WNT.
Ca icasole e al. [5] epo ha he human Po cupine locus (MG61/PORC) spans 15
exons o e app oxima ely 12 kb o genomic sequence on Xp11.23. Like i s mouse and
Xenopus homologues, MG61/PORC encodes ou p o ein iso o ms (AD) gene a ed
h ough al e na i e splicing and exp essed in a issue-speci ic ashion. They p esen
e idence indica ing ha MG61/PORC can in luence he ac i i y o a human WNT7A
exp ession cons uc in a T-cell ac o - esponsi e epo e assay.
Liu e al. [6] indica e ha pos - ansla ional modi ica ion o WNTs includes lipid
modi ica ion and glycosyla ion. The o me is pe o med by PORCN. PORCN is a
memb ane-bound O-acyl ans e ase loca ed in he endoplasmic e iculum and can add
palmi olea e g oups o WNT p o eins ha is necessa y o WNT ligand sec e ion, and
i is a membe o he memb ane-bound O-acyl ans e ases (MBOATs). Lipid modi ica-
ion is necessa y o Wn ac i i y, and he opposi e is ue o glycosyla ion as obse ed
by Wille e al. [7]. Liu e al. [8] de eloped a sc een o small molecules ha blocked
WNT sec e ion and disco e ed LGK974, a po en and speci ic small-molecule PORCN
inhibi o . They show ha LGK974 inhibi s WNT signaling, including educ ion o he
WNT-dependen LRP6 phospho yla ion and he exp ession o WNT a ge genes, like
as AXIN2. The inhibi o is e ec i e in mul iple umo models a well- ole a ed doses.
Toge he , hei indings p o ide a s a egy and and a ool o a ge ing WNT-d i en
cance s h ough he inhibi ion o PORCN. Fu he down he line, Madan e al. [9] de-
3
eloped a no el po en , o ally a ailable PORCN inhibi o , ETC-1922159 ha blocked
he sec e ion and ac i i y o all WNTs. ETC-1922159 is ema kably e ec i e in ea -
ing RSPO- ansloca ion bea ing colo ec al cance (CRC) pa ien -de i ed xenog a s.
This is he i s example o e ec i e a ge ed he apy o his subse o CRC. By his
demons a ion hey show ha inhibi ion o WNT signaling by PORCN inhibi ion holds
p omise as di e en ia ion he apy in gene ically de ined human cance s.
Su on [10], con e a ange o PORCN ela ed de elopmen al diso de s. Till now,
mos esea ch wo k has ocused on he ole o PORCN along wi h WNTs. In his
esea ch wo k, I p esen 3 d o de combina ions o PORCN wi h o he genes, apa
om he WNTs, 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 [11]. 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 [11].
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
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
4
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.
5
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 PORCN-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 [12]) and Sobol indicies (wi h 2002 implemen a ion in Sal elli [13]
and ma inez implemen a ion in Ma inez [14] and Baudin e al. [15]).
6
6.3. Conse ed machine lea ning ankings o es ed PORCN-X-X
combina ions
A o al o 2415, 3 d o de combina ions in ol ing PORCN 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 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 combi-
na 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 CXXC4-PORCN-X combina ions
Ekici e al. [16] iden i ied a homozygous splice si e mu a ion in he CCDC88C gene as
a no el cause o a complex hyd ocephalic b ain mal o ma ion, ia posi ional cloning in
a consanguineous amily wi h au osomal ecessi e hyd ocephalus. CCDC88C encodes
DAPLE (HkRP2), a Hook- ela ed p o ein wi h a binding domain o he cen al WNT
signalling pa hway p o ein DVL and DVL is inhibi ed by CXXC4 and CCDC88C, me-
dia es Wn signalling ia inhibi ion o GSK3. Looking a he ables abo e, one inds he
ollowing combina ions o CXXC4 along wi h PORCN, o be p ominen a 3 d o de
le el - CXXC4-PORCN-SENP2, CXXC4-PORCN-WNT2B, CXXC4-PORCN-TCF7,
CXXC4-PORCN-WNT4, CXXC4-PORCN-SFRP4, CXXC4-PORCN-FBXW4, CXXC4-
PORCN-PPP2R1A, CXXC4-PORCN-PPP2CA and CXXC4-PORCN-WNT5A. 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.
6.3.2. Examining he beha iou o FOSL1-PORCN-X combina ions
The abili y o he igh en icle (RV) o adap o an inc eased p essu e a e load de-
e mines su i al in pa ien s wi h pulmona y a e ial hype ension. The WNT pa hway
plays an impo an ole in he de elopmen o he RV and may also be implica ed in
adul ca diac emodeling. Nayakan i e al. [17] show ha •WNT/β-ca enin signal-
ing molecules a e up egula ed in RV o pa ien s wi h pulmona y a e ial hype ension
and animal models o RV o e load (pulmona y a e y banding-induced and monoc o-
aline a models); •Ac i a ion o WNT/β-ca enin signaling led o RV emodeling
ia ansc ip ional ac i a ion o FOSL1 and FOSL2; •Fu he , he mRNA exp ession
p o iling o WNT signaling molecules and immuno luo escence s aining o aCTNNB1
(ac i e β-ca enin) and PORCN in RV myoca dial issues om human dono s (con-
ol) and pa ien s wi h idiopa hic PAH (IPAH) demons a ed a signi ican up egula ion
o WNT/β-ca enin signaling and • inally, pha macological inhibi ion o WNT sig-
naling using inhibi o o PORCN, LGK-974 a enua ed ib osis and ca diac hype o-
phy leading o imp o emen in RV unc ion in bo h, pulmona y a e y banding- and
monoc o aline-induced RV o e load and he blockade using LGK-974 in WNT3A-
s imula ed ca diac ib oblas s esul ed in signi ican down egula ion o mRNA and p o-
7
RANKING @ iUSING HSIC - LINEAR
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CXXC4-PORCN-SENP2 10 33446 17033 17387 32253 CXXC4-PORCN-WNT4 49 6186 19448 20672 51388
CXXC4-PORCN-WNT2B 60 17097 46765 26682 32940 CXXC4-PORCN-SFRP4 80 28448 27819 28835 44315
CCND3-PORCN-WNT4 91 42809 21302 8841 38191 CCND3-PORCN-FBXW4 143 52831 15807 7893 14041
CXXC4-PORCN-TCF7 147 56042 37081 25343 32394 CXXC4-PORCN-FBXW4 168 26465 19028 12201 29004
CSNK1D-PORCN-SENP2 254 26488 43944 21480 22511 PITX2-PORCN-SENP2 270 20159 27718 25665 18827
FOSL1-PORCN-SFRP4 292 44876 11834 15903 36394 APC-PORCN-WNT4 310 33562 14239 15555 28291
FBXW2-PORCN-SFRP4 311 28602 1442 40221 38787 APC-PORCN-TCF7L1 320 33618 6586 15674 22420
FZD7-PORCN-FBXW4 331 24784 14647 7522 19704 NLK-PORCN-PPP2CA 339 30605 43435 41734 4166
FOSL1-PORCN-SENP2 349 31659 11861 10245 21849 NLK-PORCN-SFRP4 368 53128 52278 37793 4619
FZD5-PORCN-SENP2 377 32693 14759 8273 55426 FZD6-PORCN-WNT2B 379 19259 55786 24330 16739
FZD1-PORCN-SENP2 382 25494 17903 13765 16485 FZD6-PORCN-WNT4 394 39861 46523 785 6046
DKK1-PORCN-SENP2 400 29700 53693 2734 52517 CSNK1G1-PORCN-SENP2 410 36322 35831 12245 17913
BCL9-PORCN-PPP2CA 415 15959 34237 38189 34019 CXXC4-PORCN-PPP2R1A 424 27798 37533 50501 37618
FOSL1-PORCN-WNT4 455 37570 20729 10105 38487 PITX2-PORCN-WNT5A 460 36097 17787 53210 23094
APC-PORCN-SENP2 466 12387 7261 13497 19215 FRZB-PORCN-SENP2 467 13159 11733 10122 22264
LRP5-PORCN-SENP2 476 41616 8750 51278 21981 CXXC4-PORCN-PPP2CA 481 22027 38709 38555 36190
FZD6-PORCN-TLE2 482 39422 46346 2340 25087 FZD6-PORCN-SENP2 497 45212 45263 687 14394
BCL9-PORCN-SFRP4 498 29468 3887 31671 36411 PITX2-PORCN-FBXW4 499 12554 20396 26439 17842
FBXW2-PORCN-WNT4 531 21565 4445 36629 31422 CXXC4-PORCN-WNT5A 535 15961 16253 55679 46631
FZD8-PORCN-SFRP1 556 26745 7918 11285 32679 PITX2-PORCN-TCF7L1 572 42893 22702 25919 13429
CSNK1D-PORCN-WNT2B 573 51683 44617 47981 16208 FZD6-PORCN-SFRP1 615 42793 48666 4863 20350
PITX2-PORCN-WNT2B 630 42884 44910 50269 15186 FZD8-PORCN-SENP2 639 19701 11231 9109 12830
FOSL1-PORCN-WNT2B 670 19667 46545 40946 19709 KREMEN1-PORCN-WNT4 693 6753 23243 1864 44869
DKK1-PORCN-WNT4 724 36114 54617 3866 55268 NLK-PORCN-SENP2 751 51440 56864 21216 6122
FZD7-PORCN-WNT3A 780 35610 948 25632 12174 FZD8-PORCN-PPP2R1A 807 27524 31540 26322 40650
PITX2-PORCN-TLE1 813 43605 21513 22845 15786 FRAT1-PORCN-SFRP4 816 23261 18955 23358 33807
DKK1-PORCN-SFRP4 824 35293 52036 5440 53719 LRP5-PORCN-SFRP4 872 1618 3850 57012 38203
FRAT1-PORCN-SENP2 915 19198 9986 14436 18176 APC-PORCN-SFRP1 973 22402 11999 21396 30025
LRP5-PORCN-WNT2 975 5747 5037 56461 37999 CCND3-PORCN-SFRP1 984 46966 24689 11920 26237
CCND3-PORCN-TLE2 1002 48876 25152 13843 25724 PITX2-PORCN-PPP2R1A 1003 8071 39783 44256 5481
NLK-PORCN-WNT2B 1006 26349 37659 35498 4512 FBXW11-PORCN-WNT2B 1048 54134 36167 45459 15114
CSNK1D-PORCN-TLE2 1050 41629 52347 39317 20436 KREMEN1-PORCN-SENP2 1055 20253 16697 487 37387
FRAT1-PORCN-RHOU 1077 31453 10861 21530 17749 FZD1-PORCN-RHOU 1095 21176 12741 16941 18130
NLK-PORCN-SLC9A3R1 1108 35858 56545 26507 3768 FZD7-PORCN-TLE2 1111 50028 20809 22737 16490
CSNK1D-PORCN-TCF7 1115 16160 38935 28820 29405 LEF1-PORCN-PPP2R1A 1139 34004 43790 26178 5620
NLK-PORCN-TCF7 1154 48490 41769 34836 12221 FZD6-PORCN-TCF7 1180 33602 45874 5530 14682
FZD1-PORCN-WNT2B 1214 23191 49164 44140 14132 PITX2-PORCN-RHOU 1220 38816 23756 29958 13324
DKK1-PORCN-WNT2B 1222 26601 56978 25305 51044 FZD1-PORCN-SFRP4 1272 20986 27308 23520 32421
BCL9-PORCN-RHOU 1284 46597 6968 29490 21809 CSNK1G1-PORCN-TLE2 1291 31155 47884 19907 37757
CSNK1G1-PORCN-RHOU 1299 27191 33972 15284 20376 FOSL1-PORCN-RHOU 1333 44749 10281 23020 23848
APC-PORCN-WNT2B 1336 19495 29454 32718 22662 KREMEN1-PORCN-WNT3A 1377 25809 2588 12830 26801
BCL9-PORCN-WNT2B 1394 28608 33398 47599 21197 KREMEN1-PORCN-WNT2B 1401 36444 47192 17886 28451
CCND3-PORCN-TCF7L1 1408 36413 14249 8914 16004 FZD8-PORCN-WNT4 1416 27491 15836 9789 36903
FBXW11-PORCN-WNT4 1417 38911 18306 23726 35310 FZD8-PORCN-TCF7 1423 29081 35097 18363 11878
FBXW11-PORCN-SFRP4 1424 40575 3082 26157 24346 BCL9-PORCN-TCF7L1 1434 34720 6524 28798 16832
FOSL1-PORCN-TLE2 1446 44769 21226 13796 30066 DKK1-PORCN-TLE2 1461 36221 53569 8435 54639
FZD6-PORCN-SFRP4 1468 43415 46173 1426 23003 FZD7-PORCN-SFRP1 1470 54865 4185 15633 25384
DIXDC1-PORCN-SENP2 1529 21963 6981 10680 50015 FZD7-PORCN-WNT5A 1546 23763 6363 31855 40603
NLK-PORCN-WNT2 1557 46116 57071 36752 14418 FZD1-PORCN-TCF7 1572 38315 38185 25247 19741
CCND3-PORCN-TLE1 1580 36600 16976 3464 18298 CSNK1D-PORCN-SLC9A3R1 1596 41508 51420 34746 16992
PITX2-PORCN-SFRP4 1607 32189 32121 34063 21972 APC-PORCN-TCF7 1608 44043 39040 24555 20881
NLK-PORCN-TLE2 1657 49377 56092 39434 12430 FZD1-PORCN-SLC9A3R1 1698 18363 16380 21532 14659
FZD8-PORCN-PPP2CA 1713 51044 29439 20913 20485 FZD1-PORCN-FBXW4 1723 25108 19068 11515 19611
NLK-PORCN-WNT4 1742 49908 50644 30880 6042 FOSL1-PORCN-SFRP1 1757 36317 8057 17969 48972
FRZB-PORCN-SFRP4 1758 2975 26008 22234 42068 FRZB-PORCN-WNT4 1770 28522 21808 15299 35164
FRAT1-PORCN-WNT2B 1796 26246 45830 36444 11708 CSNK1G1-PORCN-SLC9A3R1 1815 10503 40046 19851 14743
FRZB-PORCN-PPP2R1A 1881 14863 41848 44601 12655 FZD7-PORCN-WNT2B 1892 48697 42677 33490 16364
GSK3B-PORCN-WNT4 1893 29701 28162 8296 19073 FOSL1-PORCN-FBXW4 1896 35711 18446 8569 19117
KREMEN1-PORCN-TCF7L1 1902 38888 15726 2313 30252 PITX2-PORCN-SFRP1 1905 39236 31192 37387 9110
CSNK1D-PORCN-SFRP1 1945 41776 54231 29005 26519 FZD1-PORCN-TLE2 1962 28422 26300 32913 23948
FZD5-PORCN-SFRP1 1980 55503 9426 16493 55566 FRAT1-PORCN-WNT4 1985 2835 18017 16053 23730
DKK1-PORCN-TCF7L1 1996 8327 51626 5019 50393 FRZB-PORCN-WNT2 2018 14494 10314 22043 37904
FZD6-PORCN-WNT2 2024 30877 41431 1558 29140 LRP5-PORCN-RHOU 2053 8242 9590 48746 20172
Table 1: Rankings o PORCN-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
ein exp ession o Wn /β-ca enin signaling and i s a ge genes (β-ca enin, PORCN,
MYC), ansc ip ion ac o s (FOSL1, FOSL2), p oli e a ion ma ke (CCND1), and
ib oblas - o-myo ib oblas s ansdi e en ia ion ma ke s (POSTN, CTGF). Looking a
he ables abo e, one inds he ollowing combina ions o FOSL1 along wi h PORCN,
8
RANKING @ iUSING HSIC - RBF
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CXXC4-PORCN-SENP2 9869 47028 41747 45009 41195 CXXC4-PORCN-WNT4 12492 2278 24920 46755 55842
CXXC4-PORCN-WNT2B 11272 21120 2288 41634 56160 CXXC4-PORCN-SFRP4 9369 30775 45417 32220 54090
CCND3-PORCN-WNT4 32692 49112 4162 52578 21791 CCND3-PORCN-FBXW4 14645 48562 10056 3289 18987
CXXC4-PORCN-TCF7 8174 50291 19771 4132 42869 CXXC4-PORCN-FBXW4 19853 43651 1014 10933 51164
CSNK1D-PORCN-SENP2 5664 26748 24402 26200 37885 PITX2-PORCN-SENP2 9499 29209 4986 29421 35908
FOSL1-PORCN-SFRP4 1126 41952 37755 38422 51768 APC-PORCN-WNT4 3592 12533 35169 40131 56018
FBXW2-PORCN-SFRP4 6999 27618 7405 7672 31324 APC-PORCN-TCF7L1 2882 26995 28827 39506 53073
FZD7-PORCN-FBXW4 8121 22895 5486 11733 22661 NLK-PORCN-PPP2CA 6640 37879 19229 30844 45007
FOSL1-PORCN-SENP2 314 29835 38646 3075 34319 NLK-PORCN-SFRP4 26548 54453 3595 31340 34837
FZD5-PORCN-SENP2 13359 46673 16639 12543 32648 FZD6-PORCN-WNT2B 47 9685 16997 36922 48852
FZD1-PORCN-SENP2 5513 34056 9744 10153 31014 FZD6-PORCN-WNT4 49 30454 13795 53236 50505
DKK1-PORCN-SENP2 2598 41263 6134 19723 13188 CSNK1G1-PORCN-SENP2 13585 41454 10606 1967 17443
BCL9-PORCN-PPP2CA 19443 12204 3989 2860 44188 CXXC4-PORCN-PPP2R1A 20998 30567 5511 22186 56640
FOSL1-PORCN-WNT4 1429 25705 30547 51837 52319 PITX2-PORCN-WNT5A 11335 32674 6548 15458 54809
APC-PORCN-SENP2 311 33317 27533 12463 51663 FRZB-PORCN-SENP2 2427 25944 18926 35699 48606
LRP5-PORCN-SENP2 11545 45801 9754 1937 37320 CXXC4-PORCN-PPP2CA 9663 20715 7491 12348 51537
FZD6-PORCN-TLE2 1065 45384 18117 3169 43333 FZD6-PORCN-SENP2 3 53444 8379 12707 32509
BCL9-PORCN-SFRP4 18390 13860 4099 36393 45375 PITX2-PORCN-FBXW4 2782 19946 19676 35972 50951
FBXW2-PORCN-WNT4 26557 1122 13989 31473 19951 CXXC4-PORCN-WNT5A 24704 5412 10695 26556 50085
FZD8-PORCN-SFRP1 11923 6846 34413 24802 45677 PITX2-PORCN-TCF7L1 13222 48332 9570 21227 51753
CSNK1D-PORCN-WNT2B 8595 53305 9816 26691 42121 FZD6-PORCN-SFRP1 1350 53618 15134 15153 53828
PITX2-PORCN-WNT2B 6802 25276 16938 13140 54357 FZD8-PORCN-SENP2 1042 32328 3606 28410 19273
FOSL1-PORCN-WNT2B 4296 5489 1279 29512 55035 KREMEN1-PORCN-WNT4 4572 591 18551 4045 46258
DKK1-PORCN-WNT4 9761 29610 8470 23618 51513 NLK-PORCN-SENP2 25839 52725 11882 9881 37272
FZD7-PORCN-WNT3A 7046 46922 42358 23913 36667 FZD8-PORCN-PPP2R1A 3136 21194 9602 10973 55135
PITX2-PORCN-TLE1 13872 39019 23792 7146 28106 FRAT1-PORCN-SFRP4 3261 12036 26076 48387 48335
DKK1-PORCN-SFRP4 10967 45207 3433 23697 54991 LRP5-PORCN-SFRP4 7636 690 3149 40164 40704
FRAT1-PORCN-SENP2 1688 40659 28876 5431 52097 APC-PORCN-SFRP1 7111 14469 39969 4242 53927
LRP5-PORCN-WNT2 19897 6038 17781 5354 56782 CCND3-PORCN-SFRP1 33184 51464 6743 7129 29071
CCND3-PORCN-TLE2 27878 51557 10879 4451 14924 PITX2-PORCN-PPP2R1A 11355 50277 26063 28070 55628
NLK-PORCN-WNT2B 30300 3466 8133 31316 44880 FBXW11-PORCN-WNT2B 4588 54697 1382 3672 49591
CSNK1D-PORCN-TLE2 12595 39793 26325 7235 43651 KREMEN1-PORCN-SENP2 2897 40815 14540 5841 26554
FRAT1-PORCN-RHOU 3460 15685 47256 50127 56007 FZD1-PORCN-RHOU 5740 25675 39166 40916 55717
NLK-PORCN-SLC9A3R1 39803 20122 9428 9998 42527 FZD7-PORCN-TLE2 38186 53192 36658 6999 30131
CSNK1D-PORCN-TCF7 38186 53192 36658 6999 30131 LEF1-PORCN-PPP2R1A 9650 37275 29706 14200 48587
NLK-PORCN-TCF7 14350 41604 26400 15610 37827 FZD6-PORCN-TCF7 9 22463 16490 29529 32076
FZD1-PORCN-WNT2B 12628 31292 8901 34846 55210 PITX2-PORCN-RHOU 11795 30595 6426 8297 54722
DKK1-PORCN-WNT2B 6263 7902 41853 840 49894 FZD1-PORCN-SFRP4 11010 1938 293 36645 52104
BCL9-PORCN-RHOU 13417 51514 7531 35538 56157 CSNK1G1-PORCN-TLE2 25416 24850 21439 2281 53031
CSNK1G1-PORCN-RHOU 18456 21677 26712 34529 54262 FOSL1-PORCN-RHOU 1550 39845 36998 42942 56120
APC-PORCN-WNT2B 3093 4702 5177 37025 54684 KREMEN1-PORCN-WNT3A 8946 29482 33980 6745 37128
BCL9-PORCN-WNT2B 7648 28196 20793 10962 34371 KREMEN1-PORCN-WNT2B 4060 34624 13586 33545 46659
CCND3-PORCN-TCF7L1 23178 26953 5435 27259 35443 FZD8-PORCN-WNT4 3177 7307 28634 31520 31714
FBXW11-PORCN-WNT4 6702 42970 13553 51464 33227 FZD8-PORCN-TCF7 3913 45328 27883 32520 22942
FBXW11-PORCN-SFRP4 4481 17010 1946 40382 32523 BCL9-PORCN-TCF7L1 23603 38078 31638 19229 41402
FOSL1-PORCN-TLE2 11375 42064 44489 3406 53873 DKK1-PORCN-TLE2 15980 45554 11547 10317 52314
FZD6-PORCN-SFRP4 58 47582 15962 31907 46706 FZD7-PORCN-SFRP1 46709 56734 39833 5383 34239
DIXDC1-PORCN-SENP2 16346 39480 19973 18502 14705 FZD7-PORCN-WNT5A 20174 37185 18191 15667 34821
NLK-PORCN-WNT2 44692 38504 8829 1995 53685 FZD1-PORCN-TCF7 2001 52600 33800 5805 49403
CCND3-PORCN-TLE1 13616 41666 12307 4061 29372 CSNK1D-PORCN-SLC9A3R1 26693 34397 22670 453 31614
PITX2-PORCN-SFRP4 7652 26224 19994 9630 41059 APC-PORCN-TCF7 671 37810 35108 9656 51194
NLK-PORCN-TLE2 41691 54802 745 25237 46608 FZD1-PORCN-SLC9A3R1 18304 25091 21402 3214 52196
FZD8-PORCN-PPP2CA 4402 55143 2005 12002 37055 FZD1-PORCN-FBXW4 15874 28222 17086 4292 47953
NLK-PORCN-WNT4 33383 45823 7542 34942 49961 FOSL1-PORCN-SFRP1 10522 38362 29766 6077 55724
FRZB-PORCN-SFRP4 6537 11064 22288 34580 50227 FRZB-PORCN-WNT4 9103 50017 36210 40277 54561
FRAT1-PORCN-WNT2B 5506 22998 20346 48317 52835 CSNK1G1-PORCN-SLC9A3R1 33423 29599 9114 6260 50642
FRZB-PORCN-PPP2R1A1 3914 23845 13959 7815 56301 FZD7-PORCN-WNT2B 35742 42851 5084 32980 11716
GSK3B-PORCN-WNT4 7755 14164 10378 27077 53726 FOSL1-PORCN-FBXW4 996 45964 6696 11811 50330
KREMEN1-PORCN-TCF7L1 5105 42564 13754 28956 27851 PITX2-PORCN-SFRP1 20244 35446 37738 24843 55456
CSNK1D-PORCN-SFRP1 36889 38723 2444 15209 50430 FZD1-PORCN-TLE2 29353 42139 4457 3385 52832
FZD5-PORCN-SFRP1 19216 56452 45353 3271 51709 FRAT1-PORCN-WNT4 6345 412 40450 45568 49626
DKK1-PORCN-TCF7L1 10025 8033 19471 39600 52807 FRZB-PORCN-WNT2 7253 15397 42587 3591 56438
FZD6-PORCN-WNT2 586 40987 4888 4733 51712 LRP5-PORCN-RHOU 12060 10648 7628 45521 55586
Table 2: Rankings o PORCN-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 - b
o be p ominen a 3 d o de le el - FOSL1-PORCN-SFRP4, FOSL1-PORCN-SENP2,
FOSL1-PORCN-WNT4, FOSL1-PORCN-WNT2B, FOSL1-PORCN-TLE2, FOSL1-
PORCN-RHOU, FOSL1-PORCN-SFRP1 and FOSL1-PORCN-FBXW4. 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.
9
[25] Z. Zhong, D. M. Vi shup, Recu en mu a ions in umo supp esso bxw7 bypass wn /β-ca enin addic ion in cance ,
Science Ad ances 10 (2024) eadk1031.
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Axel od, E. K. Vlada , A wn 4-and dkk3-d i en canonical o noncanonical wn signaling swi ch con ols mul icili-
ogenesis, Jou nal o cell science 136 (2023).
16
