WNT inhibi o y ac o 1 (WIF1) : 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
WNT inhibi o y ac o 1 (WIF1), a sec e ed p o ein ha binds o WNT p o eins and
inhibi s hei ac i i ies. 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 WIF1 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 WIF1-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 WIF1 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1Aspec s o unpublished wo k we e p esen ed in a pos e session a Cell Symposia: Technology.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 Ma ch 1, 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 WIF1 ela ed combina ions using indi idual gene exp essions mea-
su 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. 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,
2
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. WNT inhibi o y ac o 1 (WIF1)
Hsieh e al. [4] desc ibe ha WIF1 binds o WNT p o eins and inhibi s hei ac i i ies.
Using Xenopus emb yos hey show ha WIF1 o e exp ession a ec s somi ogenesis
( he gene a ion o unk mesode m segmen s), in ag eemen wi h i s no mal exp ession
in pa axial mesode m and u he , in i o, WIF1 binds o D osophila Wingless and
Xenopus WNT8 p oduced by D osophila S2 cells. Thei esul s indica e ha WNT
p o eins in e ac wi h s uc u ally di e se ex acellula inhibi o s o ine- une he spa ial
and empo al pa e ns o WNT ac i i y. Regua e al. [5] epo he iden i ica ion o
he 5’ p omo e egion ( 1.5 kb) o he human WIF1 gene, unc ional analysis o whic
shows ha a whole agmen displays high basal p omo e ac i i y in di e en cell lines,
while he unca ed o ms do no , indica ing ha in eg i y o he WIF1 p omo e egion
may be impo an o WIF1 ac i i y. Liepinsh e al. [6] and Malinauskas e al. [7],
s udy he c ys al s uc u e o WIF1 and he molecula mechanims o WNT inhibi ion
ia WIF1.
Malinauskas e al. [7] epo ha WIF1 is p esen ac oss e eb a e amilies and
consis s o an N- e minal sec e ion signal sequence, he WIF domain (WD, 143 amino
acid esidues), i e EGF-like domains (3133 esidues each) and a hyd ophilic C e mi-
nus. The WIF domain o WIF1 is su icien o inhibi Wn signalling7, bu he unc ion
o he i e EGF-like domains (EGFs IV) has emained obscu e. They used a se ies o
WIF1 cons uc s in a WNT esponse assay, o in es iga e he oles o he domains o
WIF1 in inhibi ion o WNT3A. WNT3A signaling was inhibi ed in a dose-dependen
manne (33500 nM) by WIF1∆C. WIF1WD and WIF1W D−EGF−Iwe e also inhibi o y,
consis en wi h Hsieh e al. [4] epo ha he WIF domain in isola ion can inhibi WNT
signaling, bu bo h hese cons uc s we e no ably less e ec i e han he molecules ha
con ained he WIF domain and EGFs IV.
In his esea ch wo k, I p esen 3 d o de combina ions o WIF1 wi h o he genes,
ha he machine lea ning based sea ch engine poin s o, as possible syne gis ic combi-
na 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.
3
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 [8]. 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 [8].
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
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
4
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. 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].
5
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 WIF1-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 [9]) and Sobol indicies (wi h 2002 implemen a ion in Sal elli [10]
and ma inez implemen a ion in Ma inez [11] and Baudin e al. [12]).
6.3. Conse ed machine lea ning ankings o es ed WIF1-X-X com-
bina ions
A o al o 2415, 3 d o de combina ions in ol ing WIF1 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 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-WIF1-X combina ions
Gudjonsson e al. [13] subjec ed 58 pai ed biopsies om lesional and unin ol ed pso-
ia ic skin and 64 biopsies om no mal skin o global gene exp ession p o iling. They
ound WNT5A ansc ip s up egula ed i e old in lesional skin, accompanied by in-
c eased WNT5A p o ein le els. In con as , exp ession o WIF1 mRNA was down eg-
ula ed ¿10- old in lesional skin, along wi h dec eased WIF1 immunos aining. These
esul s sugges ed a shi away om canonical Wn signaling owa d noncanonical pa h-
ways d i en by in e ac ions be ween WNT5A and i s cogna e ecep o s in pso iasis,
accompanied by impai ed homeos a ic inhibi ion o Wn signaling by WIF1 and dick-
kop . In ea ly os eochond osis (OC) ca ilage canal chond ocy es compa ed o con-
ols, Kinsley e al. [14] ound signi ican ly dec eased WNT11 and inc eased β-ca enin,
WNT5B, DKK1, LRP6, WIF1, AXIN1, and SC-PEP gene exp ession.
6
RANKING @ iUSING HSIC - LINEAR
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CTNNBIP1-WIF1-WNT2B 5 716 18217 51222 29536 TLE1-WIF1-WNT2B 65 13326 20278 36821 11947
CCND1-WIF1-WNT2B 86 32096 35653 38353 29538 CTNNBIP1-WIF1-WNT5A 128 2117 50325 55816 30661
TLE1-WIF1-WNT2 152 12574 27880 35684 24762 TLE2-WIF1-WNT2B 162 206 11704 50552 55877
CTNNBIP1-WIF1-WNT4 380 415 11991 33905 19908 NLK-WIF1-WNT2 431 13840 49796 35119 6813
CCND1-WIF1-WNT4 439 23377 41096 38262 34292 TLE1-WIF1-WNT3A 449 13164 8253 51282 7381
CTNNBIP1-WIF1-WNT3A 603 57 12000 57039 19928 FOSL1-WIF1-WNT2B 727 2770 23114 37617 17980
DVL2-JUN-WIF1 788 37918 18319 11932 34672 NLK-WIF1-WNT2B 877 15574 29869 50706 14922
FBXW11-WIF1-WNT2B 980 2151 19852 53626 35239 CTNNBIP1-WIF1-WNT3 1062 2046 28129 43847 22398
TLE1-WIF1-WNT4 1157 30379 12684 11265 1014 TLE1-WIF1-WNT5A 1188 23457 43932 51409 21021
FZD1-WIF1-WNT2B 1329 23 38111 30027 18511 CCND1-WIF1-WNT2 1543 11595 53523 46295 23076
TLE2-WIF1-WNT3A 1645 195 4085 52703 19685 CXXC4-WIF1-WNT3A 1745 353 12465 51440 34488
DKK1-JUN-WIF1 1820 23431 35933 34937 52606 FBXW11-JUN-WIF1 1901 11991 20361 28288 29058
TCF7L1-WIF1-WNT3A 2015 7414 38348 38153 24687 NKD1-WIF1-WNT3A 2028 3129 43733 48011 30914
CCND1-WIF1-WNT3A 2203 19821 39265 34450 38713 CCND1-WIF1-WNT5A 2206 17920 56231 50097 15244
TCF7L1-WIF1-WNT4 2218 10007 38673 37345 36797 SLC9A3R1-TLE1-WIF1 2489 8000 13237 31531 3962
CSNK1G1-WIF1-WNT2B 2561 1995 24404 34807 53934 CSNK1G1-WIF1-WNT4 2582 628 24563 33380 53761
CTNNB1-FRAT1-WIF1 2625 18691 37238 24416 4230 KREMEN1-WIF1-WNT3A 2762 721 11586 56871 31145
CXXC4-WIF1-WNT2 2794 318 38171 33660 55940 CXXC4-WIF1-WNT2B 2798 244 27556 44507 52219
BCL9-FGF4-WIF1 2803 15565 47332 49359 43280 FBXW2-WIF1-WNT4 2836 2416 50951 26493 30178
CTBP2-JUN-WIF1 2868 17637 22151 3690 5044 GSK3B-JUN-WIF1 2874 57004 14204 24719 995
LRP6-TCF7L1-WIF1 2890 24748 56683 45634 14436 NKD1-WIF1-WNT4 2997 2461 45561 55000 34857
AES-FOXN1-WIF1 3020 27902 1754 12067 18564 DAAM1-WIF1-WNT2B 3043 759 50931 27606 47145
FRAT1-WIF1-WNT4 3157 3802 25184 32202 1523 CSNK1D-FGF4-WIF1 3202 18099 34798 40988 22019
EP300-JUN-WIF1 3213 26743 1259 1082 53260 PYGO1-WIF1-WNT4 3238 2703 55318 32252 32949
FZD8-WIF1-WNT2B 3269 243 27377 19078 48272 FZD7-WIF1-WNT3A 3300 22512 13048 31811 10684
LRP5-WIF1-WNT2 3309 8027 54170 21981 39712 FRAT1-WIF1-WNT3A 3328 15377 26382 55074 7682
FBXW4-WIF1-WNT2B 3407 2879 36747 43254 40889 FZD1-WIF1-WNT4 3425 32 39696 18088 22320
FZD2-NKD1-WIF1 3430 39091 22109 26358 3 FZD1-WIF1-WNT2 3541 469 55529 20037 32149
FRZB-WIF1-WNT2B 3820 12763 27144 38688 14118 DIXDC1-NKD1-WIF1 3909 12873 22358 12920 23739
FBXW2-JUN-WIF1 3982 6153 53985 45810 46608 TCF7L1-WIF1-WNT5A 4007 25712 49240 53231 50932
FZD5-CTNNBIP1-WIF1 4022 52675 7175 11477 29088 FZD5-WIF1-WNT5A 4070 24066 49908 53334 34000
SFRP4-WIF1-WNT3A 4077 1667 15047 43673 14284 LEF1-WIF1-WNT3 4224 9702 36696 52931 22759
BTRC-NKD1-WIF1 4240 14000 50136 49384 38469 LRP6-PYGO1-WIF1 4293 17363 23754 6785 4390
PPP2R1A-TLE1-WIF1 4307 33741 44977 32847 32390 TCF7L1-WIF1-WNT2 4345 20158 51362 40340 48389
NLK-WIF1-WNT4 4406 21046 38575 49983 13952 KREMEN1-NKD1-WIF1 4459 12175 15117 38622 27477
AES-JUN-WIF1 4472 28415 49294 40746 21208 FRZB-WIF1-WNT4 4481 3483 22127 37869 5037
KREMEN1-WIF1-WNT4 4505 6 32895 41843 42797 CSNK1G1-WIF1-WNT3A 4524 651 24433 41940 24409
DKK1-WIF1-WNT4 4532 13090 48760 30623 55584 FRAT1-WIF1-WNT2 4559 16950 52343 25199 28909
FSHB-NKD1-WIF1 4621 8153 24750 5910 428 CCND3-JUN-WIF1 4630 5154 35719 23637 33462
CSNK1G1-JUN-WIF1 4634 18256 33517 5537 47380 FBXW11-FGF4-WIF1 4650 8304 41904 29881 15466
NLK-WIF1-WNT3A 4697 36349 45660 34357 1641 CCND3-NKD1-WIF1 4703 15466 48536 38259 5001
CTNNB1-NLK-WIF1 4707 9899 6192 11981 1923 JUN-WIF1-WNT5A 4730 23210 50885 51206 36664
FOSL1-TLE1-WIF1 4735 9994 4780 43075 2516 CSNK1A1-NLK-WIF1 4795 14710 6213 20851 31609
FZD8-JUN-WIF1 4797 14662 20872 250 14885 FZD7-NKD1-WIF1 4840 43438 23817 39330 17629
AXIN1-FZD2-WIF1 4880 56931 43233 17761 6844 GSK3B-NLK-WIF1 4909 52847 4703 44869 2761
PYGO1-WIF1-WNT5A 4948 8911 30428 21376 24898 SENP2-WIF1-WNT2 4997 18610 47165 55988 55683
PPP2R1A-WIF1-WNT4 5019 37728 49097 41364 45936 CSNK1G1-NLK-WIF1 5054 9876 3023 50217 40547
FBXW11-TLE1-WIF1 5151 21116 13884 43214 2581 CXXC4-NLK-WIF1 5268 10350 6512 1160 15363
SENP2-WIF1-WNT4 5283 14344 21051 43416 45904 BCL9-NLK-WIF1 5369 11251 10475 3676 22747
FBXW11-PYGO1-WIF1 5380 8837 55777 3899 37175 FOSL1-WIF1-WNT2 5404 15643 45844 47156 39486
CTNNB1-T-WIF1 5406 20960 19739 11635 21009 CXXC4-WIF1-WNT4 5410 19 16924 45160 54529
TCF7L1-WIF1-WNT3 5469 28902 52401 25619 27868 DVL1-JUN-WIF1 5674 37144 16904 4823 37727
FRZB-WIF1-WNT2 5709 5485 51972 46418 31405 DKK1-FGF4-WIF1 5714 42039 36616 21416 49824
FZD6-PORCN-WIF1 5717 34355 48055 274 39658 DKK1-WIF1-WNT2 5738 10295 54604 36927 57021
PPP2CA-WIF1-WNT4 5751 1807 53735 25829 47191 DAAM1-JUN-WIF1 5830 12099 53131 3838 44361
FBXW11-FOXN1-WIF1 5840 10050 554 10106 13305 EP300-FGF4-WIF1 5848 31277 41493 38422 55833
PPP2R1A-WIF1-WNT3A 5919 34346 48174 40443 24235 EP300-TLE1-WIF1 5972 16128 8443 34895 42825
LRP6-NKD1-WIF1 5998 19435 35302 21912 36590 DVL2-WIF1-WNT4 6024 27351 28400 29068 46173
FBXW2-PYGO1-WIF1 6116 9988 36252 7568 54910 PPP2R1A-WIF1-WNT2B 6135 34753 36857 36017 55555
CSNK1D-JUN-WIF1 6149 20727 36070 15822 2807 CXXC4-FRAT1-WIF1 6172 16667 52879 168 44602
SFRP1-WIF1-WNT2 6253 42208 44024 23110 51839 FOSL1-WIF1-WNT5A 6286 2387 48506 51990 25900
DAAM1-PYGO1-WIF1 6296 13073 20827 9619 26318 AXIN1-FOXN1-WIF1 6413 26633 589 11640 3200
LRP5-TLE1-WIF1 6476 8699 27950 38670 3372 FSHB-WIF1-WNT4 6540 764 36551 30104 9874
Table 1: Rankings o WIF1-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
Looking a he ables abo e, one inds he ollowing combina ions o WNT3A
along wi h WIF1, o be p ominen a 3 d o de le el - CTNNBIP1-WIF1-WNT3A,
7
RANKING @ iUSING HSIC - RBF
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CTNNBIP1-WIF1-WNT2B 38092 3733 8392 37231 50461 TLE1-WIF1-WNT2B 39953 13690 3178 37473 11178
CCND1-WIF1-WNT2B 36761 20542 11221 38644 7317 CTNNBIP1-WIF1-WNT5A 23143 5998 4289 37385 52573
TLE1-WIF1-WNT2 43453 5975 28430 42450 32889 TLE2-WIF1-WNT2B 39741 6829 13257 43555 31091
CTNNBIP1-WIF1-WNT4 28408 15354 16297 16001 53872 NLK-WIF1-WNT2 40307 10226 11647 34273 29809
CCND1-WIF1-WNT4 29821 25068 12712 33994 6600 TLE1-WIF1-WNT3A 50523 24823 48636 56307 10235
CTNNBIP1-WIF1-WNT3A 28101 8157 26911 47091 41515 FOSL1-WIF1-WNT2B 41773 13018 2276 54404 49689
DVL2-JUN-WIF1 6060 40504 15256 30934 48673 NLK-WIF1-WNT2B 20533 18090 8143 25594 25892
FBXW11-WIF1-WNT2B 38776 30910 903 8803 21329 CTNNBIP1-WIF1-WNT3 44721 9765 12738 26593 56684
TLE1-WIF1-WNT4 40180 37225 30537 13365 9063 TLE1-WIF1-WNT5A 40747 33211 3589 52410 46132
FZD1-WIF1-WNT2B 46438 3992 11382 45997 45602 CCND1-WIF1-WNT2 37082 11406 11541 14342 16511
TLE2-WIF1-WNT3A 40072 5491 24360 49488 34844 CXXC4-WIF1-WNT3A 11746 12153 2343 56809 35373
DKK1-JUN-WIF1 14470 30176 11543 7858 42039 FBXW11-JUN-WIF1 13667 34474 37922 11980 35650
TCF7L1-WIF1-WNT3A 2909 25918 43790 53902 35000 NKD1-WIF1-WNT3A 48793 3970 17300 56778 21427
CCND1-WIF1-WNT3A 22745 5551 30083 51087 4790 CCND1-WIF1-WNT5A 37414 8236 3639 32526 9840
TCF7L1-WIF1-WNT4 13995 23515 42960 42008 36503 SLC9A3R1-TLE1-WIF1 31186 3969 23029 44406 46868
CSNK1G1-WIF1-WNT2B 38910 5666 25272 47015 36127 CSNK1G1-WIF1-WNT4 16896 27273 7830 48279 26589
CTNNB1-FRAT1-WIF1 47615 22068 25131 13309 23212 KREMEN1-WIF1-WNT3A 38760 4243 33739 39807 7207
CXXC4-WIF1-WNT2 51580 27076 41572 21992 55327 CXXC4-WIF1-WNT2B 39278 29517 3444 42367 49205
BCL9-FGF4-WIF1 11263 34919 2796 10943 15683 FBXW2-WIF1-WNT4 20440 27918 8101 14377 2991
CTBP2-JUN-WIF1 8251 10577 39311 24911 56633 GSK3B-JUN-WIF1 8724 56927 50822 35202 56101
LRP6-TCF7L1-WIF1 48592 41414 27227 22690 3657 NKD1-WIF1-WNT4 20047 23652 20170 17000 48569
AES-FOXN1-WIF1 1100 27353 38089 31438 12357 DAAM1-WIF1-WNT2B 45979 2760 20066 47459 10609
FRAT1-WIF1-WNT4 11715 10008 40620 23391 16427 CSNK1D-FGF4-WIF1 2570 27850 35517 16644 26870
EP300-JUN-WIF1 11523 21819 31185 9903 31253 PYGO1-WIF1-WNT4 30659 11937 27320 45398 3025
FZD8-WIF1-WNT2B 15532 7478 16375 18773 20549 FZD7-WIF1-WNT3A 3521 32340 43606 53450 22727
LRP5-WIF1-WNT2 27791 17603 14834 26995 40760 FRAT1-WIF1-WNT3A 9771 4923 24250 54851 24596
FBXW4-WIF1-WNT2B 27391 4792 20325 52634 39190 FZD1-WIF1-WNT4 42556 11976 32015 44929 41241
FZD2-NKD1-WIF1 45250 38648 56326 24018 7601 FZD1-WIF1-WNT2 38666 2790 24054 10334 47807
FRZB-WIF1-WNT2B 12032 17926 1240 36454 45817 DIXDC1-NKD1-WIF1 44180 9421 57087 48747 10766
FBXW2-JUN-WIF1 46353 25273 18325 14967 6352 TCF7L1-WIF1-WNT5A 19561 51039 4589 44974 51657
FZD5-CTNNBIP1-WIF1 14151 52702 31378 42083 18375 FZD5-WIF1-WNT5A 8783 34105 21011 56941 51881
SFRP4-WIF1-WNT3A 43798 5901 48178 45486 27167 LEF1-WIF1-WNT3 36462 29053 27342 16772 47153
BTRC-NKD1-WIF1 40459 4738 29145 25508 9960 LRP6-PYGO1-WIF1 40589 27373 31407 1058 42246
PPP2R1A-TLE1-WIF1 18734 28938 477 39566 970 TCF7L1-WIF1-WNT2 18637 24345 47332 21762 47245
NLK-WIF1-WNT4 27894 29051 3153 6969 779 KREMEN1-NKD1-WIF1 11200 6413 56333 14493 14792
AES-JUN-WIF1 10120 24212 19751 10267 44412 FRZB-WIF1-WNT4 7084 20245 38285 19795 37188
KREMEN1-WIF1-WNT4 15263 25410 14854 30920 27336 CSNK1G1-WIF1-WNT3A 39224 8471 4045 39840 22187
DKK1-WIF1-WNT4 31737 32517 6740 28018 30494 FRAT1-WIF1-WNT2 9313 6116 22848 25187 25230
FSHB-NKD1-WIF1 24095 15522 18330 7234 28767 CCND3-JUN-WIF1 13838 6148 31656 30680 20733
CSNK1G1-JUN-WIF1 4351 22508 8866 26497 52893 FBXW11-FGF4-WIF1 5724 14852 19141 15691 14573
NLK-WIF1-WNT3A 15025 31663 634 53620 7624 CCND3-NKD1-WIF1 36891 17882 28735 49874 2688
CTNNB1-NLK-WIF1 36869 4645 37317 37303 40718 JUN-WIF1-WNT5A 17879 25683 7574 50125 47128
FOSL1-TLE1-WIF1 31047 3632 40704 50017 52759 CSNK1A1-NLK-WIF1 11282 8274 56968 38447 50254
FZD8-JUN-WIF1 21742 21278 37642 8182 16093 FZD7-NKD1-WIF1 50953 34059 55345 47706 386
AXIN1-FZD2-WIF1 7321 57022 1548 25380 17152 GSK3B-NLK-WIF1 54258 51883 54492 6800 41476
PYGO1-WIF1-WNT5A 42194 2788 21830 11541 35248 SENP2-WIF1-WNT2 32421 15895 24851 26629 35264
PPP2R1A-WIF1-WNT4 26629 52985 27249 6249 3150 CSNK1G1-NLK-WIF1 47859 22704 35817 25257 48817
FBXW11-TLE1-WIF1 14107 27186 19295 24017 3290 CXXC4-NLK-WIF1 37250 20017 55603 45686 50949
SENP2-WIF1-WNT4 21321 27321 19436 29566 8098 BCL9-NLK-WIF1 42377 8645 50877 47640 35234
FBXW11-PYGO1-WIF1 2569 13645 24651 1922 27374 FOSL1-WIF1-WNT2 45340 16844 53312 9456 53004
CTNNB1-T-WIF1 7778 26191 45773 17171 20512 CXXC4-WIF1-WNT4 42891 41168 17267 19696 42795
TCF7L1-WIF1-WNT3 34046 41878 23724 48456 52552 DVL1-JUN-WIF1 26119 22108 34781 31590 19241
FRZB-WIF1-WNT2 36167 6734 39162 17055 44934 DKK1-FGF4-WIF1 3492 49887 7655 5221 44988
FZD6-PORCN-WIF1 480 48176 21990 7324 56972 DKK1-WIF1-WNT2 16362 15213 7425 4997 43739
PPP2CA-WIF1-WNT4 17433 21585 17502 30799 13227 DAAM1-JUN-WIF1 26905 6840 9993 8788 19186
FBXW11-FOXN1-WIF1 419 2385 47172 11148 12509 EP300-FGF4-WIF1 1112 29993 9169 25908 27395
PPP2R1A-WIF1-WNT3A 17742 45653 30117 54996 1436 EP300-TLE1-WIF1 44472 4388 23964 55747 29783
LRP6-NKD1-WIF1 30969 16249 36176 44255 21690 DVL2-WIF1-WNT4 52812 33588 6800 19576 11848
FBXW2-PYGO1-WIF1 7912 12588 25947 9153 9982 PPP2R1A-WIF1-WNT2B 32326 45372 32478 24409 8115
CSNK1D-JUN-WIF1 31036 23659 55667 9066 28938 CXXC4-FRAT1-WIF1 6873 35270 49661 19416 37560
SFRP1-WIF1-WNT2 9718 49056 22258 22488 18176 FOSL1-WIF1-WNT5A 32757 9493 2822 49605 45745
DAAM1-PYGO1-WIF1 3980 697 11295 592 10924 AXIN1-FOXN1-WIF1 2440 40095 51373 27135 13422
LRP5-TLE1-WIF1 34546 9992 6916 37075 13965 FSHB-WIF1-WNT4 55011 29325 3556 5035 26747
Table 2: Rankings o WIF1-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
TLE2-WIF1-WNT3A, TCF7L1-WIF1-WNT3A, CCND1-WIF1-WNT3A, SFRP4-WIF1-
WNT3A, NLK-WIF1-WNT3A, PPP2R1A-WIF1-WNT3A, TLE1-WIF1-WNT3A, CXXC4-
WIF1-WNT3A, NKD1-WIF1-WNT3A, KREMEN1-WIF1-WNT3A, FZD7-WIF1-WNT3A,
8
RANKING @ iUSING SOBOL - 2002
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CTNNBIP1-WIF1-WNT2B 32269 9564 44982 43273 5808 TLE1-WIF1-WNT2B 42718 23842 52893 55585 8492
CCND1-WIF1-WNT2B 53452 50296 53198 44416 331 CTNNBIP1-WIF1-WNT5A 37517 8726 47830 33901 17853
TLE1-WIF1-WNT2 14466 33261 4260 1575 48694 TLE2-WIF1-WNT2B 35013 18233 37906 28769 3346
CTNNBIP1-WIF1-WNT4 19686 48738 9309 23329 39168 NLK-WIF1-WNT2 8017 43046 20756 8948 54881
CCND1-WIF1-WNT4 4841 13848 2511 11475 50379 TLE1-WIF1-WNT3A 50693 6752 56468 57096 11947
CTNNBIP1-WIF1-WNT3A 41974 54167 46904 51223 14244 FOSL1-WIF1-WNT2B 25173 2114 24567 1335 44580
DVL2-JUN-WIF1 15451 4813 8548 10559 52944 NLK-WIF1-WNT2B 49149 14168 36378 48222 2298
FBXW11-WIF1-WNT2B 29590 51803 34137 33592 22138 CTNNBIP1-WIF1-WNT3 15189 2978 10191 5960 42924
TLE1-WIF1-WNT4 24611 48165 2574 1753 54527 TLE1-WIF1-WNT5A 32505 9057 54581 55409 2636
FZD1-WIF1-WNT2B 41197 35896 29093 49255 31536 CCND1-WIF1-WNT2 3711 6976 3951 12662 56830
TLE2-WIF1-WNT3A 33475 13433 36234 29978 9382 CXXC4-WIF1-WNT3A 54553 44801 48557 52030 1570
DKK1-JUN-WIF1 6674 53375 11978 4656 40657 FBXW11-JUN-WIF1 28563 6852 14244 2120 54094
TCF7L1-WIF1-WNT3A 50706 10131 45130 48883 856 NKD1-WIF1-WNT3A 37352 21808 33337 55217 6162
CCND1-WIF1-WNT3A 30286 43921 47521 55757 2241 CCND1-WIF1-WNT5A 52311 43612 54645 45673 6949
TCF7L1-WIF1-WNT4 11430 37104 6438 4338 54134 SLC9A3R1-TLE1-WIF1 49432 25242 42714 39347 50342
CSNK1G1-WIF1-WNT2B 13733 56852 4680 24169 53252 CSNK1G1-WIF1-WNT4 53996 12035 47320 37468 7141
CTNNB1-FRAT1-WIF1 20069 13878 9022 3674 41411 KREMEN1-WIF1-WNT3A 36608 31863 33558 56397 51574
CXXC4-WIF1-WNT2 15365 18609 6335 8974 52925 CXXC4-WIF1-WNT2B 41811 38799 50795 48219 4194
BCL9-FGF4-WIF1 6521 47584 531 5681 51087 FBXW2-WIF1-WNT4 1570 2869 13912 18127 41471
CTBP2-JUN-WIF1 26632 28197 10200 26952 24504 GSK3B-JUN-WIF1 2820 53362 17047 20670 42347
LRP6-TCF7L1-WIF1 46690 44500 38326 52913 1244 NKD1-WIF1-WNT4 27161 54046 639 3320 54064
AES-FOXN1-WIF1 14926 30887 11020 27362 56513 DAAM1-WIF1-WNT2B 51968 9011 43968 43585 1804
FRAT1-WIF1-WNT4 23572 3207 18683 9445 56168 CSNK1D-FGF4-WIF1 34683 24427 28639 39649 25219
EP300-JUN-WIF1 42039 52746 44541 44510 6591 PYGO1-WIF1-WNT4 35126 29183 31527 51724 48035
FZD8-WIF1-WNT2B 56387 21556 34997 44557 31717 FZD7-WIF1-WNT3A 462 1898 24495 17586 7553
LRP5-WIF1-WNT2 26293 46706 8593 21321 39427 FRAT1-WIF1-WNT3A 38203 56268 35949 38506 8834
FBXW4-WIF1-WNT2B 40094 8029 54106 49256 2718 FZD1-WIF1-WNT4 4277 11332 28577 4077 43256
FZD2-NKD1-WIF1 48304 2115 44826 40847 8209 FZD1-WIF1-WNT2 16007 21304 28054 7826 25984
FRZB-WIF1-WNT2B 40472 54680 38479 42695 53648 DIXDC1-NKD1-WIF1 2783 6193 1919 15666 44738
FBXW2-JUN-WIF1 13125 27968 19762 1412 50668 TCF7L1-WIF1-WNT5A 45712 19992 50710 52827 3045
FZD5-CTNNBIP1-WIF1 3612 9589 10637 15392 7584 FZD5-WIF1-WNT5A 46018 34226 43880 48456 34278
SFRP4-WIF1-WNT3A 11286 51732 2804 2874 51088 LEF1-WIF1-WNT3 6586 23760 7555 20182 48604
BTRC-NKD1-WIF1 48449 54705 56221 55648 12202 LRP6-PYGO1-WIF1 44508 17042 34865 29362 9716
PPP2R1A-TLE1-WIF1 45090 23493 53498 33748 24410 TCF7L1-WIF1-WNT2 10773 36458 5086 1330 38184
NLK-WIF1-WNT4 8622 27260 19165 3572 56997 KREMEN1-NKD1-WIF1 41242 46530 54613 56937 13792
AES-JUN-WIF1 15247 17980 7285 26738 54994 FRZB-WIF1-WNT4 19577 3033 23872 23782 7044
KREMEN1-WIF1-WNT4 9057 21375 20526 13352 5900 CSNK1G1-WIF1-WNT3A 3166 45406 9828 19653 50304
DKK1-WIF1-WNT4 11135 42111 15998 24015 43039 FRAT1-WIF1-WNT2 15701 80 23990 2644 43140
FSHB-NKD1-WIF1 8501 17679 24446 9809 47619 CCND3-JUN-WIF1 24199 9395 27874 18876 36923
CSNK1G1-JUN-WIF1 50325 56104 52234 45553 1152 FBXW11-FGF4-WIF1 35293 36422 33789 54132 26098
NLK-WIF1-WNT3A 38872 26733 39808 47467 11370 CCND3-NKD1-WIF1 36042 23837 33038 45243 36980
CTNNB1-NLK-WIF1 27962 27173 4445 7873 33696 JUN-WIF1-WNT5A 11573 40788 5006 2485 37662
FOSL1-TLE1-WIF1 23465 12761 28282 7112 46249 CSNK1A1-NLK-WIF1 32459 19376 28696 36711 12615
FZD8-JUN-WIF1 9234 4498 18346 7363 52993 FZD7-NKD1-WIF1 20117 52838 9275 5598 51615
AXIN1-FZD2-WIF1 52063 20768 50568 49372 8948 GSK3B-NLK-WIF1 48655 42899 46413 40079 20496
PYGO1-WIF1-WNT5A 9422 32695 26276 12872 6210 SENP2-WIF1-WNT2 21618 32250 3233 7633 26426
PPP2R1A-WIF1-WNT4 25703 38532 8212 14678 55797 CSNK1G1-NLK-WIF1 11567 4092 1250 25403 55481
FBXW11-TLE1-WIF1 30644 52535 45101 43945 12232 CXXC4-NLK-WIF1 47523 52787 49697 39912 8695
SENP2-WIF1-WNT4 26805 33663 4825 21788 43902 BCL9-NLK-WIF1 8901 32070 18405 1896 47629
FBXW11-PYGO1-WIF1 25061 37723 9816 10733 38354 FOSL1-WIF1-WNT2 31773 4678 36771 49261 17929
CTNNB1-T-WIF1 21499 29614 11202 15378 31898 CXXC4-WIF1-WNT4 9049 33567 635 7452 53825
TCF7L1-WIF1-WNT3 6465 46841 11999 8295 56290 DVL1-JUN-WIF1 133 39629 17853 21639 41516
FRZB-WIF1-WNT2 16627 2487 18655 14490 3420 DKK1-FGF4-WIF1 46668 45941 37440 39369 52245
FZD6-PORCN-WIF1 158 1040 22006 19159 51608 DKK1-WIF1-WNT2 15360 23242 18889 22471 39072
PPP2CA-WIF1-WNT4 15333 32299 8636 19834 50303 DAAM1-JUN-WIF1 17770 14297 8451 520 24284
FBXW11-FOXN1-WIF1 22524 9008 6699 14880 46642 EP300-FGF4-WIF1 21091 2394 11152 17151 51131
PPP2R1A-WIF1-WNT3A 46290 12066 50238 34915 12432 EP300-TLE1-WIF1 24274 39167 8540 1490 50475
LRP6-NKD1-WIF1 2949 22887 2144 9835 53060 DVL2-WIF1-WNT4 21201 2424 24042 11008 43966
FBXW2-PYGO1-WIF1 23813 40455 7171 7535 53909 PPP2R1A-WIF1-WNT2B 40634 31244 45244 35349 8785
CSNK1D-JUN-WIF1 15080 11320 26129 19806 34275 CXXC4-FRAT1-WIF1 48970 56362 46322 38709 39988
SFRP1-WIF1-WNT2 15158 45628 2995 27504 34635 FOSL1-WIF1-WNT5A 22573 9683 23381 1031 51508
DAAM1-PYGO1-WIF1 14907 56052 14575 20848 37739 AXIN1-FOXN1-WIF1 5961 53853 25598 20239 32508
LRP5-TLE1-WIF1 36205 52063 56337 55035 4521 FSHB-WIF1-WNT4 31734 34663 50353 51787 17129
Table 3: Rankings o WIF1-X-X. A lis o app oxima ely i s 125 combina ions wi h ankings below 10,000
ou o 57,155. SA - SOBOL; Implemen a ion - 2002
FRAT1-WIF1-WNT3A and CSNK1G1-WIF1-WNT3A. Looking a he ables abo e,
one inds he ollowing combina ions o o he membe s o WNT amily, along wi h
WIF1, o be p ominen a 3 d o de le el - CTNNBIP1-WIF1-WNT2B, CCND1-WIF1-
9
