Add essing he needle in a hays ack p oblem in ime
beha iou al s udy o 3 d o de gene 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
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 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 mi-
g 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 WNT 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. 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 syn-
e gis ically. Howe e , he p oblem explodes combina o ially wi h e en a small se o 71
eco ded genes in he abo e s udy, when one s eps o explo e 3 d o de combina ions.
Wi h he o al numbe o C71
3(= 57155) combina ions, i becomes nea ly impossible
o any biologis o s udy he sys em wide dynamics o any pa hway. He e, I •enu-
me a e and ank all C71
3combina ions using ou di e en sensi i i y me hods; •show
he conse ed ankings o PORCN-WNT-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 he combina ions ela ed o WNT3A
esponse genes ha a e anked by he sea ch engine in ime. This s udy demons a es
how biologis s can use he machine lea ning based sea ch engine o add ess he needle
in a hays ack p oblem o disco e ing meaning ul combina ions o highe o de in a as
sea ch o es , which on u he we lab es migh assis in in e ening he pa hway a a
IBeha iou al s udy o 3-od gene 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1Aspec s o unpublished wo k we e p esen ed in a pos e session a Cell Symposia: Technology.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 Feb ua y 26, 2025
combina o ial le el, in ime.
Keywo ds: Sensi i i y analysis, Suppo ec o anking, Hilbe Schmid
Independence C i e ion indices (HSIC) and Sobol indicies, WNT3A
1. In eg a ion, Inno a ion and Insigh
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.
The p oblem explodes combina o ially wi h e en a small se o eco ded genes, when
one s eps o explo e highe (he e 3 d) o de combina ions. Wi h he huge o al numbe
o combina ions, i becomes nea ly impossible o any biologis o s udy he sys em
wide dynamics o any pa hway as well as loca e combina ions o genuine in e es . This
s udy demons a es how biologis s can use a machine lea ning based sea ch engine o
add ess he needle in a hays ack p oblem o disco e ing meaning ul combina ions o
highe o de in a as sea ch o es , while cu ing down he ime equi ed o sea ch he
same. Fu he we lab es migh assis in in e ening he pa hway a a combina o ial
le el, in ime.
2. 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 gene combina ions using indi idual gene exp essions measu ed in
ime, in WNT3A s imula ed HEK 293 cells. 2
3. 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
2Aspec s o unpublished wo k p esen ed as pos e in he Be keley Cell Symposyia : Technology, Biology
& Da a Science, 2016, Be keley, USA
2
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.
3.1. 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.
3.2. 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.
3.3. Wn signaling and sec e ion
Sha ma [4]’s acciden al disco e y o he Wingless played a pionee ing ole in he eme -
gence o a widely expanding esea ch ield o he Wn signaling pa hway. A majo i y
o he wo k has ocused on issues ela ed o • he disco e y o gene ic and epige-
ne ic ac o s a ec ing he pa hway Tho s ensen e al. [5] & Ba on and Kneissel [6],
•implica ions o mu a ions in he pa hway and i s dominan ole on cance and o he
diseases Cle e s [7], •in es iga ion in o he pa hway’s con ibu ion owa ds emb yo
de elopmen Sokol [8], homeos asis Pin o e al. [9] & Zhong e al. [10] and apop o-
sis Pe´
cina-ˇ
Slaus [11] and •sa e y and easibili y o d ug design o he Wn pa hway
3
Kahn [12], Ga be [13], Vo onko and K auss [14], Blagoda ski e al. [15] & Cu in
and Lo enzi [16].
The Wn phenomena can be oughly seg ega ed in o signaling and sec e ion pa .
The Wn signaling pa hway wo ks when he WNT ligand ge s a ached o he F iz-
zled(FZD)/LRP co ecep o complex. FZD may in e ac wi h he Dishe elled (DVL)
causing phospho yla ion. I is also hough ha Wn s cause phospho yla ion o he
LRP ia casein kinase 1 (CK1) and kinase GSK3. These de elopmen s u he lead o
a ac ion o Axin which causes inhibi ion o he o ma ion o he deg ada ion complex.
The deg ada ion complex cons i u es o AXIN, he β-ca enin anspo a ion complex
APC, CK1 and GSK3. When he pa hway is ac i e he dissolu ion o he deg ada ion
complex leads o s abiliza ion in he concen a ion o β-ca enin in he cy oplasm. As
β-ca enin en e s in o he nucleus i displaces he GROUCHO and binds wi h ansc ip-
ion cell ac o TCF hus ins iga ing ansc ip ion o Wn a ge genes. GROUCHO ac s
as lock on TCF and p e en s he ansc ip ion o a ge genes which may induce cance .
In cases when he Wn ligands a e no cap u ed by he co ecep o a he cell memb ane,
AXIN helps in o ma ion o he deg ada ion complex. The deg ada ion complex phos-
pho yla es β-ca enin which is hen ecognised by F BOX/WD epea p o ein β-TRCP.
β-TRCP is a componen o ubiqui in ligase complex ha helps in ubiqui ina ion o
β-ca enin hus ma king i o deg ada ion ia he p o easome.
Con a y o he signaling phenomena, he sec e ion phenomena is abou he e-
lease and anspo a ion o he WNT p o ein/ligand in and ou o he cell, espec i ely.
B ie ly, he WNT p o eins ha a e syn hesized wi h he endoplasmic e iculum (ER),
a e known o be palmi oylea ed ia he Po cupine (PORCN) o o m he WNT ligand,
which is hen eady o anspo a ion. I is belie ed ha hese ligands a e hen ans-
po ed ia he EVI/WNTLESS ansmemb ane complex ou o he cell B¨
anzige e al.
[17] & Ba sche e e al. [18]. The EVI/WNTLESS hemsel es a e known o eside
in he Golgi bodies and in e ac ion wi h he WNT ligands o he la e ’s glycosyla ion
Ku ayoshi e al. [19] & Gao and Hannoush [20]. Once ou side he cell, he WNTs
hen in e ac wi h he cell ecep o s, as explained in he o egoing pa ag aph, o in-
duce he Wn signaling. O impo ance is he ac ha he EVI/WNTLESS also need a
anspo e in he om o a complex e med as Re ome .
4. 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.
5. 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-
4
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 [21]. 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 [21].
6. Design o expe imen
6.1. 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 SV MRank
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
SVMRank
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
5
Sensi i i y me hod Time poin
=1h =3h =6h =12h =24h
HSIC - Linea
01234
HSIClinea − p−1
−3 −2 −1 0
HSIClinea − p−2
01234567
HSIClinea − p−3
0 1 2 3 4 5
HSIClinea − p−4
−4 −3 −2 −1 0
HSIClinea − p−5
HSIC - RBF
01234
HSIC b − p−1
−7 −6 −5 −4 −3 −2 −1 0
HSIC b − p−2
012345
HSIC b − p−3
−4 −3 −2 −1 0
HSIC b − p−4
−4 −3 −2 −1 0 1
HSIC b − p−5
SOBOL - 2002
−1e+05 0e+00 1e+05
SB2002− p−1
−600 −400 −200 0 200 400 600
SB2002− p−2
−6e+05 −4e+05 −2e+05 0e+00 2e+05 4e+05 6e+05
SB2002− p−3
−3e+06 −2e+06 −1e+06 0e+00 1e+06 2e+06 3e+06
SB2002− p−4
−200 −100 0 100 200
SB2002− p−5
SOBOL - ma inez
−4 −3 −2 −1 0 1 2
SBma inez− p−1
−2 0 2 4
SBma inez− p−2
−3 −2 −1 0 1 2 3 4
SBma inez− p−3
−2 −1 0 1 2 3
SBma inez− p−4
−150 −100 −50 0 50
SBma inez− p−5
Table 1: Rows - Sensi i i y me hods; Columns - Time poin s; A g aph shows he anking sco es o combi-
na ions being a anged in descending o de om le o igh .
o de o he gene combina ions based on he anking sco e lea ned by he SVMRank
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. Table 1 shows he anking sco es in discending o de o
3 d o de combina ions using ou di e en sensi i i y me hods (i.e ows) and a i e
di e en ime poin s (i.e columns).
7. Resul s & Discussion
7.1. 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 using 4
di e en sensi i i y indices. Ou o he C71
3combina 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 lib-
6
e 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 .
7.2. Enume a ion and anking o C71
3=57155 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. A pa icula ow ep e-
sen s a pa icula ank gi en by a numbe . Following his, a e combina ions aking up
ha pa icula ank a di e en ime poin s. The 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
[22]) and Sobol indicies (wi h 2002 implemen a ion in Sal elli [23] and ma inez im-
plemen a ion in Ma inez [24] and Baudin e al. [25]). O impo ance o no e is ha
using hese iles, one can see a which p io i y/ anking one wan s o in es iga e and
see wha combina ions a e aking up ha p io i y in ime. Changing combina ions o a
pa icula ank indica e ha a a pa icula poin in ime, a pa icula combina ion migh
be p edominan among o he s.
7.3. Conse ed machine lea ning ankings o es ed PORCN-WNT-
X combina ions
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. [26] 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,
7
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.
Liu e al. [27] 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. [28]. Liu e al. [29] 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. [30] de-
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.
Based on hese expe imen al es s and documen ed li e a u e, he syne gy o PORCN-
WNT can be used o see i he abo e machine lea ning based engine gi es app op ia e
anking o 3 d o de combina ions o PORCN-WNT-X (X, a pa icula gene/p o ein).
I he ankings a e app op ia e, hen we can in e ha he sea ch engine indeed poin s
o combina o ial syne gies, whe he es ed o unexplo ed, a biological le el. Guj al
and MacBea h [1] eco ded he egula ions o PORCN along wi h WNT1, WNT2B,
WNT3A, WNT4 and WNT5A.
He e, I p esen and demons a e he conse a ion o ankings o PORCN-WNT-X
combina ions ac oss di e en sensi i i y me hods. Using he linea ke nel and HSIC
sensi i i y analysis me hod, able 2 shows ankings o combina ions wi hin he i s
10,000 ange (wi h low nume ical alue meaning a e y high p io i y/ ole) mos ly du -
ing he i s phase (o a e = 1 hou o WNT3A s imula ion). These poin o he
possible ole o combina ions du ing he ea ly phase o WNT3A s imula ion. As ime
passes, he ankings o hese combina ions ge lowe anks (i.e hige nume ical alues)
poin ing o hei down play o ole when he e ec o WNT3A s imula ion has subsided
in he la e phase. These 3 d o de syne gies indica e he e icacy o he machine lea n-
ing based sea ch engine in inding meaning ul combina ions ha migh be o in e es
o (de elopmen al)biologis s, molecula biologis s and oncologis s.
A o al o 2415, 3 d o de combina ions in ol ing PROCN we e ob ained om a
ull se o C71
3= 57155 combina ions. Ou o hese 2415 combina ions, hose ela ed o
PORCN-WNT syne gy a e selec ed. 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 3, 4 and 5 show he ankings o he same combina-
ions as in able 2, bu using b ke nel o HSIC, 2002 implemen a ion o SOBOL and
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
CXXC4-PORCN-WNT4 49 6186 19448 20672 51388 PITX2-PORCN-WNT4 177 16891 32175 32123 27627
FZD6-PORCN-WNT2B 379 19259 55786 24330 16739 FZD6-PORCN-WNT4 394 39861 46523 785 6046
FOSL1-PORCN-WNT4 455 37570 20729 10105 38487 PITX2-PORCN-WNT2B 630 42884 44910 50269 15186
FZD5-PORCN-WNT4 646 40380 25866 12816 56710 FOSL1-PORCN-WNT2B 670 19667 46545 40946 19709
KREMEN1-PORCN-WNT4 693 6753 23243 1864 44869 FZD7-PORCN-WNT3A 780 35610 948 25632 12174
DKK1-PORCN-WNT2B 1222 26601 56978 25305 51044 KREMEN1-PORCN-WNT3A 1377 25809 2588 12830 26801
BCL9-PORCN-WNT2B 1394 28608 33398 47599 21197 FZD8-PORCN-WNT4 1416 27491 15836 9789 36903
NLK-PORCN-WNT4 1742 49908 50644 30880 6042 GSK3B-PORCN-WNT4 1893 29701 28162 8296 19073
FRAT1-PORCN-WNT4 1985 2835 18017 16053 23730 FZD6-PORCN-WNT2 2024 30877 41431 1558 29140
FZD5-PORCN-WNT2B 2123 44490 45300 33310 53770 FZD6-PORCN-WNT5A 2165 41983 26329 43017 27185
CCND3-PORCN-WNT5A 2270 38617 15634 39601 37699 CXXC4-PORCN-WNT3 2291 2240 24537 6255 30135
FZD6-PORCN-WNT3A 2394 56979 41510 33895 6602 CSNK1D-PORCN-WNT5A 2899 17376 34214 55252 32946
BCL9-PORCN-WNT2 2978 30124 2987 21306 45043 DKK1-PORCN-WNT3A 3027 51411 42480 14175 39772
EP300-PORCN-WNT4 3047 52212 12666 11882 56673 LRP5-PORCN-WNT5A 3051 25077 6874 53519 30711
FZD8-PORCN-WNT2 3084 38943 6461 12608 17348 CSNK1A1-PORCN-WNT4 3257 26979 26665 9094 28864
DIXDC1-PORCN-WNT2B 3266 11238 38406 37800 51881 CSNK1G1-PORCN-WNT2 3410 20366 30313 12508 34531
FOSL1-PORCN-WNT5A 3631 16428 9587 43895 35656 DAAM1-PORCN-WNT4 3680 47587 5186 9818 24761
FZD1-PORCN-WNT2 3737 14464 10387 26137 31141 EP300-PORCN-WNT2B 3826 37202 48507 42391 54306
DIXDC1-PORCN-WNT5A 3885 26867 8379 47688 52084 FOSL1-PORCN-WNT3A 3900 15019 1518 39920 12124
FZD2-PORCN-WNT3 3994 23668 24913 3556 38793 CSNK1A1-PORCN-WNT2B 4109 24272 43637 30113 14274
BCL9-PORCN-WNT3A 4125 17834 1540 51723 23039 FOSL1-PORCN-WNT2 4144 48973 6608 18938 40921
LEF1-PORCN-WNT3 4220 6502 35317 5065 1556 LRP6-PORCN-WNT2B 4288 11513 52986 43798 7888
CTNNB1-PORCN-WNT2B 4381 41494 54608 33159 44891 FZD5-PORCN-WNT3A 4393 44820 4226 33407 54333
GSK3B-PORCN-WNT2B 4525 24848 40685 28860 9721 FZD2-PORCN-WNT4 4576 26380 31174 13954 52829
FZD5-PORCN-WNT2 4674 42137 9005 17361 56340 EP300-PORCN-WNT5A 4719 30282 10559 49731 55789
FRAT1-PORCN-WNT5A 4744 35332 12577 52285 31329 FRAT1-PORCN-WNT3A 4941 28915 3063 37414 10241
KREMEN1-PORCN-WNT2 4959 36712 10209 2355 46390 CTNNBIP1-PORCN-WNT4 5017 38878 13233 4965 42568
FZD7-PORCN-WNT2 5063 48509 3534 18543 37452 FBXW2-PORCN-WNT5A 5093 9753 1927 56299 23944
CSNK1A1-PORCN-WNT5A 5243 23800 15741 37419 31250 FRZB-PORCN-WNT5A 5316 15372 16217 53391 42789
FZD2-PORCN-WNT2 5319 35217 4925 18448 50496 FZD6-PORCN-WNT3 5539 17206 33991 301 6205
DVL2-PORCN-WNT2B 5842 46277 40915 44683 55710 LEF1-PORCN-WNT4 5938 6340 32575 15016 39684
DIXDC1-PORCN-WNT2 6166 9846 4217 17714 53792 DVL1-PORCN-WNT2B 6171 16317 38040 29254 5289
FBXW11-PORCN-WNT2 6311 39888 7951 33180 19070 CTNNB1-PORCN-WNT5A 6382 34261 18812 36691 51406
DVL1-PORCN-WNT4 6631 47068 9083 4176 6383 FRAT1-PORCN-WNT3 6706 18258 19680 8889 11973
DAAM1-PORCN-WNT5A 6758 49371 3391 50318 25339 FBXW11-PORCN-WNT3 6762 31256 9446 8712 8411
FBXW2-PORCN-WNT2 6905 25689 1063 38513 34061 DVL1-PORCN-WNT2 7032 39563 1823 5185 12571
DKK1-PORCN-WNT3 7165 12201 52957 1425 47839 FSHB-PORCN-WNT4 7187 35341 51879 43751 30960
DIXDC1-PORCN-WNT3A 7226 9557 1088 34837 45504 APC-PORCN-WNT3 7285 26324 14843 5204 12325
CSNK2A1-PORCN-WNT2 7317 28374 7626 21080 31795 DVL2-PORCN-WNT5A 7381 46344 27348 46664 56984
NLK-PORCN-WNT3 7444 40963 56870 11439 3041 GSK3B-PORCN-WNT3A 7574 34492 6475 23367 8516
FRZB-PORCN-WNT3A 7687 8222 4498 44883 17262 CTNNBIP1-PORCN-WNT5A 7693 15781 8108 34940 32551
CSNK1G1-PORCN-WNT3A 7824 36551 31135 32075 7370 FZD7-PORCN-WNT3 7919 50229 13866 3977 19719
FBXW2-PORCN-WNT3A 8007 29570 331 44149 23392 CTNNBIP1-PORCN-WNT3 8175 33782 15052 3217 10272
FZD8-PORCN-WNT3 8198 42890 20340 2880 17514 DVL2-PORCN-WNT3A 8315 32904 22980 44056 50976
PORCN-SFRP1-WNT2B 8374 33217 32367 38609 43781 EP300-PORCN-WNT3 8497 44763 16497 4191 45957
PORCN-SFRP1-WNT5A 8531 30769 38133 56398 46745 CSNK1A1-PORCN-WNT3 8682 9887 21818 2357 12384
LRP5-PORCN-WNT3 8787 10685 15101 51335 9714 FOSL1-PORCN-WNT3 8888 41174 18861 4616 20787
AXIN1-PORCN-WNT4 9013 31986 17718 11205 34131 PORCN-WNT4-WNT5A 9093 21416 44185 36030 52780
FRAT1-PORCN-WNT2 9314 30043 8901 28853 31633 CTNNB1-PORCN-WNT3 9325 40433 31660 954 26533
GSK3B-PORCN-WNT2 9371 40431 15296 6282 27880 AES-PORCN-WNT5A 9395 43267 5747 17185 30918
FRZB-PORCN-WNT3 9560 6430 26600 4539 19524 CTBP1-PORCN-WNT3A 9567 4412 1206 29048 13053
MYC-PORCN-WNT2 9597 42141 37704 21380 33950 DAAM1-PORCN-WNT2 9600 49958 2043 12313 45710
CTNNBIP1-PORCN-WNT2 9847 23180 4750 9800 36378 FGF4-PORCN-WNT2B 9991 29929 44511 25174 44265
Table 2: Rankings o PORCN-WNT-X. SA - HSIC; Ke nel - linea
ma inez implemen a ion o SOBOL, espec i ely. As on 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 syn-
e gy, whe he he combina ion has been es ed o unexplo ed/un es ed. A leas a he
2nd o de , conside ing he combina ions o PORCN-WNT which ha e al eady been
es ablished in we lab expe imen s (in abo e li e a u e), he abula ed combina ions
wi h hei app op ia e anks show he p omise o he machine lea ning sea ch engine in
e ec i ely loca ing he PORCN-WNT combina ions. Fu he , he p esen ed ankings
poin o combina ions o PORCN-WNT-X, i.e he 3 d o de combina ions. So, con-
side ing all o he C71
3combina ions, he machine lea ning sea ch engine quickly anks
9
7.4.6. low densi y lipop o ein ecep o - ela ed p o ein (LRP)
Fo LRP6, he e a e 4 combina ions in ol ing F-box and WD epea domain con aining
11 (FBXW11) wi h LRP6. This depic s he possible syne gy be ween LRP6-FBXW11
ha need o explo ed. Wang e al. [42] s a e ha upon ac i a ion o he pa hway by he
binding o Wn ligand o F izzled and LRP5LRP6 ecep o s, he axin complex is in-
hibi ed and esul s in he accumula ion o soluble β-ca enin ha can en e he nucleus,
whe e i in e ac s wi h ansc ip ion ac o s o he TCF/LEF1 amily o egula e a se ies
o a ge genes. I is assumed ha APC helps phospho yla ed β-ca enin o dissocia e
om AXIN, c ea ing a ca aly ic cycle o binding and elease o he subs a e. O h-
e s ha e sugges ed ha APC ac s ei he ups eam o he phospho yla ion eac ions, by
anspo ing β-ca enin o he complex o downs eam o he phospho yla ion eac ions,
by ec ui ing he ubiqui in ligase bT CP (FBXW11) o he complex. Hol e al. [43]
obse e ha FBXW11 a ge s include β-ca enin, key media o o WNT signaling, c i -
ical o digi al, neu ological, and eye de elopmen . The e migh be an indi ec syne gy
be ween LRP6-FBXW11. Guj al and MacBea h [1], LRP6 was ound o be up egu-
la ed (+i e numbe s), along wi h FBXW11. The sea ch engine con i ms he possible
exis ence o he biological syne gy be ween he abo e componen s by poin ing ou 3 d
o de combina ions in ol ing LRP6-FBXW11 in e ac ion.
7.4.7. C- e minal binding p o ein (CTBP)
Fo CTBP1, he e a e 6 combina ions in ol ing ib oblas g ow h ac o 4 (FGF4)
wi h CTBP1. Fo CTBP2, he e a e 5 combina ions in ol ing ca enin β1 (CTNNB1)
wi h CTBP2. This depic s he possible syne gy be ween CTBP1-FGF4 and CTBP2-
CTNNB1 ha need o explo ed. Wang e al. [42] obse e ha du ing he epi helialmes-
enchymal ansi ion (EMT) p ocess, TGFβinduced iso o m swi ching o FGF ecep-
o s, causing he cells o become sensi i e o FGF2. Addi ion o FGF2 o TGFβ- ea ed
cells pe u bed EMyoT by eac i a ing he MEK-E k pa hway and subsequen ly en-
hanced EMT h ough he o ma ion o MEK-E k-dependen complexes o he an-
sc ip ion ac o δEF1/ZEB1 wi h he ansc ip ional co ep esso CTBP1. Kim e al.
[44] demons a e ha CTBP2 associa es wi h majo componen s o he β-ca enin (CTNNB1)
des uc ion complex and limi s he accessibili y o β-ca enin o co e ansc ip ion ac-
o s in undi e en ia ed emb yonic s em cells (ESCs). Thus he syne gies be ween he
componen s ha e been es ablished. Guj al and MacBea h [1], CTBP-1/2 and CTNNB1
we e ound o be up egula ed (+i e numbe s), while FGF4 was down egula ed o a
majo pe iod o ime (apa om being up egula ed). The sea ch engine con i ms he
possible exis ence o he biological syne gy be ween he abo e componen s by poin -
ing ou 3 d o de combina ions in ol ing CTBP1-FGF4 and CTBP2-CTNNB1 in e -
ac ions.
7.4.8. cyclin D (CCND)
Fo CCND1, he e a e 7 combina ions in ol ing ib oblas g ow h ac o 4 (FGF4) wi h
CCND1. Fo CCND-2/3, he e a e 4 combina ions each in ol ing izzled class ecep-
o 5 (FZD5) wi h CCND-1/2. This depic s he possible syne gy be ween CCND1-
FGF4 and CCND-1/2-FZD5 ha need o explo ed. Bao e al. [45] show ha CCND1
16
co-localizes wi h FGF3, FGF4, and FGF19 a ch omosome loca ion 11q13. B and
e al. [46] show ha exp ession le els o p e iously desc ibed endo helial a ge genes
o β-ca enin we e s udied using qPCR, bu no di e ences was obse ed in he exp es-
sion o CCND1 a e knockdown o FZD5. Bu his migh no be he case wi h CCND-
2/3. Guj al and MacBea h [1], CCND-1/2/3 was ound o be up egula ed (+i e num-
be s) along wi h FGF4, while FZD5 was ound o be down egula ed (−i e numbe s).
The sea ch engine con i ms he possible exis ence o he biological syne gy be ween
he abo e componen s by poin ing ou 3 d o de combina ions in ol ing CCND1-FGF4
and CCND-2/3-FZD5 in e ac ions.
7.4.9. Wn amily membe (WNT)
One peculia i y ha we can ind in he able unde he i le o WNT1 is ha he machine
poin s o syne gis ic combina ions o WNT1 wi h o he amilies o WNT. This pa e n
eme ged in all he op 10 anked combina ions. I migh be o in e es o in es iga e
whe he WNT1 wo ks in andem wi h o he WNT amily membe s, as i one obse es
in he o he columns such beha iou is no obse ed.
8. Conclusion
This s udy demons a es how biologis s can use he machine lea ning based sea ch
engine o add ess he needle in a hays ack p oblem o disco e ing meaning ul com-
bina ions o highe o de in a as sea ch o es , which on u he we lab es migh
assis in in e ening he pa hway a a combina o ial le el, in ime. The p oblem ex-
plodes combina o ially wi h e en a small se o eco ded genes in he abo e s udy,
when one s eps o explo e 3 d o de combina ions. Wi h he o al numbe o C71
3(=
57155) combina ions in his s udy, i becomes nea ly impossible o any biologis o
s udy he sys em wide dynamics o any pa hway. The manusc ip add esses hese is-
sues by enume a ing and anking a huge lis o 3 d o de combina ions, demons a ing
conse ed machine lea ning ankings o we lab es ablished combina ions ac oss he
di e en sensi i i y me hods used and p esen ing some o he pa e ns in he beha iou
o some o he es ablished combina ions ela ed o WNT3A esponse genes. In sum-
ma y, he wo k p esen s a solu ion o he undamen al needle in a hays ack p oblem
o loca ing highe o de gene combina ions in a as sea ch o es , ia use o powe ul
machine lea ning based sea ch engine. Use o his engine is bound o assis many biolo-
gis s/oncologis s in sea ch o meaning ul highe o de gene combina ions ha wo k in
cell biology and make po en ial disco e ies necessa y o ad ancemen in he s udy o
cell/de elopmen al biology as well as de elopemen o he apeu ics in diseased cells.
Compe ing in e es s
No compe ing in e es is decla ed.
17
WNT3 s imula ed esponse genes
Response gene amily Gene amily membe 3 d o de combina ions
adenoma osis polyposis coli APC-PITX2-SFRP4 APC-FZD6-SENP2 APC-PITX2-SENP2 APC-DIXDC1-WNT2B APC-PITX2-TCF7 APC-FZD6-TLE2
(APC) egula o o WNT signaling pa hway APC-FZD2-TCF7L1 APC-PITX2-PPP2CA APC-PORCN-SENP2 APC-PITX2-WNT4
-myc a ian myelocy oma osis CSNK2A1-MYC-SENP2 CSNK2A1-MYC-SFRP4 AES-AXIN1-MYC CSNK2A1-MYC-TCF7L1 FRZB-MYC-SENP2 CSNK2A1-MYC-PPP2CA
i al oncogene homolog (MYC) DKK1-MYC-SENP2 FZD5-MYC-SENP2 CSNK2A1-MYC-WNT4 DVL1-MYC-SENP2
izzled class ecep o (FZD) FZD1 FZD2 FZD5 FZD6 FZD7 FZD8
FZD1-NLK-SENP2 FSHB-FZD2-SENP2 FZD5-JUN-WNT2 APC-FZD6-FZD8 FZD7-NKD1-SENP2 FZD8-FBXW4-WNT3A
AES-AXIN1-FZD1 FSHB-FZD2-WNT4 FZD5-JUN-FBXW4 APC-FZD6-TLE2 CXXC4-FZD7-PPP2CA AES-AXIN1-FZD8
DVL1-FRZB-FZD1 FSHB-FZD2-FZD7 FZD5-CCND2-FBXW11 AES-AXIN1-FZD6 FZD7-PPP2CA-SFRP4 FZD8-LRP6-RHOU
FZD1-FZD7-PPP2CA FSHB-FZD2-KREMEN1 FZD5-CCND2-SENP2 FZD6-PORCN-WNT2B CXXC4-FZD7-SFRP4 FZD8-PORCN-SFRP1
FZD1-FZD7-SFRP4 DKK1-FZD2-LRP5 FZD5-CCND2-FRZB FZD6-PORCN-WNT4 FZD1-FZD7-PPP2CA DIXDC1-FOXN1-FZD8
AES-EP300-FZD1 APC-FZD2-TCF7L1 FZD5-CCND3-SENP2 FZD6-GSK3A-WNT2 FZD1-FZD7-SFRP4 FZD8-PORCN-SENP2
DKK1-DVL2-FZD1 FSHB-FZD2-TLE2 FZD5-JUN-WNT5A CCND1-CTBP1-FZD6 FZD7-PORCN-SENP2 CXXC4-FRAT1-FZD8
CXXC4-FRAT1-FZD1 FSHB-FZD2-LRP5 FZD5-PITX2-SENP2 FZD6-PORCN-TLE2 CSNK1D-FGF4-FZD7 BTRC-FOXN1-FZD8
DVL1-EP300-FZD1 FRZB-FZD2-SENP2 FZD5-CCND2-DKK1 FZD6-PORCN-SENP2 FSHB-FZD2-FZD7 FZD8-LRP6-TCF7
FRAT1-FZD1-SFRP4 FSHB-FZD2-SFRP4 FZD5-MYC-SENP2 FZD6-PORCN-SFRP1 FZD7-PORCN-FBXW4 FZD8-GSK3A-KREMEN1
glycogen syn hase kinase 3 (GSK3) GSK3A GSK3B
FRZB-GSK3A-SENP2 CSNK1D-FGF4-GSK3B
FRZB-GSK3A-PPP2R1A FBXW11-GSK3B-WNT2B
DKK1-GSK3A-LRP5 FOSL1-FOXN1-GSK3B
FZD6-GSK3A-WNT2 GSK3B-LRP6-SLC9A3R1
BTRC-GSK3A-T CTBP2-GSK3B-RHOU
FRZB-GSK3A-LRP5 CSNK1G1-GSK3B-SLC9A3R1
FZD5-GSK3A-SENP2 GSK3B-RHOU-SENP2
DKK1-GSK3A-WNT2B FSHB-FZD2-GSK3B
BTRC-GSK3A-NLK GSK3B-JUN-TLE1
CSNK1D-GSK3A-LEF1 CTBP1-FGF4-GSK3B
dishe elled segmen
pola i y p o ein (DVL) DVL1 DVL2
DVL1-EP300-FRZB DKK1-DVL2-SENP2
AXIN1-DVL1-FBXW2 DKK1-DVL2-FRZB
AXIN1-DVL1-FBXW11 DVL2-JUN-FBXW4
DVL1-FRZB-FZD1 DKK1-DVL2-FZD1
DVL1-EP300-GSK3B DVL2-JUN-WNT3A
DVL1-EP300-WNT2B DVL2-JUN-WNT2B
DVL1-FBXW11-SLC9A3R1 CXXC4-DVL2-FRZB
DVL1-EP300-WNT4 DKK1-DVL2-FBXW11
AXIN1-DVL1-RHOU DVL2-JUN-TCF7
DVL1-EP300-FZD1 FZD5-DVL2-FRZB
low densi y lipop o ein ecep o
ela ed p o ein (LRP) LRP5 LRP6
DVL1-EP300-LRP5 FBXW11-LRP6-SENP2
DKK1-JUN-LRP5 FBXW11-LRP6-TCF7
LRP5-NLK-WNT4 FBXW11-LRP6-SLC9A3R1
FOXN1-KREMEN1-LRP5 LRP6-TCF7-WNT2B
DKK1-FZD2-LRP5 FBXW11-LRP6-SFRP4
FZD5-FOXN1-LRP5 DKK1-LRP6-SENP2
FSHB-FZD2-LRP5 DAAM1-LRP6-SENP2
DKK1-GSK3A-LRP5 CCND2-LRP6-RHOU
LRP5-SFRP1-WNT2B DAAM1-LRP6-SLC9A3R1
FRZB-GSK3A-LRP5 CCND2-LRP6-TCF7
C- e minal binding p o ein (CTBP) CTBP1 CTBP2
CCND1-CTBP1-KREMEN1 CTBP2-CTNNB1-FOSL1
CSNK2A1-CTBP1-PPP2R1A CTBP2-CTNNB1-WNT4
CCND1-CTBP1-FZD6 CTBP2-T-TLE2
CTBP1-FGF4-FBXW4 CTBP2-FOXN1-SENP2
CTBP1-FGF4-FZD1 CTBP2-CTNNB1-FBXW4
CTBP1-FGF4-WNT5A CTBP2-CTNNB1-TLE1
CTBP1-GSK3A-PPP2CA CTBP2-CTNNB1-WNT2B
CTBP1-FGF4-TCF7L1 CTBP2-T-WNT2B
CTBP1-FGF4-FRZB CTBP2-GSK3B-RHOU
CTBP1-FGF4-RHOU CSNK1A1-CTBP2-KREMEN1
cyclin D (CCND) CCND1 CCND2 CCND3
CCND1-FGF4-GSK3B CCND2-LRP6-SENP2 CCND3-PORCN-WNT4
CCND1-FGF4-RHOU FZD5-CCND2-FBXW11 CCND3-PORCN-FBXW4
CCND1-WIF1-WNT2B FZD5-CCND2-SENP2 FZD5-CCND3-SENP2
CCND1-FGF4-SFRP1 FZD5-CCND2-FRZB FZD5-CCND3-FRZB
CCND1-FGF4-WNT5A CCND2-LRP6-RHOU AES-AXIN1-CCND3
CCND1-FGF4-FOSL1 CCND2-FBXW11-SLC9A3R1 CCND3-WNT1-WNT4
CCND1-PYGO1-WNT2 CCND2-LRP6-TCF7 CCND3-PORCN-SFRP1
CCND1-FGF4-FBXW4 FZD5-CCND2-DKK1 CCND3-PORCN-TLE2
CCND1-FGF4-PPP2R1A CCND2-LRP6-FBXW4 FZD5-CCND3-CSNK1D
CCND1-CTBP1-KREMEN1 CCND2-WNT1-WNT4 FZD5-CCND3-SFRP4
Wn amily membe (WNT) WNT1 WNT2B WNT3A WNT4 WNT5A
TLE2-WNT1-WNT2B CTNNBIP1-WIF1-WNT2B CSNK1D-FGF4-WNT3A CXXC4-PORCN-WNT4 CSNK1D-FGF4-WNT5A
AXIN1-WNT1-WNT4 AES-AXIN1-WNT2B FZD8-FBXW4-WNT3A CSNK1D-FGF4-WNT4 FSHB-T-WNT5A
AXIN1-WNT1-WNT2 LRP6-TCF7-WNT2B DKK1-JUN-WNT3A LRP5-NLK-WNT4 CTNNBIP1-WIF1-WNT5A
CCND2-WNT1-WNT4 CXXC4-PORCN-WNT2B AES-AXIN1-WNT3A PITX2-PORCN-WNT4 CCND1-FGF4-WNT5A
TLE1-WNT1-WNT2B TLE1-WIF1-WNT2B DVL2-JUN-WNT3A FSHB-FZD2-WNT4 FZD5-JUN-WNT5A
TCF7L1-WNT1-WNT2B CCND1-WIF1-WNT2B CCND1-FGF4-WNT3A AXIN1-WNT1-WNT4 CCND2-LRP6-WNT5A
CCND2-WNT1-WNT5A APC-DIXDC1-WNT2B FBXW2-WNT3A-WNT4 DVL1-EP300-WNT4 PITX2-PORCN-WNT5A
TCF7L1-WNT1-WNT4 FBXW11-LRP6-WNT2B JUN-PYGO1-WNT3A FSHB-T-WNT4 CXXC4-PORCN-WNT5A
TLE1-WNT1-WNT4 FZD7-NKD1-WNT2B CTNNBIP1-WIF1-WNT3A APC-PORCN-WNT4 LEF1-T-WNT5A
AXIN1-WNT1-WNT3 TLE2-WIF1-WNT2B PPP2CA-WNT1-WNT3A DKK1-JUN-WNT4 CXXC4-PORCN-WNT5A
Table 6: Top 10 3 d o de combina ions wi h conse ed machine lea ning ankings o WNT3 s imula ed
esponse genes, ac oss di e en sensi i i y indices.
Au ho con ibu ions s a emen
SS concei ed and designed he expe imen s; w o e he code; pe o med he expe i-
men s; analyzed he da a; w o e he manusc ip .
18
A ailabili y o code
Code o ime se ies da a a ailable a CERN based Zenodo on h ps://zenodo.o g/
eco ds/14637456.
Acknowledgmen s
Special hanks o M s. Ri a Sinha and la e M . P abha Sinha o suppo ing he au ho
inancially, wi hou which his wo k could no ha e been made possible.
Supplemen a y
The ollowing iles (ending wi h .R and can be opened in R o in simple ex p ocessing
p og am) wi h hese names a e made a ailable wi h his manusc ip . (1) HSIClinea -
TP-Choose-3-NSc-D.R, (2) HSIC b -TP-Choose-3-NSc-D.R, (3) SB2002-TP-Choose-
3-NSc-D.R, and (4) SBma inez-TP-Choose-3-NSc-D.R, con ain ankings o 3 d o -
de combina ions ac oss each ime poin o , HSIC (linea ke nel), HSIC ( b ke nel),
SOBOL (2002 implemen a ion) and SOBOL (ma inez implemen a ion), espec i ely.
Re e ences
[1] T. S. Guj al, G. MacBea h, A sys em-wide in es iga ion o he dynamics o wn signaling e eals no el phases o
ansc ip ional egula ion, PloS one 5 (2010) e10024.
[2] S. Sinha, Machine lea ning anking o plausible (un) explo ed syne gis ic gene combina ions using sensi i i y indices
o ime se ies measu emen s o wn signaling pa hway, In eg a i e Biology 16 (2024) zyae020.
[3] T. Joachims, T aining linea s ms in linea ime, in: P oceedings o he 12 h ACM SIGKDD in e na ional con e ence
on Knowledge disco e y and da a mining, ACM, 2006, pp. 217–226.
[4] R. Sha ma, Wingless a new mu an in d osophila melanogas e , D osophila in o ma ion se ice 50 (1973) 134–134.
[5] L. Tho s ensen, G. E. Lind, T. Lø ig, C. B. Diep, G. I. Meling, T. O. Rognum, R. A. Lo he, Gene ic and epigene ic
changes o componen s a ec ing he wn pa hway in colo ec al ca cinomas s a i ied by mic osa elli e ins abili y,
Neoplasia 7 (2005) 99–108.
[6] R. Ba on, M. Kneissel, Wn signaling in bone homeos asis and disease: om human mu a ions o ea men s, Na u e
medicine 19 (2013) 179–192.
[7] H. Cle e s, Wn /[β]-ca enin signaling in de elopmen and disease, Cell 127 (2006) 469–480.
[8] S. Sokol, Wn Signaling in Emb yonic De elopmen , olume 17, Else ie , 2011.
[9] D. Pin o, A. G ego ie , H. Beg hel, H. Cle e s, Canonical wn signals a e essen ial o homeos asis o he in es inal
epi helium, Genes & de elopmen 17 (2003) 1709–1713.
[10] Z. Zhong, N. J. E hen, B. O. Williams, Wn signaling in bone de elopmen and homeos asis, Wiley In e disciplina y
Re iews: De elopmen al Biology 3 (2014) 489–500.
[11] N. Pe´
cina-ˇ
Slaus, Wn signal ansduc ion pa hway and apop osis: a e iew, Cance Cell In e na ional 10 (2010) 1–5.
[12] M. Kahn, Can we sa ely a ge he wn pa hway?, Na u e Re iews D ug Disco e y 13 (2014) 513–532.
19
[13] K. Ga be , D ugging he wn pa hway: p oblems and p og ess, Jou nal o he Na ional Cance Ins i u e 101 (2009)
548–550.
[14] A. Vo onko , S. K auss, Wn /be a-ca enin signaling and small molecule inhibi o s, Cu en pha maceu ical design
19 (2012) 634.
[15] A. Blagoda ski, D. Po e yae , V. Ka anae , Ta ge ing he wn pa hways o he apies, Mol Cell The 2 (2014) 28.
[16] J. C. Cu in, M. V. Lo enzi, D ug disco e y app oaches o a ge wn signaling in cance s em cells, Onco a ge 1
(2010) 552.
[17] C. B¨
anzige , D. Soldini, C. Sch¨
u , P. Zippe len, G. Hausmann, K. Basle , Wn less, a conse ed memb ane p o ein
dedica ed o he sec e ion o wn p o eins om signaling cells, Cell 125 (2006) 509–522.
[18] K. Ba sche e , N. Pel e, D. Ingel inge , M. Bou os, Sec e ion o wn ligands equi es e i, a conse ed ansmem-
b ane p o ein, Cell 125 (2006) 523–533.
[19] M. Ku ayoshi, H. Yamamo o, S. Izumi, A. Kikuchi, Pos - ansla ional palmi oyla ion and glycosyla ion o wn -5a
a e necessa y o i s signalling, Biochemical Jou nal 402 (2007) 515–523.
[20] X. Gao, R. N. Hannoush, Single-cell imaging o wn palmi oyla ion by he acyl ans e ase po cupine, Na u e
chemical biology 10 (2014) 61–68.
[21] S. Sinha, Hilbe -schmid and sobol sensi i i y indices o s a ic and ime se ies wn signaling measu emen s in
colo ec al cance -pa a, BMC sys ems biology 11 (2017) 120.
[22] S. Da Veiga, Global sensi i i y analysis wi h dependence measu es, Jou nal o S a is ical Compu a ion and Simula-
ion 85 (2015) 1283–1305.
[23] A. Sal elli, Making bes use o model e alua ions o compu e sensi i i y indices, Compu e physics communica ions
145 (2002) 280–297.
[24] J. Ma inez, Analyse de sensibili e globale pa decomposi ion de la a iance, P esen a ion in Jou n´
ee des GdR
Ondes & Masco 13 (2011) 207.
[25] M. Baudin, K. Boumhaou , T. Delage, B. Iooss, J.-M. Ma inez, Nume ical s abili y o sobolindices es ima ion
o mula, in: P oceedings o he 8 h In e na ional Con e ence on Sensi i i y Analysis o Model Ou pu (SAMO
2016), olume 30, 2016, pp. 50–51.
[26] K. Tanaka, K. Okabayashi, M. Asashima, N. Pe imon, T. Kadowaki, The e olu iona ily conse ed po cupine gene
amily is in ol ed in he p ocessing o he wn amily, Eu opean Jou nal o Biochemis y 267 (2000) 4300–4311.
[27] J. Liu, Q. Xiao, J. Xiao, C. Niu, Y. Li, X. Zhang, Z. Zhou, G. Shu, G. Yin, Wn /β-ca enin signalling: unc ion,
biological mechanisms, and he apeu ic oppo uni ies, Signal ansduc ion and a ge ed he apy 7 (2022) 3.
[28] K. Wille , J. D. B own, E. Danenbe g, A. W. Duncan, I. L. Weissman, T. Reya, J. R. Ya es III, R. Nusse, Wn
p o eins a e lipid-modi ied and can ac as s em cell g ow h ac o s, Na u e 423 (2003) 448–452.
[29] J. Liu, S. Pan, M. H. Hsieh, N. Ng, F. Sun, T. Wang, S. Kasibha la, A. G. Schulle , A. G. Li, D. Cheng, e al.,
Ta ge ing wn -d i en cance h ough he inhibi ion o po cupine by lgk974, P oceedings o he Na ional Academy
o Sciences 110 (2013) 20224–20229.
[30] B. Madan, Z. Ke, N. Ha ms on, S. Y. Ho, A. F ois, J. Alam, D. A. Jeya aj, V. Pendha ka , K. Ghosh, I. H. Vi shup,
e al., Wn addic ion o gene ically de ined cance s e e sed by po cn inhibi ion, Oncogene 35 (2016) 2197–2207.
[31] P. D. McC ea, C. W. Tu ck, B. Gumbine , A homolog o he a madillo p o ein in d osophila (plakoglobin) associa ed
wi h e-cadhe in, Science 254 (1991) 1359–1361.
[32] M. Pei e , C. Rauskolb, M. Williams, B. Riggleman, E. Wieschaus, The segmen pola i y gene a madillo in e ac s
wi h he wingless signaling pa hway in bo h emb yonic and adul pa e n o ma ion, De elopmen 111 (1991)
1029–1043.
[33] R. Kemle , F om cadhe ins o ca enins: cy oplasmic p o ein in e ac ions and egula ion o cell adhesion, T ends in
Gene ics 9 (1993) 317–321.
20
[34] M. Ku aguchi, X.-P. Wang, R. T. B onson, R. Ro henbe g, N. Y. Ohene-Baah, J. J. Lund, M. Kuche lapa i, R. L.
Maas, R. Kuche lapa i, Adenoma ous polyposis coli (apc) is equi ed o no mal de elopmen o skin and hymus,
PLoS gene ics 2 (2006) e146.
[35] X.-P. Wang, D. J. O’Connell, J. J. Lund, I. Saadi, M. Ku aguchi, A. Tu be-Doan, R. Ca allesco, H. Kim, P. J. Pa k,
H. Ha ada, e al., Apc inhibi ion o wn signaling egula es supe nume a y oo h o ma ion du ing emb yogenesis
and h oughou adul hood (2009).
[36] B. Yang, J. Zhang, J. Wang, W. Fan, L. Ba bie -To es, X. Yang, M. A. R. Jus o, T. Liu, Y. Chen, J. S egge da, e al.,
Csnk2a1-media ed max phospho yla ion up egula es hmgb1 and il-6 exp ession in cholangioca cinoma p og ession,
Hepa ology Communica ions 7 (2023) e00144.
[37] X.-X. Sun, Y. Chen, Y. Su, X. Wang, K. M. Chauhan, J. Liang, C. J. Daniel, R. C. Sea s, M.-S. Dai, Sumo p o ease
senp1 desumoyla es and s abilizes c-myc, P oceedings o he Na ional Academy o Sciences 115 (2018) 10983–
10988.
[38] S. R. Ghimi e, M. R. Deans, F izzled3 and izzled6 coope a e wi h angl2 o di ec cochlea inne a ion by ype ii
spi al ganglion neu ons, Jou nal o Neu oscience 39 (2019) 8013–8023.
[39] O. Jaka, L. Casas-F aile, M. Azpi a e, A. Aias ui, A. L. De Munain, A. Saenz, F zb and melusin, o e exp essed
in lgmd2a, egula e in eg in β1d iso o m eplacemen al e ing myoblas usion and he in eg in-signalling pa hway,
Expe Re iews in Molecula Medicine 19 (2017) e2.
[40] Z. Zhong, N. Ha ms on, K. C. Wood, B. Madan, D. M. Vi shup, e al., A p300/ga a6 axis de e mines di e en ia ion
and wn dependency in panc ea ic cance models, The Jou nal o Clinical In es iga ion 132 (2022).
[41] X.-q. Gan, J.-y. Wang, Y. Xi, Z.-l. Wu, Y.-p. Li, L. Li, Nuclea d l, c-jun, β-ca enin, and c o m a complex leading
o s abiliza ion o β-ca enin– c in e ac ion, The Jou nal o cell biology 180 (2008) 1087–1100.
[42] L. Wang, X. Liu, E. Guse , C. Wang, F. Fago o, Regula ion o he phospho yla ion and nuclea impo and expo
o β-ca enin by apc and i s cance - ela ed unca ed o m, Jou nal o cell science 127 (2014) 1647–1659.
[43] R. J. Hol , R. M. Young, B. C espo, F. Ce oni, C. J. Cu y, E. Bellacchio, D. A. Bax, A. Ciol i, M. Simon, C. R.
Fage be g, e al., De no o missense a ian s in bxw11 cause di e se de elopmen al pheno ypes including b ain,
eye, and digi anomalies, The Ame ican Jou nal o Human Gene ics 105 (2019) 640–657.
[44] T. W. Kim, S. Kwak, J. Shin, B.-H. Kang, S.-E. Lee, M. Y. Suh, J.-H. Kim, I.-Y. Hwang, J.-H. Lee, J. Choi, e al.,
C bp2-media ed β-ca enin egula ion is equi ed o exi om plu ipo ency, Expe imen al & molecula medicine 49
(2017) e385–e385.
[45] Y. Bao, J. Gab ielpillai, J. Die ich, R. Za bl, S. S ie h, F. Sch ¨
ock, D. Die ich, Fib oblas g ow h ac o ( g ), g
ecep o ( g ), and cyclin d1 (ccnd1) dna me hyla ion in head and neck squamous cell ca cinomas is associa ed wi h
ansc ip ional ac i i y, gene ampli ica ion, human papilloma i us (hp ) s a us, and sensi i i y o y osine kinase
inhibi o s, Clinical Epigene ics 13 (2021) 1–18.
[46] M. M. B and , C. G. Van Dijk, I. Ch i i, H. M. Kool, P. E. B¨
u gisse , L. Louzao-Ma inez, J. Pei, R. J. Ro ie , M. C.
Ve haa , D. J. Duncke , e al., Endo helial loss o zd5 s imula es pkc/e s1-media ed ansc ip ion o angp 2 and l 1,
Angiogenesis 21 (2018) 805–821.
21
