NKD inhibi o o WNT signaling pa hway 1 / naked cu icle
homolog 1 (NKD1) : 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
NKD1 is a membe o naked cu icle (NKD) amily ha inhibi s he WNT signaling
pa hway, by binding o Dishe elled (DVL) amily o p o eins. 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 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 ecog-
nized 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 es-
sion measu emen s a e singula in na u e. He e, I •enume a e and ank all 2415 NKD1
ela ed 3 d o de combina ions in a o es o 71C3combina ions using ou di e en sen-
si i i y me hods; •show he conse ed ankings o NKD1-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 en-
gine (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 NKD1 comb. in WNT3A s imula ed cells
1Aspec s o unpublished wo k we e p esen ed in a pos e session a Cell Symposia: Technology. Biology.
Da a Science, 9-11 Oc obe 2016, Be keley, Cali o nia, USA.
P ep in submi ed o P ep in Ma ch 2, 2025
1. Signi icance
Sinha [2] ecen ly demons a ed he use o machine lea ning based sea ch engine o
ank/ e eal gene combina ions a 2nd o de o he ime se ies da a by Guj al and
MacBea h [1] and showed how i is possible o loca e combina ions o p io i y ha
migh be wo king syne gis ically, using sensi i i y me hods and powe ul suppo ec-
o anking algo i hm. Howe e , he p oblem explodes combina o ially wi h e en a
small se o 71 eco ded genes in he s udy by Guj al and MacBea h [1], when one
s eps o explo e 3 d o de combina ions. Wi h he o al numbe o 71C3(= 57155) com-
bina ions, i becomes nea ly impossible o any biologis o s udy he sys em wide dy-
namics o any pa hway. Also, he amoun o ime usually needed o sea ch o and es
a combina ion is a mo e han he sea ch down by he machine lea ning based sea ch
engine. He e, I ex end he esea ch wo k by Sinha [2] o conduc a beha io al s udy o
3 d o de NKD1 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. 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. NKD inhibi o o WNT signaling pa hway 1 / naked cu icle ho-
molog 1 (NKD1)
Naked cu icle (NKD) is a conse ed amily o in acellula p o eins encoded in mos
animal genomes, he o iginal mu an s o which we e disco e ed by 1995 Nobel lau e-
a es Ch is iane Nusslein-Volha d and E ic F. Wieschaus and colleagues in hei gene ic
sc eens o pa e n- o ma ion mu an s in D osophila melanogas e Ju gens e al. [4].
Du ing animal de elopmen , cells ha e o espond app op ia ely o localized sec e ed
signals and WNT signals ha e been ound o be c ucial in de elopmen and neopla-
sia. Zeng e al. [5] show ha NKD, a D osophila segmen -pola i y gene, encodes an
inducible an agonis o he WNT signal Wingless (WG). In ly emb yos and imaginal
discs nkd ansc ip ion is induced by WG while, o e p oduc ion o NKD in D osophila
and misexp ession o NKD in he e eb a e Xenopus lae is, esul in pheno ypes e-
sembling hose o loss o WG/Wn unc ion. Using ec opic exp ession, Rousse e al.
[6] ound ha NKD a ec ed, in a cell-au onomous manne , a ansduc ion s ep be ween
he WNT signaling componen s D osophila Dishe elled (DSH) and Zes e-whi e 3 ki-
nase (ZW3). Thei esul s showed ha NKD ac ed di ec ly h ough DSH o limi WG
ac i i y and de e mined how e icien ly WNT signals s abilized A madillo (A m)/β-
ca enin and ac i a ed downs eam genes.
In he ui ly D osophila, emb yos de ec i e in signaling media ed by he WNT
p o ein Wingless (WG) exhibi se e e segmen a ion de ec s. The D osophila segmen
pola i y gene NKD encodes an EF hand p o ein ha egula es ea ly WG ac i i y by
ac ing as an inducible an agonis . NKD an agonizes WG ia a di ec in e ac ion wi h
he Wn signaling componen D osophila Dishe elled (DSH). Wha on J e al. [7] de-
sc ibe wo mouse and human p o eins, NKD-1/2, ela ed o ly NKD. They obse e
ha he mos conse ed egion among he ly and e eb a e p o eins, he EFX domain,
includes he pu a i e EF hand and lanking sequences whe e EFX co esponds o a
minimal domain equi ed o ly o e eb a e NKD o in e ac wi h he basic/PDZ do-
mains o ly DSH o e eb a e DVL p o eins in he yeas wo-hyb id assay. Ka oh [8]
cloned and cha ac e ized human NKD-1/2. Bo h we e p edic ed o encode 470- and
451- amino-acid polypep ide, espec i ely. NKD-1/2, showed 43.8% o al amino-acid
iden i y, we e mo e homologous in he NH1, NH2, NH3, and NH4 domains. The con-
se ed sequence blocks, om N- e minal o C- e minal, a e as ollows: •a N- e minal
memb ane ancho ing mo i , which in mammals is subjec o my is oyla ion; Li e al.
[9] demons a e ha a membe o he NKD amil is my is oyla ed. Bo h NKD1 and
3
NKD2 con ain he consensus sequence o N-my is oyl ans e ase (Me -Gly-X-X-X-
Se /Th ), along wi h adjacen basic esidues and a polyhis idine ac a hei C e mini.
Thei s udy iden i ied an unexpec ed unc ion o NKD2 ha is no sha ed by NKD1,
ha is, my is oyla ion-dependen esco ing o TGFα o he basola e al su ace o po-
la ized epi helial cells. Mammalian NKD homologs ha e N- e minal consensus se-
quences ha di ec he pos - ansla ional addi ion o a lipophilic my is oyl moie y, bu
ly and mosqui o NKD, while sha ing N- e minal sequence homology, lack a my is-
oyla ion consensus sequence. Chan e al. [10] p o ide e idence ha ly NKD ac s
cell-au onomously in he emb yo, wi h i s N- e minus able o con e unique unc ional
p ope ies and memb ane associa ion ha canno be mimicked in i o by he e olo-
gous my is oyla ion consensus sequences. •a single, ex ended EF hand mo i (called
”EFX” o ”NH2”) ha binds DSH/DVL p o eins; in Wha on J e al. [7] as men ioned
ea lie and Yan e al. [11] iden i ied an in e ac ing p o ein, mNKD, ha is 30% iden ical
o D osophila NKD and bo h mNKD and D osophila NKD con ain a single EF-hand
(common helix-loop-helix calcium-binding mo i ) calcium-binding mo i which has
he mos simila i y o he EF-hand ound in he Reco e in amily o calcium-binding
p o eins. The domain o mNKD ha in e ac s wi h mDVL in he yeas wo-hyb id ex-
pe imen s is loca ed be ween amino acids 107 and 230 and includes he EF-hand. •a
hi y amino acid mo i in he ly NKD p o ein media es nuclea ansloca ion; Nkd can
bind and inhibi he WNT signal ansduce Dishe elled (DSH), bu he mechanism
by which NKD limi s Wn signaling in he ly emb yo is no unde s ood. Wald op
e al. [12] show ha NKD mu an s exhibi ele a ed le els o he be a-ca enin homolog
A madillo bu no al e a ion in DSH abundance o dis ibu ion. While DSH-binding
egions o NKD con ibu e o i s ac i i y, hey iden i ied a conse ed 30-amino-acid
mo i , sepa able om DSH-binding egions, ha is essen ial o NKD unc ion and nu-
clea localiza ion. Replacemen o he 30-amino-acid mo i wi h a con en ional nuclea
localiza ion sequence escued a small ac ion o NKD mu an animals o adul hood.
And, Guo e al. [13] show ha one unc ion o he e eb a e NKD 30-amino-acid mo-
i is o oppose NKD1-EFX/DVL in e ac ions, which is i sel appa en ly opposed by
u he C- e minal sequence ha is dele ed in hei MSI-CRC umo s. •a C- e minal
His idine- ich sequence o unknown unc ion.
Wn signaling con ols a wide ange o de elopmen al p ocesses and i s abe an
egula ion can lead o disease. To be e unde s and he egula ion o his pa hway,
Van Raay e al. [14] iden i ied zeb a ish homologues o NKD, i.e NKD-1/2, which ha e
p e iously been shown o inhibi canonical WNT/β-ca enin signaling. They obse ed
ha zeb a ish NKD1 exp ession inc eased subs an ially a e he mid-blas ula ansi ion
in a pa e n mi o ing ha o ac i a ed canonical WNT/β-ca enin signaling, being ex-
p essed in bo h he en ola e al blas ode m ma gin and also in he axial mesendode m.
In con as , zeb a ish NKD2 was ma e nally and ubiqui ously exp essed. O e exp es-
sion o NKD-1/2A supp essed canonical WNT/β-ca enin signaling a mul iple s ages
o ea ly zeb a ish de elopmen and also exace ba ed he cyclopia and axial mesendo-
de m con e gence and ex ension (C&E) de ec in he non-canonical WNT/PCP mu an
silbe blick (SLB/WNT11). Fu he , he es ablishmen o he le - igh (LR) axis in
zeb a ish emb yos elies on signals om he do sal o e unne cells (DFC) and he
Kup e ’s esicle (KV). Schneide e al. [15] analyzed he exp ession pa e ns o h ee
zeb a ish NKD homologs and ound en iched exp ession o NKD1 in DFCs and KV.
4
They ound DVL deg aded upon NKD1 o e exp ession in zeb a ish. Thei indings
showed ha NKD1 ac ed as a β-ca enin an agonis in he DFCs necessa y o LR pa -
e ning.
I p esen 3 d o de combina ions o NKD1 wi h o he genes, ha he machine lea n-
ing 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 [16]. 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 [16].
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
5
in mainSc ip -1-1.R). A e he da a has been ans o med, ec o ized p og amming
is employed o densi y based sensi i i y analysis and looping is employed o a i-
ance based sensi i i y analysis o compu e he equi ed sensi i i y indices o each o
he pcombina ions. This p ocedu e is done o di e en kinds o sensi i i y analysis
me hods.
A e he abo e sensi i i y indices ha e been s o ed o each o he p h combina-
ion, he nex s ep in he design o expe imen is conduc ed. Since he e is only one
eco ding o sensi i i y index pe combina ion, each combina ion o ms a aining ex-
ample which is allo ed a aining index and he sensi i i y indices o he indi idual
gene ic ac o s o m he aining example. Thus he e a e Cn
k aining examples o k h
o de in e ac ion. Using his aining se SVMRank
lea n Joachims [3] is used o gene a e a
model on de aul alue C alue o 20. In he cu en expe imen on oy model C alue
has no been unned. The aining se helps in he gene a ion o he model as he di -
e en gene combina ions a e numbe ed in o de which a e used as ank indices. The
model is hen used o gene a e sco e on he obse a ions in he es ing se using he
SV MRank
classi y Joachims [3]. No e ha due o a ailabili y o only one example pe com-
bina ion, a e he model has been buil , he same aining da a is used as es da a o
gene a es he sco es. This p ocedu e is execu ed o each and e e y sensi i i y analysis
me hod. This is ollowed by so ing o hese sco es along wi h he ank indices (i.e he
aining indices) al eady assigned o he gene combina ions. The end esul is a so ed
o de o he gene combina ions based on he anking sco e lea ned by he SV MRank
algo i hm. Finally, his en i e p ocedu e is compu ed o sensi i i y indices gene a ed
o each and e e y old change a ime poin and de ia ions in old change a di e en
du a ions. Obse ing he changing ank o a pa icula combina ion a di e en imes
and di e en ime pe iods will e eal how a combina ion is beha ing.
No e ha he ollowing is he o de in which he iles should be execu ed in R, in
o de , o ob aining he desi ed esul s (No e ha he code will no be explained he e) - •
use sou ce(”mainSc ip -1-1.R”) wi h a gumen s o Dynamic da a •sou ce(”SVMRank-
Resul s-D.R”), o ank he in e ac ions (again his needs o be done sepa a ely o
di e en kinds o SA me hods), •use sou ce(”Combine-Time- iles.R”), i compu -
ing indices sepa a ely ia p e ious ile, •sou ce(”So -n-Plo -D.R”) o so he in e -
ac ions. No e ha he so ing is chages he in e ac ion anking in ime. Thus •use
sou ce(”In e ac ion-P io i y-In ime.R”) o ind he p io i ized anking o each and e -
e y in e ac ion o e he di e en ime poin s and inally •use sou ce(”P in -Ranking-
AND-In e ac ion-Rank.R”) o p in indi idual anking o he equi ed inpu ac o wi h
o he in e ac ion ac o s.
6. 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-
6
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 NKD1-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 [17]) and Sobol indicies (wi h 2002 implemen a ion in Sal elli [18]
and ma inez implemen a ion in Ma inez [19] and Baudin e al. [20]).
6.3. Conse ed machine lea ning ankings o es ed NKD1-X-X com-
bina ions
A o al o 2415, 3 d o de combina ions in ol ing NKD1 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.
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
FZD7-NKD1-SENP2 78 10179 4761 28020 28474 FSHB-NKD1-PPP2R1A 134 11978 48147 4744 11658
DIXDC1-NKD1-SENP2 139 26878 5252 13422 20937 FZD7-NKD1-WNT2B 140 22580 30435 30959 23507
DIXDC1-NKD1-TLE2 211 181 25309 23711 748 DIXDC1-NKD1-TCF7L1 239 17174 2661 14197 5839
FZD7-NKD1-PPP2CA 369 8802 35791 35537 25608 FZD7-NKD1-SFRP4 384 21227 4937 21897 25651
FSHB-NKD1-TLE2 425 30274 24343 8644 12849 DIXDC1-NKD1-PPP2CA 440 13162 40123 35144 6197
FZD5-NKD1-WNT2B 450 18227 31166 30382 5811 FSHB-NKD1-SENP2 574 7025 14205 7566 35992
DKK1-NKD1-SENP2 575 5975 43246 35996 27099 FBXW11-NKD1-SENP2 618 34583 6281 9193 28276
FZD7-NKD1-TCF7L1 657 23179 2067 50336 28795 FSHB-NKD1-WNT2B 699 45757 26960 8191 17214
FRZB-NKD1-SENP2 705 6025 7511 12942 30682 FZD7-NKD1-FBXW4 729 9858 18476 41281 18997
FZD5-NKD1-TLE2 785 4126 18422 33090 3434 FZD2-NKD1-WNT2 792 33006 2260 28026 532
LEF1-NKD1-PPP2R1A 793 3084 55944 23057 25903 FRZB-NKD1-WNT2B 861 8764 29474 26264 14733
FZD1-NKD1-SENP2 865 3117 15529 25963 26289 FOSL1-NKD1-SFRP4 875 160 5276 11851 11033
DIXDC1-NKD1-WNT2 883 442 1751 18827 1642 DKK1-NKD1-WNT2B 912 10412 49963 52787 8425
CSNK1G1-NKD1-PPP2CA 926 17356 35232 35369 12912 FSHB-NKD1-RHOU 974 40540 14067 9128 35039
FSHB-NKD1-SFRP1 1011 27987 21471 7065 1983 FBXW11-NKD1-WNT2B 1027 51970 24642 25865 43366
CCND3-NKD1-WNT2B 1067 19542 49729 33902 7166 FZD7-NKD1-WNT2 1099 15793 1721 33173 28181
FZD7-NKD1-TLE1 1127 6936 12734 50934 40716 FZD5-NKD1-SFRP4 1137 15039 9065 28525 21751
FSHB-NKD1-WNT5A 1146 8921 29165 19619 2206 CSNK1G1-NKD1-TCF7L1 1194 9892 6186 28656 13545
FZD1-NKD1-SFRP4 1200 13902 31686 31642 11656 CSNK1G1-NKD1-SENP2 1257 16631 15972 26700 19860
FZD1-NKD1-WNT2B 1274 10870 41498 34943 5517 FRZB-NKD1-SFRP4 1296 647 21775 12472 26405
FZD7-NKD1-RHOU 1307 26801 3329 51286 46329 FZD2-NKD1-RHOU 1310 19610 4807 33843 1134
FSHB-NKD1-TCF7L1 1387 37613 10650 8338 29279 KREMEN1-NKD1-WNT2B 1400 34496 34759 43275 20181
LRP5-NKD1-SENP2 1447 1797 8631 4376 40581 KREMEN1-NKD1-SENP2 1463 18745 6060 20808 42111
CSNK1G1-NKD1-SFRP4 1474 513 13103 24557 6931 LRP5-NKD1-SFRP4 1486 21467 6314 10196 31377
FZD2-NKD1-TLE2 1505 29421 21252 27865 2130 FZD1-NKD1-TLE2 1523 3791 21524 33601 4582
FSHB-NKD1-TCF7 1528 46050 40792 9733 32939 DIXDC1-NKD1-WNT4 1536 13509 3143 4994 28564
FBXW2-NKD1-WNT2B 1547 22973 29232 13160 53054 FZD7-NKD1-TCF7 1550 5115 43100 44210 33757
FZD7-NKD1-WNT3A 1664 5491 2056 28279 37124 LRP5-NKD1-WNT2B 1686 21363 28403 16564 24813
KREMEN1-NKD1-TCF7L1 1699 28241 2070 41242 30439 DIXDC1-NKD1-RHOU 1798 6195 3765 22405 3157
LRP5-NKD1-TCF7L1 1804 29713 4980 13354 42899 DIXDC1-NKD1-WNT5A 1830 5103 33835 49403 2232
FOSL1-NKD1-PPP2CA 1845 14335 40783 24581 23211 FZD5-NKD1-TCF7L1 1914 20430 1935 26746 22679
FRZB-NKD1-PPP2CA 1923 12714 42040 19751 23511 APC-NKD1-TLE2 1939 24 20649 13050 16733
CCND3-NKD1-WNT3A 1995 32953 30709 40159 23393 NKD1-WIF1-WNT3A 2028 3129 43733 48011 30914
FZD8-NKD1-WNT2B 2038 34027 33288 19731 46263 FZD5-NKD1-FBXW4 2042 6515 20216 24601 16637
CTBP1-NKD1-SFRP4 2057 1716 14512 24063 41784 FZD7-NKD1-SLC9A3R1 2065 23275 9662 24185 39745
FZD5-NKD1-RHOU 2086 9792 3471 18764 2521 DIXDC1-NKD1-PPP2R1A 2140 5484 54992 25998 568
DKK1-NKD1-PPP2CA 2158 21388 52610 49493 9273 FZD1-NKD1-RHOU 2176 20088 11316 49737 2429
CXXC4-NKD1-WNT2B 2217 9878 36698 23848 1631 FRZB-NKD1-TLE2 2272 121 33128 21637 12907
CSNK1G1-NKD1-RHOU 2328 3565 14141 34128 1880 FOSL1-NKD1-SENP2 2466 6869 5781 10026 30259
FZD2-NKD1-SENP2 2523 36940 7846 15207 17515 FSHB-NKD1-WNT2 2558 23961 6398 3570 16109
KREMEN1-NKD1-TLE2 2619 18016 16139 44657 37610 FZD5-NKD1-WNT4 2642 3099 2732 32040 47167
KREMEN1-NKD1-WNT3A 2675 23678 2816 47552 40285 DIXDC1-NKD1-TCF7 2704 16324 46726 24262 6288
FZD5-NKD1-TCF7 2753 4697 38384 26960 22996 FBXW2-NKD1-PPP2CA 2839 23721 34814 16169 56279
CTBP1-NKD1-TCF7L1 2845 7922 3120 35646 35460 CTBP2-FZD7-NKD1 2976 52126 40799 40259 46777
GSK3B-NKD1-TLE2 2977 22800 23954 42499 38689 FBXW2-NKD1-SENP2 2988 37184 10657 11033 56876
NKD1-WIF1-WNT4 2997 2461 45561 55000 34857 FZD5-NKD1-WNT5A 3021 6206 35575 52940 2092
CXXC4-NKD1-SENP2 3069 14633 9774 13334 17352 CCND3-NKD1-SFRP4 3074 31551 41849 39607 12267
DVL1-NKD1-WNT2B 3089 2831 24130 36326 51502 KREMEN1-NKD1-FBXW4 3108 22301 16832 29059 23025
CSNK2A1-NKD1-WNT2B 3148 4519 40339 22219 23905 CXXC4-NKD1-TLE2 3160 26 22413 13930 94
NKD1-PPP2CA-SFRP4 3169 46409 13326 29656 43339 CTNNBIP1-NKD1-RHOU 3194 27112 11412 35287 15481
CCND3-NKD1-PPP2CA 3285 34449 42225 49257 26308 NKD1-WNT2B-WNT4 3336 43254 28275 6099 51615
CCND1-NKD1-PPP2CA 3363 11274 37598 54652 44854 FZD7-NKD1-WNT5A 3371 2073 37837 34079 40424
FZD2-NKD1-WIF1 3430 39091 22109 26358 3 FZD2-NKD1-WNT2B 3444 30135 33767 29289 1990
NKD1-WNT2B-WNT3A 3477 51633 33941 7298 45111 FRZB-NKD1-RHOU 3499 2171 5014 35449 27330
CSNK1G1-NKD1-WNT2 3527 1109 9218 26094 482 FZD5-NKD1-PPP2R1A 3621 21515 54524 36048 1557
CCND3-NKD1-WNT2 3637 32192 36071 49096 2809 FSHB-NKD1-FBXW4 3657 26327 16817 8776 23172
FZD8-NKD1-PPP2CA 3681 49836 33279 27543 15965 FZD7-NKD1-WNT4 3704 14766 3963 41558 50663
FBXW11-NKD1-TCF7L1 3783 32677 2358 19136 41733 LEF1-NKD1-WNT3 3813 14659 40690 18495 25196
FBXW2-NKD1-WNT4 3822 22628 8291 3237 57029 KREMEN1-NKD1-WNT4 3871 11426 4535 41285 47213
DIXDC1-NKD1-WIF1 3909 12873 22358 12920 23739 DAAM1-NKD1-WNT2B 3944 45573 30236 23673 33353
CXXC4-NKD1-RHOU 3957 5011 6876 36465 23781 LEF1-NKD1-SFRP1 3999 1638 28264 15491 1219
GSK3B-NKD1-TCF7L1 4012 30306 1476 36252 37466 CSNK2A1-NKD1-PPP2CA 4025 15782 45180 27270 33423
FBXW2-NKD1-TLE2 4091 22177 18065 12184 55575 CSNK2A1-NKD1-PPP2R1A 4118 2001 56920 13318 8736
Table 1: Rankings o NKD1-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
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
FZD7-NKD1-SENP2 22248 3166 47262 13293 2567 FSHB-NKD1-PPP2R1A 25236 3206 25555 29398 54336
DIXDC1-NKD1-SENP2 24325 22750 54264 38554 4248 FZD7-NKD1-WNT2B 47917 26281 13366 54412 1630
DIXDC1-NKD1-TLE2 22103 8452 55942 25492 11873 DIXDC1-NKD1-TCF7L1 32308 45794 57018 24322 3679
FZD7-NKD1-PPP2CA 15127 35957 31673 37533 1778 FZD7-NKD1-SFRP4 22923 15141 38823 43517 2354
FSHB-NKD1-TLE2 17403 24824 7167 5397 44661 DIXDC1-NKD1-PPP2CA 9807 43231 37477 30170 1078
FZD5-NKD1-WNT2B 18497 19475 22567 24649 24247 FSHB-NKD1-SENP2 14879 5325 16207 3306 6877
DKK1-NKD1-SENP2 7012 22034 30235 20793 14207 FBXW11-NKD1-SENP2 3968 23882 33729 15929 5877
FZD7-NKD1-TCF7L1 40741 32897 48058 29669 1354 FSHB-NKD1-WNT2B 24792 50507 25909 42911 36692
FRZB-NKD1-SENP2 3644 10458 50187 29431 36573 FZD7-NKD1-FBXW4 39942 9295 41002 45990 5647
FZD5-NKD1-TLE2 3831 2363 53067 35683 47894 FZD2-NKD1-WNT2 54548 26947 57006 32814 25385
LEF1-NKD1-PPP2R1A 24944 9286 39491 44583 37109 FRZB-NKD1-WNT2B 26947 18964 19602 32120 37731
FZD1-NKD1-SENP2 16283 248 42563 17609 26499 FOSL1-NKD1-SFRP4 38557 1693 50390 24818 21820
DIXDC1-NKD1-WNT2 30452 9192 55932 6605 10010 DKK1-NKD1-WNT2B 33321 46336 43515 12948 3783
CSNK1G1-NKD1-PPP2CA 8799 37693 42013 33688 15900 FSHB-NKD1-RHOU 13620 39126 15440 38560 46234
FSHB-NKD1-SFRP1 28217 31095 6105 12696 47885 FBXW11-NKD1-WNT2B 42436 56089 5208 5851 6025
CCND3-NKD1-WNT2B 31750 9905 43256 46510 4045 FZD7-NKD1-WNT2 38995 9386 56253 3799 2844
FZD7-NKD1-TLE1 27415 7679 53298 43858 894 FZD5-NKD1-SFRP4 15328 9399 47362 16033 40262
FSHB-NKD1-WNT5A 45339 3228 1592 43013 28219 CSNK1G1-NKD1-TCF7L1 6006 22577 49200 31622 30401
FZD1-NKD1-SFRP4 43048 8656 45237 21687 17892 CSNK1G1-NKD1-SENP2 4079 7354 54740 12528 13804
FZD1-NKD1-WNT2B 35381 16131 32653 43586 18237 FRZB-NKD1-SFRP4 30663 4537 52953 18729 25710
FZD7-NKD1-RHOU 29725 14170 51670 56277 8735 FZD2-NKD1-RHOU 50910 12898 54711 9572 46912
FSHB-NKD1-TCF7L1 29187 51071 22006 21070 31900 KREMEN1-NKD1-WNT2B 10715 45017 15095 25349 17172
LRP5-NKD1-SENP2 14990 3717 34426 11779 16566 KREMEN1-NKD1-SENP2 730 3287 51067 20876 22424
CSNK1G1-NKD1-SFRP4 10332 8994 35937 45547 19919 LRP5-NKD1-SFRP4 26254 21185 21350 26108 17079
FZD2-NKD1-TLE2 24712 20087 50718 44876 38227 FZD1-NKD1-TLE2 24945 3728 49365 3491 46221
FSHB-NKD1-TCF7 16167 43862 3127 18402 9845 DIXDC1-NKD1-WNT4 28297 20930 51455 19765 821
FBXW2-NKD1-WNT2B 33781 33859 11109 13486 210 FZD7-NKD1-TCF7 37444 15437 35879 47781 305
FZD7-NKD1-WNT3A 16651 467 45031 55399 13378 LRP5-NKD1-WNT2B 32145 41013 38068 34089 24010
KREMEN1-NKD1-TCF7L1 6544 33167 55781 7544 9258 DIXDC1-NKD1-RHOU 22817 19488 48855 52946 7640
LRP5-NKD1-TCF7L1 17394 31853 35078 16573 14922 DIXDC1-NKD1-WNT5A 50477 15744 20410 52735 35648
FOSL1-NKD1-PPP2CA 21934 29546 42661 35675 17456 FZD5-NKD1-TCF7L1 18061 23794 54846 25790 41167
FRZB-NKD1-PPP2CA 1942 36043 22753 20309 35265 APC-NKD1-TLE2 23869 4453 50209 22108 50421
CCND3-NKD1-WNT3A 19177 14820 26493 56175 64 NKD1-WIF1-WNT3A 48793 3970 17300 56778 21427
FZD8-NKD1-WNT2B 49791 35392 25199 27885 3968 FZD5-NKD1-FBXW4 9460 12253 43946 48270 55667
CTBP1-NKD1-SFRP4 34262 7238 53046 16240 32125 FZD7-NKD1-SLC9A3R1 40405 7627 50823 42113 3058
FZD5-NKD1-RHOU 17419 5033 39813 31860 48308 DIXDC1-NKD1-PPP2R1A 41282 2633 37452 52221 22216
DKK1-NKD1-PPP2CA 845 43108 38644 15851 21492 FZD1-NKD1-RHOU 9230 9523 50610 53836 44264
CXXC4-NKD1-WNT2B 33112 30020 8852 27851 43373 FRZB-NKD1-TLE2 14829 3484 49881 39277 47223
CSNK1G1-NKD1-RHOU 7968 13163 45029 45281 48042 FOSL1-NKD1-SENP2 15372 3697 55084 25337 9352
FZD2-NKD1-SENP2 25897 35442 55987 51047 12409 FSHB-NKD1-WNT2 18619 15105 23935 22810 37921
KREMEN1-NKD1-TLE2 2919 14915 47965 33551 33612 FZD5-NKD1-WNT4 12678 521 57060 25537 26670
KREMEN1-NKD1-WNT3A 9700 7837 52991 45907 10853 DIXDC1-NKD1-TCF7 22420 28291 44348 38473 4381
FZD5-NKD1-TCF7 16271 1612 53778 20615 31084 FBXW2-NKD1-PPP2CA 15124 44885 17926 12733 2217
CTBP1-NKD1-TCF7L1 22297 13060 56917 8766 27600 CTBP2-FZD7-NKD1 31868 50353 6812 34202 44114
GSK3B-NKD1-TLE2 7424 17188 52854 26876 49828 FBXW2-NKD1-SENP2 11695 33380 11958 18807 1265
NKD1-WIF1-WNT4 20047 23652 20170 17000 48569 FZD5-NKD1-WNT5A 33749 1909 44565 56409 39882
CXXC4-NKD1-SENP2 23566 21575 56539 18663 8724 CCND3-NKD1-SFRP4 21810 15481 41109 37803 2086
DVL1-NKD1-WNT2B 38080 13959 43055 47296 2221 KREMEN1-NKD1-FBXW4 16975 10848 31634 30290 26950
CSNK2A1-NKD1-WNT2B 17855 5115 19163 36411 21386 CXXC4-NKD1-TLE2 14475 5894 51388 28114 51127
NKD1-PPP2CA-SFRP4 40324 48641 51898 9183 19710 CTNNBIP1-NKD1-RHOU 49378 32634 47683 47402 32347
CCND3-NKD1-PPP2CA 19772 35706 47585 36014 3731 NKD1-WNT2B-WNT4 31109 52225 48686 5473 15716
CCND1-NKD1-PPP2CA 31094 31919 45839 10804 5523 FZD7-NKD1-WNT5A 53120 6594 44749 54824 2305
FZD2-NKD1-WIF1 45250 38648 56326 24018 7601 FZD2-NKD1-WNT2B 53572 28271 33551 10732 5520
NKD1-WNT2B-WNT3A 50905 55634 51652 46273 6139 FRZB-NKD1-RHOU 9972 3765 49769 37400 50607
CSNK1G1-NKD1-WNT2 6387 6428 51082 8449 39348 FZD5-NKD1-PPP2R1A 23335 9105 47323 31744 56453
CCND3-NKD1-WNT2 36776 17718 45542 2330 4094 FSHB-NKD1-FBXW4 37869 19703 30672 38958 40988
FZD8-NKD1-PPP2CA 31727 55399 17443 4434 10950 FZD7-NKD1-WNT4 19019 5699 47235 25398 489
FBXW11-NKD1-TCF7L1 8257 42198 35700 9053 14548 LEF1-NKD1-WNT3 33634 12910 24295 24445 28299
FBXW2-NKD1-WNT4 15630 22910 34768 11469 618 KREMEN1-NKD1-WNT4 1146 12492 44039 43786 11253
DIXDC1-NKD1-WIF1 44180 9421 57087 48747 10766 DAAM1-NKD1-WNT2B 21385 46690 24575 48240 1108
CXXC4-NKD1-RHOU 49373 16254 50519 35698 48470 LEF1-NKD1-SFRP1 33942 6111 31628 47136 38942
GSK3B-NKD1-TCF7L1 43296 37741 56267 44754 33094 CSNK2A1-NKD1-PPP2CA 6422 22743 30647 42195 19402
FBXW2-NKD1-TLE2 16737 27286 16157 17903 3635 CSNK2A1-NKD1-PPP2R1A 19188 9240 34119 49629 44582
Table 2: Rankings o NKD1-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
6.3.1. Examining he beha iou o DIXDC1-NKD1-X combina ions
Dishe elled (DVL-1/2/3) a e DIX-domain p o eins implica ed in he WNT signal-
ing pa hway. NKD1 is a membe o naked cu icle (NKD) amily ha inhibi s he
9
