nemo like kinase (NLK) : Time beha iou al s udy o 3 d
o de combina ions in WNT3A s imula ed HEK 293 cells
sh ip akash sinha
Independen Resea che ; O cid ID : o cid.o g/0000-0001-7027-5788
104-Madhu isha Heigh s Phase 1, Risali, Bhilai-490006, India
Abs ac
Nemo-Like Kinase (NLK) is a se ine/ h eonine p o ein kinase , Nemo (NMO) being
he D osophila o holog o he mammalian NLK gene. I s ac i a ion mechanism and
downs eam a ge s a e s ill no well cha ac e ized. 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 ex-
hibi simila exp ession dynamics and unco e ed p e iously un ecognized posi i e and
nega i e eedback loops. Howe e , hei s udy depic s/uses singula measu emen s o
indi idual gene exp ession a di e en ime snapsho s/poin s o in e he sys em wide
analysis o he pa hway. A any pa icula ime poin , i is o en he case ha genes a e
wo king syne gis ically in 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 NLK ela ed 3 d o de
combina ions in a o es o 71C3combina ions using ou di e en sensi i i y me hods;
•show he conse ed ankings o NLK-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 NLK 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1Aspec s o unpublished wo k we e p esen ed in a pos e session a Cell Symposia: Technology.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 27, 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 NLK 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. nemo like kinase (NLK)
The D osophila eye consis s o a ei e a i e hexagonal a ay o pho o ecep o cell clus-
e s, he omma idia. Du ing no mal mo phogenesis, he clus e s in he do sal o en al
hal es o he disc o a e 90◦in opposi e di ec ions, o ming mi o images ac oss a
do so en al equa o . In he mu an nemo (NMO), he e is an ini ial u ning o ap-
p oxima ely 45◦, bu u he o a ion is blocked. Choi and Benze [4] indica e ha he
NMO ac s upon each clus e as a whole; no mal nmo unc ion in one o mo e pho o e-
cep o cells appea s o be su icien o induce ull o a ion. The NMO gene sequence
is equi ed o ini ia e he second s ep o o a ion, ia and an encoded se ine/ h eonine
p o ein kinase homolog. They show ha in ano he mu an , oule e, excessi e o a ion
h ough a ying angles occu s in many omma idia, which is supp essed by NMO, hus
indica ing ha NMO ac s ups eam in a o a ion- egula ing pa hway.
Ex acellula -signal egula ed kinases/mic o ubule-associa ed p o ein kinases (ERK/MAPKs)
and cyclin-di ec ed kinases (CDKs) a e key egula o s o many aspec s o cell g ow h
and di ision, as well as apop osis. B o e al. [5] cloned NLK, whe e he NLK amino
acid sequence is 54.5% simila and 41.7% iden ical o mu ine ERK2, and 49.6% sim-
ila and 38.4% iden ical o human CDC2. A ea u e ha dis inguishes NLK om
ERL/MAPKs, CDKs, and also NMO, is i s ex ended amino- e minal domain, ha is
e y ich in glu amine, alanine, p oline, and his idine. Mu a ion o he ATP-binding
Lys-155 o me hionine abolishes i s abili y o au ophospho yla e, as does mu a ion o
a pu a i e ac i a ing h eonine in kinase domain VIII, o aline, aspa ic, o glu amic
acid. NLK and NMO may be he i s membe s o a amily o kinases wi h homol-
ogy o bo h ERK/MAPKs and CDKs. Mi ogen-ac i a ed p o ein (MAP) kinases a e
a amily o se ine/ h eonine kinases ha ansduce ex acellula cues in o a a ie y o
in acellula esponses anging om lineage speci ica ion o cell di ision and adap a-
ion. Coulombe and Meloche [6] classi y MAP kinases in o con en ional o a ypical
enzymes, based on hei abili y o ge phospho yla ed and ac i a ed by he MAP kinase
kinase (MAPKK)/MEK amily. Con en ional MAP kinases comp ise ERK1/ERK2,
p38s, JNKs, and ERK5, which a e all subs a es o MAPKKs, while a ypical MAP ki-
nases include ERK3/ERK4, NLK and ERK7. Much less is known abou he egula ion,
subs a e speci ici y and physiological unc ions o a ypical MAP kinases.
Conside ing he s uc u e o NLK, i s C- e minal ex ension is conse ed om wo m
o human (45% iden i y be ween LIT-1 and human NLK) and may con ibu e o he in-
e ac ion o he kinase wi h speci ic subs a es o a ge s as shown by Ishi ani e al.
[7]. The WNT signalling pa hway egula es many de elopmen al p ocesses h ough
3
a complex o β-ca enin and he T-cell ac o / lymphoid enhance ac o (TCF/LEF)
amily. WNT s abilizes cy osolic β-ca enin, which hen binds o TCF and ac i a es
gene ansc ip ion. In Caeno habdi is elegans, he p o eins MOM4 and LIT1 eg-
ula e WNT signalling o pola ize esponding cells du ing emb yogenesis as shown
by Meneghini e al. [8]. MOM4 and LIT1 a e homologous o TAK1 (a kinase ac i-
a ed by ans o ming g ow h ac o -β) mi ogenac i a ed p o ein-kinase-kinase kinase
(MAP3K) and MAPK- ela ed NLK, espec i ely, in mammalian cells. Ishi ani e al. [7]
hypo hesize he possibili y ha TAK1 and NLK a e also in ol ed in WNT signalling
in mammalian cellsand show ha TAK1 ac i a ion s imula es NLK ac i i y and down-
egula es ansc ip ional ac i a ion media ed by β-ca enin and TCF. They demos a e
ha injec ion o NLK supp esses he induc ion o axis duplica ion by mic oinjec ed β-
ca enin in Xenopus emb yos. NLK phospho yla es TCF/LEF ac o s and inhibi s he
in e ac ion o he β-ca enin-TCF complex wi h DNA. Thus, he TAK1-NLK-MAPK-
like pa hway nega i ely egula es he WNT signalling pa hway. Yamada e al. [9] and
Yamada e al. [10], also show simila esul s o NLK in e ac ion wi h TCF/LEF amily
membe s.
Mo e speci ically, c-myb p o o-oncogene (c-MYB) egula es bo h he p oli e a ion
and apop osis o hema opoie ic cells by inducing he ansc ip ion o a g oup o a ge
genes. Kanei-Ishii e al. [11] epo ha c-MYB p o ein is phospho yla ed and de-
g aded by WNT1 signal ia he pa hway in ol ing TGF-β-ac i a ed kinase (TAK1),
homeodomain-in e ac ing p o ein kinase 2(HIPK2), and NLK. They show ha WNT1
signal causes he nuclea en y o TAK1, which hen ac i a es HIPK2 and NLK. Fu -
he , NLK binds di ec ly o c-MYB oge he wi h HIPK2, which esul s in he phos-
pho yla ion o c-MYB a mul iple si es, ollowed by i s ubiqui ina ion and p o easome-
dependen deg ada ion. Fu he mo e, o e exp ession o NLK in M1 cells ab oga ed he
abili y o c-MYB o main ain he undi e en ia ed s a e o hese cells. Finally, Ishi ani
e al. [12] show ha phospho yla ion o TCF4 by NLK inhibi ed DNA binding by he
β-ca enin-TCF4 complex. These esul s sugges ed ha NLK phospho yla ion on hese
si es con ibu ed o he down- egula ion o LEF1/TCF ansc ip ional ac i i y.
Ishi ani and Ishi ani [13] summa ize he cu en unde s anding o he unc ion and
egula ion o NLK and discuss he aspec s o NLK egula ion ha emain o be e-
sol ed. In his esea ch wo k, I p esen 3 d o de combina ions o NLK wi h o he
genes, ha he machine lea ning based sea ch engine poin s o, as possible syne gis ic
combina ions ha migh be wo king in ime.
3. Me hods
Please e e o sec ions o Sinha [2] o me hods, design o s udy and analysis o da a
o 2nd o de combina ions. The same me hod and design o s udy is used o gene a e
esul s o 3 d o de combina ions p esen ed in his s udy.
4
4. Time se ies da a
Guj al and MacBea h [1] p esen a se o 71 WNT- ela ed gene exp ession alues o 6
di e en imes poin s o e a ange o 24-hou pe iod using qPCR. The changes ep e-
sen he old-change in he exp ession le els o genes in 200 ng/mL WNT3A-s imula ed
HEK 293 cells in ime ela i e o hei le els in uns imula ed, se um-s a ed cells a 0-
hou . Guj al and MacBea h [1] s a e ha qPCR da a a e he means o h ee biological
eplica es. Only genes whose mean ansc ip le els changed by mo e han wo- old a
one o mo e ime poin s du ing he 24-hou ime cou se we e conside ed signi ican .
Posi i e (nega i e) numbe s ep esen up (down) - egula ion. We ha e al eady co e ed
he issues ela ed o hese da a se s in de ail in Sinha [14]. Reade s a e eques ed o
go h ough hem in he poin ed e e ence. The ools o s udy which a e used he e ha e
been published in ano he ounda ional wo k in Sinha [14].
5. Design o expe imen
5.1. Pipeline o ime se ies da a
Fo he case o ime se ies da a, in e ac ions among he con ibu ing ac o s a e s udied
by compa ing iple s o old-changes a single ime poin s. The p odecu e begins wi h
he gene a ion o dis ibu ion a ound measu emen s a single ime poin s wi h added
noise is done o es ima e he indices. A dis ibu ion is gene a ed o he old changes
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
5
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
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.
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].
6
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 NLK-X-X combina ions om
Guj al and MacBea h [1]
In he supplemen a y sec ion, I p esen ou iles, each con aining he ankings o 3 d
o de combina ions, ha wa y in ime (shown o 5 ime poin s). Each ile ep esen s
he ankings compu ed using a pa icula sensi i i y me hod. The changing ankings
in ime o a pa icula combina ion ep esen s he impo ance o con ibu ion/ ole ha
combina ion plays in he cell s imula ed wi h WNT3A. The sensi i i y me hods used
a e Hilbe Schmid Independence C i e ion indices (HSIC) indices (wi h b and linea
ke nel in Da Veiga [15]) and Sobol indicies (wi h 2002 implemen a ion in Sal elli [16]
and ma inez implemen a ion in Ma inez [17] and Baudin e al. [18]).
6.3. Conse ed machine lea ning ankings o es ed NLK-X-X com-
bina ions
A o al o 2415, 3 d o de combina ions in ol ing NLK 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-NLK-X combina ions
Kanei-Ishii e al. [11] epo ha c-MYB p o ein is phospho yla ed and deg aded by
WNT1 signal ia he pa hway in ol ing TGF-β-ac i a ed kinase (TAK1), homeodomain-
in e ac ing p o ein kinase 2 (HIPK2), and NLK. They show ha WNT1 signal causes
he nuclea en y o TAK1, which hen ac i a es HIPK2 and NLK. Looking a he ables
abo e, one inds he ollowing combina ions o membe s o he WNT amily along
wi h NLK, o be p ominen a 3 d o de le el - LRP5-NLK-WNT4, FOSL1-NLK-
WNT4, CXXC4-NLK-WNT4, CTNNBIP1-NLK-WNT5A, NLK-PORCN-WNT2B, NLK-
PORCN-WNT2, LRP5-NLK-WNT2B, NLK-SFRP1-WNT5A, NLK-SFRP1-WNT2,
NLK-SFRP1-WNT3, DIXDC1-NLK-WNT4, FRZB-NLK-WNT4, CSNK1G1-NLK-
WNT2B, FZD1-NLK-WNT5A, CTNNBIP1-NLK-WNT2B, LRP5-NLK-WNT5A, NLK-
FBXW4-WNT3A, FZD5-NLK-WNT4, FGF4-NLK-WNT2B, CSNK1G1-NLK-WNT4,
NLK-WIF1-WNT2, FRAT1-NLK-WNT4, NLK-WIF1-WNT2B, FRAT1-NLK-WNT3A,
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
FZD1-NLK-SENP2 66 7254 6519 12561 16204 CSNK1G1-NLK-SENP2 74 35675 3308 48520 19328
LRP5-NLK-SENP2 99 17426 20510 156 54321 NLK-SFRP1-TCF7 125 43152 40831 35451 28596
LRP5-NLK-WNT4 173 5427 19931 576 56700 CSNK1D-FGF4-NLK 182 13641 35785 54873 12126
FRAT1-NLK-SENP2 308 14795 5137 12639 16597 CSNK1G1-NLK-WNT4 321 20710 3312 50831 31403
NLK-PORCN-PPP2CA 339 30605 43435 41734 4166 NLK-PORCN-SFRP4 368 53128 52278 37793 4619
FOSL1-NLK-WNT4 378 3397 2566 2260 40025 NLK-WIF1-WNT2 431 13840 49796 35119 6813
CXXC4-NLK-WNT4 491 167 4767 2069 15953 FRAT1-NLK-WNT4 534 1131 4271 13789 39755
CXXC4-NLK-FBXW4 591 19400 24702 2318 5774 CCND1-FGF4-NLK 650 37617 39188 40111 26729
BTRC-GSK3A-NLK 685 15173 52709 30778 8565 NLK-PORCN-SENP2 751 51440 56864 21216 6122
NLK-FBXW4-SLC9A3R1 760 5112 22367 45665 21602 FZD1-NLK-FBXW4 834 6168 26326 20481 40535
CTNNBIP1-NLK-WNT5A 840 10869 21909 56571 16909 LRP5-NLK-FBXW4 847 9156 37860 589 53712
CTNNBIP1-NLK-SFRP1 852 523 6419 55912 26165 NLK-WIF1-WNT2B 877 15574 29869 50706 14922
FZD1-NLK-SFRP1 923 208 3403 10308 46968 NLK-SFRP1-SFRP4 967 54433 34929 9753 40373
NLK-TLE1-TLE2 993 36487 34168 46840 34475 FRAT1-NLK-WNT3A 1005 19771 7884 9479 10249
NLK-PORCN-WNT2B 1006 26349 37659 35498 4512 FBXW2-FGF4-NLK 1060 19103 48572 41780 1397
LRP5-NLK-SFRP1 1066 2 18438 235 53114 NLK-PORCN-SLC9A3R1 1108 35858 56545 26507 3768
FZD1-NLK-TLE1 1147 12376 4310 27950 16973 NLK-PORCN-TCF7 1154 48490 41769 34836 12221
FBXW11-FGF4-NLK 1172 27458 51060 40627 25175 CSNK1G1-NLK-TLE1 1270 15559 1608 53075 20188
DKK1-NLK-SENP2 1343 20532 9328 35918 23556 FOSL1-NLK-WNT2B 1425 3331 440 49507 31594
CXXC4-NLK-TLE2 1467 3249 13379 2815 22591 FOSL1-NLK-WNT3A 1512 2335 4160 3374 12963
CXXC4-NLK-SFRP1 1520 3860 3645 1038 15312 DKK1-FGF4-NLK 1530 30108 32527 40415 19377
NLK-PORCN-WNT2 1557 46116 57071 36752 14418 FRAT1-NLK-FBXW4 1570 6400 25113 13146 24103
DAAM1-FGF4-NLK 1615 51287 55713 52792 17270 NLK-PORCN-TLE2 1657 49377 56092 39434 12430
LRP5-NLK-WNT2B 1725 4903 8642 34617 54453 NLK-PORCN-WNT4 1742 49908 50644 30880 6042
AES-AXIN1-NLK 1775 49282 47808 50035 53907 FZD1-NLK-WNT2B 1840 1616 1306 53698 22012
FOSL1-NLK-SFRP1 1846 2471 1853 521 54004 FZD7-NLK-WNT3A 1957 2219 4173 15212 30086
NLK-SFRP1-WNT5A 2032 55480 32725 47613 26430 FGF4-NLK-WNT4 2033 3044 4724 33423 28154
NLK-SFRP1-WNT2 2043 53015 46284 12054 33556 DVL2-JUN-NLK 2045 6588 32911 20097 18489
NLK-SFRP1-WNT3 2049 43102 31587 4584 28785 FZD8-NLK-WNT2B 2126 25291 1834 45776 56354
DIXDC1-NLK-WNT4 2128 13920 3978 2846 15403 CXXC4-NLK-WNT2B 2202 5290 1484 56489 12898
CTNNB1-NLK-TLE1 2322 31661 2654 17390 15058 FZD8-NLK-SFRP1 2340 2987 4568 21448 52792
CTBP1-FGF4-NLK 2373 24017 40861 28523 25856 NLK-PORCN-TCF7L1 2400 38016 56402 27460 3015
CSNK1G1-NLK-TCF7L1 2409 13940 8988 50696 40050 DVL1-FGF4-NLK 2505 55303 42133 41000 49492
FRZB-NLK-WNT4 2520 1556 5592 7221 22356 FRAT1-NLK-TLE2 2530 6281 12625 8358 38149
DVL2-FGF4-NLK 2539 9068 35433 35003 33783 FZD5-FGF4-NLK 2548 25184 37573 26783 23902
AES-EP300-NLK 2549 52374 48380 27425 55437 CSNK1D-NLK-WNT4 2750 2726 9906 45186 25621
BCL9-FGF4-NLK 2765 16506 49200 35441 40551 CXXC4-FGF4-NLK 2780 22054 41988 28791 40205
FBXW11-FOXN1-NLK 2897 3423 17764 15937 45601 FSHB-FZD2-NLK 3007 15229 33503 42544 8088
CSNK1G1-NLK-WNT2B 3057 20612 364 49392 38971 FZD1-NLK-PPP2R1A 3063 6647 16715 10003 26509
GSK3B-NLK-TLE1 3123 28197 2579 41126 15983 LRP5-NLK-SFRP4 3199 217 20954 446 56950
FZD1-NLK-WNT5A 3220 14961 17555 36449 16975 CTNNBIP1-NLK-FBXW4 3223 10049 26324 48138 19000
CTNNBIP1-NLK-WNT2B 3262 12256 1539 46850 31899 CSNK1A1-NLK-TLE1 3280 2505 5178 30696 38811
LRP5-NLK-WNT5A 3296 15243 30086 6594 47805 CTNNBIP1-NLK-RHOU 3322 501 7291 43407 48933
NLK-PORCN-TLE1 3414 46190 49745 10954 11706 DIXDC1-NLK-FBXW4 3436 6471 26909 5680 17650
FBXW2-JUN-NLK 3505 12581 49210 43684 51663 CTNNBIP1-NLK-WNT4 3546 4416 6989 50022 30148
FZD5-NLK-SENP2 3647 23886 4036 3124 1472 CSNK1D-NLK-WNT3A 3672 3466 7618 26301 5357
LRP5-NLK-PPP2R1A 3749 6866 25722 95 55900 CSNK1G1-NLK-PPP2R1A 3754 21618 10600 22928 48421
NLK-FBXW4-WNT3A 3762 18958 12589 35118 5530 CXXC4-NLK-TCF7L1 3843 4771 10375 1945 20127
FZD5-NLK-WNT4 3897 19032 2692 1966 40749 EP300-GSK3A-NLK 3902 24187 13268 22163 37611
CCND1-FRAT1-NLK 3929 35214 17635 44956 38660 CXXC4-NLK-WNT5A 3932 2627 16679 25816 15722
NLK-SFRP1-TLE2 3952 54493 39629 26154 50386 DKK1-GSK3A-NLK 3968 22383 24849 47754 29762
FGF4-NLK-WNT2B 3978 2527 804 55492 27607 FOSL1-NLK-SFRP4 3991 8084 2347 4123 43458
FRAT1-NLK-RHOU 4074 18571 5441 22722 18400 FRAT1-NLK-PPP2R1A 4096 7150 14882 4380 42041
CTNNBIP1-NLK-PPP2R1A 4168 17696 21970 43414 47292 NLK-PYGO1-WNT2 4229 27445 40800 13988 7354
AXIN1-FZD2-NLK 4347 26298 10959 26949 9217 NLK-WIF1-WNT4 4406 21046 38575 49983 13952
NLK-SFRP1-FBXW4 4416 23473 46584 11984 39379 GSK3A-JUN-NLK 4439 45904 37849 40408 18195
AXIN1-FOXN1-NLK 4448 7290 24395 14630 18096 FZD1-NLK-SFRP4 4509 3076 5015 18937 38268
CXXC4-NLK-RHOU 4522 5467 5985 8707 24421 DVL1-FOXN1-NLK 4529 51079 27843 11249 56056
FZD1-NLK-TCF7L1 4642 24230 11921 14016 23504 CCND3-FGF4-NLK 4644 49910 36053 48791 53135
DAAM1-FRAT1-NLK 4668 52014 25172 20469 49769 NLK-WIF1-WNT3A 4697 36349 45660 34357 1641
CTNNB1-NLK-WIF1 4707 9899 6192 11981 1923 FOSL1-NLK-TCF7L1 4743 4810 5264 1752 28982
CSNK1D-NLK-SENP2 4773 12377 9957 43796 3597 CSNK1A1-NLK-WIF1 4795 14710 6213 20851 31609
FRAT1-NLK-TCF7 4821 5072 6111 23919 29394 CCND1-NLK-WNT2B 4835 38149 1102 53863 38938
Table 1: Rankings o NLK-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
FOSL1-NLK-WNT2B, FOSL1-NLK-WNT3A, NLK-PORCN-WNT4, FZD1-NLK-WNT2B,
FZD7-NLK-WNT3A, FGF4-NLK-WNT4, FZD8-NLK-WNT2B, CXXC4-NLK-WNT2B,
CSNK1D-NLK-WNT4, CTNNBIP1-NLK-WNT4, CSNK1D-NLK-WNT3A, CXXC4-
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
FZD1-NLK-SENP2 4216 33313 50995 20046 16713 CSNK1G1-NLK-SENP2 34480 34469 25805 4202 8014
LRP5-NLK-SENP2 28404 31921 48677 23545 26406 NLK-SFRP1-TCF7 8841 43619 30305 17506 12968
LRP5-NLK-WNT4 34513 16387 35220 5468 37281 CSNK1D-FGF4-NLK 5343 27561 8638 8497 51980
FRAT1-NLK-SENP2 47712 35472 55874 27952 35046 CSNK1G1-NLK-WNT4 37117 32429 26444 1650 27288
NLK-PORCN-PPP2CA 6640 37879 19229 30844 45007 NLK-PORCN-SFRP4 26548 54453 3595 31340 34837
FOSL1-NLK-WNT4 46914 7268 50547 1274 44200 NLK-WIF1-WNT2 40307 10226 11647 34273 29809
CXXC4-NLK-WNT4 22955 3089 37410 121 47163 FRAT1-NLK-WNT4 32436 4345 56234 697 36071
CXXC4-NLK-FBXW4 36361 6924 5576 32715 39457 CCND1-FGF4-NLK 23150 32232 22665 42559 12440
BTRC-GSK3A-NLK 8965 2718 45185 45189 49869 NLK-PORCN-SENP2 25839 52725 11882 9881 37272
NLK-FBXW4-SLC9A3R1 56671 1861 38594 29352 5573 FZD1-NLK-FBXW4 20283 8207 32619 27566 30042
CTNNBIP1-NLK-WNT5A 43965 11033 40662 17048 49376 LRP5-NLK-FBXW4 48704 10826 12482 34528 35402
CTNNBIP1-NLK-SFRP1 33298 2286 54426 26390 24484 NLK-WIF1-WNT2B 20533 18090 8143 25594 25892
FZD1-NLK-SFRP1 24451 9305 49446 19196 22902 NLK-SFRP1-SFRP4 25125 53640 1360 15834 31791
NLK-TLE1-TLE2 54439 46207 309 27068 8231 FRAT1-NLK-WNT3A 51049 30143 52377 44271 42168
NLK-PORCN-WNT2B 30300 3466 8133 31316 44880 FBXW2-FGF4-NLK 1671 979 163 29649 18596
LRP5-NLK-SFRP1 38815 3342 52455 23786 33500 NLK-PORCN-SLC9A3R1 39803 20122 9428 9998 42527
FZD1-NLK-TLE1 32959 8717 41662 33327 32893 NLK-PORCN-TCF7 14350 41604 26400 15610 37827
FBXW11-FGF4-NLK 2114 16567 7954 26999 37518 CSNK1G1-NLK-TLE1 51469 19124 38302 32990 19686
DKK1-NLK-SENP2 2831 28851 33433 831 12425 FOSL1-NLK-WNT2B 20492 705 35136 30860 53018
CXXC4-NLK-TLE2 21331 11904 46279 1885 30976 FOSL1-NLK-WNT3A 51755 5242 44005 49978 52983
CXXC4-NLK-SFRP1 49331 4153 49861 27131 33193 DKK1-FGF4-NLK 3129 15113 40241 34444 48762
NLK-PORCN-WNT2 44692 38504 8829 1995 53685 FRAT1-NLK-FBXW4 50800 21515 31927 26376 27004
DAAM1-FGF4-NLK 1482 50392 22580 43523 38010 NLK-PORCN-TLE2 41691 54802 745 25237 46608
LRP5-NLK-WNT2B 28396 1960 19941 23600 55297 NLK-PORCN-WNT4 33383 45823 7542 34942 49961
AES-AXIN1-NLK 32068 45433 3161 29821 53403 FZD1-NLK-WNT2B 28935 4414 27054 36546 52981
FOSL1-NLK-SFRP1 34233 941 55096 25592 35663 FZD7-NLK-WNT3A 23365 3018 51679 44843 19133
NLK-SFRP1-WNT5A 22263 52123 16817 33554 46452 FGF4-NLK-WNT4 4835 2733 36815 3654 11745
NLK-SFRP1-WNT2 33812 54135 6702 29330 45088 DVL2-JUN-NLK 17072 6052 41009 20313 44474
NLK-SFRP1-WNT3 51886 35916 3457 20064 40670 FZD8-NLK-WNT2B 50248 4499 42098 23442 25585
DIXDC1-NLK-WNT4 5010 8900 42377 1999 3181 CXXC4-NLK-WNT2B 28869 300 28004 21112 54426
CTNNB1-NLK-TLE1 55950 22712 28147 35986 13653 FZD8-NLK-SFRP1 54470 72 56582 18335 33221
CTBP1-FGF4-NLK 3746 33288 10452 55841 49146 NLK-PORCN-TCF7L1 31569 44836 10175 2151 43393
CSNK1G1-NLK-TCF7L1 38665 6811 44713 7792 48500 DVL1-FGF4-NLK 2306 54597 5405 53929 25428
FRZB-NLK-WNT4 6001 9443 53325 4130 50442 FRAT1-NLK-TLE2 26675 24348 52446 8545 15016
DVL2-FGF4-NLK 2327 15184 45235 14257 45259 FZD5-FGF4-NLK 2239 33059 12033 52334 51042
AES-EP300-NLK 38886 52106 1233 23736 42435 CSNK1D-NLK-WNT4 1538 21775 47534 6449 28873
BCL9-FGF4-NLK 6693 29487 24244 44096 45853 CXXC4-FGF4-NLK 1507 4569 5986 44776 54536
FBXW11-FOXN1-NLK 345 17553 4941 12084 9525 FSHB-FZD2-NLK 17474 18226 16777 16181 28351
CSNK1G1-NLK-WNT2B 53434 5922 42619 33337 50690 FZD1-NLK-PPP2R1A 20834 8886 52092 12766 24248
GSK3B-NLK-TLE1 45736 20255 50690 4684 15971 LRP5-NLK-SFRP4 42299 6001 52599 18512 34951
FZD1-NLK-WNT5A 28100 15641 23012 14962 49066 CTNNBIP1-NLK-FBXW4 44996 19802 33841 25211 38562
CTNNBIP1-NLK-WNT2B 23541 1910 34449 30631 55521 CSNK1A1-NLK-TLE1 16274 1109 56566 37347 24936
LRP5-NLK-WNT5A 33250 14809 24503 18293 46276 CTNNBIP1-NLK-RHOU 20208 392 56468 42238 24576
NLK-PORCN-TLE1 37435 39499 5549 31543 47543 DIXDC1-NLK-FBXW4 25837 3880 29684 25017 18802
FBXW2-JUN-NLK 29577 33489 631 40952 3561 CTNNBIP1-NLK-WNT4 27403 2923 45312 850 52767
FZD5-NLK-SENP2 9566 34294 49065 9629 25330 CSNK1D-NLK-WNT3A 12770 9632 43802 42949 37641
LRP5-NLK-PPP2R1A 22739 10079 12169 17484 38120 CSNK1G1-NLK-PPP2R1A 35195 9424 21823 20710 43474
NLK-FBXW4-WNT3A 26514 5505 28475 52773 4096 CXXC4-NLK-TCF7L1 38206 4994 56442 3145 46853
FZD5-NLK-WNT4 18569 6862 45684 649 46844 EP300-GSK3A-NLK 1488 36811 54049 43805 46079
CCND1-FRAT1-NLK 26521 15175 17461 50164 8676 CXXC4-NLK-WNT5A 46697 2350 52931 39870 42513
NLK-SFRP1-TLE2 44300 56949 757 34474 28195 DKK1-GSK3A-NLK 28 36037 55819 40750 50385
FGF4-NLK-WNT2B 13475 808 24001 38421 32951 FOSL1-NLK-SFRP4 56020 1030 45227 15474 45886
FRAT1-NLK-RHOU 52049 4579 56808 43475 33170 FRAT1-NLK-PPP2R1A 47257 5675 39028 27369 25057
CTNNBIP1-NLK-PPP2R1A 27842 23336 43647 19091 40032 NLK-PYGO1-WNT2 7759 3583 13307 7257 24124
AXIN1-FZD2-NLK 17740 18892 23208 35290 20140 NLK-WIF1-WNT4 27894 29051 3153 6969 7790
NLK-SFRP1-FBXW4 21614 5912 9190 38148 35118 GSK3A-JUN-NLK 12859 53370 40655 43079 36718
AXIN1-FOXN1-NLK 9541 19853 27767 42655 28011 FZD1-NLK-SFRP4 28087 13170 30488 13854 38484
CXXC4-NLK-RHOU 43136 740 51616 39219 36924 DVL1-FOXN1-NLK 3090 52566 51110 49483 15813
FZD1-NLK-TCF7L1 6486 13405 43996 6473 42827 CCND3-FGF4-NLK 277 51087 6136 52041 3116
DAAM1-FRAT1-NLK 48108 52925 26046 49813 10162 NLK-WIF1-WNT3A 15025 31663 634 53620 7624
CTNNB1-NLK-WIF1 36869 4645 37317 37303 40718 FOSL1-NLK-TCF7L1 10193 14999 53644 2916 50012
CSNK1D-NLK-SENP2 2789 23569 46292 12953 16278 CSNK1A1-NLK-WIF1 11282 8274 56968 38447 50254
FRAT1-NLK-TCF7 46859 4510 41103 2141 38466 CCND1-NLK-WNT2B 9124 21736 38415 27714 2883
Table 2: Rankings o NLK-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
NLK-WNT5A, NLK-PYGO1-WNT2, NLK-WIF1-WNT4, NLK-WIF1-WNT3A and
CCND1-NLK-WNT2B. All hese combina ions indica e he exis ence o a possible
syne gy when hey ake a highe ank in he lis o combina ions.
9
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