CXXC- ype zinc inge p o ein 4 (CXXC4) : 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
CXXC4 (o Dishe elled DVL-binding p o ein - inhibi ion o he DVL and AXIN com-
plex (IDAX)) encodes a CXXC- ype zinc inge domain-con aining p o ein ha an ag-
onizes he canonical WNT signaling pa hway. This domain con ains eigh conse ed
cys eine esidues ha bind o wo zinc ions. The encoded p o ein nega i ely egula es
WNT signaling h ough in e ac ion wi h he pos synap ic densi y p o ein (PSD95) /
D osophila disc la ge umo supp esso (DlgA) / zonula occludens-1 p o ein (ZO-1) o
(PDZ) p o ein domain o DVL, ha is equi ed o he s abiliza ion o he ansc ip-
ional co-ac i a o β-ca enin. 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 us-
ing sel -o ganizing maps, hey iden i ied clus e s o genes ha exhibi simila exp es-
sion dynamics and unco e ed p e iously un ecognized posi i e and nega i e eedback
loops. Howe e , hei s udy depic s/uses singula measu emen s o indi idual gene
exp ession a di e en ime snapsho s/poin s o in e he sys em wide analysis o he
pa hway. A any pa icula ime poin , i is o en he case ha genes a e wo king syne -
gis ically in combina ions, e en hough hei exp ession measu emen s a e singula in
na u e. He e, I •enume a e and ank all 2415 CXXC4 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 CXXC4-X-X combina ions, which poin o exis ence o bio-
logical 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.
ITime beha iou al s udy o 3-od CXXC4 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1Aspec s o unpublished wo k we e p esen ed in a pos e session a Cell Symposia: Technology.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 8, 2025
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. 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 CXXC4 ela ed combina ions using indi idual gene exp essions measu ed in
ime, in WNT3A s imula ed HEK 293 cells.
2. In oduc ion
The de ails o he machine lea ning based sea ch engine has been ecen ly published in
Sinha [2] and deployed o explo e he 2nd o de combina ions o genes in he da a se
p o ided by Guj al and MacBea h [1]. Ne e heless, he e, I poin o he undamen als
o he published wo k o comple eness.
2.1. A combina o ial p oblem
Sensi i i y analysis plays a majo ole in compu ing he s eng h o he in luence o
in ol ed ac o s in any phenomena unde in es iga ion. When applied o exp ession
p o iles o a ious in a/ex acellula ac o s ha o m an in eg al pa o a signaling
pa hway, he a iance and densi y based analysis yields a ange o sensi i i y indices
o indi idual as well as a ious combina ions o ac o s. These combina ions deno e
he highe o de in e ac ions among he in ol ed ac o s. Compu a ion o highe o -
de in e ac ions is o en ime consuming bu i gi es a chance o explo e he a ious
combina ions ha migh be o in e es in he wo king mechanism o he pa hway. Fo
example, in a ange o ou h o de combina ions among he a ious ac o s o he Wn
pa hway, i would be easy o assess he in luence o he des uc ion complex o med by
APC, AXIN, CSKI and GSK3 in e ac ion. Bu he e ec o hese combina ions a y
o e ime as measu emen s o old changes and de ia ions in old changes a y. So
i is impe a i e o know how an in e ac ion o a combina ion o he in ol ed ac o s
beha e in ime and Sinha [2] de elops a p ocedu e o ack he beha iou by exploi ing
he in luences o hese in ol ed ac o s.
2
2.2. A possible solu ion
In his wo k, a e es ima ing he indi idual e ec s o ac o s o a highe o de combi-
na ion, he indi idual indices a e conside ed as disc imina i e ea u es. A combina ion,
hen, is a ea u e se in highe o de (≥2 ,i.e mul i a ia e). Wi h an excessi ely la ge
numbe o ac o s in ol ed in he pa hway, i is di icul o sea ch o impo an com-
bina ions in a wide sea ch space o e di e en o de s. Exploi ing he analogy wi h
he issues o p io i izing webpages using anking algo i hms, o a pa icula o de , a
ull se o combina ions o in e ac ions can hen be p io i ized based on hese ea u es
using a powe ul anking algo i hm ia suppo ec o s Joachims [3]. Reco ding he
changing ankings o he combina ions o e ime e eals how highe o de in e ac ions
beha e wi hin he pa hway and when an in e en ion migh be necessa y o in luence
he in e ac ion wi hin he pa hway.
2.3. CXXC- ype zinc inge p o ein 4 (CXXC4)
CXXC4 is belongs o he class o Zinc inge s. A zinc inge is a small p o ein s uc-
u al mo i which con ain mul iple inge -like p o usions ha make con ac s wi h hei
a ge molecule and a e cha ac e ized by he coo dina ion o one o mo e zinc ions
(Zn2+) which s abilizes he old. Some o hese domains bind zinc, bu many do no ;
ins ead binding o he me als such as i on, o no me al a all. This domain con ains
eigh conse ed cys eine esidues ha bind o wo zinc ions. The CXXC domain is
ound in a a ie y o ch oma in-associa ed p o eins and binds o non-me hyla ed CpG
dinucleo ides. The domain is cha ac e ised by wo CGXCXXC epea s.
In a emp ing o cla i y he oles o DVL in he WNT signaling pa hway, Hino
e al. [4] iden i ied a no el p o ein which binds o he PDZ domain o DVL and named
i IDAX ( o inhibi ion o he D l and Axin complex o CXXC4). IDAX and AXIN
compe ed wi h each o he o he binding o DVL and immunocy ochemical analy-
ses showed ha he o me was localized o he same place as DVL in cells and ha
exp ession o he la e inhibi ed he colocaliza ion o DVL and IDAX. Fu he , WNT-
induced accumula ion o β-ca enin and ac i a ion o T-cell ac o in mammalian cells
we e supp essed by exp ession o Idax. Since DVL is a posi i e egula o in he WNT
signaling pa hway and ha he PDZ domain is impo an o his ac i i y, hei esul s
sugges ed ha IDAX ac ed as a nega i e egula o o he WNT signaling pa hway by
di ec ly binding o he PDZ domain o D l.
Kojima e al. [5] iden i ied a CXXC4 homozygous dele ion a 4q24 in an agg es-
si e enal cell ca cinoma (RCC) using single-nucleo ide polymo phism (SNP) a ays.
They ound signi ican ly lowe CXXC4 mRNA le els in umo samples in pa ien s wi h
me as ases compa ed wi h hose wi hou . Fu he , knockdown o CXXC4 induced he
nuclea ansloca ion o β-ca enin and al e ed exp ession o a se o genes in ol ed in
cell p oli e a ion, in asion and su i al.
I p esen 3 d o de combina ions o CXXC4 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
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 [6]. 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 [6].
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
4
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
SV MRank
classi y Joachims [3]. No e ha due o a ailabili y o only one example pe com-
bina ion, a e he model has been buil , he same aining da a is used as es da a o
gene a es he sco es. This p ocedu e is execu ed o each and e e y sensi i i y analysis
me hod. This is ollowed by so ing o hese sco es along wi h he ank indices (i.e he
aining indices) al eady assigned o he gene combina ions. The end esul is a so ed
o de o he gene combina ions based on he anking sco e lea ned by he SV MRank
algo i hm. Finally, his en i e p ocedu e is compu ed o sensi i i y indices gene a ed
o each and e e y old change a ime poin and de ia ions in old change a di e en
du a ions. Obse ing he changing ank o a pa icula combina ion a di e en imes
and di e en ime pe iods will e eal how a combina ion is beha ing.
No e ha he ollowing is he o de in which he iles should be execu ed in R, in
o de , o ob aining he desi ed esul s (No e ha he code will no be explained he e) - •
use sou ce(”mainSc ip -1-1.R”) wi h a gumen s o Dynamic da a •sou ce(”SVMRank-
Resul s-D.R”), o ank he in e ac ions (again his needs o be done sepa a ely o
di e en kinds o SA me hods), •use sou ce(”Combine-Time- iles.R”), i compu -
ing indices sepa a ely ia p e ious ile, •sou ce(”So -n-Plo -D.R”) o so he in e -
ac ions. No e ha he so ing is chages he in e ac ion anking in ime. Thus •use
sou ce(”In e ac ion-P io i y-In ime.R”) o ind he p io i ized anking o each and e -
e y in e ac ion o e he di e en ime poin s and inally •use sou ce(”P in -Ranking-
AND-In e ac ion-Rank.R”) o p in indi idual anking o he equi ed inpu ac o wi h
o he in e ac ion ac o s.
6. Resul s & Discussion
6.1. Time se ies da a by Guj al and MacBea h [1]
NOTE - Ranking was assigned on sco es ha we e so ed in DECREASING alues.
So, 1 was assigned o highes sco e and ice e sa.
Resul s o he 3 d o de in e ac ions a e p esen ed he e. The esul s i s discuss
he beha iou o in e ac ions ac oss he snapsho s o ime using he compu ed sensi-
i i ies on old change measu emen s pe ime snapsho . The analysis was done us-
ing 4 di e en sensi i i y indices. Ou o he 71C3combina ions, I conside /p esen
only hose combina ions ha show a anking wi hin i s 10,000 ou o 57,155. This
choice is libe al and biologis s/oncologis s can ha e a mo e s ic e choice as pe need.
Two obse a ions a e made, • he anking o a pa icula combina ion is conse ed (i.e
wi hin he 10,000 ange) in a pa icula ime poin o in he ea ly phase o la e phase
o WNT3A s imula ion, ac oss he majo i y o he ou sensi i i y me hods, which is a
5
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 CXXC4-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 [7]) and Sobol indicies (wi h 2002 implemen a ion in Sal elli [8] and
ma inez implemen a ion in Ma inez [9] and Baudin e al. [10]).
6.3. Conse ed machine lea ning ankings o es ed CXXC4-X-X
combina ions
A o al o 2415, 3 d o de combina ions in ol ing CXXC4 we e ob ained om a ull
se o 71C3= 57155 combina ions. Fu he , om his selec ed se , using he abo e c i-
e ia o conse ed ankings, I epo / abula e he meaning ul combina ions ha migh
be wo king syne gis ically. Tables 2, 3 and 4 show he ankings o he same combi-
na ions as in able 1, bu using b ke nel o HSIC, 2002 implemen a ion o SOBOL
and ma inez implemen a ion o SOBOL, espec i ely. As one allies he ankings o
ac oss hese ables o a pa icula combina ion, one inds ha he ole o he combina-
ion o in e es is conse ed. This conse a ion poin s o he exis ence o he biological
syne gy, whe he he combina ion has been es ed o unexplo ed/un es ed.
6.3.1. Examining he beha iou o DVL-CXXC4-X combina ions
I is known om abo e li e a u e ha CXXC4 binds wi h DVL o an agonize he WNT
signaling pa hway. Looking a he ables abo e, one inds he ollowing combina ions
o membe s o DVL amily along wi h CXXC4, o be p ominen a 3 d o de le el -
CXXC4-DVL2-FRZB, CXXC4-DVL2-SFRP4, CXXC4-DVL2-LRP5, CXXC4-DVL2-
RHOU, CXXC4-DVL2-WNT2B, CXXC4-DVL2-FZD1 and CXXC4-DVL2-WNT3A.
6
RANKING @ iUSING HSIC - LINEAR
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CXXC4-PORCN-SENP2 10 33446 17033 17387 32253 CXXC4-PORCN-WNT4 49 6186 19448 20672 51388
CXXC4-PORCN-WNT2B 60 17097 46765 26682 32940 CXXC4-FRAT1-FRZB 64 19925 35266 282 20625
CXXC4-PORCN-SFRP4 80 28448 27819 28835 44315 CXXC4-FOSL1-SENP2 88 36639 18548 29008 12844
CXXC4-FZD7-PPP2CA 90 9819 23105 12397 36836 CXXC4-FZD7-SFRP4 136 18277 38915 34583 33873
CXXC4-PORCN-TCF7 147 56042 37081 25343 32394 CXXC4-PORCN-FBXW4 168 26465 19028 12201 29004
CXXC4-FRAT1-TLE2 212 18126 46011 57 25507 CXXC4-FOSL1-PPP2R1A 255 24314 35136 31526 39110
CXXC4-FRAT1-FZD1 296 10717 21805 2575 15715 CXXC4-FRAT1-FBXW4 304 26037 23203 450 10918
CXXC4-FGF4-SENP2 325 44612 33138 54156 47148 CXXC4-PORCN-PPP2R1A 424 27798 37533 50501 37618
CXXC4-FGF4-FRZB 461 19762 30000 22761 54575 CXXC4-FZD7-WNT2B 472 12278 44001 31202 33433
CXXC4-DVL2-FRZB 479 9516 3524 8282 38815 CXXC4-PORCN-PPP2CA 481 22027 38709 38555 36190
CXXC4-NLK-WNT4 491 167 4767 2069 15953 CXXC4-FRAT1-TCF7L1 519 13366 30568 2083 18784
CXXC4-PORCN-WNT5A 535 15961 16253 55679 46631 CXXC4-FGF4-RHOU 583 24551 34633 53319 56248
CXXC4-NLK-FBXW4 591 19400 24702 2318 5774 CXXC4-DVL2-RHOU 703 7173 6556 19343 52966
CXXC4-FOSL1-FRAT1 731 20058 29538 14504 27891 CXXC4-JUN-TLE2 764 1040 837 11709 30876
CXXC4-FGF4-LRP5 826 10603 47963 24020 51425 CXXC4-FRAT1-FZD8 827 10881 39520 3401 24688
CXXC4-JUN-SENP2 843 21048 50347 6595 9660 CXXC4-FGF4-TLE2 870 21534 50726 38272 53250
CXXC4-JUN-RHOU 881 1789 43156 41625 53423 CXXC4-FGF4-WNT3A 905 28520 52397 52668 30693
CXXC4-FGF4-WNT5A 957 4552 41511 51712 55041 CXXC4-JUN-LRP5 971 1353 33173 6860 26690
CXXC4-FGF4-PPP2R1A 1044 30931 36251 44472 52608 CXXC4-FOXN1-SLC9A3R1 1089 2458 1605 6818 34700
CXXC4-FGF4-TCF7 1091 38819 31734 49434 48726 CSNK1G1-CXXC4-FOSL1 1094 46700 26853 25310 54546
CXXC4-JUN-FBXW4 1138 13192 17971 6537 17461 CXXC4-FOXN1-RHOU 1258 949 4951 19719 52102
CSNK1D-CXXC4-FZD1 1263 2919 24873 24770 29960 CXXC4-JUN-SFRP4 1308 4014 25558 7639 24982
CXXC4-DVL2-SFRP4 1347 5287 2872 6219 37139 CXXC4-DVL2-WNT2B 1361 15018 7269 31481 39016
CXXC4-FGF4-FOSL1 1368 22243 14796 45725 54959 CXXC4-JUN-TCF7 1379 21025 34076 34379 37036
CXXC4-FRAT1-WNT3A 1421 24998 29856 17406 1342 CXXC4-NLK-TLE2 1467 3249 13379 2815 22591
CXXC4-JUN-PYGO1 1496 10929 38139 43065 17470 CXXC4-FOXN1-FRZB 1502 99 9554 17642 46105
CXXC4-NLK-SFRP1 1520 3860 3645 1038 15312 CXXC4-JUN-TCF7L1 1561 16594 47993 27451 26786
CXXC4-FZD2-LEF1 1642 3090 9287 23149 51524 CXXC4-GSK3A-WNT2 1689 13832 6873 29230 43303
CXXC4-WIF1-WNT3A 1745 353 12465 51440 34488 CXXC4-FGF4-WNT4 1747 5857 34419 49599 54246
CXXC4-FGF4-FZD1 1751 11265 20257 55084 52255 CXXC4-FOXN1-SENP2 1771 9020 6263 7094 11868
CXXC4-FZD7-RHOU 1774 20795 27044 52150 54907 CXXC4-JUN-PPP2R1A 1782 11540 37923 13434 43762
CXXC4-FOSL1-WNT5A 1800 15338 42242 52718 32578 CXXC4-FRAT1-LRP5 1810 3252 48463 383 12590
CXXC4-JUN-SLC9A3R1 1862 8225 23228 21414 44419 CXXC4-FGF4-KREMEN1 1948 42829 14565 52294 56300
CXXC4-FZD2-SFRP4 1951 1938 36455 2988 50465 CXXC4-DVL2-FZD1 2007 11971 18762 3053 35259
CXXC4-FZD1-SENP2 2050 40723 10326 38271 17504 CXXC4-FGF4-SFRP4 2200 21598 27619 50838 52265
CXXC4-NLK-WNT2B 2202 5290 1484 56489 12898 CXXC4-NKD1-WNT2B 2217 9878 36698 23848 1631
CXXC4-GSK3A-RHOU 2262 20534 4082 47103 49826 CXXC4-PORCN-WNT3 2291 2240 24537 6255 30135
CXXC4-FZD2-RHOU 2317 6671 22273 26084 55079 CXXC4-FGF4-GSK3B 2336 2158 53607 41323 48886
CXXC4-FOXN1-FZD8 2405 10212 3200 15737 15007 CXXC4-FOXN1-SFRP4 2487 1405 7515 14548 25337
CSNK1G1-CXXC4-DKK1 2488 45829 37872 27388 55403 CSNK1G1-CXXC4-FRAT1 2496 24384 49297 7946 49881
CXXC4-FZD7-SENP2 2507 35237 27610 27855 26307 CXXC4-SFRP1-WNT2B 2551 24274 44184 31848 27946
BCL9-CXXC4-FZD7 2587 37095 21041 33971 29584 CXXC4-GSK3A-SFRP4 2604 10596 14291 21482 35934
CXXC4-FZD2-PPP2CA 2607 29974 9988 18663 50107 CXXC4-JUN-WNT4 2688 13375 46722 2824 3108
CXXC4-DVL2-LRP5 2699 16595 48005 8211 27106 CXXC4-WNT1-WNT3A 2734 34306 282 36977 4488
CSNK1D-CXXC4-FRAT1 2744 18327 34701 8594 2661 CXXC4-JUN-PITX2 2757 3424 36286 40345 36376
CXXC4-FGF4-NLK 2780 22054 41988 28791 40205 CXXC4-WIF1-WNT2 2794 318 38171 33660 55940
CXXC4-FOXN1-WNT3A 2796 53 5860 22254 12575 CXXC4-GSK3A-LRP5 2801 2556 3529 23047 42324
CXXC4-FGF4-FRAT1 2842 9594 30978 23790 51147 CXXC4-FZD7-KREMEN1 2872 42910 42232 51357 48270
CXXC4-FRAT1-WNT2 2894 23698 18152 32 32646 CXXC4-FZD2-SENP2 2916 26793 21261 5858 39928
CXXC4-FZD2-LRP5 2946 717 14065 26069 44141 CXXC4-FZD1-LRP5 2998 7300 42894 19351 29464
CXXC4-FZD2-GSK3B 3060 14042 29298 42224 44272 CXXC4-NKD1-SENP2 3069 14633 9774 13334 17352
CXXC4-FOXN1-WNT5A 3109 8816 13105 18798 36097 CXXC4-NKD1-TLE2 3160 26 22413 13930 94
CXXC4-FOXN1-FBXW4 3181 4297 20629 11517 21464 CXXC4-DVL2-WNT3A 3186 7341 5733 24584 2313
CSNK1A1-CTBP2-CXXC4 3187 741 15084 41906 44957 CXXC4-GSK3A-SENP2 3196 30564 1921 32171 26223
CXXC4-FOXN1-PPP2CA 3277 19301 19575 24116 33763 CXXC4-FGF4-PPP2CA 3340 9402 29074 35299 53290
CXXC4-JUN-TLE1 3367 30489 24344 6356 85 CXXC4-GSK3A-SLC9A3R1 3506 9586 9125 48353 50314
CXXC4-FOXN1-WNT2 3532 201 7409 18120 37271 CXXC4-FRAT1-KREMEN1 3542 41044 29584 5685 51990
CXXC4-FZD1-FZD7 3585 25420 10832 32645 23514 CXXC4-FGF4-WNT3 3619 587 35000 56680 49419
CXXC4-FOXN1-LRP5 3643 1872 9789 44781 31650 CXXC4-JUN-PPP2CA 3661 32213 26859 462 30021
CXXC4-FGF4-LRP6 3678 11467 49324 42483 34171 CXXC4-FZD7-TCF7 3714 44164 27210 52158 40111
CXXC4-FOXN1-FZD6 3727 251 19904 12481 33219 CXXC4-FZD2-WNT2B 3800 9215 15294 40680 45553
CXXC4-FGF4-FZD8 3802 3981 51255 45882 40409 CXXC4-NLK-TCF7L1 3843 4771 10375 1945 20127
CXXC4-FZD1-WNT4 3921 4043 24475 36885 25822 CXXC4-NLK-WNT5A 3932 2627 16679 25816 15722
Table 1: Rankings o CXXC4-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
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.
7
RANKING @ iUSING HSIC - RBF
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CXXC4-PORCN-SENP2 9869 47028 41747 45009 41195 CXXC4-PORCN-WNT4 12492 2278 24920 46755 55842
CXXC4-PORCN-WNT2B 11272 21120 2288 41634 56160 CXXC4-FRAT1-FRZB 4615 7359 56816 34657 49785
CXXC4-PORCN-SFRP4 9369 30775 45417 32220 54090 CXXC4-FOSL1-SENP2 27232 42351 44650 16863 48178
CXXC4-FZD7-PPP2CA 7569 8146 8359 8809 29695 CXXC4-FZD7-SFRP4 20307 23535 39439 24195 53332
CXXC4-PORCN-TCF7 8174 50291 19771 4132 42869 CXXC4-PORCN-FBXW4 19853 43651 1014 10933 51164
CXXC4-FRAT1-TLE2 38894 11877 48833 6512 54567 CXXC4-FOSL1-PPP2R1A 52227 34156 6226 46113 43359
CXXC4-FRAT1-FZD1 7404 4364 36104 35047 22551 CXXC4-FRAT1-FBXW4 14668 46919 1016 36914 42585
CXXC4-FGF4-SENP2 252 42683 39239 31323 30294 CXXC4-PORCN-PPP2R1A 20998 30567 5511 22186 56640
CXXC4-FGF4-FRZB 275 29756 38685 40122 49864 CXXC4-FZD7-WNT2B 3497 13030 1072 53710 54739
CXXC4-DVL2-FRZB 4886 7544 48054 28005 23326 CXXC4-PORCN-PPP2CA 9663 20715 7491 12348 51537
CXXC4-NLK-WNT4 22955 3089 37410 121 47163 CXXC4-FRAT1-TCF7L1 14983 16373 55100 8101 42887
CXXC4-PORCN-WNT5A 24704 5412 10695 26556 50085 CXXC4-FGF4-RHOU 2335 25378 25285 54463 41595
CXXC4-NLK-FBXW4 36361 6924 5576 32715 39457 CXXC4-DVL2-RHOU 24302 4880 47885 35622 25708
CXXC4-FOSL1-FRAT1 46607 15174 26086 25252 40912 CXXC4-JUN-TLE2 2337 10507 41107 15818 46481
CXXC4-FGF4-LRP5 1846 12123 15671 39128 29876 CXXC4-FRAT1-FZD8 6745 11128 54253 54080 39603
CXXC4-JUN-SENP2 1851 32478 55139 8858 43014 CXXC4-FGF4-TLE2 591 38121 27919 26190 19771
CXXC4-JUN-RHOU 7270 2533 37155 46380 45935 CXXC4-FGF4-WNT3A 376 11041 597 49220 57138
CXXC4-FGF4-WNT5A 6438 9457 13415 42775 42269 CXXC4-JUN-LRP5 15539 1611 30933 39991 28813
CXXC4-FGF4-PPP2R1A 1192 9614 5570 26405 23051 CXXC4-FOXN1-SLC9A3R1 5835 4242 55138 22461 50612
CXXC4-FGF4-TCF7 1232 32544 24487 22245 56783 CSNK1G1-CXXC4-FOSL1 18872 46435 17556 11771 54033
CXXC4-JUN-FBXW4 14457 30498 1036 36322 33651 CXXC4-FOXN1-RHOU 4808 4398 51558 29746 40158
CSNK1D-CXXC4-FZD1 7144 1734 27303 7250 11481 CXXC4-JUN-SFRP4 8489 12877 51306 12233 26552
CXXC4-DVL2-SFRP4 16351 4938 49667 29954 34883 CXXC4-DVL2-WNT2B 14916 7821 10829 36605 32745
CXXC4-FGF4-FOSL1 553 41867 29836 8057 53097 CXXC4-JUN-TCF7 2896 16477 22826 15141 21339
CXXC4-FRAT1-WNT3A 5682 22392 33504 50525 42228 CXXC4-NLK-TLE2 21331 11904 46279 1885 30976
CXXC4-JUN-PYGO1 15268 3842 31367 43633 53074 CXXC4-FOXN1-FRZB 2132 6567 49876 23824 32081
CXXC4-NLK-SFRP1 49331 4153 49861 27131 33193 CXXC4-JUN-TCF7L1 5069 16399 50288 29076 25853
CXXC4-FZD2-LEF1 38950 1181 32681 4532 22634 CXXC4-GSK3A-WNT2 1230 15380 52831 13794 54110
CXXC4-WIF1-WNT3A 11746 12153 2343 56809 35373 CXXC4-FGF4-WNT4 299 4403 10799 6662 56255
CXXC4-FGF4-FZD1 412 10632 11544 31326 47937 CXXC4-FOXN1-SENP2 515 15255 52769 4140 43381
CXXC4-FZD7-RHOU 8290 22007 17701 54867 39963 CXXC4-JUN-PPP2R1A 8147 19410 4343 32567 48732
CXXC4-FOSL1-WNT5A 53822 4385 5771 55698 30961 CXXC4-FRAT1-LRP5 23317 429 29024 48013 32482
CXXC4-JUN-SLC9A3R1 13688 4927 33829 15408 20050 CXXC4-FGF4-KREMEN1 1514 40573 41207 46205 49688
CXXC4-FZD2-SFRP4 16662 2511 31631 1790 20964 CXXC4-DVL2-FZD1 6039 15880 42432 32927 19633
CXXC4-FZD1-SENP2 34090 36346 54606 22792 22438 CXXC4-FGF4-SFRP4 1800 28754 47520 10479 30525
CXXC4-NLK-WNT2B 28869 300 28004 21112 54426 CXXC4-NKD1-WNT2B 33112 30020 8852 27851 43373
CXXC4-GSK3A-RHOU 258 9516 53313 35938 49928 CXXC4-PORCN-WNT3 37775 8521 7319 54045 46168
CXXC4-FZD2-RHOU 10828 29932 33193 7959 25644 CXXC4-FGF4-GSK3B 2513 1585 2338 49143 54753
CXXC4-FOXN1-FZD8 2538 22024 56449 30002 56254 CXXC4-FOXN1-SFRP4 2063 2782 54618 3345 15870
CSNK1G1-CXXC4-DKK1 18870 49739 2762 48160 29218 CSNK1G1-CXXC4-FRAT1 10676 6045 28407 52045 39223
CXXC4-FZD7-SENP2 1262 39914 29126 38452 45236 CXXC4-SFRP1-WNT2B 9023 37294 3518 45010 56925
BCL9-CXXC4-FZD7 9941 29991 34446 25812 41178 CXXC4-GSK3A-SFRP4 170 13696 53514 4388 43098
CXXC4-FZD2-PPP2CA 11564 33338 12458 3001 54858 CXXC4-JUN-WNT4 4946 4363 31447 4600 32510
CXXC4-DVL2-LRP5 11745 7304 42550 26847 15371 CXXC4-WNT1-WNT3A 1236 41816 5972 30693 33822
CSNK1D-CXXC4-FRAT1 14134 8276 23947 22453 12908 CXXC4-JUN-PITX2 5093 2871 54929 54382 25342
CXXC4-FGF4-NLK 1507 4569 5986 44776 54536 CXXC4-WIF1-WNT2 51580 27076 41572 21992 55327
CXXC4-FOXN1-WNT3A 2235 1906 54317 41438 43489 CXXC4-GSK3A-LRP5 385 9378 49161 34343 36785
CXXC4-FGF4-FRAT1 4283 5655 31886 10011 47555 CXXC4-FZD7-KREMEN1 3201 51583 32100 52166 52493
CXXC4-FRAT1-WNT2 31513 32492 56401 22069 45177 CXXC4-FZD2-SENP2 11373 32779 36118 41772 48711
CXXC4-FZD2-LRP5 17864 7669 25949 15071 31594 CXXC4-FZD1-LRP5 50587 2520 47210 49401 49419
CXXC4-FZD2-GSK3B 11449 20532 5769 43469 53376 CXXC4-NKD1-SENP2 23566 21575 56539 18663 8724
CXXC4-FOXN1-WNT5A 6575 17827 51655 52301 55304 CXXC4-NKD1-TLE2 14475 5894 51388 28114 51127
CXXC4-FOXN1-FBXW4 3459 16395 8588 13912 10169 CXXC4-DVL2-WNT3A 5548 8944 24906 33696 42805
CSNK1A1-CTBP2-CXXC4 6148 356 31122 45700 47540 CXXC4-GSK3A-SENP2 74 32451 54211 24002 33327
CXXC4-FOXN1-PPP2CA 1922 14941 49768 109 32177 CXXC4-FGF4-PPP2CA 896 24972 12137 33837 43059
CXXC4-JUN-TLE1 12052 20822 44884 32576 24749 CXXC4-GSK3A-SLC9A3R1 467 8014 47156 13152 55436
CXXC4-FOXN1-WNT2 4136 8477 52268 544 46007 CXXC4-FRAT1-KREMEN1 9306 45373 50696 51816 46911
CXXC4-FZD1-FZD7 49954 12547 56459 23869 41132 CXXC4-FGF4-WNT3 3561 311 5182 29806 42876
CXXC4-FOXN1-LRP5 960 9617 46621 12430 9349 CXXC4-JUN-PPP2CA 2697 40480 12704 20114 45550
CXXC4-FGF4-LRP6 2697 40480 12704 20114 45550 CXXC4-FZD7-TCF7 7210 39983 16805 19991 41633
CXXC4-FOXN1-FZD6 4475 608 35118 18286 44561 CXXC4-FZD2-WNT2B 20369 10806 14946 7965 25615
CXXC4-FGF4-FZD8 292 11900 36098 42761 36334 CXXC4-NLK-TCF7L1 38206 4994 56442 3145 46853
CXXC4-FZD1-WNT4 34012 9183 32309 19082 29352 CXXC4-NLK-WNT5A 46697 2350 52931 39870 42513
Table 2: Rankings o CXXC4-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
6.3.2. Examining he beha iou o GSK3-CXXC4-X combina ions
In gas ic cance , Lu e al. [11] show ha CXXC4 in e ac s wi h DVL1 di ec ly and
he mu a ion o c i ical esidues in he DVL-in e ac ing domain ab oga ed i s in e ac-
8
RANKING @ iUSING SOBOL - 2002
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CXXC4-PORCN-SENP2 4981 10546 9375 17394 34482 CXXC4-PORCN-WNT4 9600 4879 1294 6463 37839
CXXC4-PORCN-WNT2B 39582 44080 51571 43634 12796 CXXC4-FRAT1-FRZB 13855 16693 7772 24610 15521
CXXC4-PORCN-SFRP4 3428 54623 4989 9629 43028 CXXC4-FOSL1-SENP2 9857 21302 3091 25681 49127
CXXC4-FZD7-PPP2CA 6148 28592 25213 26202 44025 CXXC4-FZD7-SFRP4 8226 37912 21420 24728 27141
CXXC4-PORCN-TCF7 2527 11671 4576 9976 25876 CXXC4-PORCN-FBXW4 53747 2497 52161 47571 14085
CXXC4-FRAT1-TLE2 8172 787 10839 18520 17014 CXXC4-FOSL1-PPP2R1A 33024 20784 45045 33319 8066
CXXC4-FRAT1-FZD1 9682 502 6322 25277 1837 CXXC4-FRAT1-FBXW4 25898 41741 14499 23277 897
CXXC4-FGF4-SENP2 56902 51611 35174 38140 4316 CXXC4-PORCN-PPP2R1A 44156 3317 53822 38916 15985
CXXC4-FGF4-FRZB 655 16082 9480 20416 46553 CXXC4-FZD7-WNT2B 49726 31087 32815 31314 18255
CXXC4-DVL2-FRZB 6421 47272 15558 23096 47407 CXXC4-PORCN-PPP2CA 13026 53831 3318 18245 41235
CXXC4-NLK-WNT4 53246 51233 55370 49749 15337 CXXC4-FRAT1-TCF7L1 18548 15555 6549 27894 2409
CXXC4-PORCN-WNT5A 47497 52019 55859 50726 19154 CXXC4-FGF4-RHOU 252 5480 21939 19031 52845
CXXC4-NLK-FBXW4 5974 6674 24560 10110 44194 CXXC4-DVL2-RHOU 13662 45063 23761 15178 35600
CXXC4-FOSL1-FRAT1 13778 2749 16108 6403 43145 CXXC4-JUN-TLE2 47401 2576 46879 53365 10616
CXXC4-FGF4-LRP5 19668 6338 18685 9517 51966 CXXC4-FRAT1-FZD8 19654 576 4332 16136 19365
CXXC4-JUN-SENP2 8825 8401 12932 7871 27023 CXXC4-FGF4-TLE2 2464 6054 13953 11679 56111
CXXC4-JUN-RHOU 43332 26892 49071 46614 1986 CXXC4-FGF4-WNT3A 7493 411 15315 24389 48926
CXXC4-FGF4-WNT5A 4008 46378 14592 16580 56090 CXXC4-JUN-LRP5 33040 7608 43755 38567 13643
CXXC4-FGF4-PPP2R1A 6382 430 21801 13251 51268 CXXC4-FOXN1-SLC9A3R1 3959 7438 19286 25956 7951
CXXC4-FGF4-TCF7 45370 46737 48467 45014 23299 CSNK1G1-CXXC4-FOSL1 25168 1437 11571 16056 25721
CXXC4-JUN-FBXW4 49484 2831 37278 49282 3845 CXXC4-FOXN1-RHOU 49343 54575 54627 33981 50794
CSNK1D-CXXC4-FZD1 15838 20986 27843 15827 35450 CXXC4-JUN-SFRP4 7686 54368 19771 7870 53296
CXXC4-DVL2-SFRP4 40484 4674 42806 42655 30934 CXXC4-DVL2-WNT2B 6744 50339 17055 22295 46522
CXXC4-FGF4-FOSL1 52810 50470 34544 37927 3516 CXXC4-JUN-TCF7 1115 20606 6634 9559 44618
CXXC4-FRAT1-WNT3A 7869 2751 20454 26029 9961 CXXC4-NLK-TLE2 9628 4363 7425 17260 48958
CXXC4-JUN-PYGO1 13879 27252 8058 10543 55180 CXXC4-FOXN1-FRZB 47727 56222 50026 44836 51771
CXXC4-NLK-SFRP1 17728 56469 8386 24896 33148 CXXC4-JUN-TCF7L1 56040 37157 50497 47616 12624
CXXC4-FZD2-LEF1 43791 16576 35344 56737 19650 CXXC4-GSK3A-WNT2 55861 49041 34404 46788 7541
CXXC4-WIF1-WNT3A 54553 44801 48557 52030 1570 CXXC4-FGF4-WNT4 49638 56741 41820 32756 8361
CXXC4-FGF4-FZD1 10610 51496 17191 13677 52657 CXXC4-FOXN1-SENP2 20619 376 16314 23024 6715
CXXC4-FZD7-RHOU 42809 25100 32087 29550 5695 CXXC4-JUN-PPP2R1A 44274 1712 51774 45829 14514
CXXC4-FOSL1-WNT5A 45823 54747 52368 41434 48001 CXXC4-FRAT1-LRP5 14447 55550 4187 25428 10791
CXXC4-JUN-SLC9A3R1 3663 5023 4043 7111 47297 CXXC4-FGF4-KREMEN1 9212 1819 7168 7601 47095
CXXC4-FZD2-SFRP4 50903 14206 47616 54449 8766 CXXC4-DVL2-FZD1 8469 13264 13510 23889 17063
CXXC4-FZD1-SENP2 12809 49359 6206 3069 42315 CXXC4-FGF4-SFRP4 44465 38386 38344 41294 134
CXXC4-NLK-WNT2B 17363 10111 1772 5324 38194 CXXC4-NKD1-WNT2B 15436 10525 10086 1323 45129
CXXC4-GSK3A-RHOU 14260 7037 2619 8274 28887 CXXC4-PORCN-WNT3 13 8251 9046 18094 39176
CXXC4-FZD2-RHOU 6780 8109 9925 14270 49006 CXXC4-FGF4-GSK3B 9304 6529 4812 8493 41990
CXXC4-FOXN1-FZD8 55264 46656 51687 38480 50201 CXXC4-FOXN1-SFRP4 13446 237 16807 20244 1750
CSNK1G1-CXXC4-DKK1 29722 16090 47827 56588 1654 CSNK1G1-CXXC4-FRAT1 27618 3778 3433 676 48257
CXXC4-FZD7-SENP2 4691 36054 25571 25112 38500 CXXC4-SFRP1-WNT2B 5270 10347 14597 16518 33006
BCL9-CXXC4-FZD7 12890 55435 14964 14600 32799 CXXC4-GSK3A-SFRP4 42048 44931 50649 47022 11196
CXXC4-FZD2-PPP2CA 48257 39680 46070 54823 47811 CXXC4-JUN-WNT4 11461 1911 4636 18755 45271
CXXC4-DVL2-LRP5 12022 50320 14484 24733 24341 CXXC4-WNT1-WNT3A 46602 51045 38468 51607 4562
CSNK1D-CXXC4-FRAT1 34042 35885 29812 41264 26139 CXXC4-JUN-PITX2 7081 3972 8713 3640 32183
CXXC4-FGF4-NLK 18745 698 6566 18659 49649 CXXC4-WIF1-WNT2 15365 18609 6335 8974 52925
CXXC4-FOXN1-WNT3A 51263 50390 30984 42574 46666 CXXC4-GSK3A-LRP5 2369 28526 3451 15002 30988
CXXC4-FGF4-FRAT1 50820 53673 45701 44615 8451 CXXC4-FZD7-KREMEN1 38479 27988 31220 33378 4766
CXXC4-FRAT1-WNT2 41126 2126 46459 30168 34144 CXXC4-FZD2-SENP2 50382 48962 47212 42891 8509
CXXC4-FZD2-LRP5 10970 45825 5695 222 27035 CXXC4-FZD1-LRP5 51552 42608 31364 30529 12998
CXXC4-FZD2-GSK3B 7116 23758 13803 1131 52308 CXXC4-NKD1-SENP2 53247 30638 52373 44913 3619
CXXC4-FOXN1-WNT5A 45779 49880 48086 39298 56659 CXXC4-NKD1-TLE2 667 11124 4405 10259 37949
CXXC4-FOXN1-FBXW4 43717 56917 40334 36937 55377 CXXC4-DVL2-WNT3A 17336 51748 14847 23229 36228
CSNK1A1-CTBP2-CXXC4 32731 6104 30912 45061 27995 CXXC4-GSK3A-SENP2 42993 50176 54509 48854 28496
CXXC4-FOXN1-PPP2CA 3477 1511 1989 21870 13869 CXXC4-FGF4-PPP2CA 45268 56658 41145 41538 2318
CXXC4-JUN-TLE1 9806 54580 10229 3795 46539 CXXC4-GSK3A-SLC9A3R1 55602 51900 49035 38962 23048
CXXC4-FOXN1-WNT2 20914 24314 16648 24201 21980 CXXC4-FRAT1-KREMEN1 17526 25193 23946 23550 12450
CXXC4-FZD1-FZD7 11040 53941 8320 18995 41701 CXXC4-FGF4-WNT3 37990 37288 42279 35654 7889
CXXC4-FOXN1-LRP5 42375 52933 50994 41421 52542 CXXC4-JUN-PPP2CA 12942 55409 5351 11313 42743
CXXC4-FGF4-LRP6 37441 50826 38434 47652 5185 CXXC4-FZD7-TCF7 7168 23159 23535 24415 44261
CXXC4-FOXN1-FZD6 50432 53386 52863 37651 44074 CXXC4-FZD2-WNT2B 9145 29828 19209 12741 40862
CXXC4-FGF4-FZD8 2927 5577 12374 5513 30264 CXXC4-NLK-TCF7L1 20204 45005 6311 11503 39338
CXXC4-FZD1-WNT4 18374 14688 10406 5900 46576 CXXC4-NLK-WNT5A 12448 41748 17765 12599 37639
Table 3: Rankings o CXXC4-X-X. A lis o app oxima ely i s 125 combina ions wi h ankings below
10,000 ou o 57,155. SA - SOBOL; Implemen a ion - 2002
ion wi h DVL1. Impo an ly, he associa ion o DVL1 wi h AXIN1 and GSK3βwas
dis up ed upon he exp ession o wild- ype bu no he mu a ed CXXC4 ha ailed o
in e ac wi h DVL1. Fu he , he wild- ype bu no he mu a ed CXXC4 educed he
amoun o β-ca enin and inhibi ed he phospho yla ion o GSK3β, while knockdown
9
