Casein kinase-1(α1/δ/γ1) & 2α1 (CSNK) : 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 : 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
Casein kinase (CSNK) a e se ine/ h eonine-selec i e p o ein kinase, which selec i ely
modi ies o he p o eins by co alen ly adding phospha es o hem (phospho yla ion) as
opposed o kinases which modi y lipids, ca bohyd a es, o o he molecules. 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 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 CSNK ( amily membe ) ela ed 3 d o de combina ions in a o es o 71C3com-
bina ions using ou di e en sensi i i y me hods; •show he conse ed ankings o
CSNK-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 CSNK 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1Aspec s o unpublished wo k we e p esen ed in a pos e session a Cell Symposia: Technology.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 26, 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 FOXN1 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,
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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. The ea lies esea ch using Casein
A phosphop o ein is a p o ein ha is pos - ansla ionally modi ied by he a achmen
o ei he a single phospha e g oup, o a complex molecule such as 5’-phospho-DNA,
h ough a phospha e g oup. In euka yo es, he a ge amino acid is mos ly se ine, h e-
onine, o y osine esidues,while in p oka yo es, i is aspa ic acid o his idine esidues.
Cozzone [4] summa izes and documen s he phospho yla ion o p o eins, as a majo
egula o y mechanism in cells.
In a li e mi ochond ia, Bu ne and Kennedy [5] disco e ed an enzyme capable
o ca alyzing he ans e o phospha e om ATP o p o ein. O a numbe o p o eins
es ed, hey obse ed ha only casein was phospho yla ed a an app eciable a e. α-
casein was obse ed o phospho yla e a abou 4 imes he a e o β-casein. Fu he ,
nea ly all o he adioac i i y ans e ed om ATP labeled wi h P32 o casein could
be accoun ed o as adioac i e phosphose ine in acid hyd olysa es o he casein. F ee
phosphose ine did no appea o be an in e media e in he eac ion.
Casein is a amily o ela ed phosphop o eins, known in he o m o α-S1 (encoded
by CSN1S1), α-S2 (encoded by CSN1S2), β(encoded by CSN2) and κ(encoded by
CSN3), casein. Fujiwa a e al. [6] isola ed and cha ac e ized 5 yeas a i icial ch o-
mosome (YAC) clones con aining he human casein gene amily, o s udy he con ol
mechanisms o he exp ession o hese genes. They pe o med, pa ial es ic ion anal-
ysis in conjunc ion wi h he ch omosomal agmen a ion me hod and luo escence in
si u hyb idiza ion (FISH) analysis, o cons uc a de ailed physical map o he casein
gene amily and de e mined he ch omosomal localiza ion o hese genes. The isola ed
YAC clones 748F3, 882G11, 886B3 and 960D2 con ained he en i e casein gene am-
ily, while he κ-casein gene was absen in 750D11. The human αS1-, β- and κ-casein
genes we e ound o be closely linked and a anged in he o de αS1-β-κ. The casein
gene amily was localized o ch omosome 4q21.1 by FISH analysis.
2.4. Casein kinase (CSNK)
The Casein kinase amily o p o ein kinases a e se ine/ h eonine-selec i e enzymes,
which selec i ely modi ies o he p o eins by co alen ly adding phospha es o hem (i.e
phospho yla ion, Cohen [7]) as opposed o kinases which modi y lipids, ca bohyd a es,
o o he molecules.
In he Golgi appa a us o lac a ing a mamma y gland, Bingham and Fa ell J [8]
ound a casein kinase ha ca alyzed he phospho yla ion o dephospho yla ed α-S1-
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casein by ATP. They epo ha dephospho yla ed β- and κ-caseins we e also phos-
pho yla ed by his enzyme, while o he milk p o eins (β-lac oglobulin, α-lac albumin,
na i e α-S1-, β-, and κ-casein, and p o eins o he a globule memb ane) we e phos-
pho yla ed o a limi ed ex en . They obse ed ha he op imum pH o phospha e
inco po a ion in o dephospho yla ed casein was 7.6; he Km o dephospho yla ed α-
S1-casein was 12 µm (.27 mg pe ml), whe eas he Km o ATP was 80 µm. Fu he ,
he casein kinase equi ed a di alen ca ion o maximum ac i i y (bo h Ca2+and Mg2+
could sa is y his equi emen ). These indings sugges ed ha he phospho yla ion o
casein (a ood p o ein), was qui e di e en om he phospho yla ion o cellula en-
zymes, which equi ed cyclic AMP, was inhibi ed by Ca2+and was in ol ed in con ol
mechanisms.
Hanks and Hun e [9] ca ied ou a monumen al ask o analyzing and colla ing
he amino acid sequences o all p o ein kinases and de ining he conse ed s uc u al
ea u es ha cha ac e ize he po ion o hese p o eins ha is esponsible o ca aly ic
ac i i y. In hei e iew, hey p esen in o ma ion abou he euka yo ic p o ein kinases
(a la ge supe amily o homologous p o eins), which a e ela ed by hei kinase do-
mains (also known as ca aly ic domains), which consis o ≈250-300 amino acid
esidues. They obse e ha he kinase domains ha de ine his g oup o enzymes
con ain 12 conse ed subdomains ha old in o a common ca aly ic co e s uc u e, as
e ealed by he 3-dimensional s uc u es o se e ed p o einse ine kinases. The e a e
wo main sub-di isions wi hin he supe amily: he p o ein-se ine/ h eonine kinases
and he p o ein- y osine kinases. Fu he , hey sugges ha a classi ica ion scheme can
be ounded on a kinase domain phylogeny, which e eals amilies o enzymes ha ha e
ela ed subs a e speci ici ies and modes o egula ion.
2.4.1. Casein kinase 1 (CSNK1 / CK1)
CSNK1A1 - Tapia e al. [10] isola ed and sequenced, a cDNA clone coding o hu-
man p o ein kinase CK1 (casein kinase 1), hus demons a ing ha i co esponded o a
homolog o he CK1α(CSNK1A1) o m ound in bo ine b ain. Using his cDNA se-
quence and PCR ampli ica ion, hey u he isola ed YAC genomic clones ha con ain
his human CK1αsequence. These YACs we e used o luo escen in si u hyb idiza-
ion in o de o localize he human CK1αgene o ch omosome 13q13.
Fish e al. [11] epo ed he cloning and cha ac e iza ion o a no el iso o m o CKI
om a human placen al cDNA lib a y. The cDNA o his iso o m, hCKIε(CSNK1E),
p edic ed a basic polypep ide o 416 amino acids and a molecula mass o 47.3 kDa.
They obse ed ha i encoded a co e kinase domain o 285 amino acids and a ca boxyl-
e minal ail o 123 amino acids. The kinase domain was 53-98% iden ical o he kinase
domains o o he CKI amily membe s and was mos closely ela ed o he δiso o m.
Localiza ion o he hCKIεgene o ch omosome 22q12-13 and he hCKIδ(CSNK1D)
gene o ch omosome 17q25 con i med ha hese we e dis inc genes in he CKI amily.
In summa y, hCKIεwas a no el CKI iso o m wi h p ope ies ha o e lapped hose o
p e iously desc ibed CKI iso o ms.
CSNK1D - Rowles e al. [12] pu i ied casein kinase I (CKI) o e 6000- old om
bo ine hymus and sequenced se en yp ic pep ides ha accoun ed o nea ly 25% o
he p ima y sequence o he enzyme. They isola ed pa ial cDNAs encoding CKI and
4
a ela ed enzyme (CKIδ), by using PCR. Fu he , hey used he CKI PCR p oduc o
p obe a bo ine b ain cDNA lib a y om which cDNAs co esponding o CKI (CKIα)
and wo homologous enzymes (CKIβand CKIγ) we e iden i ied. Thei inding o he
exis ence o leas ou CKI-like enzymes sugges ed ha CKI ac i i y in issues/cell
ex ac s may be composed o mul iple ela ed bu dis inc p o ein kinases. Based on
his, hey sugges ha his g oup o enzymes was no simila o any o he known p o ein
kinases and may, he e o e, ep esen an addi ional b anch o he p o ein kinase amily.
G a es e al. [13] epo ed he molecula cloning and cha ac e iza ion o a 49-kDa
o m o casein kinase I om a es is. A cDNA clone encoding he enzyme, designa ed
casein kinase I δ(CSNK1D), con ained an open eading ame o 1284 nucleo ides ha
p edic ed a polypep ide o 428 amino acids wi h a M , o 49,121. The p edic ed amino
acid sequence sha ed 76% iden i y wi h casein kinase I α, a 37-kDa o m ha was
cloned om bo ine b ain by Rowles e al. [12]. Fu he , exp ession o he casein kinase
IδcDNA in Esche ichia coli esul ed in ac i e enzyme ha phospho yla ed casein,
phos i in, and he pep ide subs a e DDDDVASLPGLRRR. They obse ed ah Casein
kinase I δ ep esen ed a sepa a e membe o he casein kinase I amily dis inguished
by i s la ge size and unique kine ic beha io wi h espec o hepa in.
Kusuda e al. [14] isola ed and sequenced a cDNA clone coding o human ca-
sein kinase I (CK1). They ound ha he en i e amino acid sequence o human CK1
was 97% homologous o ha o a CK1δ, and hei sequences in he kinase domain
(284 amino acid esidues) we e comple ely iden ical, hus p edic ing ha he ob ained
cDNA was o a human homolog o he CK1δiso o m (CSNK1D). The human CK1δ
gene was mapped o ch omosome 17q25.2q25.3 by luo escencein si uhyb idiza ion
and polyme ase chain eac ion analysis o he human/ oden hyb id cell panels.
CSNK1G1 - Kusuda e al. [15] isola ed wo ypes o cDNA o human casein
kinase 1 γ1 (hCK1 γ1). They ound hCK1γ1S o encode a polypep ide consis ing
o 393 amino acids, which was highly homologous wi h al eady epo ed a CK1γ1
( CK1γ1), while he o he ype o cDNA (hCK1γ1L) encoded a polypep ide consis ing
o 422 amino acids, which was qui e iden ical in he kinase domain, bu di e en in he
C- e minal sequence om hCK1γ1S. Fu he , hCK1γ1L had a cha ac e is ic sequence
o 50 amino acids a he C- e minal end and his mo i was shown o be sha ed by he
casein kinase γ2 and γ3 om a and human, hus sugges ing ha i was a signa u e
sequence o he gamma-iso o ms. RT-PCR analysis e ealed ha hCK1γ1S mRNA
was p edominan ly p esen in he es is, whe eas he abundance o hCK1γ1L mRNA
was nea ly he same in he wel e issues examined. Finally, he human hCK1γ1 gene
(CSNK1G1) was mapped o ch omosome 15q22.1–>q22.31 by luo escence in si u
hyb idiza ion.
2.4.2. Casein kinase 2 (CSNK2 / CK2)
By immunological sc eening o λg 11 exp ession lib a ies, Saxena e al. [16] isola ed
cloned cDNAs encoding bo h subuni s o D osophila melanogas e casein kinase II,
and he comple e amino acid sequence o bo h polypep ides was deduced by DNA
sequencing. The alpha cDNA con ained an open eading ame o 336 amino acid
esidues and he expec ed semi-in a ian esidues p esen in he ca aly ic domain o
p e iously sequenced p o ein kinases, con i ming ha i was he ca aly ic subuni o he
5
enzyme. On he o he hand, he be a subuni was de i ed om an open eading ame o
215 amino acid esidues and exhibi ed no ex ensi e homology o o he p o eins whose
sequences we e known a he ime o his esea ch.
Using a D osophila casein kinase II cDNA p obe, Meisne e al. [17] isola ed a hu-
man cDNA encoding he alpha subuni o casein kinase II and a pa ial cDNA encoding
he a homologue. The D osophila enzyme sequence was ound o be 90% iden ical
wi h he human casein kinase II sequence, and he e was only a single amino acid di -
e ence be ween he published pa ial bo ine sequence and he human sequence. These
esul s we e consis en wi h he possibili y ha wo genes could encode he alpha sub-
uni s.
Casein kinase II holoenzyme appea s o be a e ame , con aining wo αo α’
subuni s (o one o each) and wo be a subuni s. S udy by Lozeman e al. [18], show
ha he e a e wo dis inc ca aly ic subuni s o casein kinase II (alpha and alpha’) and
ha he sequence o hese subuni s was la gely conse ed be ween he bo ine and he
human.
Yang-Feng e al. [19] localized he human CKII-αDNA sequence o wo loci:
11p15.5p15.4 and 20p13, using a combina ion o seg ega ion analysis o oden -human
hyb id cells and ch omosomal in si u hyb idiza ion. In con as , hey mapped he CKll-
α’ gene o ch omosome 16, by soma ic cell hyb id analysis. Taken oge he wi h hei
p e ious assignmen o he CKII egula o y β-subuni gene o 6p12p21, hese esul s
indica ed ha al hough he p oduc s o hese genes o med a single biological complex,
hey we e encoded on di e en human ch omosomes.
CSNK2A1 - Finally, Wi kne e al. [20] isola ed and cha ac e ized a 18.9-kb ge-
nomic clone ep esen ing a cen al po ion o he human casein kinase II (CKII) subuni
αgene (CSNK2A1). Using he whole clone as a p obe, he gene was localized on ch o-
mosome 20p13. The clone con ained eigh exons whose sequences comp ised bases
102 o 824 o he coding egion o he human CKIIαand he exon/in on splice junc-
ions con o med o he g /ag ule. Th ee o he nine in ons we e loca ed a posi ions
co esponding o hose in he CKIIαgene o he nema ode Caeno habdi is elegans. The
in ons con ained eigh comple e and eigh incomple e Alu epea s. Some o he Alu
sequences we e a anged in andems o wo o h ee, which seemed o o igina e om
inse ions o younge Alu sequences in o he poly(A) egion o p e iously in eg a ed
Alu sequences, as indica ed by lanking di ec epea s.
I p esen 3 d o de combina ions o CSNK 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.
6
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 [21]. Reade s a e eques ed o
go h ough hem in he poin ed e e ence. The ools o s udy which a e used he e ha e
been published in ano he ounda ional wo k in Sinha [21].
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
7
model is hen used o gene a e sco e on he obse a ions in he es ing se using he
SV MRank
classi y Joachims [3]. No e ha due o a ailabili y o only one example pe com-
bina ion, a e he model has been buil , he same aining da a is used as es da a o
gene a es he sco es. This p ocedu e is execu ed o each and e e y sensi i i y analysis
me hod. This is ollowed by so ing o hese sco es along wi h he ank indices (i.e he
aining indices) al eady assigned o he gene combina ions. The end esul is a so ed
o de o he gene combina ions based on he anking sco e lea ned by he SV MRank
algo i hm. Finally, his en i e p ocedu e is compu ed o sensi i i y indices gene a ed
o each and e e y old change a ime poin and de ia ions in old change a di e en
du a ions. Obse ing he changing ank o a pa icula combina ion a di e en imes
and di e en ime pe iods will e eal how a combina ion is beha ing.
No e ha he ollowing is he o de in which he iles should be execu ed in R, in
o de , o ob aining he desi ed esul s (No e ha he code will no be explained he e) - •
use sou ce(”mainSc ip -1-1.R”) wi h a gumen s o Dynamic da a •sou ce(”SVMRank-
Resul s-D.R”), o ank he in e ac ions (again his needs o be done sepa a ely o
di e en kinds o SA me hods), •use sou ce(”Combine-Time- iles.R”), i compu -
ing indices sepa a ely ia p e ious ile, •sou ce(”So -n-Plo -D.R”) o so he in e -
ac ions. No e ha he so ing is chages he in e ac ion anking in ime. Thus •use
sou ce(”In e ac ion-P io i y-In ime.R”) o ind he p io i ized anking o each and e -
e y in e ac ion o e he di e en ime poin s and inally •use sou ce(”P in -Ranking-
AND-In e ac ion-Rank.R”) o p in indi idual anking o he equi ed inpu ac o wi h
o he in e ac ion ac o s.
6. Resul s & Discussion
6.1. Time se ies da a by Guj al and MacBea h [1]
NOTE - Ranking was assigned on sco es ha we e so ed in DECREASING alues.
So, 1 was assigned o highes sco e and ice e sa.
Resul s o he 3 d o de in e ac ions a e p esen ed he e. The esul s i s discuss
he beha iou o in e ac ions ac oss he snapsho s o ime using he compu ed sensi-
i i ies on old change measu emen s pe ime snapsho . The analysis was done us-
ing 4 di e en sensi i i y indices. Ou o he 71C3combina ions, I conside /p esen
only hose combina ions ha show a anking wi hin i s 10,000 ou o 57,155. This
choice is libe al and biologis s/oncologis s can ha e a mo e s ic e choice as pe need.
Two obse a ions a e made, • he anking o a pa icula combina ion is conse ed (i.e
wi hin he 10,000 ange) in a pa icula ime poin o in he ea ly phase o la e phase
o WNT3A s imula ion, ac oss he majo i y o he ou sensi i i y me hods, which is a
s ic c i e ia o assessmen o • he anking o a pa icula combina ion is conse ed
ac oss ime poin s/phase (i.e hey a e wi hin he 10,000 ange) and he majo i y o he
ou sensi i i y me hods, which is elaxed c i e ia o assessmen . Applying his il e
helps e eal impo an combina ions o in e es ha migh be wo king syne gis ically
a a highe o de le el in he cell.
Rega ding echnical poin s o implemen a ion, he ankings we e gene a ed wi h-
ou scaling/no malizing he ime se ies da a p o ided by Guj al and MacBea h [1].
8
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 CSNK1A1-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 [22]) and Sobol indicies (wi h 2002 implemen a ion in Sal elli [23]
and ma inez implemen a ion in Ma inez [24] and Baudin e al. [25]).
6.3. Conse ed machine lea ning ankings o es ed CSNK1A1-X-
X combina ions
A o al o 2415, 3 d o de combina ions in ol ing CSNK1A1 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-CSNK1A1-X combina ions
Dishe elled (DVL) p o ein plays a cen al ole in WNT pa hway by ansducing he
signal om he Wn ecep o complex o he β-ca enin des uc ion complex. DVL
also plays a pi o al ole in he plana cell pola i y pa hway ha in ol es he c-JUN
N- e minal kinase (JNK). JNKs we e o iginally iden i ied as kinases ha bind and
phospho yla e c-JUN on Se -63 and Se -73 wi hin i s ansc ip ional ac i a ion domain.
Cong e al. [26] ound ha casein kinase I (CKI), a posi i e egula o o WNT signaling,
s imula ed DVL ac i i y in he WNT pa hway, bu d ama ically inhibi ed DVL ac i i y
in he JNK pa hway. Consis en wi h his, hey obse ed ha o e exp ession o CKI
in D osophila melanogas e s imula ed WNT signaling and dis up ed plana cell pola -
i y. Fu he mo e, by using RNA in e e ence, hey demons a ed ha he D osophila
CKI homologue double ime posi i ely egula ed he β-ca enin pa hway ia DVL and
nega i ely egula ed he DVL-induced JNK pa hway. They hus sugges ed ha CKI
9
di ec ly o , β-ca enin. The s uc u al and biochemical da a sugges ed a no el model
o how APC unc ions in β-ca enin deg ada ion.
Looking a he ables abo e, one inds he ollowing combina ions o APC along
wi h CSNK1A1, o be p ominen a 3 d o de le el - APC-CSNK1A1-DAAM1, APC-
CSNK1A1-TCF7L1, APC-CSNK1A1-WNT2, APC-BCL9-CSNK1A1, APC-CSNK1A1-
DKK1, APC-CSNK1A1-FBXW11, APC-CSNK1A1-SENP2, APC-CSNK1A1-TCF7,
APC-CSNK1A1-FBXW4, APC-CSNK1A1-FZD1, APC-CSNK1A1-FZD8, APC-CSNK1A1-
GSK3B and APC-CSNK1A1-FRZB. 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.
6.4. Conse ed machine lea ning ankings o es ed CSNK1D-X-X
combina ions
A o al o 2415, 3 d o de combina ions in ol ing CSNK 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 6, 7 and 8 show he ankings o he same combina-
ions as in able 5, 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.
NOTE - We conside he same ac o s which ac ed in combina ion o CSNK1A1,
in he p e ious sec ions, as we ha e e idence o li e a u e ha ha e e i ied he exis-
ence o combina o ial syne gy wi h CSNK1A1. He e we see i he e exis s combina-
ions o CSNK1D, o no .
6.4.1. Examining he beha iou o DVL-CSNK1D-X combina ions
Looking a he ables abo e, one inds he ollowing combina ions o membe s o DVL
amily along wi h CSNK1D, o be p ominen a 3 d o de le el - BCL9-CSNK1D-
DVL1 and CSNK1D-DVL2-LEF1. 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.
6.4.2. Examining he beha iou o TCF-CSNK1D-X combina ions
Looking a he ables abo e, one inds he ollowing combina ions o membe s o
TCF amily along wi h CSNK1D, o be p ominen a 3 d o de le el - CSNK1D-FGF4-
TCF7L1, CSNK1D-FGF4-TCF7, CSNK1D-PORCN-TCF7, CSNK1D-PPP2R1A-TCF7L1,
CSNK1D-PPP2R1A-TCF7, CSNK1D-FOXN1-TCF7L1, CSNK1D-JUN-TCF7L1, CSNK1D-
FOXN1-TCF7, CSNK1D-JUN-TCF7, CSNK1D-GSK3A-TCF7L1 and CSNK1D-LRP6-
TCF7. 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.
16
RANKING @ iUSING HSIC - LINEAR
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CSNK1D-FGF4-SENP2 12 15434 36642 38886 8419 CSNK1D-FGF4-FOSL1 30 6054 51426 42593 32863
CSNK1D-FGF4-TCF7L1 44 18859 55201 32920 17618 CSNK1D-FGF4-WNT5A 59 12095 43366 47094 42796
CSNK1D-FGF4-WNT3A 62 3435 29950 56252 22054 CSNK1D-FGF4-LRP5 68 8358 23265 46644 15156
CSNK1D-FGF4-PPP2R1A 72 17401 22364 53716 30729 CSNK1D-FGF4-WNT2B 82 23581 20638 52449 10903
CSNK1D-FGF4-WNT4 98 6482 43663 41124 12062 CSNK1D-FGF4-SFRP1 103 1452 48498 52465 14299
CSNK1D-FGF4-TCF7 114 16725 32161 19689 28545 CSNK1D-FGF4-SFRP4 120 325 44939 34338 20617
CSNK1D-FGF4-RHOU 137 7470 45846 49163 20155 CSNK1D-FGF4-FRAT1 154 4058 50213 49903 6296
CSNK1D-FGF4-NLK 182 13641 35785 54873 12126 CSNK1D-FGF4-GSK3B 194 12598 37191 52378 26164
CSNK1D-FGF4-LEF1 219 1576 38743 22056 7921 CSNK1D-FGF4-FZD7 220 17662 38625 44699 22997
CSNK1D-PORCN-SENP2 254 26488 43944 21480 22511 CSNK1D-SFRP1-WNT2B 268 48716 36593 46538 17001
AES-AXIN1-CSNK1D 336 51649 23870 47953 1427 CSNK1D-FOXN1-LEF1 437 1005 10226 23334 20989
CSNK1D-FGF4-FZD8 505 12071 27989 37578 9827 CSNK1D-FZD2-LEF1 522 392 1270 40271 30141
CSNK1D-FGF4-KREMEN1 529 10037 50110 50880 28493 CSNK1D-FSHB-LEF1 553 21733 36403 3295 16135
CSNK1D-FOSL1-FZD1 568 999 47773 10250 51091 CSNK1D-PORCN-WNT2B 573 51683 44617 47981 16208
CSNK1D-FOXN1-SENP2 624 4830 5783 7469 36423 CSNK1D-GSK3A-LEF1 723 313 2418 21648 1291
CSNK1D-FGF4-WNT3 740 18961 36184 50414 8143 CSNK1D-FGF4-TLE1 799 22825 47823 41761 7069
CSNK1D-JUN-LEF1 823 6859 47543 11454 29458 CSNK1D-PPP2R1A-WNT5A 992 931 1207 30631 56811
FZD5-CCND3-CSNK1D 1013 2704 4480 48146 19 CSNK1D-PORCN-TLE2 1050 41629 52347 39317 20436
CSNK1D-FGF4-FZD6 1063 5699 37365 32586 26789 CSNK1D-PORCN-TCF7 1115 16160 38935 28820 29405
CSNK1D-FOXN1-KREMEN1 1122 3656 11331 13933 38262 CSNK1D-PPP2R1A-TCF7L1 1128 12625 3602 38061 56712
CSNK1D-FOXN1-PPP2CA 1252 17427 16752 21509 34632 CSNK1D-CXXC4-FZD1 1263 2919 24873 24770 29960
CSNK1D-FOXN1-WNT2B 1328 17615 2986 7052 5219 CSNK1D-CTNNB1-T 1338 17969 13628 49746 36181
CSNK1D-FOXN1-FZD8 1359 10239 4066 27563 3347 CSNK1D-PPP2R1A-TCF7 1430 4169 153 38743 7414
CSNK1D-FGF4-LRP6 1476 6459 24160 48759 14140 CSNK1D-PORCN-SLC9A3R1 1596 41508 51420 34746 16992
CSNK1D-FGF4-SLC9A3R1 1680 16334 34504 26928 33064 CSNK1D-FOXN1-TCF7L1 1701 17694 5920 17923 11937
CSNK1D-TLE1-TLE2 1724 21275 41549 44598 15361 CSNK1D-WNT1-WNT2B 1760 3377 3805 17345 50447
CSNK1D-FOXN1-FZD7 1784 13446 5253 17028 40495 CSNK1D-FOXN1-MYC 1836 2577 20627 16019 40465
CSNK1D-SFRP1-SFRP4 1855 34480 36277 39100 23037 CSNK1D-PORCN-SFRP1 1945 41776 54231 29005 26519
CSNK1D-FGF4-PPP2CA 2103 20756 11349 39534 15407 CSNK1D-FOXN1-SLC9A3R1 2107 11939 2569 12418 40459
CSNK1D-PORCN-FBXW4 2224 25065 31330 23189 19480 CSNK1D-JUN-TCF7L1 2260 26231 56724 39559 1567
CSNK1D-FOXN1-FZD1 2304 904 14917 34472 44382 CSNK1D-FGF4-FSHB 2441 17927 45150 34061 11599
CSNK1D-FZD6-SFRP4 2540 1448 2060 26618 40843 FZD5-CCND2-CSNK1D 2569 50084 31913 44030 55296
CSNK1D-GSK3A-SFRP4 2717 1830 17275 20425 6307 CSNK1D-WNT3-WNT3A 2727 49625 22336 55596 44252
CSNK1D-JUN-WNT3A 2740 3878 56083 44551 46162 CSNK1D-CXXC4-FRAT1 2744 18327 34701 8594 2661
CSNK1D-NLK-WNT4 2750 2726 9906 45186 25621 CSNK1D-WNT1-WNT2 2884 830 8568 25186 5895
CSNK1D-FOXN1-RHOU 2891 4517 7734 29359 18640 CSNK1D-PORCN-PPP2R1A 2896 17111 34991 43683 19157
CSNK1D-PORCN-WNT5A 2899 17376 34214 55252 32946 CSNK1D-FGF4-PYGO1 2967 23307 41918 28164 3925
CSNK1D-GSK3A-SENP2 3013 17698 1355 31846 6960 CSNK1D-FOXN1-TCF7 3058 2324 2856 25009 48032
CSNK1D-FGF4-PITX2 3093 11417 24874 53815 30793 CSNK1D-FGF4-WIF1 3202 18099 34798 40988 22019
CSNK1D-FOXN1-LRP5 3219 4054 11922 50036 24583 CSNK1D-JUN-TCF7 3439 2738 31647 25028 51027
CSNK1D-FOSL1-FRZB 3460 9515 54696 17041 40782 CSNK1D-GSK3A-WNT2B 3478 33755 3658 52438 24593
CSNK1D-FRAT1-FZD1 3569 4219 52992 30046 47083 CSNK1D-WNT1-WNT4 3618 317 9161 25363 16241
CSNK1D-NLK-WNT3A 3672 3466 7618 26301 5357 CSNK1D-GSK3A-WNT2 3764 1816 4728 34640 8679
CSNK1D-FOXN1-PITX2 3778 6280 4678 21772 36345 CSNK1D-FOXN1-LRP6 3780 5416 14616 20732 36025
CSNK1D-JUN-WNT2B 3782 39855 36594 49047 2280 BCL9-CSNK1D-DVL1 3917 28513 23552 3666 9410
FZD5-CSNK1D-WNT5A 3923 32577 23307 47873 6444 CSNK1D-JUN-PYGO1 3934 1849 39438 23725 46933
CSNK1D-SFRP1-WNT5A 3998 16473 29590 51130 13720 CSNK1D-JUN-SENP2 4050 19615 50185 29822 41231
CSNK1D-GSK3A-PPP2CA 4064 22624 794 37163 9946 CSNK1D-FOXN1-GSK3B 4159 13828 5801 31044 53930
CSNK1D-GSK3A-KREMEN1 4185 9426 5865 52232 3987 CCND3-CSNK1D-FGF4 4247 56969 5553 44696 25096
BCL9-CSNK1D-FOSL1 4412 39895 11612 3219 55102 CSNK1D-FZD2-PPP2CA 4453 21686 1861 42323 46897
CSNK1D-SFRP1-WNT3A 4551 19558 52514 48069 19184 CSNK1D-LRP6-RHOU 4592 17007 12476 52979 3340
CSNK1D-CTBP2-LEF1 4610 223 28103 22239 7005 BCL9-CSNK1D-SENP2 4632 37058 3181 4534 51855
CSNK1D-FOXN1-WNT3A 4647 1495 8738 24005 46405 CSNK1D-DVL2-LEF1 4662 5034 10825 440 37937
CSNK1D-JUN-TLE2 4736 22202 35404 30933 11826 CCND3-CSNK1D-WNT5A 4753 43030 22446 46977 51854
CSNK1D-FOSL1-FZD7 4768 31561 48499 37364 37254 CSNK1D-NLK-SENP2 4773 12377 9957 43796 3597
CSNK1D-SFRP1-TLE2 4922 46547 38030 46678 31499 CSNK1D-GSK3A-TCF7L1 5032 24389 11966 40967 20883
CSNK1D-PITX2-SFRP4 5096 37446 11233 10582 41257 CSNK1D-FZD2-LRP5 5122 962 3101 54072 26208
CSNK1D-GSK3A-RHOU 5141 8223 4832 44949 10510 CSNK1D-CTNNB1-FRZB 5197 24993 56239 40597 28537
CSNK1D-FGF4-MYC 5235 14215 44901 39123 23202 CSNK1D-JUN-WNT4 5251 20001 51942 21538 52316
BCL9-CSNK1D-EP300 5259 34971 18070 4629 41428 CSNK1D-FOXN1-PPP2R1A 5317 3754 8571 14144 18670
FZD5-CCND1-CSNK1D 5355 24059 52933 18167 50576 CSNK1D-FZD2-SFRP4 5362 1855 17483 13582 54971
CSNK1D-FOXN1-WNT4 5440 3392 11967 26112 53280 APC-BTRC-CSNK1D 5442 10883 12646 22647 6204
CSNK1D-CTBP2-SFRP4 5542 334 31924 37036 44498 CSNK1D-LRP6-TCF7 5593 12297 32989 31678 26667
Table 5: Rankings o CSNK1D-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
6.4.3. Examining he beha iou o PP2A-CSNK1D-X combina ions
Looking a he ables abo e, one inds he ollowing combina ions o membe s o
PPP2A amily along wi h CSNK1D, o be p ominen a 3 d o de le el - CSNK1D-
FGF4-PPP2R1A, CSNK1D-FOXN1-PPP2CA, CSNK1D-FGF4-PPP2CA, CSNK1D-
17
RANKING @ iUSING HSIC - RBF
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CSNK1D-FGF4-SENP2 2542 27165 19967 35638 32914 CSNK1D-FGF4-FOSL1 3694 6645 6799 4138 45840
CSNK1D-FGF4-TCF7L1 4541 25809 20278 40264 36271 CSNK1D-FGF4-WNT5A 16991 26760 1497 11585 17580
CSNK1D-FGF4-WNT3A 866 6634 43990 20734 56058 CSNK1D-FGF4-LRP5 8844 18263 430 12232 23605
CSNK1D-FGF4-PPP2R1A 3004 29048 12442 15684 23801 CSNK1D-FGF4-WNT2B 2842 20288 7801 35728 43120
CSNK1D-FGF4-WNT4 2044 17655 11902 17351 48590 CSNK1D-FGF4-SFRP1 17187 352 5460 18719 36092
CSNK1D-FGF4-TCF7 2578 13286 34 28753 54402 CSNK1D-FGF4-SFRP4 6151 154 43125 29798 22993
CSNK1D-FGF4-RHOU 3836 6390 11977 25185 40250 CSNK1D-FGF4-FRAT1 4624 3572 29726 25608 46279
CSNK1D-FGF4-NLK 5343 27561 8638 8497 51980 CSNK1D-FGF4-GSK3B 2870 6165 39093 37995 35649
CSNK1D-FGF4-LEF1 16885 889 16278 22379 29256 CSNK1D-FGF4-FZD7 3708 1492 23721 12408 17016
CSNK1D-PORCN-SENP2 5664 26748 24402 26200 37885 CSNK1D-SFRP1-WNT2B 7873 54928 11692 34070 52974
AES-AXIN1-CSNK1D 33513 47832 7845 51708 6743 CSNK1D-FOXN1-LEF1 6150 3755 45826 20298 28446
CSNK1D-FGF4-FZD8 1068 28301 13813 37144 30865 CSNK1D-FZD2-LEF1 38842 5216 13377 4337 12007
CSNK1D-FGF4-KREMEN1 2147 22653 25065 18882 43497 CSNK1D-FSHB-LEF1 55374 14244 35230 8216 18460
CSNK1D-FOSL1-FZD1 14359 1015 37515 5753 14234 CSNK1D-PORCN-WNT2B 8595 53305 9816 26691 42121
CSNK1D-FOXN1-SENP2 1289 8520 39455 7070 25852 CSNK1D-GSK3A-LEF1 6720 14350 53714 3942 23987
CSNK1D-FGF4-WNT3 2419 18531 38096 22623 37111 CSNK1D-FGF4-TLE1 1651 32994 23493 5014 41934
CSNK1D-JUN-LEF1 20901 8723 38740 12713 27687 CSNK1D-PPP2R1A-WNT5A 27528 4279 14277 4265 42405
FZD5-CCND3-CSNK1D 4293 24482 51150 40471 36385 CSNK1D-PORCN-TLE2 12595 39793 26325 7235 43651
CSNK1D-FGF4-FZD6 6737 6408 6417 30228 39254 CSNK1D-PORCN-TCF7 4035 1408 266 23788 31209
CSNK1D-FOXN1-KREMEN1 3060 1922 41865 30003 8137 CSNK1D-PPP2R1A-TCF7L1 34388 5648 48876 25681 52823
CSNK1D-FOXN1-PPP2CA 677 25144 54449 22625 44186 CSNK1D-CXXC4-FZD1 7144 1734 27303 7250 11481
CSNK1D-FOXN1-WNT2B 2477 5135 39962 11954 23525 CSNK1D-CTNNB1-T 51919 2142 9666 39801 16008
CSNK1D-FOXN1-FZD8 484 13507 45944 36021 49258 CSNK1D-PPP2R1A-TCF7 34317 14103 3740 45791 33515
CSNK1D-FGF4-LRP6 18101 5680 13351 25149 10621 CSNK1D-PORCN-SLC9A3R1 26693 34397 22670 453 31614
CSNK1D-FGF4-SLC9A3R1 10617 29302 26992 4647 42618 CSNK1D-FOXN1-TCF7L1 1853 19094 49475 40364 5085
CSNK1D-TLE1-TLE2 28280 37833 12666 39269 5835 CSNK1D-WNT1-WNT2B 3674 5014 26127 3017 32922
CSNK1D-FOXN1-FZD7 2580 12602 43323 15316 39137 CSNK1D-FOXN1-MYC 463 3569 42774 40411 28606
CSNK1D-SFRP1-SFRP4 5865 32490 29157 40625 43609 CSNK1D-PORCN-SFRP1 36889 38723 2444 15209 50430
CSNK1D-FGF4-PPP2CA 3187 47005 13018 23779 39413 CSNK1D-FOXN1-SLC9A3R1 9628 8268 42958 15342 21726
CSNK1D-PORCN-FBXW4 5373 20376 20328 22365 50987 CSNK1D-JUN-TCF7L1 22113 18400 27177 33962 5630
CSNK1D-FOXN1-FZD1 186 1437 42030 14270 8269 CSNK1D-FGF4-FSHB 8876 10878 93 40281 25736
CSNK1D-FZD6-SFRP4 28948 9871 56626 33341 10920 FZD5-CCND2-CSNK1D 2174 48901 29308 29035 26999
CSNK1D-GSK3A-SFRP4 3312 9861 54850 25114 31433 CSNK1D-WNT3-WNT3A 4832 51374 56476 26830 11649
CSNK1D-JUN-WNT3A 3991 7790 52423 12387 1862 CSNK1D-CXXC4-FRAT1 14134 8276 23947 22453 12908
CSNK1D-NLK-WNT4 1538 21775 47534 6449 28873 CSNK1D-WNT1-WNT2 3841 8374 55936 27925 28491
CSNK1D-FOXN1-RHOU 3693 1529 28226 32793 21419 CSNK1D-PORCN-PPP2R1A 16940 28022 22571 2476 54099
CSNK1D-PORCN-WNT5A 17071 12074 1312 10487 50936 CSNK1D-FGF4-PYGO1 35224 24194 35705 42726 4974
CSNK1D-GSK3A-SENP2 679 19695 54356 47357 23687 CSNK1D-FOXN1-TCF7 526 3006 24338 37412 29080
CSNK1D-FGF4-PITX2 21808 22200 7826 55044 47261 CSNK1D-FGF4-WIF1 2570 27850 35517 16644 26870
CSNK1D-FOXN1-LRP5 3643 4399 15957 9681 3346 CSNK1D-JUN-TCF7 19796 346 649 20621 7941
CSNK1D-FOSL1-FRZB 19966 5694 21191 35654 5540 CSNK1D-GSK3A-WNT2B 537 38319 50713 23870 15104
CSNK1D-FRAT1-FZD1 30515 10291 41362 5174 7792 CSNK1D-WNT1-WNT4 2475 13139 28187 2712 22029
CSNK1D-NLK-WNT3A 12770 9632 43802 42949 37641 CSNK1D-GSK3A-WNT2 1633 16051 53761 28401 27543
CSNK1D-FOXN1-PITX2 11143 1695 49037 55776 7145 CSNK1D-FOXN1-LRP6 13480 3544 42500 13963 13814
CSNK1D-JUN-WNT2B 36826 33885 13766 40492 6501 BCL9-CSNK1D-DVL1 43892 32546 30461 1264 19067
FZD5-CSNK1D-WNT5A 10782 25515 25535 29067 55122 CSNK1D-JUN-PYGO1 46732 424 46278 41608 30058
CSNK1D-SFRP1-WNT5A 7931 18053 3281 19001 33260 CSNK1D-JUN-SENP2 2653 23718 38996 40186 21869
CSNK1D-GSK3A-PPP2CA 1046 40897 47094 14850 34061 CSNK1D-FOXN1-GSK3B 1758 13445 40737 47921 44449
CSNK1D-GSK3A-KREMEN1 1238 5197 49343 17131 39680 CCND3-CSNK1D-FGF4 53833 56236 13403 31362 5509
BCL9-CSNK1D-FOSL1 47904 42624 47654 3433 45846 CSNK1D-FZD2-PPP2CA 3053 36451 19189 15273 40108
CSNK1D-SFRP1-WNT3A 1694 2663 18831 24025 39031 CSNK1D-LRP6-RHOU 9238 26733 38518 37191 35303
CSNK1D-CTBP2-LEF1 8883 17823 28631 13435 18163 BCL9-CSNK1D-SENP2 44308 43457 33874 30051 32611
CSNK1D-FOXN1-WNT3A 174 2450 50841 26734 14997 CSNK1D-DVL2-LEF1 53540 4763 36760 14495 51756
CSNK1D-JUN-TLE2 17254 7221 33658 28649 27279 CCND3-CSNK1D-WNT5A 26184 41606 8103 12634 19595
CSNK1D-FOSL1-FZD7 39520 47576 23109 9945 26122 CSNK1D-NLK-SENP2 2789 23569 46292 12953 16278
CSNK1D-SFRP1-TLE2 13034 42315 14660 41421 27119 CSNK1D-GSK3A-TCF7L1 789 29786 54140 26077 36093
CSNK1D-PITX2-SFRP4 4175 45358 33459 4847 37993 CSNK1D-FZD2-LRP5 31249 14000 540 14876 15989
CSNK1D-GSK3A-RHOU 557 7015 53157 22185 43573 CSNK1D-CTNNB1-FRZB 15856 15227 48531 37431 9414
CSNK1D-FGF4-MYC 4085 24182 15055 21582 25623 CSNK1D-JUN-WNT4 23623 7470 42887 14337 2015
BCL9-CSNK1D-EP300 52623 25888 25234 6007 31047 CSNK1D-FOXN1-PPP2R1A 783 2341 30370 5693 20193
FZD5-CCND1-CSNK1D 4682 17735 35223 18136 46595 CSNK1D-FZD2-SFRP4 8632 6917 25028 10001 13916
CSNK1D-FOXN1-WNT4 712 1876 41088 1961 29254 APC-BTRC-CSNK1D 2236 12178 36083 5029 45903
CSNK1D-CTBP2-SFRP4 5497 10895 29317 34539 10978 CSNK1D-LRP6-TCF7 5176 36559 1881 36347 12983
Table 6: Rankings o CSNK1D-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
GSK3A-PPP2CA, CSNK1D-PPP2R1A-WNT5A, CSNK1D-PPP2R1A-TCF7L1, CSNK1D-
PPP2R1A-TCF7, CSNK1D-PORCN-PPP2R1A, CSNK1D-FZD2-PPP2CA and CSNK1D-
FOXN1-PPP2R1A. 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.
18
RANKING @ iUSING SOBOL - 2002
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CSNK1D-FGF4-SENP2 45011 27585 30267 41354 22081 CSNK1D-FGF4-FOSL1 31433 17351 34702 49796 3779
CSNK1D-FGF4-TCF7L1 25851 23703 28531 9955 26240 CSNK1D-FGF4-WNT5A 27276 41074 28302 22360 34593
CSNK1D-FGF4-WNT3A 26097 37629 27746 14081 26558 CSNK1D-FGF4-LRP5 2955 43397 25413 16078 42368
CSNK1D-FGF4-PPP2R1A 16041 36350 23034 23038 36186 CSNK1D-FGF4-WNT2B 28074 51541 15533 12033 30048
CSNK1D-FGF4-WNT4 31095 19365 29428 42965 30788 CSNK1D-FGF4-SFRP1 17254 46015 24945 24496 39736
CSNK1D-FGF4-TCF7 47373 33208 33019 35060 24479 CSNK1D-FGF4-SFRP4 39876 11006 32217 32622 17395
CSNK1D-FGF4-RHOU 12115 29224 26900 15818 35002 CSNK1D-FGF4-FRAT1 43307 19656 33814 44501 13085
CSNK1D-FGF4-NLK 11305 41185 24087 8932 35872 CSNK1D-FGF4-GSK3B 4128 7853 22532 14175 38412
CSNK1D-FGF4-LEF1 35712 40912 31537 37596 9192 CSNK1D-FGF4-FZD7 38718 29241 32518 33630 10048
CSNK1D-PORCN-SENP2 26180 49740 24174 6964 30394 CSNK1D-SFRP1-WNT2B 14464 28189 8702 8326 25216
AES-AXIN1-CSNK1D 17614 20399 2658 23007 32892 CSNK1D-FOXN1-LEF1 18416 22419 26392 15687 40976
CSNK1D-FGF4-FZD8 10015 39491 25159 24198 38526 CSNK1D-FZD2-LEF1 31519 19029 30167 30946 20994
CSNK1D-FGF4-KREMEN1 21369 16424 25622 19556 47905 CSNK1D-FSHB-LEF1 17557 28861 26741 15958 23463
CSNK1D-FOSL1-FZD1 33939 40307 29863 45255 32407 CSNK1D-PORCN-WNT2B 39627 20751 32331 36708 28715
CSNK1D-FOXN1-SENP2 22145 41275 26967 5135 47598 CSNK1D-GSK3A-LEF1 36973 16169 28985 41996 5916
CSNK1D-FGF4-WNT3 29097 5562 41695 44969 27058 CSNK1D-FGF4-TLE1 31338 33282 28628 47096 30909
CSNK1D-JUN-LEF1 25658 26247 28008 9195 29514 CSNK1D-PPP2R1A-WNT5A 26135 44357 28294 20860 36948
FZD5-CCND3-CSNK1D 46351 3330 50103 35023 9366 CSNK1D-PORCN-TLE2 40721 9512 29575 32383 21204
CSNK1D-FGF4-FZD6 18376 27935 24677 23494 47063 CSNK1D-PORCN-TCF7 10132 38975 27387 12057 30165
CSNK1D-FOXN1-KREMEN1 31821 16389 28671 30403 11306 CSNK1D-PPP2R1A-TCF7L1 25967 41054 27430 10798 32868
CSNK1D-FOXN1-PPP2CA 18148 46116 27668 8407 45131 CSNK1D-CXXC4-FZD1 15838 20986 27843 15827 35450
CSNK1D-FOXN1-WNT2B 34971 36541 30580 44435 4295 CSNK1D-CTNNB1-T 42761 39366 30573 52126 13625
CSNK1D-FOXN1-FZD8 31892 7178 33756 49005 20364 CSNK1D-PPP2R1A-TCF7 41472 28978 28805 36435 24561
CSNK1D-FGF4-LRP6 54180 13585 31741 41058 14672 CSNK1D-PORCN-SLC9A3R1 22475 41256 24969 21096 28384
CSNK1D-FGF4-SLC9A3R1 43276 13827 31871 40076 15155 CSNK1D-FOXN1-TCF7L1 35334 23957 30050 36064 4998
CSNK1D-TLE1-TLE2 19455 40358 5030 19470 26781 CSNK1D-WNT1-WNT2B 42719 30480 50555 50603 27505
CSNK1D-FOXN1-FZD7 25311 49876 23413 8098 36669 CSNK1D-FOXN1-MYC 44307 29810 29915 52115 22248
CSNK1D-SFRP1-SFRP4 32021 30603 35439 41782 29994 CSNK1D-PORCN-SFRP1 30977 7376 32969 50220 26759
CSNK1D-FGF4-PPP2CA 45504 35247 32816 42764 13525 CSNK1D-FOXN1-SLC9A3R1 23368 50212 27896 7855 37916
CSNK1D-PORCN-FBXW4 40912 20587 30104 44920 20175 CSNK1D-JUN-TCF7L1 40981 24954 29837 33199 13509
CSNK1D-FOXN1-FZD1 36474 18523 28735 38842 16102 CSNK1D-FGF4-FSHB 37586 23188 30054 39574 14949
CSNK1D-FZD6-SFRP4 37025 20562 29540 31061 17840 FZD5-CCND2-CSNK1D 39639 19905 41415 55029 16947
CSNK1D-GSK3A-SFRP4 38998 40109 29848 46577 10900 CSNK1D-WNT3-WNT3A 36262 46174 50463 43303 12247
CSNK1D-JUN-WNT3A 41685 14518 29055 33675 22133 CSNK1D-CXXC4-FRAT1 34042 35885 29812 41264 26139
CSNK1D-NLK-WNT4 41521 25413 31966 31421 31114 CSNK1D-WNT1-WNT2 14398 26421 6595 6539 29319
CSNK1D-FOXN1-RHOU 31392 16873 29114 44729 3759 CSNK1D-PORCN-PPP2R1A 38585 10367 29409 42259 26713
CSNK1D-PORCN-WNT5A 33173 15133 30807 39641 18354 CSNK1D-FGF4-PYGO1 41090 20740 34158 34168 20857
CSNK1D-GSK3A-SENP2 45946 48851 30360 53837 19511 CSNK1D-FOXN1-TCF7 21839 33109 27126 21035 52156
CSNK1D-FGF4-PITX2 45761 16034 33072 48233 21295 CSNK1D-FGF4-WIF1 34683 24427 28639 39649 25219
CSNK1D-FOXN1-LRP5 38778 34796 30801 41436 16166 CSNK1D-JUN-TCF7 16160 32149 27332 23912 43544
CSNK1D-FOSL1-FRZB 31318 38355 31685 44774 22524 CSNK1D-GSK3A-WNT2B 9527 37019 28419 11178 37958
CSNK1D-FRAT1-FZD1 20960 29768 28275 10710 43347 CSNK1D-WNT1-WNT4 20721 8116 11826 6782 37040
CSNK1D-NLK-WNT3A 15647 31281 25207 25693 26652 CSNK1D-GSK3A-WNT2 37628 15354 32710 30271 18583
CSNK1D-FOXN1-PITX2 18384 31000 27911 15993 34137 CSNK1D-FOXN1-LRP6 12836 27102 27262 5010 34889
CSNK1D-JUN-WNT2B 35800 33697 28958 34580 16565 BCL9-CSNK1D-DVL1 5169 2531 9866 16638 46496
FZD5-CSNK1D-WNT5A 21298 15129 1430 366 40105 CSNK1D-JUN-PYGO1 24772 39437 27678 10274 47704
CSNK1D-SFRP1-WNT5A 11269 25479 3686 15976 27188 CSNK1D-JUN-SENP2 19786 39894 26516 17689 39326
CSNK1D-GSK3A-PPP2CA 38964 24815 30788 42585 4984 CSNK1D-FOXN1-GSK3B 33934 15919 31085 51592 27046
CSNK1D-GSK3A-KREMEN1 20093 40861 28185 15145 51111 CCND3-CSNK1D-FGF4 25501 41888 19350 4356 36845
BCL9-CSNK1D-FOSL1 10419 8445 20713 5953 54355 CSNK1D-FZD2-PPP2CA 40401 31133 29816 40542 23445
CSNK1D-SFRP1-WNT3A 19952 32710 12566 7366 35990 CSNK1D-LRP6-RHOU 34637 26415 30562 44183 17446
CSNK1D-CTBP2-LEF1 35436 36626 30114 35212 1936 BCL9-CSNK1D-SENP2 7894 55225 16856 28157 9757
CSNK1D-FOXN1-WNT3A 36731 14201 28962 47587 13902 CSNK1D-DVL2-LEF1 37733 42004 32019 35022 16190
CSNK1D-JUN-TLE2 35323 15737 30487 31236 19521 CCND3-CSNK1D-WNT5A 26753 51792 5466 20864 48578
CSNK1D-FOSL1-FZD7 25294 25065 27511 18532 28438 CSNK1D-NLK-SENP2 40143 16432 28881 34696 27936
CSNK1D-SFRP1-TLE2 14852 25401 8318 13409 27386 CSNK1D-GSK3A-TCF7L1 23592 41249 27328 22703 35101
CSNK1D-PITX2-SFRP4 26609 44292 24260 17256 33381 CSNK1D-FZD2-LRP5 21506 19923 24132 16640 35889
CSNK1D-GSK3A-RHOU 11202 8387 26821 3303 37553 CSNK1D-CTNNB1-FRZB 35537 12277 40549 47197 15377
CSNK1D-FGF4-MYC 24133 31913 27203 19416 39013 CSNK1D-JUN-WNT4 24170 35809 26365 15414 39425
BCL9-CSNK1D-EP300 3311 5825 20711 3984 45817 CSNK1D-FOXN1-PPP2R1A 39046 11003 29491 48744 12072
FZD5-CCND1-CSNK1D 14887 40746 19201 997 4727 CSNK1D-FZD2-SFRP4 35660 24193 30365 46109 21000
CSNK1D-FOXN1-WNT4 23873 38225 27206 12028 40601 APC-BTRC-CSNK1D 42702 43953 47146 33780 8438
CSNK1D-CTBP2-SFRP4 35574 12520 29543 31811 17639 CSNK1D-LRP6-TCF7 14059 30348 28213 14212 32048
Table 7: Rankings o CSNK1D-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
6.4.4. Examining he beha iou o LRP-CSNK1D-X combina ions
Looking a he ables abo e, one inds he ollowing combina ions o membe s o
LRP amily along wi h CSNK1D, o be p ominen a 3 d o de le el - CSNK1D-FGF4-
LRP6, CSNK1D-FOXN1-LRP5, CSNK1D-FGF4-LRP5, CSNK1D-FOXN1-LRP6, CSNK1D-
19
RANKING @ iUSING SOBOL - MARTINEZ
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CSNK1D-FGF4-SENP2 55119 28784 753 23302 53897 CSNK1D-FGF4-FOSL1 39220 16866 389 23848 23132
CSNK1D-FGF4-TCF7L1 40859 12468 13114 42874 33245 CSNK1D-FGF4-WNT5A 39875 34325 26022 14242 1408
CSNK1D-FGF4-WNT3A 11042 19248 28222 21505 8886 CSNK1D-FGF4-LRP5 44011 14327 27863 30216 18989
CSNK1D-FGF4-PPP2R1A 32236 18431 4861 24170 28783 CSNK1D-FGF4-WNT2B 11099 33067 21662 18628 9514
CSNK1D-FGF4-WNT4 30931 24624 1645 40905 44453 CSNK1D-FGF4-SFRP1 24988 7332 20614 11103 14523
CSNK1D-FGF4-TCF7 56903 23341 587 8096 54144 CSNK1D-FGF4-SFRP4 51948 20558 476 17213 54793
CSNK1D-FGF4-RHOU 25547 26286 25711 24726 4948 CSNK1D-FGF4-FRAT1 56865 12006 918 21628 54532
CSNK1D-FGF4-NLK 33940 4625 12426 23698 5080 CSNK1D-FGF4-GSK3B 37094 8199 21044 25936 22668
CSNK1D-FGF4-LEF1 50110 29395 2034 27280 54041 CSNK1D-FGF4-FZD7 54587 3593 2262 16940 46019
CSNK1D-PORCN-SENP2 1456 4258 8869 32822 29157 CSNK1D-SFRP1-WNT2B 45504 25704 37754 9982 35219
AES-AXIN1-CSNK1D 35852 3680 25566 9981 7313 CSNK1D-FOXN1-LEF1 32374 24326 23110 46046 3210
CSNK1D-FGF4-FZD8 23206 13656 45564 35305 9821 CSNK1D-FZD2-LEF1 29724 23302 1126 4556 23508
CSNK1D-FGF4-KREMEN1 24857 20786 27757 39745 8714 CSNK1D-FSHB-LEF1 19222 39228 21058 21493 6562
CSNK1D-FOSL1-FZD1 41680 37855 2054 46155 46394 CSNK1D-PORCN-WNT2B 54547 33746 2831 17934 52535
CSNK1D-FOXN1-SENP2 38843 9650 25689 48746 11032 CSNK1D-GSK3A-LEF1 27984 32214 780 18412 15578
CSNK1D-FGF4-WNT3 27141 43301 10716 18079 36761 CSNK1D-FGF4-TLE1 30313 3293 20586 21005 55995
CSNK1D-JUN-LEF1 36389 9478 48851 37502 3819 CSNK1D-PPP2R1A-WNT5A 34799 46397 27927 38367 6548
FZD5-CCND3-CSNK1D 24425 35427 11357 16458 13140 CSNK1D-PORCN-TLE2 53642 34642 1349 6256 56564
CSNK1D-FGF4-FZD6 25549 14281 21210 22546 3415 CSNK1D-PORCN-TCF7 25748 22359 21805 36766 4140
CSNK1D-FOXN1-KREMEN1 32146 2230 14527 12211 48112 CSNK1D-PPP2R1A-TCF7L1 1420 17934 41275 37855 4684
CSNK1D-FOXN1-PPP2CA 35792 53371 27044 46895 15279 CSNK1D-CXXC4-FZD1 28112 48535 48166 35007 4846
CSNK1D-FOXN1-WNT2B 40727 20657 11342 28759 54605 CSNK1D-CTNNB1-T 55697 37457 1377 24186 53282
CSNK1D-FOXN1-FZD8 40606 42498 22468 13908 52376 CSNK1D-PPP2R1A-TCF7 50128 22951 5812 8544 53759
CSNK1D-FGF4-LRP6 56364 10127 2296 23831 56682 CSNK1D-PORCN-SLC9A3R1 15731 15687 5737 23413 32643
CSNK1D-FGF4-SLC9A3R1 52818 9841 830 24865 56433 CSNK1D-FOXN1-TCF7L1 51221 5285 6459 25508 51438
CSNK1D-TLE1-TLE2 42315 43646 33134 2508 54333 CSNK1D-WNT1-WNT2B 31537 11063 42528 38828 9460
CSNK1D-FOXN1-FZD7 33029 31601 24563 26553 33641 CSNK1D-FOXN1-MYC 50924 26721 3557 20447 56671
CSNK1D-SFRP1-SFRP4 21268 21314 35721 28006 9257 CSNK1D-PORCN-SFRP1 18994 35477 42 21142 50577
CSNK1D-FGF4-PPP2CA 55329 26273 1032 21669 55925 CSNK1D-FOXN1-SLC9A3R1 33119 17256 36353 44743 32463
CSNK1D-PORCN-FBXW4 54457 32031 1944 26924 56516 CSNK1D-JUN-TCF7L1 48658 28221 1848 12654 36298
CSNK1D-FOXN1-FZD1 55202 51315 557 15388 55873 CSNK1D-FGF4-FSHB 53386 36653 4663 24262 56290
CSNK1D-FZD6-SFRP4 51105 5714 720 31166 44306 FZD5-CCND2-CSNK1D 7223 27121 23185 31108 21218
CSNK1D-GSK3A-SFRP4 47899 34099 4951 23576 49750 CSNK1D-WNT3-WNT3A 11520 29889 44430 29706 9625
CSNK1D-JUN-WNT3A 49779 33157 919 18538 52334 CSNK1D-CXXC4-FRAT1 18469 1863 38915 19191 36580
CSNK1D-NLK-WNT4 55088 4562 19617 29935 54873 CSNK1D-WNT1-WNT2 40567 28297 16569 6336 51007
CSNK1D-FOXN1-RHOU 34252 18639 2074 27005 35628 CSNK1D-PORCN-PPP2R1A 46494 24460 5959 26920 56966
CSNK1D-PORCN-WNT5A 22402 4216 2288 18135 42734 CSNK1D-FGF4-PYGO1 53782 7577 1845 21026 56561
CSNK1D-GSK3A-SENP2 52934 31036 1324 14474 42126 CSNK1D-FOXN1-TCF7 32381 26851 38448 50093 9452
CSNK1D-FGF4-PITX2 44579 43462 767 11821 46293 CSNK1D-FGF4-WIF1 43363 48941 1472 39959 56626
CSNK1D-FOXN1-LRP5 52584 42034 6817 14398 37913 CSNK1D-JUN-TCF7 22295 36468 17276 29939 515
CSNK1D-FOSL1-FRZB 41028 37740 6910 31880 54766 CSNK1D-GSK3A-WNT2B 28987 44289 19857 45245 10158
CSNK1D-FRAT1-FZD1 35866 8723 28263 47919 5986 CSNK1D-WNT1-WNT4 4934 23696 3275 40685 48358
CSNK1D-NLK-WNT3A 30261 5484 6297 36145 38245 CSNK1D-GSK3A-WNT2 44075 10874 7758 16421 56183
CSNK1D-FOXN1-PITX2 39725 19950 32730 49412 6271 CSNK1D-FOXN1-LRP6 42807 7879 23909 46855 44003
CSNK1D-JUN-WNT2B 41000 35594 890 25093 56672 BCL9-CSNK1D-DVL1 13131 24654 56866 21285 11397
FZD5-CSNK1D-WNT5A 22240 8729 8905 8361 14874 CSNK1D-JUN-PYGO1 5673 24084 17393 28564 30653
CSNK1D-SFRP1-WNT5A 46232 40726 39677 8395 43436 CSNK1D-JUN-SENP2 31303 34385 30502 38156 4556
CSNK1D-GSK3A-PPP2CA 49948 27496 4120 13149 30348 CSNK1D-FOXN1-GSK3B 44857 1620 1103 5943 42753
CSNK1D-GSK3A-KREMEN1 8331 36538 18893 45935 39059 CCND3-CSNK1D-FGF4 33645 25729 11171 4259 2969
BCL9-CSNK1D-FOSL1 6994 56975 54633 36841 20797 CSNK1D-FZD2-PPP2CA 49236 39754 539 34368 52220
CSNK1D-SFRP1-WNT3A 36490 53621 5052 7047 50254 CSNK1D-LRP6-RHOU 34336 2691 1633 17028 44197
CSNK1D-CTBP2-LEF1 48968 10726 6135 22249 56309 BCL9-CSNK1D-SENP2 7818 31418 33113 7222 1844
CSNK1D-FOXN1-WNT3A 47715 2711 5484 26364 53183 CSNK1D-DVL2-LEF1 49081 18658 2603 29361 56933
CSNK1D-JUN-TLE2 55996 3817 12011 19143 52700 CCND3-CSNK1D-WNT5A 36336 364 51360 31612 43178
CSNK1D-FOSL1-FZD7 32946 26115 27641 53780 8204 CSNK1D-NLK-SENP2 54274 1758 35987 36243 51006
CSNK1D-SFRP1-TLE2 41155 46372 37122 5380 40515 CSNK1D-GSK3A-TCF7L1 2372 2561 26389 42919 28709
CSNK1D-PITX2-SFRP4 783 12794 45331 28854 43563 CSNK1D-FZD2-LRP5 4958 19633 32139 50415 4916
CSNK1D-GSK3A-RHOU 16007 10231 17105 47130 31183 CSNK1D-CTNNB1-FRZB 51258 45759 3242 19204 39592
CSNK1D-FGF4-MYC 27747 53740 29653 32287 2134 CSNK1D-JUN-WNT4 28813 34671 41857 33835 1136
BCL9-CSNK1D-EP300 37357 52675 55940 48065 6089 CSNK1D-FOXN1-PPP2R1A 53170 6227 2620 23711 53082
FZD5-CCND1-CSNK1D 31474 38575 10040 10604 7111 CSNK1D-FZD2-SFRP4 51918 14988 1412 33035 37704
CSNK1D-FOXN1-WNT4 40130 54610 25402 49876 4689 APC-BTRC-CSNK1D 56835 26515 42490 50974 18375
CSNK1D-CTBP2-SFRP4 49397 12922 932 7503 56132 CSNK1D-LRP6-TCF7 31280 19096 22465 41381 4029
Table 8: Rankings o CSNK1D-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 - ma inez
LRP6-RHOU, CSNK1D-FZD2-LRP5, and CSNK1D-LRP6-TCF7. All hese combi-
na ions indica e he exis ence o a possible syne gy when hey ake a highe ank in he
lis o combina ions.
20
6.4.5. Examining he beha iou o CTNNB1-CSNK1D-X combina ions
Looking a he ables abo e, one inds he ollowing combina ions o CTNNB1 along
wi h CSNK1D, o be p ominen a 3 d o de le el - CSNK1D-CTNNB1-T and CSNK1D-
CTNNB1-FRZB. 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.
6.4.6. Examining he beha iou o APC-CSNK1D-X combina ions
Looking a he ables abo e, one inds he ollowing combina ions o APC along wi h
CSNK1D, o be p ominen a 3 d o de le el - APC-BTRC-CSNK1D. All hese com-
bina ions indica e he exis ence o a possible syne gy when hey ake a highe ank in
he lis o combina ions.
6.5. Conse ed machine lea ning ankings o es ed CSNK1G1-X-
X combina ions
A o al o 2415, 3 d o de combina ions in ol ing CSNK1G1 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 10, 11 and 12 show he ankings o he same com-
bina ions as in able 9, 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.
NOTE - We conside he same ac o s which ac ed in combina ion o CSNK1A1,
in he p e ious sec ions, as we ha e e idence o li e a u e ha ha e e i ied he exis-
ence o combina o ial syne gy wi h CSNK1A1. He e we see i he e exis s combina-
ions o CSNK1G1, o no .
6.5.1. Examining he beha iou o DVL-CSNK1G1-X combina ions
Looking a he ables abo e, one inds he ollowing combina ions o membe s o DVL
amily along wi h CSNK1G1, o be p ominen a 3 d o de le el - CSNK1G1-DVL2-
WNT2, CSNK1G1-DVL2-TCF7, CSNK1G1-DVL2-FBXW11, CSNK1G1-DVL2-TCF7L1,
CSNK1G1-DVL2-TLE2, CSNK1G1-DVL2-SENP2, CSNK1G1-DVL2-FOSL1, CSNK1G1-
DVL2-FZD1 and CSNK1G1-DVL2-FRZB. 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.
6.5.2. Examining he beha iou o TCF-CSNK1G1-X combina ions
Looking a he ables abo e, one inds he ollowing combina ions o membe s o
TCF amily along wi h CSNK1G1, o be p ominen a 3 d o de le el - CSNK1G1-
DVL2-TCF7, CSNK1G1-NKD1-TCF7L1, CSNK1G1-FOXN1-TCF7L1, CSNK1G1-
DVL2-TCF7L1, CSNK1G1-FZD1-TCF7L1, CSNK1G1-FGF4-TCF7L1, CSNK1G1-
FOXN1-TCF7, CSNK1G1-NLK-TCF7L1, CSNK1G1-CTNNBIP1-TCF7L1, CSNK1G1-
21
RANKING @ iUSING HSIC - LINEAR
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CSNK1G1-NLK-SENP2 74 35675 3308 48520 19328 CSNK1G1-FOXN1-TLE2 226 3994 5316 18517 42187
CSNK1G1-NLK-WNT4 321 20710 3312 50831 31403 CSNK1G1-FOXN1-KREMEN1 390 10815 10745 12917 12924
CSNK1G1-FOXN1-SLC9A3R1 395 1314 2366 9985 14166 CSNK1G1-PORCN-SENP2 410 36322 35831 12245 17913
CSNK1G1-FZD2-SENP2 430 26396 20526 35632 16355 CSNK1G1-FSHB-LEF1 506 19332 10676 684 44215
CSNK1G1-DVL2-WNT2 512 22400 27124 6214 39864 CSNK1G1-FSHB-SFRP4 577 21679 6780 1575 25615
CSNK1G1-FZD2-TLE2 600 1430 44384 54164 52337 CSNK1G1-DVL2-SENP2 708 9805 19546 23999 8201
CSNK1G1-LRP5-SENP2 821 46576 17464 17352 30361 CSNK1G1-JUN-SENP2 855 23957 55112 11084 3256
CSNK1G1-NKD1-PPP2CA 926 17356 35232 35369 12912 CSNK1G1-FZD2-FZD7 944 16232 24487 55399 23887
CSNK1G1-FOXN1-PPP2R1A 960 4562 8931 10045 26824 CSNK1G1-CTNNBIP1-TCF7L1 999 13063 17121 18913 53234
CSNK1G1-FGF4-TLE2 1023 22382 54317 54503 47054 CSNK1G1-FZD2-SFRP4 1035 1065 32773 38790 38245
CSNK1G1-FSHB-SENP2 1054 47479 13640 1228 8996 CSNK1G1-DVL2-FOSL1 1061 14048 12622 34641 48959
CSNK1G1-DVL2-TCF7 1070 8709 15200 25653 4958 CSNK1G1-FZD2-PPP2CA 1082 23722 6311 56537 35909
CSNK1G1-JUN-WNT2 1087 1305 52762 5894 31347 CSNK1G1-CXXC4-FOSL1 1094 46700 26853 25310 54546
CSNK1G1-CTNNBIP1-DKK1 1133 14650 36806 5792 53273 CSNK1G1-JUN-TCF7L1 1134 10933 47748 13909 25134
CSNK1G1-FZD2-WNT2B 1144 10281 11030 49965 37172 CSNK1G1-CTNNBIP1-TLE2 1189 14302 22595 16694 56930
CSNK1G1-NKD1-TCF7L1 1194 9892 6186 28656 13545 CSNK1G1-FOXN1-FBXW4 1201 11491 20301 17590 26677
CSNK1G1-DVL2-FBXW11 1204 11366 47774 39156 34516 CSNK1G1-GSK3B-SLC9A3R1 1210 17915 3146 1251 20930
CSNK1G1-FGF4-KREMEN1 1239 30116 44329 46230 30098 CSNK1G1-NKD1-SENP2 1257 16631 15972 26700 19860
CSNK1G1-FOXN1-TCF7L1 1281 8663 5550 16139 11644 CSNK1G1-T-TLE2 1289 7716 26938 1980 47468
CSNK1G1-PORCN-TLE2 1291 31155 47884 19907 37757 CSNK1G1-PORCN-RHOU 1299 27191 33972 15284 20376
CSNK1G1-JUN-TLE2 1365 2675 25875 17296 52928 CSNK1G1-NKD1-SFRP4 1474 513 13103 24557 6931
CSNK1G1-FSHB-PPP2CA 1518 8523 49087 1235 27660 CSNK1G1-FOXN1-FRZB 1549 4678 4300 19697 7337
CSNK1G1-JUN-KREMEN1 1571 14622 52390 27682 7035 CSNK1G1-FOXN1-RHOU 1587 4796 8477 31603 16974
CSNK1G1-DVL2-TCF7L1 1594 26605 24282 21676 30138 CSNK1G1-SFRP1-WNT5A 1618 12629 47126 54603 30299
CSNK1G1-CTNNB1-KREMEN1 1675 48319 35467 28250 6432 CSNK1G1-SFRP1-TLE2 1712 35952 51589 41916 56964
CSNK1G1-JUN-FBXW4 1720 14629 26207 15285 48296 CSNK1G1-FZD1-SENP2 1791 37257 52309 26522 36929
CSNK1G1-PORCN-SLC9A3R1 1815 10503 40046 19851 14743 CSNK1G1-CTNNB1-SENP2 1823 48308 39023 36622 2971
CSNK1G1-CTNNB1-FBXW11 1832 37454 31263 43989 30890 CSNK1G1-CTNNB1-DAAM1 1863 29150 40706 29346 30532
CSNK1G1-JUN-RHOU 1898 1165 55257 34817 23988 CSNK1G1-DVL2-FZD1 1899 31769 26103 8981 50719
CSNK1G1-FZD1-TCF7L1 1928 14834 43931 28975 44251 CSNK1G1-FGF4-FOSL1 1936 28205 33826 36195 48093
CSNK1G1-FZD2-WNT4 1942 1607 11956 46269 29169 CSNK1G1-FZD2-LEF1 1947 1417 8944 51456 47383
CSNK1G1-GSK3A-TLE2 1958 19247 20416 54079 54261 CSNK1G1-FOXN1-FZD6 1966 10515 13241 17759 18874
CSNK1G1-JUN-PPP2R1A 1986 10228 52696 13904 47706 CSNK1G1-JUN-PYGO1 2002 4879 55264 32395 18429
CSNK1G1-DVL2-TLE2 2047 13079 24517 18237 55667 CSNK1G1-PORCN-TCF7L1 2073 14966 30891 15229 14200
CSNK1G1-FGF4-SENP2 2112 49038 53530 48190 17709 CSNK1G1-JUN-TCF7 2167 22852 38657 32689 6608
CSNK1G1-JUN-PPP2CA 2194 17201 31808 2244 24092 CSNK1G1-FZD1-FZD7 2236 8972 51512 19066 10647
CSNK1G1-CSNK2A1-MYC 2268 42433 43512 35352 51992 CSNK1G1-PORCN-FBXW4 2284 27821 27627 9377 23266
CSNK1G1-FGF4-TCF7L1 2285 10862 41090 54745 25393 CSNK1G1-FGF4-FBXW4 2297 23073 41204 39779 38778
CSNK1G1-FOXN1-TCF7 2327 21226 4505 21767 3917 CSNK1G1-NKD1-RHOU 2328 3565 14141 34128 1880
CSNK1G1-FZD2-FZD8 2338 18572 33760 38917 40049 CSNK1G1-JUN-WNT2B 2402 5466 39576 33692 34944
CSNK1G1-NLK-TCF7L1 2409 13940 8988 50696 40050 CSNK1G1-FZD2-SLC9A3R1 2430 12072 31728 53760 44963
CSNK1G1-GSK3B-LRP6 2470 3965 12186 1024 16413 CSNK1G1-PORCN-WNT2B 2472 8559 45236 34464 18734
CSNK1G1-CXXC4-DKK1 2488 45829 37872 27388 55403 CSNK1G1-CXXC4-FRAT1 2496 24384 49297 7946 49881
CSNK1G1-FGF4-PPP2R1A 2535 19539 51865 57137 46652 CSNK1G1-WIF1-WNT2B 2561 1995 24404 34807 53934
CSNK1G1-WIF1-WNT4 2582 628 24563 33380 53761 CSNK1G1-DIXDC1-WNT2B 2602 9079 34225 44850 51306
CSNK1G1-T-WNT2B 2676 4730 9390 14824 25293 CSNK1G1-T-TCF7L1 2695 8773 21250 845 15712
CSNK1G1-PORCN-PPP2R1A 2697 18740 49826 20704 24737 CSNK1G1-PORCN-WNT5A 2747 5935 22657 45224 29673
CSNK1G1-PORCN-SFRP1 2795 18557 36114 17627 42050 CSNK1G1-DVL2-FRZB 2830 11776 15278 32095 12867
CSNK1G1-JUN-SLC9A3R1 2848 7013 49399 24901 32991 CSNK1G1-JUN-WNT4 2974 622 48857 6464 4596
CSNK1G1-FSHB-MYC 2987 47541 16749 1201 23454 CSNK1G1-NLK-WNT2B 3057 20612 364 49392 38971
CSNK1G1-JUN-WNT5A 3068 8191 56989 38952 10438 CSNK1G1-SFRP1-WNT2B 3077 12559 37776 32807 54829
CSNK1G1-FGF4-FRAT1 3087 3833 51164 49600 29524 CSNK1G1-CTNNB1-FRZB 3107 38284 22901 35739 3612
CSNK1G1-CTBP2-DKK1 3146 194 46088 31304 49535 CSNK1G1-GSK3B-RHOU 3190 3405 4726 1433 8406
CSNK1G1-CTBP2-SLC9A3R1 3240 166 52122 36860 45086 CSNK1G1-DIXDC1-RHOU 3247 13611 55894 17887 29476
CSNK1G1-GSK3A-RHOU 3261 12094 4223 43874 25027 CSNK1G1-FZD2-WNT5A 3333 14640 38705 56952 5899
CSNK1G1-CTNNBIP1-FOSL1 3338 21173 6659 21711 53461 CSNK1G1-FSHB-WNT2B 3357 9060 28997 6593 37362
APC-CSNK1G1-FZD1 3390 30189 28290 1457 54900 CSNK1G1-PORCN-WNT2 3410 20366 30313 12508 34531
CSNK1G1-CTNNBIP1-FBXW11 3415 22265 9012 12002 52077 CSNK1G1-DIXDC1-DKK1 3474 22358 26349 38523 54006
CSNK1G1-FOXN1-FZD1 3475 2066 8269 14457 23102 CSNK1G1-FGF4-SFRP1 3511 22139 54017 39144 48180
CSNK1G1-NKD1-WNT2 3527 1109 9218 26094 482 CSNK1G1-JUN-SFRP4 3548 4317 53039 9482 18106
CSNK1G1-FGF4-SLC9A3R1 3554 8200 55502 49949 42703 CSNK1G1-PYGO1-TLE2 3565 24569 56894 5227 16188
CSNK1G1-FGF4-WNT4 3583 9743 47387 43850 34383 CSNK1G1-FOXN1-WNT3A 3634 7199 9792 30313 10861
CSNK1G1-FSHB-T 3636 19798 35345 312 15515 CSNK1G1-GSK3A-SENP2 3671 35222 2760 48687 25616
Table 9: Rankings o CSNK1G1-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
JUN-TCF7L1, CSNK1G1-PORCN-TCF7L1, CSNK1G1-JUN-TCF7 and CSNK1G1-
T-TCF7L1. 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.
22
RANKING @ iUSING HSIC - RBF
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CSNK1G1-NLK-SENP2 34480 34469 25805 4202 8014 CSNK1G1-FOXN1-TLE2 3512 4562 37294 11299 13219
CSNK1G1-NLK-WNT4 37117 32429 26444 1650 27288 CSNK1G1-FOXN1-KREMEN1 7103 1710 43024 36832 31611
CSNK1G1-FOXN1-SLC9A3R1 4227 955 39936 15459 33468 CSNK1G1-PORCN-SENP2 13585 41454 10606 1967 17443
CSNK1G1-FZD2-SENP2 16568 22383 10213 6975 36119 CSNK1G1-FSHB-LEF1 46458 5148 44690 1362 34271
CSNK1G1-DVL2-WNT2 26581 25977 21694 30622 18019 CSNK1G1-FSHB-SFRP4 49673 9604 39425 16774 51741
CSNK1G1-FZD2-TLE2 14214 390 12996 12800 24140 CSNK1G1-DVL2-SENP2 10060 33044 6346 24081 29517
CSNK1G1-LRP5-SENP2 14135 47074 22615 10563 18356 CSNK1G1-JUN-SENP2 2057 43819 27038 14070 17638
CSNK1G1-NKD1-PPP2CA 8799 37693 42013 33688 15900 CSNK1G1-FZD2-FZD7 21108 3606 11500 6373 21026
CSNK1G1-FOXN1-PPP2R1A 3415 1125 22606 474 39586 CSNK1G1-CTNNBIP1-TCF7L1 43171 9916 19650 22573 25909
CSNK1G1-FGF4-TLE2 12643 19305 27429 4012 34111 CSNK1G1-FZD2-SFRP4 27829 5976 9290 19601 31081
CSNK1G1-FSHB-SENP2 41253 35360 30966 2443 33408 CSNK1G1-DVL2-FOSL1 24608 32567 25022 2699 31491
CSNK1G1-DVL2-TCF7 15740 15189 43760 1824 49105 CSNK1G1-FZD2-PPP2CA 21192 37740 25191 13344 44898
CSNK1G1-JUN-WNT2 10147 5580 32401 33214 37290 CSNK1G1-CXXC4-FOSL1 18872 46435 17556 11771 54033
CSNK1G1-CTNNBIP1-DKK1 45274 12532 2085 28807 30170 CSNK1G1-JUN-TCF7L1 827 11310 28918 27910 3674
CSNK1G1-FZD2-WNT2B 31344 5642 34740 5475 23273 CSNK1G1-CTNNBIP1-TLE2 43515 18510 14805 25265 22352
CSNK1G1-NKD1-TCF7L1 6006 22577 49200 31622 30401 CSNK1G1-FOXN1-FBXW4 6456 4971 6852 14306 22075
CSNK1G1-DVL2-FBXW11 14851 14553 29808 12160 18195 CSNK1G1-GSK3B-SLC9A3R1 24505 22540 7318 7896 7232
CSNK1G1-FGF4-KREMEN1 12312 33122 8653 27029 51700 CSNK1G1-NKD1-SENP2 4079 7354 54740 12528 13804
CSNK1G1-FOXN1-TCF7L1 2258 13561 45680 37954 10050 CSNK1G1-T-TLE2 15349 28608 40369 17566 47898
CSNK1G1-PORCN-TLE2 25416 24850 21439 2281 53031 CSNK1G1-PORCN-RHOU 18456 21677 26712 34529 54262
CSNK1G1-JUN-TLE2 3633 15390 39684 2796 27092 CSNK1G1-NKD1-SFRP4 10332 8994 35937 45547 19919
CSNK1G1-FSHB-PPP2CA 50070 6934 23453 5427 21042 CSNK1G1-FOXN1-FRZB 4205 5593 40227 150 17600
CSNK1G1-JUN-KREMEN1 6491 2240 25073 41585 18357 CSNK1G1-FOXN1-RHOU 5126 2277 43717 34280 32087
CSNK1G1-DVL2-TCF7L1 8430 32795 20312 16548 46597 CSNK1G1-SFRP1-WNT5A 26848 12013 30115 7944 48214
CSNK1G1-CTNNB1-KREMEN1 12259 40883 18405 45871 37363 CSNK1G1-SFRP1-TLE2 38330 13700 14458 10263 44078
CSNK1G1-JUN-FBXW4 6418 15849 3058 18441 29387 CSNK1G1-FZD1-SENP2 32058 40787 30927 4374 20821
CSNK1G1-PORCN-SLC9A3R1 33423 29599 9114 6260 50642 CSNK1G1-CTNNB1-SENP2 8473 45202 18386 8358 20498
CSNK1G1-CTNNB1-FBXW11 8081 32056 33348 27118 24593 CSNK1G1-CTNNB1-DAAM1 13837 35555 36581 34030 48851
CSNK1G1-JUN-RHOU 2915 263 26104 42711 34946 CSNK1G1-DVL2-FZD1 5036 24181 26002 2834 17734
CSNK1G1-FZD1-TCF7L1 26757 20001 35110 22673 40307 CSNK1G1-FGF4-FOSL1 30497 29781 8021 11753 43558
CSNK1G1-FZD2-WNT4 13040 11367 14247 4325 36477 CSNK1G1-FZD2-LEF1 37628 651 37780 9885 25711
CSNK1G1-GSK3A-TLE2 21880 3846 34786 4128 44853 CSNK1G1-FOXN1-FZD6 9597 4725 31350 6692 33022
CSNK1G1-JUN-PPP2R1A 2410 8342 5954 20586 31871 CSNK1G1-JUN-PYGO1 17775 1546 36260 46060 22759
CSNK1G1-DVL2-TLE2 25707 7774 19195 28772 13026 CSNK1G1-PORCN-TCF7L1 19446 5592 14959 30431 50377
CSNK1G1-FGF4-SENP2 4616 45273 3041 10902 17063 CSNK1G1-JUN-TCF7 2531 27001 37335 13108 9426
CSNK1G1-JUN-PPP2CA 3740 31530 16470 29436 25461 CSNK1G1-FZD1-FZD7 42202 2356 44114 48791 35670
CSNK1G1-CSNK2A1-MYC 46238 56607 42725 857 38125 CSNK1G1-PORCN-FBXW4 10477 26670 1604 31235 52570
CSNK1G1-FGF4-TCF7L1 3125 11336 9840 33926 40511 CSNK1G1-FGF4-FBXW4 20873 40154 1525 33082 24319
CSNK1G1-FOXN1-TCF7 6103 15997 49902 11757 46472 CSNK1G1-NKD1-RHOU 7968 13163 45029 45281 48042
CSNK1G1-FZD2-FZD8 22757 27942 6185 40310 30385 CSNK1G1-JUN-WNT2B 7913 15753 39919 50228 16435
CSNK1G1-NLK-TCF7L1 38665 6811 44713 7792 48500 CSNK1G1-FZD2-SLC9A3R1 28704 8977 9734 10319 26207
CSNK1G1-GSK3B-LRP6 44943 8879 13860 8331 10201 CSNK1G1-PORCN-WNT2B 15765 2688 26141 22189 56019
CSNK1G1-CXXC4-DKK1 18870 49739 2762 48160 29218 CSNK1G1-CXXC4-FRAT1 10676 6045 28407 52045 39223
CSNK1G1-FGF4-PPP2R1A 8938 29139 2598 16353 38899 CSNK1G1-WIF1-WNT2B 38910 5666 25272 47015 36127
CSNK1G1-WIF1-WNT4 16896 27273 7830 48279 26589 CSNK1G1-DIXDC1-WNT2B 56105 5718 34204 36658 46240
CSNK1G1-T-WNT2B 7308 15374 20596 23413 32785 CSNK1G1-T-TCF7L1 2357 14811 41736 25166 36605
CSNK1G1-PORCN-PPP2R1A 16024 19421 9392 5370 55173 CSNK1G1-PORCN-WNT5A 8541 17540 20517 6560 46815
CSNK1G1-PORCN-SFRP1 27236 23068 16848 13318 54516 CSNK1G1-DVL2-FRZB 11203 3943 12156 18643 14086
CSNK1G1-JUN-SLC9A3R1 8199 8824 12860 16832 13385 CSNK1G1-JUN-WNT4 3575 5 23478 28885 6190
CSNK1G1-FSHB-MYC 43747 46283 35580 1289 17413 CSNK1G1-NLK-WNT2B 53434 5922 42619 33337 50690
CSNK1G1-JUN-WNT5A 1627 9471 37716 21278 33763 CSNK1G1-SFRP1-WNT2B 46506 17719 30569 35787 55375
CSNK1G1-FGF4-FRAT1 3622 6775 28403 42516 41038 CSNK1G1-CTNNB1-FRZB 9877 40304 14569 3677 31442
CSNK1G1-CTBP2-DKK1 12379 37559 2412 41433 4051 CSNK1G1-GSK3B-RHOU 31434 1254 24292 12304 14579
CSNK1G1-CTBP2-SLC9A3R1 25333 8891 16800 22800 25629 CSNK1G1-DIXDC1-RHOU 49459 11518 16506 41618 49774
CSNK1G1-GSK3A-RHOU 19387 9576 34864 29016 31935 CSNK1G1-FZD2-WNT5A 20419 29433 26502 7708 18760
CSNK1G1-CTNNBIP1-FOSL1 35395 8179 16803 17088 24295 CSNK1G1-FSHB-WNT2B 43414 19138 41449 6694 6668
APC-CSNK1G1-FZD1 7749 26824 42227 42495 14246 CSNK1G1-PORCN-WNT2 21543 32722 24973 9534 56929
CSNK1G1-CTNNBIP1-FBXW11 40429 22735 27221 29186 11089 CSNK1G1-DIXDC1-DKK1 26769 29764 1454 44361 36145
CSNK1G1-FOXN1-FZD1 1030 2372 37367 366 6405 CSNK1G1-FGF4-SFRP1 15656 24142 6725 14523 42132
CSNK1G1-NKD1-WNT2 6387 6428 51082 8449 39348 CSNK1G1-JUN-SFRP4 6927 6984 24622 46197 4920
CSNK1G1-FGF4-SLC9A3R1 10241 16030 4176 25778 44518 CSNK1G1-PYGO1-TLE2 21495 24434 29013 7562 53728
CSNK1G1-FGF4-WNT4 8298 17662 14155 26871 50395 CSNK1G1-FOXN1-WNT3A 7916 4786 40233 7694 33821
CSNK1G1-FSHB-T 51659 22786 44198 2191 56498 CSNK1G1-GSK3A-SENP2 17955 35543 38041 9692 22046
Table 10: Rankings o CSNK1G1-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
6.5.3. Examining he beha iou o PPP2A-CSNK1G1-X combina ions
Looking a he ables abo e, one inds he ollowing combina ions o membe s o
PPP2A amily along wi h CSNK1G1, o be p ominen a 3 d o de le el - CSNK1G1-
NKD1-PPP2CA, CSNK1G1-FOXN1-PPP2R1A, CSNK1G1-FSHB-PPP2CA, CSNK1G1-
JUN-PPP2R1A, CSNK1G1-JUN-PPP2CA, CSNK1G1-FGF4-PPP2R1A, CSNK1G1-
23
RANKING @ iUSING SOBOL - 2002
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CSNK1G1-NLK-SENP2 14817 11675 2225 15674 28868 CSNK1G1-FOXN1-TLE2 21537 42757 2336 15141 32041
CSNK1G1-NLK-WNT4 7646 8437 104 10192 43063 CSNK1G1-FOXN1-KREMEN1 12568 9848 1206 5693 56612
CSNK1G1-FOXN1-SLC9A3R1 29604 29598 56041 56960 9679 CSNK1G1-PORCN-SENP2 43281 37454 56745 49095 6460
CSNK1G1-FZD2-SENP2 11142 28642 7792 15597 42963 CSNK1G1-FSHB-LEF1 38254 27148 47701 53981 4899
CSNK1G1-DVL2-WNT2 27910 12643 15697 4994 46665 CSNK1G1-FSHB-SFRP4 49169 3805 44567 32085 3551
CSNK1G1-FZD2-TLE2 42543 28177 42687 36354 12646 CSNK1G1-DVL2-SENP2 22798 50683 12430 15447 46966
CSNK1G1-LRP5-SENP2 20952 26227 18132 5105 9267 CSNK1G1-JUN-SENP2 49955 51075 54767 43231 2180
CSNK1G1-NKD1-PPP2CA 2818 12720 1066 16639 39238 CSNK1G1-FZD2-FZD7 7158 42378 658 9668 56103
CSNK1G1-FOXN1-PPP2R1A 26102 33906 21109 71 51037 CSNK1G1-CTNNBIP1-TCF7L1 28112 7321 13375 27783 55812
CSNK1G1-FGF4-TLE2 38171 54018 38464 53649 27611 CSNK1G1-FZD2-SFRP4 23075 10268 7269 4789 48739
CSNK1G1-FSHB-SENP2 47318 7617 44202 35329 27387 CSNK1G1-DVL2-FOSL1 13304 16111 11364 20166 55668
CSNK1G1-DVL2-TCF7 22581 2224 18751 13174 56823 CSNK1G1-FZD2-PPP2CA 7371 1821 2940 12583 54147
CSNK1G1-JUN-WNT2 43215 54139 50622 48011 1250 CSNK1G1-CXXC4-FOSL1 25168 1437 11571 16056 25721
CSNK1G1-CTNNBIP1-DKK1 12140 38448 9541 5556 54479 CSNK1G1-JUN-TCF7L1 6017 14337 20145 21380 48232
CSNK1G1-FZD2-WNT2B 43957 8905 55685 37469 3334 CSNK1G1-CTNNBIP1-TLE2 25127 3237 10881 7849 46732
CSNK1G1-NKD1-TCF7L1 44067 52737 54968 47023 15857 CSNK1G1-FOXN1-FBXW4 27569 27578 1117 197 47485
CSNK1G1-DVL2-FBXW11 32525 55485 49860 43897 62 CSNK1G1-GSK3B-SLC9A3R1 17837 1282 3936 19428 55642
CSNK1G1-FGF4-KREMEN1 49711 51438 57107 44900 43052 CSNK1G1-NKD1-SENP2 8054 22379 116 14940 56704
CSNK1G1-FOXN1-TCF7L1 24011 53828 1796 3138 42955 CSNK1G1-T-TLE2 33761 15546 56982 41993 4590
CSNK1G1-PORCN-TLE2 7372 47733 19657 27924 17147 CSNK1G1-PORCN-RHOU 13901 19785 413 8056 50675
CSNK1G1-JUN-TLE2 6833 1066 4928 11587 56004 CSNK1G1-NKD1-SFRP4 10766 6807 490 4170 32258
CSNK1G1-FSHB-PPP2CA 45864 55377 47231 36646 7302 CSNK1G1-FOXN1-FRZB 16921 42333 17206 26037 35243
CSNK1G1-JUN-KREMEN1 6923 4884 26325 13483 55790 CSNK1G1-FOXN1-RHOU 22734 36628 1885 6243 38820
CSNK1G1-DVL2-TCF7L1 34613 54955 38410 43971 335 CSNK1G1-SFRP1-WNT5A 30598 12429 52931 54526 8133
CSNK1G1-CTNNB1-KREMEN1 8399 6622 8923 3958 38591 CSNK1G1-SFRP1-TLE2 36104 28241 56956 55279 6687
CSNK1G1-JUN-FBXW4 13976 51841 1693 18282 49989 CSNK1G1-FZD1-SENP2 46940 54887 56179 52112 3649
CSNK1G1-PORCN-SLC9A3R1 33650 47676 46612 33574 30645 CSNK1G1-CTNNB1-SENP2 47712 45420 46499 43561 3144
CSNK1G1-CTNNB1-FBXW11 1940 20675 21938 18791 49322 CSNK1G1-CTNNB1-DAAM1 12750 37186 12892 1955 43684
CSNK1G1-JUN-RHOU 7215 6024 2384 13893 54958 CSNK1G1-DVL2-FZD1 35203 16601 30820 51262 6952
CSNK1G1-FZD1-TCF7L1 13950 21245 2033 8324 25283 CSNK1G1-FGF4-FOSL1 8963 28835 12476 27024 48361
CSNK1G1-FZD2-WNT4 7022 898 12245 15373 35027 CSNK1G1-FZD2-LEF1 13090 29157 20896 15256 44016
CSNK1G1-GSK3A-TLE2 43557 47135 32471 29032 1778 CSNK1G1-FOXN1-FZD6 15112 29912 14213 23427 38252
CSNK1G1-JUN-PPP2R1A 17390 9694 2316 9148 46335 CSNK1G1-JUN-PYGO1 39719 47416 54841 47973 10949
CSNK1G1-DVL2-TLE2 36214 52629 39421 48657 6369 CSNK1G1-PORCN-TCF7L1 8742 30765 16154 23864 24961
CSNK1G1-FGF4-SENP2 2157 16345 1663 19346 36353 CSNK1G1-JUN-TCF7 43538 48608 50508 47527 4924
CSNK1G1-JUN-PPP2CA 49728 12194 55667 43794 1187 CSNK1G1-FZD1-FZD7 42817 7109 51146 49529 157
CSNK1G1-CSNK2A1-MYC 18695 1708 3446 13091 35254 CSNK1G1-PORCN-FBXW4 23515 9545 10526 23569 26078
CSNK1G1-FGF4-TCF7L1 47918 55844 55366 54508 35878 CSNK1G1-FGF4-FBXW4 44225 4355 54630 48647 959
CSNK1G1-FOXN1-TCF7 34219 34310 44976 35510 7051 CSNK1G1-NKD1-RHOU 40596 5950 54719 48495 7475
CSNK1G1-FZD2-FZD8 50007 14985 56494 47469 1059 CSNK1G1-JUN-WNT2B 12092 24688 5587 16813 56343
CSNK1G1-NLK-TCF7L1 44331 44573 53183 44188 4910 CSNK1G1-FZD2-SLC9A3R1 21480 38407 5615 17975 40405
CSNK1G1-GSK3B-LRP6 6438 18957 418 9590 54912 CSNK1G1-PORCN-WNT2B 8407 8013 15451 27068 11666
CSNK1G1-CXXC4-DKK1 29722 16090 47827 56588 1654 CSNK1G1-CXXC4-FRAT1 27618 3778 3433 676 48257
CSNK1G1-FGF4-PPP2R1A 48874 4935 46376 33919 6326 CSNK1G1-WIF1-WNT2B 13733 56852 4680 24169 53252
CSNK1G1-WIF1-WNT4 53996 12035 47320 37468 7141 CSNK1G1-DIXDC1-WNT2B 12114 7749 26029 14404 44639
CSNK1G1-T-WNT2B 39877 28951 37196 37502 2391 CSNK1G1-T-TCF7L1 33501 6689 34325 48942 815
CSNK1G1-PORCN-PPP2R1A 15949 51267 916 23706 44599 CSNK1G1-PORCN-WNT5A 10356 8876 25975 28454 18185
CSNK1G1-PORCN-SFRP1 7246 7363 14462 20174 36420 CSNK1G1-DVL2-FRZB 30588 38887 41771 49656 1919
CSNK1G1-JUN-SLC9A3R1 43202 5406 55467 38845 7125 CSNK1G1-JUN-WNT4 33107 46065 50016 51102 7862
CSNK1G1-FSHB-MYC 10008 29873 20279 26881 48302 CSNK1G1-NLK-WNT2B 49065 6850 56800 44447 6716
CSNK1G1-JUN-WNT5A 21479 39247 6333 24156 52648 CSNK1G1-SFRP1-WNT2B 34525 31075 56473 56358 3840
CSNK1G1-FGF4-FRAT1 23308 12898 577 6288 40499 CSNK1G1-CTNNB1-FRZB 11010 41399 10677 9362 28958
CSNK1G1-CTBP2-DKK1 36737 50084 41906 46380 7431 CSNK1G1-GSK3B-RHOU 41655 54814 54139 46702 874
CSNK1G1-CTBP2-SLC9A3R1 2953 39509 10302 16583 49929 CSNK1G1-DIXDC1-RHOU 16058 1799 7780 18030 48278
CSNK1G1-GSK3A-RHOU 47412 26494 53128 51332 7632 CSNK1G1-FZD2-WNT5A 50135 56267 44911 41731 22635
CSNK1G1-CTNNBIP1-FOSL1 28695 47395 40486 51217 12008 CSNK1G1-FSHB-WNT2B 6562 41743 11739 18943 50322
APC-CSNK1G1-FZD1 32683 26130 40629 37958 20743 CSNK1G1-PORCN-WNT2 50216 4601 38088 29252 9325
CSNK1G1-CTNNBIP1-FBXW11 27997 6997 10059 3785 44390 CSNK1G1-DIXDC1-DKK1 5009 2538 5529 18100 16388
CSNK1G1-FOXN1-FZD1 11929 3765 872 10484 55805 CSNK1G1-FGF4-SFRP1 54991 41009 55503 37797 21039
CSNK1G1-NKD1-WNT2 15676 18894 5930 17029 46372 CSNK1G1-JUN-SFRP4 42953 29268 37702 44736 6880
CSNK1G1-FGF4-SLC9A3R1 7617 19617 897 10351 45255 CSNK1G1-PYGO1-TLE2 17136 9155 11518 17890 32040
CSNK1G1-FGF4-WNT4 18545 9815 5216 15463 13843 CSNK1G1-FOXN1-WNT3A 18175 14967 2698 926 50456
CSNK1G1-FSHB-T 6318 9942 3904 6835 49975 CSNK1G1-GSK3A-SENP2 9667 52049 9371 22981 45654
Table 11: Rankings o CSNK1G1-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
PORCN-PPP2R1A and CSNK1G1-FZD2-PPP2CA. 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.
24
RANKING @ iUSING SOBOL - MARTINEZ
3 d o de comb. 1 3 6 12 24 3 d o de comb. 1 3 6 12 24
CSNK1G1-NLK-SENP2 1023 28963 23752 12006 13662 CSNK1G1-FOXN1-TLE2 4073 26473 32009 15332 6483
CSNK1G1-NLK-WNT4 9882 34667 14911 20141 31237 CSNK1G1-FOXN1-KREMEN1 4187 16379 10411 17376 49738
CSNK1G1-FOXN1-SLC9A3R1 11281 33656 17132 33702 26731 CSNK1G1-PORCN-SENP2 15610 15039 24692 32268 17031
CSNK1G1-FZD2-SENP2 23323 8023 15244 20763 9314 CSNK1G1-FSHB-LEF1 8757 48545 39614 32449 13625
CSNK1G1-DVL2-WNT2 2134 29301 54842 50984 15101 CSNK1G1-FSHB-SFRP4 39476 50249 41873 33694 14579
CSNK1G1-FZD2-TLE2 21805 41649 20523 9228 19247 CSNK1G1-DVL2-SENP2 2829 8071 56530 44158 5270
CSNK1G1-LRP5-SENP2 430 22598 40400 16862 29795 CSNK1G1-JUN-SENP2 53562 32056 34894 40476 27708
CSNK1G1-NKD1-PPP2CA 19784 21076 9213 14040 31099 CSNK1G1-FZD2-FZD7 20133 14733 25644 20740 34303
CSNK1G1-FOXN1-PPP2R1A 2180 53719 33104 7285 38261 CSNK1G1-CTNNBIP1-TCF7L1 5806 12198 11262 5166 48378
CSNK1G1-FGF4-TLE2 8296 22216 32082 2863 23370 CSNK1G1-FZD2-SFRP4 3975 35697 43472 32265 3691
CSNK1G1-FSHB-SENP2 32972 50887 28581 8306 20113 CSNK1G1-DVL2-FOSL1 8083 52720 54665 44734 52383
CSNK1G1-DVL2-TCF7 1931 11355 48637 47697 45338 CSNK1G1-FZD2-PPP2CA 6902 15684 9374 21259 4565
CSNK1G1-JUN-WNT2 26112 36147 34970 53598 32760 CSNK1G1-CXXC4-FOSL1 3540 41011 53892 1277 30939
CSNK1G1-CTNNBIP1-DKK1 3286 20741 29442 46391 49878 CSNK1G1-JUN-TCF7L1 20659 31359 42235 11222 25258
CSNK1G1-FZD2-WNT2B 16988 38740 33148 19223 15749 CSNK1G1-CTNNBIP1-TLE2 3609 28632 45678 10368 21084
CSNK1G1-NKD1-TCF7L1 25433 42313 19013 1420 12490 CSNK1G1-FOXN1-FBXW4 2305 4668 32121 14002 38175
CSNK1G1-DVL2-FBXW11 18902 31099 45042 20063 7907 CSNK1G1-GSK3B-SLC9A3R1 13151 10808 29139 7865 15618
CSNK1G1-FGF4-KREMEN1 23388 19547 27651 18744 8543 CSNK1G1-NKD1-SENP2 5658 19388 11502 16684 22979
CSNK1G1-FOXN1-TCF7L1 20619 35523 15458 17164 22105 CSNK1G1-T-TLE2 21536 24813 30561 665 19587
CSNK1G1-PORCN-TLE2 23956 39888 45808 29516 4037 CSNK1G1-PORCN-RHOU 156 28220 17621 19760 27625
CSNK1G1-JUN-TLE2 3654 15612 6612 7680 23323 CSNK1G1-NKD1-SFRP4 3477 44788 33518 12420 52257
CSNK1G1-FSHB-PPP2CA 40612 43508 22826 3439 25861 CSNK1G1-FOXN1-FRZB 757 4827 23287 8957 51220
CSNK1G1-JUN-KREMEN1 21900 17437 22609 16420 7910 CSNK1G1-FOXN1-RHOU 2715 42081 23816 12990 28784
CSNK1G1-DVL2-TCF7L1 35932 38409 51352 32104 7019 CSNK1G1-SFRP1-WNT5A 18728 41171 27916 27826 21302
CSNK1G1-CTNNB1-KREMEN1 7668 39456 50237 10228 44604 CSNK1G1-SFRP1-TLE2 30635 31136 34280 5452 10126
CSNK1G1-JUN-FBXW4 35891 19352 22587 4046 48570 CSNK1G1-FZD1-SENP2 44823 32702 37344 23873 20064
CSNK1G1-PORCN-SLC9A3R1 9278 49182 53553 52071 36096 CSNK1G1-CTNNB1-SENP2 42637 17246 37340 28255 10424
CSNK1G1-CTNNB1-FBXW11 47591 47761 24648 52706 42288 CSNK1G1-CTNNB1-DAAM1 640 14671 43332 53397 11882
CSNK1G1-JUN-RHOU 22504 10065 14728 48707 5692 CSNK1G1-DVL2-FZD1 29822 52079 42226 21023 15435
CSNK1G1-FZD1-TCF7L1 3657 17738 32058 2877 3452 CSNK1G1-FGF4-FOSL1 3966 11339 26512 6277 5337
CSNK1G1-FZD2-WNT4 10410 34283 49819 8764 3839 CSNK1G1-FZD2-LEF1 25439 42050 48188 18015 7710
CSNK1G1-GSK3A-TLE2 15953 48553 26146 34236 29429 CSNK1G1-FOXN1-FZD6 465 20038 14379 3608 44811
CSNK1G1-JUN-PPP2R1A 23606 19004 7535 6758 46881 CSNK1G1-JUN-PYGO1 15049 21562 26708 38509 8167
CSNK1G1-DVL2-TLE2 25461 39155 51026 50993 10360 CSNK1G1-PORCN-TCF7L1 22705 5536 55332 52452 7332
CSNK1G1-FGF4-SENP2 15585 3966 9710 959 24750 CSNK1G1-JUN-TCF7 24936 47488 33304 8067 17856
CSNK1G1-JUN-PPP2CA 52121 39360 27268 41319 22355 CSNK1G1-FZD1-FZD7 23551 51418 20988 43171 26341
CSNK1G1-CSNK2A1-MYC 816 53067 52527 17682 54911 CSNK1G1-PORCN-FBXW4 5765 9868 51683 56209 13206
CSNK1G1-FGF4-TCF7L1 41064 41146 28605 3115 12570 CSNK1G1-FGF4-FBXW4 24615 51440 29249 42766 24693
CSNK1G1-FOXN1-TCF7 28811 39294 26956 517 23711 CSNK1G1-NKD1-RHOU 13195 46913 28099 45919 38961
CSNK1G1-FZD2-FZD8 55692 33791 38801 40579 16150 CSNK1G1-JUN-WNT2B 6543 12806 10942 2276 34250
CSNK1G1-NLK-TCF7L1 25249 40044 11018 25277 24236 CSNK1G1-FZD2-SLC9A3R1 72 11838 29010 16078 46306
CSNK1G1-GSK3B-LRP6 38011 14409 17563 26578 29511 CSNK1G1-PORCN-WNT2B 28382 5688 53042 54668 30496
CSNK1G1-CXXC4-DKK1 21335 46326 26057 31544 22681 CSNK1G1-CXXC4-FRAT1 2838 20322 35155 3949 37439
CSNK1G1-FGF4-PPP2R1A 51350 42511 16585 6456 20879 CSNK1G1-WIF1-WNT2B 2279 53121 35371 56846 2011
CSNK1G1-WIF1-WNT4 56789 43140 52845 54585 19132 CSNK1G1-DIXDC1-WNT2B 40930 25751 23698 20111 41840
CSNK1G1-T-WNT2B 41593 45959 12146 13197 24503 CSNK1G1-T-TCF7L1 18966 48845 25610 157 14816
CSNK1G1-PORCN-PPP2R1A 503 35730 3044 6124 43150 CSNK1G1-PORCN-WNT5A 46413 14655 30449 49521 13435
CSNK1G1-PORCN-SFRP1 28402 40020 24656 8442 10906 CSNK1G1-DVL2-FRZB 19883 55733 37226 45418 8700
CSNK1G1-JUN-SLC9A3R1 29086 31057 29189 10809 56936 CSNK1G1-JUN-WNT4 7327 52583 35808 38813 18150
CSNK1G1-FSHB-MYC 16803 10241 15398 7414 1214 CSNK1G1-NLK-WNT2B 51130 36723 22493 41024 14440
CSNK1G1-JUN-WNT5A 90 18823 34308 8819 39419 CSNK1G1-SFRP1-WNT2B 25407 48375 4565 5611 20190
CSNK1G1-FGF4-FRAT1 17863 11935 14252 19547 33993 CSNK1G1-CTNNB1-FRZB 2473 1895 48867 55068 18412
CSNK1G1-CTBP2-DKK1 9933 53999 48020 51075 12322 CSNK1G1-GSK3B-RHOU 12634 48456 37726 40555 19173
CSNK1G1-CTBP2-SLC9A3R1 10860 22491 33788 2639 39302 CSNK1G1-DIXDC1-RHOU 37350 50752 24433 17248 3736
CSNK1G1-GSK3A-RHOU 38032 48019 31225 42299 34354 CSNK1G1-FZD2-WNT5A 47509 40249 19979 4150 23159
CSNK1G1-CTNNBIP1-FOSL1 11949 32749 12277 6351 7950 CSNK1G1-FSHB-WNT2B 24679 21316 37424 4944 42965
APC-CSNK1G1-FZD1 21185 37153 44 28557 44726 CSNK1G1-PORCN-WNT2 44086 52040 53679 46699 15576
CSNK1G1-CTNNBIP1-FBXW11 8978 49664 28961 11257 11947 CSNK1G1-DIXDC1-DKK1 32455 51113 13061 32408 39336
CSNK1G1-FOXN1-FZD1 5809 24046 13888 4092 54967 CSNK1G1-FGF4-SFRP1 54217 40967 27315 4034 12736
CSNK1G1-NKD1-WNT2 584 24793 8285 23891 20671 CSNK1G1-JUN-SFRP4 18558 44438 31265 34955 26920
CSNK1G1-FGF4-SLC9A3R1 3812 15818 13512 15179 25323 CSNK1G1-PYGO1-TLE2 6707 43365 50722 55108 11091
CSNK1G1-FGF4-WNT4 2235 6629 11645 21643 241 CSNK1G1-FOXN1-WNT3A 8675 49134 21528 19393 15926
CSNK1G1-FSHB-T 25656 40734 22557 25924 2702 CSNK1G1-GSK3A-SENP2 8587 27952 42504 7797 12650
Table 12: Rankings o CSNK1G1-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 - ma inez
6.5.4. Examining he beha iou o LRP-CSNK1G1-X combina ions
Looking a he ables abo e, one inds he ollowing combina ions o membe s o LRP
amily along wi h CSNK1G1, o be p ominen a 3 d o de le el - CSNK1G1-LRP5-
SENP2 and CSNK1G1-GSK3B-LRP6. 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.
25
Acknowledgmen s
Special hanks o M s. Ri a Sinha and la e M . P abha Sinha o suppo ing he au ho
inancially, wi hou which his wo k could no ha e been made possible.
Supplemen a y
The ollowing iles (ending wi h . x and can be opened in R o in simple ex p o-
cessing p og am) wi h hese names a e made a ailable wi h his manusc ip . Fo
CSNK, (1) -3-od -TP- anking-linea . x , (2) -3-od -TP- anking- b . x , (3) -3-od -
TP- anking-2002. x , and (4) -3-od -TP- anking-ma inez. x , con ain ankings o
3 d o de combina ions ac oss each ime poin o , HSIC (linea ke nel), HSIC ( b
ke nel), SOBOL (2002 implemen a ion) and SOBOL (ma inez implemen a ion), e-
spec i ely.
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