si . oyalsocie ypublishing.o g
Re iew
Ci e his a icle: Al onso JCL, Talkenbe ge K,
Sei e M, Klink B, Hawkins-Daa ud A, Swanson
KR, Ha ziki ou H, Deu sch A. 2017 The biology
and ma hema ical modelling o glioma
in asion: a e iew. J. R. Soc. In e ace 14:
20170490.
h p://dx.doi.o g/10.1098/ si .2017.0490
Recei ed: 6 July 2017
Accep ed: 17 Oc obe 2017
Subjec Ca ego y:
Li e Sciences–Ma hema ics in e ace
Subjec A eas:
bioma hema ics, sys ems biology
Keywo ds:
glioma in asion, cell pheno ypic plas ici y,
malignan p og ession, in il a i e umou
mo phology, ma hema ical modelling
Au ho o co espondence:
A. Deu sch
e-mail: and eas.deu sch@ u-d esden.de
The biology and ma hema ical modelling
o glioma in asion: a e iew
J. C. L. Al onso1,2, K. Talkenbe ge 2, M. Sei e 3,5, B. Klink4,5,6,7,
A. Hawkins-Daa ud8, K. R. Swanson8, H. Ha ziki ou1,2 and A. Deu sch2
1
Depa men o Sys ems Immunology and B aunschweig In eg a ed Cen e o Sys ems Biology, Helmhol z Cen e
o In ec ion Resea ch, B aunschweig, Ge many
2
Cen e o In o ma ion Se ices and High Pe o mance Compu ing,
3
Ins i u e o Medical In o ma ics and
Biome y, and
4
Ins i u e o Clinical Gene ics, Facul y o Medicine Ca l Gus a Ca us, Technische Uni e si a
¨
D esden, Ge many
5
Na ional Cen e o Tumo Diseases (NCT), D esden, Ge many
6
Ge man Cance Conso ium (DKTK), pa ne si e, D esden, Ge many
7
Ge man Cance Resea ch Cen e (DKFZ), Heidelbe g, Ge many
8
P ecision Neu o he apeu ics Inno a ion P og am, Mayo Clinic, Phoenix, AZ, USA
JCLA, 0000-0003-2432-5953; AD, 0000-0002-9005-6897
Adul gliomas a e agg essi e b ain umou s associa ed wi h low pa ien su -
i al a es and limi ed li e expec ancy. The mos impo an hallma k o his
ype o umou is i s in asi e beha iou , cha ac e ized by a ma kedly pheno-
ypic plas ici y, in il a i e umou mo phologies and he abili y o malignan
p og ession om low- o high-g ade umou ypes. Indeed, he widesp ead
in il a ion o heal hy b ain issue by glioma cells is la gely esponsible o
poo p ognosis and he di icul y o inding cu a i e he apies. Meanwhile,
ma hema ical models ha e been es ablished o analyse po en ial mechanisms
o glioma in asion. In his e iew, we s a wi h a b ie in oduc ion o cu en
biological knowledge abou glioma in asion, and hen c i ically e iew and
highligh u u e challenges o ma hema ical models o glioma in asion.
1. In oduc ion
Gliomas a e he mos common p ima y umou s o he cen al ne ous sys em
(CNS) in adul s. They comp ise a clinically, his ologically and gene ically e y he -
e ogeneous b ain umou ca ego y. Un il ecen ly, glioma classi ica ion was la gely
based on mic oscopic examina ion o his ological sec ions o umou specimens by
expe pa hologis s, dis inguishing umou s acco ding o hei mic oscopic simi-
la i ies o di e en ypes o glial cells in o as ocy omas, oligodend oglioma o
ependymomas, he main sub ypes o gliomas [1]. The cu en 2016 Wo ld Heal h
O ganiza ion (WHO) Classi ica ion o Tumou s o he CNS o he i s ime in e-
g a es molecula bioma ke s oge he wi h classic his ological ea u es o de ine
dis inc glioma en i ies [1]. This pa adigm shi in glioma diagnos ics e lec s he
majo p og ess in ou unde s anding o he molecula biology o b ain umou s,
which has emendously inc eased in he pas wo decades due o genome-wide
molecula -p o iling s udies ha ha e cla i ied he gene ic basis o gliomas. Fo
example, di use gliomas wi h his ologically oligodend oglial ea u es a e gene i-
cally cha ac e ized by mu a ions in he IDH gene and 1p/19q codele ion, while
he diagnosis as ocy oma is usually accompanied by mu a ions in IDH in combi-
na ion wi h ATRX and/o TP53 mu a ions bu in ac 1p and 19q. By con as ,
classical p ima y glioblas omas usually do no show mu a ions in he IDH genes
and a e he e o e e e ed o as glioblas oma IDH wild- ype. In addi ion, he
WHO classi ica ion dis inguishes ou p ognos ic g ades ha e lec he deg ee o
malignancy: WHO g ade I is assigned o he mo e ci cumsc ibed, benign umou s
wi h low p oli e a i e po en ial ha mainly occu du ing childhood and in young
adul s; WHO g ade II–IV umou s a e di usely in il a i e wi h inc eased cellula
abno mali ies (di use gliomas); WHO g ade III umou s also show dedi e en ia-
ion and mi o ic cell ac i i y; and WHO g ade IV umou s exhibi , in addi ion o
&2017 The Au ho (s) Published by he Royal Socie y. All igh s ese ed.
he ea u es p esen in he o he g ades, pa hological p oli e a ion
o small essels and/o nec osis. WHO g ade II–IV umou s
a e cha ac e ized by ex ensi e, di use in il a ion o glioma
cells in o he hos b ain issue, and a e he e o e e e ed o as
di use gliomas. These agg essi e b ain umou s a e ypically
associa ed wi h a poo p ognosis, sha p de e io a ion in he
pa ien s’ quali y o li e and ma kedly low su i al a es. In pa -
icula , IDH wild- ype glioblas oma, he mos common (app ox.
45% o all gliomas) and malignan p ima y b ain umou (WHO
g ade IV), has a 5-yea su i al o abou 5% om he ime
o diagnosis [2,3]. E en o pa ien s wi h di use low-g ade
IDH-mu an gliomas (WHO g ade II), al hough su i al
canbemo e han10yea s, hep ognosis is un a ou able,
as hese umou s e en ually p og ess o a high-g ade
malignan lesion (WHO g ade III o IV) [4]. Despi e signi ican
ad ances in su gical and medical imaging echniques, as well
as in adju an adio-, chemo- and immuno he apy [5–10], he
inhe en endency o glioma cells o widely dissemina e wi hin
no mal b ain pa enchyma se e ely limi s ea men esponses
[11–13]. The e o e, a be e unde s anding o he mechanisms
ha igge andgo e ngliomain asioniso highclinicalimpo -
ance o he de elopmen o mo e e ec i e and less oxic
he apeu ic s a egies.
Al hough he e is a conside able amoun o in o ma ion
abou he clinical and biological beha iou o gliomas, he high
complexi y o he in asion mechanisms emains a majo chal-
lenge in clinical neu o-oncology. His ologically, glioma cells
closely esemble glial p ogeni o cells, which ha e he abili y o
p oli e a e and di e en ia e in o di e en glial cell ypes. These
cells ha e a high mig a o y beha iou in he de eloping CNS
[11,12,14]. This sugges s ha mechanisms con ibu ing o
mig a ion o neu oepi helial cells du ing emb yogenesis a e
also ele an o glioma in asion [14]. In addi ion, accumula ing
e idence indica es ha spa ial and empo al a ia ions in signal-
ling pa hways lead o unc ional and pheno ypic changes in
glioma cells, which hen a ec in e ac ions wi h neighbou ing
malignan and non-malignan cells along wi h o he componen s
o he su ounding b ain issue. The exac consequences o he
dynamic in e play be ween he e ogeneous cellula en i ies and
hei esponse o al e a ions in he ex acellula mic oen i on-
men ha e no ye been elucida ed. Mo eo e , i emains
unclea why me as ases ou side he CNS a e ex emely a e in di -
use gliomas [15,16]. F om a biological and medical pe spec i e, i
is di icul o in es iga e he connec ions be ween clinically obse -
able glioma beha iou and he unde lying molecula and
cellula p ocesses. The challenge is o in eg a e he heo e ically
and empi ically acqui ed knowledge o be e unde s and he
mechanisms and ac o s ha con ibu e o glioma in asion.
In his con ex , ma hema ical models p o ide use ul ools
owa ds iden i ying dependencies and a ge s o cance cell
mig a ion and in asion. Ma hema ical models and compu-
a ional app oaches ha e become inc easingly abundan in
cance esea ch o s udy umou dynamics and esponses
o ea men modali ies such as chemo- and adio he apy
[17–20]. Ma hema ical modelling p o ides a use ul heo e ical
amewo k o pe o m in silico expe imen s, as well as
o e alua e assump ions and make p edic ions ha can be
expe imen ally es ed [21–32]. In he las wo decades, se e al
ma hema ical models ha e been de eloped o in es iga e key
mechanisms go e ning glioma g ow h and in asion [23,33–35].
Ten yea s ago, se e al o he cu en co-au ho s e iewed
ma hema ical models o glioma de elopmen , g ow h and
p og ession [34]. Since hen, he ield o glioma esea ch has
signi ican ly g own. In his e iew we exclusi ely ocus on
ma hema ical models o glioma in asion. We i s in oduce
cu en biological knowledge abou glioma in asion.
Then, we desc ibe biological model sys ems, in pa icula ,
in i o expe imen s and in i o animal models o he analy-
sis o glioma in asion, and medical imaging echniques. We
hen c i ically e iew ma hema ical models o glioma in a-
sion, and highligh u u e challenges o ma hema ical and
compu a ional modelle s in his esea ch a ea.
2. Biology o glioma in asion
In il a ion o he b ain pa enchyma is a p ominen ea u e o
di use gliomas, making comple e su gical esec ion almos
impossible [36]. Di use gliomas in ade ex ensi ely as single
cells anywhe e wi hin he hos b ain issue, wi h some p e e -
ence o in il a e along whi e ma e ac s and he pe iphe y o
blood essel walls [16]. The in il a ion o he su ounding
b ain issue is de e mined by complex in e ac ions be ween
glioma cells and he ex acellula mic oen i onmen [37].
He e, we e iew cell in insic mechanisms and ex insic ac o s
ha sus ain and os e glioma in asion.
2.1. In insic mechanisms: pheno ypic plas ici y and
gene ic a iabili y
2.1.1. Epi helial–mesenchymal ansi ion and mig a ion
Glioma cells ha e he abili y o acqui e a mesenchymal pheno-
ype in esponse o mic oen i onmen al cues and mig a e
h ough he ex acellula ma ix (ECM) exhibi ing an elonga ed,
o en wedge-shaped pheno ype [14,38,39]. Mig a ion and in a-
sion o glioma cells a e ela ed, mul is ep p ocesses. Mig a ion is
de ined as he mo emen o cells om one si e o ano he ,
o en in esponse o speci ic ex e nal signals such as chemical
g adien s o mechanical o ces. Epi helial- o-mesenchymal
ansi ion (EMT) is an essen ial p ocess in wound healing,
emb yonic de elopmen and issue emodelling, consis ing in
he ansdi e en ia ion o pola ized epi helial cells in o mo ile
mesenchymal cells (o igina ed om he mesode mal emb yonic
issue which de elops in o connec i e and skele al issues).
Accumula ing e idence highligh s he c i ical ole o EMT
du ing glioma p og ession and i s associa ion wi h inc eased
glioma cell mig a ion [40]. Indi idual glioma cells sp ead by
ac i e cell mig a ion a he han by passi e mo emen . In asion
encompasses glioma cell mig a ion, bu also in ol es deg a-
da ion o he ECM [38]. I is a mul i ac o ial p ocess ha
consis s o in e ac ions be ween adjacen cance cells wi h he
ECM coupled wi h biochemical p ocesses suppo i e o ac i e
cell mig a ion. In gene al, glioma cell in asion in ol es ou dis-
inc s eps [14,38,39]: (1) de achmen o in ading cells om he
p ima y umou mass, (2) adhesion o he ECM, (3) deg ada ion
o he ECM and (4) cell mo ili y and con ac ili y (ac i e cell
mig a ion) ( igu e 1).
A he subcellula le el, sec e ion o p o eases, cell adhesion
molecules and ela ed signals play an impo an ole in
glioma cell mig a ion [37]. De achmen o glioma cells om
he p ima y umou mass in ol es se e al e en s, including
des abiliza ion and diso ganiza ion o cell–cell adhesion
complexes (cadhe in-media ed junc ions), loss o exp ession
o neu al cell adhesion molecules and clea age o CD44, a
cell-su ace p o ein which ancho s he p ima y umou mass
o he ECM by he me allop o einase ADAM [16,38]. In eg ins
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a e he mos common molecules ha allow glioma cells o
adhe e o he ECM, and ma ix-me allop o einases (MMPs)
a e he mos common p o eases ha deg ade he ECM c ea ing
mig a ion ou es. Se e al glioma-exp essed molecula ac o s,
such as ocal adhesion kinase and u okinase- ype plasminogen
ac i a o (an enzyme pa icipa ing in ECM deg ada ion), ha e
been ound o egula e hei exp ession [38]. Glioma cells
mig a e simila ly as non- ans o med neu al p ogeni o cells,
wi h myosin II as he majo sou ce o cy oplasmic con ac ili y
[41]. In ading glioma cells al e hei shape, ex ending a p omi-
nen leading cy oplasmic p o usion ollowed by a bu s o
o wa d mo emen o he cell body. The complex molecula
mechanisms and changes in signalling pa hways ha occu
du ing glioma in asion a e s ill la gely unknown. A majo di -
icul y in unde s anding he oncogenomics o glioma cell
in asion is o de e mine how and when gene ic al e a ions
and signalling cascades in e ac [42]. Only a ew speci ic pa h-
ways ha e been consis en ly iden i ied, and he e exis mul iple
possible in e ac ions along wi h addi ional unknown ac o s o
be elucida ed.
2.1.2. Mig a ion–p oli e a ion dicho omy
A he ime o diagnosis, gliomas a e al eady widely dissemi-
na ed, as hey ypically g ow and in ade ex ensi ely be o e
he pa ien expe iences any symp oms. This hidden dissemina-
ion is a majo eason ha makes gliomas di icul o ea
success ully and a cu e almos impossible. Cu en ea men
s a egies mainly ocus on he highly p oli e a i e umou
mass, bu local in asion e en ually leads o ecu ence o he
disease. Eno mous e o s ha e been de o ed o iden i ying
he main signalling e en s ha egula e glioma cell mo ili y
and in asion. Howe e , he apeu ically a ge ing in asion
dynamics is complica ed, because i has been obse ed
ha mig a o y and p oli e a i e beha iou s o glioma cells
a e mu ually exclusi e p ocesses and in e sely co ela ed
[11,43,44]. In pa icula , highly mig a o y cells ha e a lowe
p oli e a ion a e compa ed o ac i ely p oli e a ing cells ha
mo e slowly. This ei he –o beha iou o p oli e a i e and
in asi e glioma cells is suppo ed by bo h in i o and
in i o expe imen s [11] and is e e ed o as he mig a ion–
p oli e a ion dicho omy (o ‘Go-o -G ow’ mechanism) [43,44].
The ‘Go-o -G ow’ beha iou has been linked o me abolic
s ess by se e al expe imen al indings. Godlewski e al. [45]
iden i ied a glioma-exp essed mic oRNA (small non-coding
RNAs ha egula e gene exp ession) ha egula es he balance
be ween glioma cell p oli e a ion and mig a ion in esponse o
changes in he a ailable ene gy. Thei expe imen al da a
e ealed ha , in addi ion o inhibi ing glioma cell mig a ion,
he mic oRNA exp ession also p omo es cell p oli e a ion.
This sugges s ha mig a o y and p oli e a i e e en s sha e
common signalling pa hways, de ining a unique in acellula
mechanism ha egula es bo h phenomena. Mo e ecen ly,
Ho
¨ ing e al. [46] in es iga ed he e ec s o ca boxypep idase
E (CPE), a neu opep ide-p ocessing enzyme, on glioma in a-
sion by means o in i o and in i o s udies. Thei esul s
indica e an oxygen- and nu ien -dependen an i-mig a o y,
bu p o-p oli e a i e ole o CPE in glioma in asion. Addi ion-
ally, expe imen s wi h glioblas oma-de i ed neu osphe es
p o ided u he insigh in o he ‘Go-o -G ow’ mechanism.
EphB2, a ecep o o he y osine kinase amily was ound o
ha e bo h p o-mig a o y and an i-p oli e a i e e ec s in i o
[47]. These no el indings sugges ha glioma in asion could
be a acked by a ge ing speci ic cellula and molecula mech-
anisms associa ed wi h he mig a ion–p oli e a ion dicho omy.
Howe e , u he in es iga ions a e equi ed o un a el
he unde lying signalling pa hways egula ing glioma cell
mig a ion and p oli e a ion.
2.1.3. Cell me abolic plas ici y
A common ea u e o cance cells is hei al e ed glucose
me abolism [48,49]. Unlike non-neoplas ic cells ha ely on
oxida i e phospho yla ion o gene a e he ene gy needed
o cellula p ocesses, cance cells can shi hei me abolism
om espi a ion owa ds glycolysis p oducing lac ic acid.
Indeed, cance cells end o up egula e ae obic glycolysis
e en in he p esence o su icien oxygen, a phenomenon
known as ae obic glycolysis o he Wa bu g e ec , which is
a cha ac e is ic me abolic hallma k o umou de elopmen
[50–52]. Al hough he Wa bu g e ec has ecen ly egained
a en ion as a possible he apeu ic a ge [53,54], i s biological
basis emains elusi e. Compa ed o mi ochond ial oxida i e
me abolism, ae obic glycolysis is an ine icien way o gain
ene gy [55]. Howe e , inc eased glycolysis c ea es a hos ile
acidic en i onmen , in which cance cells ha e an e olu ion-
a y ad an age wi h espec o no mal pa enchyma [56]. The e
is accumula ing e idence ha acid-induced oxici y is an
essen ial componen equi ed o umou in asion, and he e-
o e a hallma k o in asi e cance s [56,57]. Glioma cells a e
speci ically cha ac e ized by a high a e o glycolysis and lac-
a e ex usion, wi h he abili y o lou ish in a ela i ely
(1) (3)(2) (4)
Figu e 1. Glioma cell mig a ion. Schema ic o he p ocess o glioma cell in asion in o hos b ain issue. In asion o glioma cells in ol es ou dis inc s eps: (1)
de achmen o in ading cells om he p ima y umou mass, a p ocess igge ed by down egula ion o cell–cell adhesion molecules and mic oen i onmen al
changes, (2) in eg in-media ed adhesion o he ex acellula ma ix (ECM), (3) sec e ion o p o eases, which locally deg ade ECM componen s c ea ing ou es
along which glioma cells in ade he b ain and (4) mig a ion by ex ending a p ominen leading cy oplasmic p o usion, ollowed by a bu s o o wa d mo emen
o he cell body. Figu e adap ed om [39].
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3
hypoxic en i onmen [58]. In ac , many o he in asi e ea-
u es o gliomas may depend on dis o ed me abolic
unc ions, which makes he s udy o me abolic al e a ions
and hei e ec s on in asion p ocesses a g owing ield in
cance esea ch wi h po en ial he apeu ic bene i s.
2.1.4. In a- and in e - umou al he e ogenei y
Tumou he e ogenei y con ibu es o disease p og ession and
de elopmen o he apy esis ance [59,60]. Ex ensi e gene ic
and pheno ypic a ia ions exis among glioma cells wi hin
a single umou (in a- umou al he e ogenei y) and be ween
pa ien s (in e - umou al he e ogenei y) due o ex ensi e mol-
ecula di e si y and mic oen i onmen al he e ogenei y
[37,61–68]. I is commonly assumed ha umou he e ogen-
ei y a ises ei he om a sel - enewing cance s em cell
popula ion o due o clonal compe i ion o common
esou ces d i en by he acquisi ion and expansion o
mu a ions in cance cells [61,69–71]. Recen clinical and
expe imen al indings ha e e ealed ex ensi e gene ic a i-
a ions in glioma cells due o in a- umou al e olu ion
[63,64,67,72]. Besides he la ge gene ic he e ogenei y, in e -
ac ions be ween glioma cells and wi h he su ounding
b ain pa enchyma lead o unc ional and pheno ypic di e -
si y. E idence indica es ha dis inc clones wi hin a umou
may ha bo gene ic and epigene ic al e a ions ha p omo e
cance cell mig a ion and in asion. Recen ly, expe imen s
wi h mix u es o di e en cell ypes o mimic pheno ypic he -
e ogenei y ha e e ealed ha in asion is d i en by he
coope a ion o mul iple umou -cell subpopula ions [73,74].
Pa e ns o co-in asion we e obse ed wi h inhe en ly in a-
si e cells ac ing as he leade and subpopula ions o poo ly
in asi e cells as ollowe s. This ‘di ision o labou ’ may
acili a e no only umou in asion, bu also malignan p o-
g ession. Al hough he e is inc easing app ecia ion ha
in a- umou al he e ogenei y is cen al o glioma beha iou ,
li le is known abou he empo al sequence o gene ic and
mic oen i onmen al changes o how genomic ins abili ies
and adap a ion o mic oen i onmen al condi ions con ibu e
o glioma in asi eness.
2.2. Cell-ex insic ac o s
2.2.1. Guidance mechanisms
The pa icula s uc u es o he b ain such as blood essels,
whi e ma e ac s and b ain pa enchyma, and speci ic
umou cell–ECM adhe ence mechanisms a e c ucial ac o s
in glioma in asion [75,76]. A any s age o in asion, glioma
cells a e con on ed wi h non-neoplas ic b ain issue com-
posed o mul iple cell ypes and a ious ECM componen s.
The ECM in he CNS is di e en om he ECM in o he is-
sues in ha i has low ib ous p o ein con en and high
ca bohyd a e concen a ions [77]. In pa icula , he b ain
ECM is mainly p oduced by as ocy es and oligodend ocy es,
comp ises an es ima ed 20% o he b ain olume in adul s
and consis s p ima ily o hyalu onic acid, excep a ound
blood essels and a he pial su ace ( he bounda y be ween
g ey ma e and ce eb ospinal luid) [76]. The in asion o
glioma cells in o he adjacen b ain issue is guided by a com-
bina ion o mul iple molecula and physical mechanisms
along p e-exis ing acks o leas esis ance. The majo in a-
sion ou es a e basemen memb anes and in e cellula
acks p o ided by myelina ed axons and as ocy e p ocesses
[76,78]. Glioma cells mig a e along blood essels by using he
ou wa d essel–pa enchyma in e ace and he lumen o he
pe i ascula space [76]. Mo e p ecisely, blood essels guide
in ading glioma cells ia laminin- and collagen-IV-media ed
in eg in engagemen (ECM p o eins media ed), whe eas
whi e ma e acks guide by cell–cell con ac s and
mechanisms egula ing cell–ECM adhesion o ces [76]. How-
e e , he speci ic guidance ac o s and ela ed molecula
mechanisms o mos dissemina ion ou es emain unclea .
2.2.2. Hypoxia-induced mig a ion
Uncon olled glioma cell p oli e a ion leads o he de elop-
men o hypoxic egions. This mic o egional change
p oduces a local milieu ha a ou s ce ain glioma cell beha-
iou s such as in asion [60]. A commonly held iew is ha
cons i u i e up egula ion o glycolysis is likely o be an adap-
a ion o he lack o oxygen [57]. Acco ding o he WHO
classi ica ion, de ec ion o ascula p oli e a ion wi h highly
pa hological blood essels and umou nec osis is essen ial
o he diagnosis o g ade IV gliomas [1]. These umou -
induced ea u es a e o en spa ially and empo ally ela ed,
wi h si es o pa hological neo ascula iza ion indica i e o
he o ma ion o hypoxic and nec o ic egions. Quan i a i e
immunohis ochemical analysis e ealed ha while high-
g ade gliomas may locally show a s ong angiogenic ac i i y,
many egions o bo h low- and high-g ade gliomas display
ascula densi ies in he ange o no mal ce eb al g ey o
whi e ma e , indica ing limi ed angiogenesis [79–81]. This
suppo s he obse a ion ha in high-g ade gliomas di e en
in asi e and p o-angiogenic umou cell pheno ypes coexis
[39]. O e exp ession o p o-angiogenic ac o s by umou
cells esul s in local ascula o e g ow h wi h de ec i e
blood essels, which ha e signi ican ly la ge diame e s
and hicke basemen memb anes han hose in no mal
b ain issue [82]. I has been obse ed in i o ha unde
oxygen-limi ing condi ions due o ascula abno mali ies,
glioma cells ac i ely mig a e away om hypoxic egions [83].
Di e en pa hological and expe imen al obse a ions
sugges ha aso-occlusion could eadily explain he apid
pe iphe al expansion and di usely in il a i e g ow h beha -
iou o high-g ade gliomas [84,85]. Occlusion o ascula u e
mainly occu s due o inc eased mechanical p essu e by
ei he umou cells o by in a ascula p o- h ombo ic mech-
anisms [83,84,86]. Occluded o collapsed blood essels
induce pe i ascula umou hypoxia and nec osis in glio-
blas oma, which ypically o m lines wi h pe i ocally
inc eased cell densi y, e med pseudopalisades [83–85,87].
Pseudopalisades a ound nec o ic oci, a common ea u e o
high-g ade gliomas, a e se e ely hypoxic and linked o
wa es o glioma cells ac i ely mig a ing away om such
oxygen-de icien egions [83–85,87]. Expe imen al s udies
u he sugges ha umou hypoxia esul s in inc eased
glioma cell mig a ion and in asion, and s ongly co ela es
wi h umou malignancy [39,88,89]. The exac pa hophysiolo-
gical ac o s and mechanisms unde lying hypoxia-induced
cell mig a ion in gliomas a e s ill no known, and u he
in es iga ion is equi ed o unde s and he complex molecula
pa hways in ol ed in hypoxic esponses and me abolic con ol
by glioma cells.
2.2.3. Blood–b ain ba ie
An impo an s uc u al componen o he b ain ascula u e is
he blood b ain ba ie (BBB), which is essen ial o supplying
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he b ain issue wi h oxygen and glucose, media ing e lux o
was e p oduc s, and main aining a p ecisely egula ed mic oen-
i onmen o eliable neu onal signalling [90]. The BBB is
composed o igh ly bound endo helial cells and pe i ascula
as ocy es ha es ic he exchange o molecules om he blood-
s eam much mo e han capilla ies anywhe e else in he body.
High-g ade gliomas ha e he abili y o dis up he in eg i y o
he BBB, which is associa ed wi h inc eased umou g ow h
and di use in asion in o he su ounding b ain pa enchyma
[16,91–93]. Recen s udies ha e shown ha he BBB can be he -
e ogeneously dis up ed in high-g ade gliomas, and he deg ee
o BBB dis up ion is ela ed o umou malignancy [92]. How-
e e , he p ecise ela ionship be ween glioma-induced BBB
dys egula ion and cell in asion is s ill no clea [91]. On he
o he hand, expe imen al e idence shows ha one o he majo
obs acles o s anda d an i-cance d ug deli e y in he b ain is
he BBB, which limi s he e icacy o chemo he apy [16,92]. In
ac , he p esence o an almos in ac BBB is one o he main ac o s
ha makes he ea men o low-g ade gliomas wi h chemo he -
apy challenging. Al hough he BBB may be dis up ed a he co e
o high-g ade gliomas, i can be ela i ely in ac a he umou
pe iphe y whe e in ading glioma cells a e loca ed [92]. This pe -
mi s in il a i e glioma cells o escape chemo he apy-induced
dea h, which can esul in umou ecu ence.
2.2.4. Immune sys em engagemen
Tumou s ha e long been ecognized as wounds ha do no
heal [94]. Bo h ca cinogenesis and wound healing in ol e
cell p oli e a ion, mig a ion, in asion, angiogenesis, in lam-
ma ion and as ocy e ac i a ion in esponse o inju ies
[76,95]. The mic oen i onmen o high-g ade gliomas
esembles in many ways a ch onic wound [95]. In pa icula ,
he ex ensi e cell mig a ion and in asion obse ed in gliomas
also accompanies eac i e gliosis, a non-speci ic eac ion
whe e as ocy es a e ac i a ed in esponse o inju ies o he
CNS as pa o a healing p ocess. The bo de o gliomas exhi-
bi s an inc eased numbe o eac i e as ocy es, which
oge he wi h glioma cells sec e e a ious p o-mig a o y sig-
nalling molecules [76]. Recen ly, a p o ein (connec i e issue
g ow h ac o ) p oduced a high le els by eac i e as ocy es
has been iden i ied o s imula e mig a ion o glioma cells [95].
Indeed, he sec e ed ac o modula es nea ly all aspec s o he
signalling mechanisms ha egula e cell in asion, such as
modi ica ion o g ow h ac o ac i i ies, ECM composi ion,
in eg in ( ansmemb ane cell-ma ix adhesion ecep o s)
and E-cadhe in exp ession (a ansmemb ane p o ein ha
media es cell–cell adhesion). Thus, he iden i ica ion o p o-
cesses in ol ed in glial eac i a ion may con ibu e o a
be e unde s anding o glioma cell in asion wi h po en ial
he apeu ic implica ions.
Accumula ed his opa hological da a ha e es ablished ha
issue- esiden mic oglia and mac ophages a e he p edomi-
nan in il a ing immune cells in gliomas, accoun ing o up
o 30–50% o he o al umou mass [96]. Monocy es ci cula e
in he bloods eam and a e con inuously ec ui ed in o
umou s in esponse o se e al umou -de i ed chemo-
a ac an s. Once inside he umou , monocy es apidly
di e en ia e in o umou -associa ed mac ophages (TAMs),
and hen accumula e in hypoxic/nec o ic a eas [96]. TAMs
p oduce se e al ac o s ha no only s imula e he su i al
and p oli e a ion o umou cells, bu also supp ess an i-
umou immuni y [96,97]. The e is g owing e idence ha
TAMs a e also in ol ed in egula ing glioma cell mig a ion
and in asion [96,98–100]. Mo eo e , TAMs con ibu e o
malignan p og ession o gliomas h ough sec e ion o a -
ious chemical ac o s ha a ec angiogenesis and ECM
emodelling, which p omo es glioma in asion [96,97,101].
Mo e p ecisely, TAMs can display wo majo pheno ypes,
he classically (M1) and al e na i ely (M2) ac i a ed, which
can be iewed as wo ex eme pheno ypes [102,103].
Unlike TAMs displaying an M1-like pheno ype wi h p o-
in lamma o y and an i- umou unc ions, M2 mac ophages
a e immunosupp essi e, p oduce p o-angiogenic ac o s,
con ibu e o he ECM- emodelling, and hus c ea e a a ou -
able mic oen i onmen o glioma g ow h and in asion.
Al hough he e is g owing accep ance ha he M1 and M2
s a es a e no dicho omous bu a he ep esen ex emes o
a con inuum o pheno ypes, a majo i y o mac ophages in
gliomas a e mac ophages wi h M2-like pheno ype which
exhibi p o-in asi e p ope ies, pa icula ly in la e s ages o
disease p og ession [104,105]. Recen e idence indica es ha
he colony s imula ing ac o -1 (CSF-1) sec e ed by glioma
cells induces TAMs o p omo e in asion [104]. I has been
obse ed ha CSF-1 le els a e ele a ed in high-g ade glio-
mas, which is associa ed wi h he exp ession o M2
mac ophage ma ke s. In addi ion, he cy okine in e leukin-
10 (IL-10) is also commonly associa ed wi h mac ophages
o he M2 pheno ype and has been ound o s imula e
glioma cell in asion [104]. Toge he , chemokines, cy okines
and g ow h ac o s sec e ed by TAMs ac i a e di e en sig-
nalling pa hways ha can swi ch glioma cells owa ds mo e
agg essi e beha iou .
3. Biological model sys ems
As i is cu en ly impossible o moni o he en i e p ocess o
glioma in asion in he human b ain, di e en biological
model sys ems ha e been in oduced. In i o cell cul u es
p o ide he oppo uni y o gene a e insigh s in o molecula
and cellula pa hways ela ed o glioma in asion unde con-
olled condi ions. Va ious in i o models ha e been
in oduced which allow a mo e ealis ic ep esen a ion and
moni o ing o he complex glioma dynamics.
3.1. In i o expe imen s
Expe imen al p o ocols in i o a e a ailable o independen ly
obse e and con ol a iables o in e es a a ious scales,
om single-cell mo emen o mul icellula clonal g ow h
and cance cell popula ion dynamics [106]. In asion s udies
ha e been pe o med in bo h wo-dimensional (2D) umou
monolaye s and h ee-dimensional (3D) mul icellula sphe -
oids, combining glioma cell mig a ion and p oli e a ion
assays, and conside ing di e en ECM composi ions and
subs a e igidi ies [107]. Howe e , he e a e signi ican
di e ences be ween umou cell mig a ion on a 2D su ace
and in a 3D ma ix [108], and e en mo e be ween in i o
and in i o expe imen s [106]. Unde con olled expe imen al
condi ions, glioma cells may exhibi a mo e ib oblas ic shape
wi h a b oad lamellipodium and an undis o ed nucleus,
whe e he o wa d mo emen is con inuous and unimpeded
[41]. By con as , glioma cells mig a ing h ough he complex
he e ogeneous b ain pa enchyma a e highly pola ized and
elonga ed [38,39]. The mechanical cons ain s due o small
in e cellula spaces impede he o wa d mo emen o nucleus
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and cell body un il necessa y con ac ion o ces a e p o ided
[41]. This abili y o glioma cells o adap hei mo ili y o he
pa icula mic oen i onmen ein o ces he need o assays
ai h ully ep esen ing he en i onmen al condi ions o he
b ain o imp o e ou unde s anding o in asion mechanisms.
Using so-called no mal b ain cell agg ega es de i ed om
e al a b ains o u iliza ion o oden o o he mammalian
b ain slices migh p esen a p omising comp omise o pe -
o m 3D in i o s udies ha can be mo e s anda dized and
a oid e hical issues a ached o animal s udies [109–112].
3.2. In i o models
Animal models a e essen ial o in es iga ing he in e ac ions
be ween glioma cells and he complex b ain mic oen i on-
men . The adi ional use o animal models in ol es injec ing
es ablished umou cell lines ei he in a enously o a he
a ge si e and hen wai ing o a umou o de elop be o e es -
ing a he apy o a gi en hypo hesis. While he complex
mic oen i onmen s in he animal models mimic he human
b ain s uc u e much be e han in i o s udies, e y ew
es ablished cell lines a e able o ep esen he his opa hological
cha ac e is ics o human gliomas, pa icula ly hei in asi e
na u e. Recen ly, me hods ha e been de eloped o ha es
cells om pa ien s o use in animal models. These a e e e ed
o as pa ien -de i ed umou agg ega es and a e be e able o
ecapi ula e pa e ns o umou cell in asion obse ed in
pa ien s [113]. Mo eo e , xenog a models ha e been
ex ensi ely employed o assess he e icacy o he apies
a ge ing glioma cells, such as he in a- umou al adminis-
a ion o IL13-PE oxin (a usion p o ein composed o IL-13
and a mu a ed o m o Pseudomonas exo oxin), o moni o
glioblas oma angiogenesis and o e alua e an i-angiogenic
he apeu ical app oaches [114]. The main d awback o
xenog a s is ha he his ology and gene ics o he o iginal
umou a e equen ly no main ained. Mo eo e , high-
esolu ion imaging o single glioma cell in asion in xenog a s
emains labo ious, cos ly and ime-consuming.
Tumou s can also be induced in animals using e o-
i uses. Two no able cases use cells in ec ed wi h
e o i uses enginee ed o o e exp ess ei he cons i u i ely
ac i a ed epide mal g ow h ac o ecep o (EGFR) [115] o
pla ele -de i ed g ow h ac o (PDGF) [116]. Bo h e o-
i uses a e able o ini ia e umou g ow h wi h human
glioblas oma cha ac e is ics when injec ed in o a a o
mouse b ain. In addi ion o p o iding a good model sys em
o d ug he apy, hey also shed ligh on he umou ini ia ing
p ocess. Ano he de elopmen in animal models is he c e-
a ion o ansgenic mice, whe e gene ic enginee ing
echniques a e used o c ea e mice wi h ubiqui ous mu a ions
ha a e p edisposed o de eloping gliomas [117].
Many in i o expe imen al echniques exis , he mos
common in ol es sac i icing he animal o allow o s aining
o he b ain issue, bu his only p o ides a empo al snapsho
o umou composi ion. Ano he echnique is e e ed o as ex
i o imaging whe e b ain issue is ha es ed and hin slices
a e placed on nu ien - illed media. This allows o mic o-
scopically obse e cell mo emen o a ime pe iod up o 24
h [116]. A u he op ion ha allows longe obse a ion is
he use o bioluminescence (o bio luo escence) a he cell
popula ion scale, o mul ipho on mic oscopy a he single-
cell le el. While any o he a o emen ioned animal models
p o ides expe imen al condi ions close o he human
b ain, he abili y o ully moni o ing he cance dynamics is
s ill challenging.
Addi ionally, he ui ly D osophila melanogas e has been
conside ed as an al e na i e in i o glioma model because
many molecula pa hways and cellula unc ions a e unda-
men ally conse ed [118,119]. Ad an ages include easy
handling, a ully sequenced genome, a wide ange o a ailable
gene ic echniques and a well-known ana omical si ua ion
[118,120]. Model o ganisms such as D. melanogas e ha e been
use ul no only o isualize umou cell mig a ion and o in es-
iga e he e ec s o induced me as asis, bu also o iden i y
glioma signalling cascades ia ad anced gene ic echniques.
Howe e , he D. melanogas e model also has some limi a ions.
In asion s udies in D. melanogas e lack an accu a e ep esen-
a ion o he human b ain pa enchyma, including he absence
o blood essels and an adap i e immune sys em.
4. Medical imaging and his opa hology
Con en ional compu e omog aphy scanning e eals mo pho-
logical in o ma ion o gliomas, bu umou s a ea ly s ages o
small me as a ic lesions a e o en no de ec ed. This echnique
has been g adually eplaced by magne ic esonance imaging
(MRI), which is signi ican ly mo e sensi i e o he p esence o
umou s and has become he s anda d imaging modali y in
he e alua ion o b ain umou s [121,122]. MRI c ea es non-
in asi e images by exploi ing he magne ic p ope ies o
wa e molecules in he body. By changing he in ensi y,
iming and du a ion o adio equency pulses and di ec ional
g adien s, my iad non-in asi e images wi h a ying con as s
and in o ma ion can be c ea ed [123]. The mo e common
T1- and T2-weigh ed MRI sequences a e mainly used o dis-
playing gene al ana omic ea u es o gliomas; howe e , he
wo ypes o sequences emphasize ea u es di e en ly (e.g. ce -
eb al spinal luid (CSF) is b igh on T2-weigh ed images and
da k on T1-weigh ed images). The T1-weigh ed image can be
used o highligh he leaky blood essels cha ac e is ic o
glioblas oma by acqui ing he image a e adminis a ion
o gadolinium, a con as agen ha appea s b igh on
T1-weigh ed images. Gadolinium seeps ou om he leaky
ascula u e haphaza dly c ea ed by he umou , highligh ing
wha is belie ed o be he mos ac i e/agg essi e umou
egion on T1-weigh ed gadolinium-enhanced MRI (T1Gd).
The T1Gd and T2 sequences a e mos commonly used o deli-
nea ing umou egions, bu i is well known ha nei he o
hese sequences is able o p o ide a p ecise isualiza ion o
umou abno mali y due o he ex ensi e in asion o he
umou cells [124]. In ac , in one s udy o high-g ade
gliomas, i was demons a ed ha human gliomas g ow in a-
si ely, wi h umou cells demons able o e 4 cm om he
g oss umou [125].
While T1- and T2-weigh ed MRI sequences emain he
dominan images clinically used, he e a e many o he
ad anced MRI echniques ha a e being explo ed such as
ascula pe usion imaging, di usion-weigh ed imaging
(DWI) and p o on magne ic esonance spec oscopy (MRS)
[126]. Vascula pe usion imaging highligh s egions o high
ascula i y and has been shown o be use ul in p edic ing
which pa ien s a e esponding o an i-angiogenic he apies
[127,128]. DWI can be used o a ious pu poses, bu o glio-
blas oma i is mos commonly used o quan i y he appa en
di usion coe icien , which is hough o be in e sely
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co ela ed wi h cell densi y [129,130]. MRS uses he p o on
signals o de e mine ela i e concen a ions o a ge me ab-
oli es a he han an ana omical image. In a ious s udies,
MRS has been shown capable o iden i ying egions o
issue en iched wi h s em-like cell-en iched oci [131], de ec -
ing umou s wi h mu a ions in he isoci a e dehyd ogenase
(IDH) genes [132,133], and assessing esponse o a ious
he apies such as adia ion and PI3K/mTOR inhibi o s
[134,135]. Fu he , he use o hype pola ized (HP) con as
agen s can signi ican ly inc ease he sensi i i y o MRS by
enhancing he signal- o-noise a io [136,137]. Mo e gene ally,
MRS has opened up he p omising ields o me abolomics
( he s udy o me abolomic signa u es in umou s) [138] and
adiomics ( he use o imaging echnology o ex apola e mol-
ecula umou da a) [139]. These s udies a e encou aging,
bu one mus no e ha he esolu ion o a s anda d MRS is
much lowe han on a s anda d MRI, oxel sizes being
app oxima ely 10 10 10 mm
3
e sus 1 11mm
3
.
Thus, while he e a e many p omising ad anced magne ic
esonance me hods o de e mining a ious umou cha ac-
e is ics, di e en ia ing be ween no mal and pa hological
issue on he basis o MRI indings alone is complica ed.
Func ional imaging echniques like posi on emission
omog aphy (PET) scans a e use ul in p o iding deepe
insigh s in o he biology o gliomas [140,141]. PET imaging
is inc easingly implemen ed in neu o-oncology, because i
o e s unique da a abou me abolic and physiologic p ocesses
such as glucose me abolism, p o ein/DNA syn hesis, cell
p oli e a ion and apop osis, as well as angiogenesis and
hypoxia ha can e lec he changes in a neoplasm. Assess-
men o he s a us o hese p ocesses has been shown
help ul in delinea ion o umou ma gins, and co ela es
wi h clinical me ics such as umou g ade, pa ien su i al
and he apy esponse [140,142,143]. Clinically, his ype o
in o ma ion is iewed as complemen a y o he ana omical
MRI, as PET scans gene ally lack ana omic con ex , and
ha e a ela i ely low spa ial esolu ion [144].
Diagnosis and classi ica ion o glioma is based on his o-
pa hology, e e ing o he mic oscopic examina ion o issue
sec ions by an expe ienced pa hologis , e.g. neu opa hologis .
Addi ionally, his opa hology analysis o issue samples has
some po en ial o p o ide u he in o ma ion a he single-
cell le el ha is ex emely impo an o quan i y and classi y
in a- umou al he e ogenei y. His ological and immunohis o-
chemical analyses a e ou inely pe o med by pa hologis s
o con i ma ion o he p esence o absence o disease, de e -
mining glioma g ading and assessing disease p og ession
[1,145,146]. Howe e , issue biopsies can be seen as ‘snap-
sho ’-like ozen scenes o dynamic biological p ocesses
p o iding da a se e ely limi ed in bo h space and ime.
Thus, despi e he cons an expansion o medical imaging ech-
nology, he iden i ica ion o umou s a an ea ly s age,
assessmen o in a- umou al he e ogenei y, educ ion o adi-
a ion exposu e and imp o emen o esolu ion a e challenging
o ana omic, unc ional and me abolic imaging alike.
5. Ma hema ical modelling o glioma cell
mig a ion and in asion
A wide a ie y o ma hema ical models ha e been p oposed
o in es iga e he mechanisms o glioma in asion, which is
cha ac e ized by in asi e cell mig a ion, pheno ypic
plas ici y, in il a i e umou mo phologies and he abili y
o malignan p og ession. Model ypes include disc e e and
con inuous app oaches such as cellula au oma on (CA), la -
ice-gas cellula au oma on (LGCA), cellula Po s model
(CPM), pa ial di e en ial equa ions (PDE), agen -based
models (ABM) and e olu iona y game heo y models (EGT)
[17–20,35,147–153]. We subsequen ly e iew ma hema ical
models o in asi e cell mig a ion, in asi e e ec s o pheno-
ypic plas ici y, in il a i e umou mo phologies and
malignan p og ession. Table 1 p o ides an o e iew o he
e iewed models.
5.1. In asi e cell mig a ion
Based mainly on in i o expe imen s, se e al ma hema ical
models ha e been de eloped o in es iga e he e ec s o
cell–cell adhesion s eng h unde dis inc mic oen i onmen-
al condi ions on he in asi e beha iou o glioma cells.
Khain e al. [27] in es iga ed, bo h heo e ically and expe -
imen ally, he e ec o cell–cell adhesion on glioma on
p opaga ion and he s uc u e o he in asi e in e ace.
Mig a ion cha ac e is ics o U87-MG cells we e measu ed
using a sc a ch wound-healing assay, and in asion on
pa e ns we e simula ed by means o bo h a 2D disc e e
la ice-based s ochas ic model and a con inuum app oach.
Simula ions o he con inuum model show ha a small e ec-
i e cell–cell adhesion change does no in luence he
p opaga ing on speed, and clus e s o glioma cells we e
no o med ( igu e 2a). By con as , he mic oscopic disc e e
model shows ha a cell–cell adhesion s eng h exceeding a
c i ical h eshold leads o clus e o ma ion in he in asi e
zone esul ing in inge ing-like on p opaga ion pa e ns
( igu e 2b). The expe imen al ime was cha ac e ized as a
ansien egime, which coincides wi h he pe iod equi ed
o a ela i ely sha p ini ial cell densi y p o ile o de elop
in o a p opaga ing on . Al hough simula ions success ully
ep oduced he maximal dis ance o mig a ion o glioma
cells on a plas ic subs a e, his model unde es ima ed he
mig a ion o he main mass o umou cells, sugges ing he
p esence o chemo ac ic s imuli.
Glioma cell mig a ion on a subs a e o collagen was
in es iga ed by Aube e al. [162]. The p oposed 2D CA
model indica es ha chemo axis o cell–cell communica ion
h ough gap junc ions (specialized in e cellula channels
ha pe mi di ec cell–cell ans e o ions and molecules)
is necessa y o ep oduce expe imen al densi y p o iles o
glioma cell dis ibu ions in umou sphe oids. In a ollow-
up s udy, mig a ion pa e ns o glioma cells in he p esence
o as ocy es we e s udied by Aube e al. [154]. An ex ended
e sion o he model p oposed in [162] was used o analyse
he opposi e e ec s o homo ypic (be ween glioma cells)
and he e o ypic (be ween glioma cells and su ounding as o-
cy es) gap junc ion communica ion on he in asi eness o
gliomas. Lowe ing glioma cell–cell in e ac ions on a passi e
subs a e o collagen was p edic ed o enhance he mig a o y
po en ial, whe eas he simul aneous inhibi ion o glioma
cell–cell and glioma cell–no mal as ocy e gap junc ion com-
munica ion leads o educed cell mig a ion. This sugges s
ha he in e ac ions be ween glioma cells and as ocy es
play an impo an ole in glioma in asion, due o he e ec
o he e o ypic gap junc ion inhibi ion which domina es ha
o homo ypic inhibi ion. Model simula ions a e consis en
wi h expe imen al da a o glioma mig a ion pa e ns in bo h
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7
Table 1. O e iew o e iewed ma hema ical modelling app oaches. Cellula au oma on (CA), la ice-gas cellula au oma on (LGCA), cellula Po s model (CPM), pa ial di e en ial equa ions (PDE), agen -based model (ABM) and
e olu iona y game heo y (EGT).
ma hema ical modelling app oach
Khain e al.
[27]
Aube
e al.
[154]
Khain
e al.
[155]
Szabo
´
e al.
[156]
Kim
e al.
[157]
Kim
[158]
Tek onidis
e al. [25]
Ha ziki ou
e al. [31]
Bo
¨ ge
e al.
[28]
Pham
e al.
[29]
Ge lee
e al. [30]
Al onso
e al.
[32]
Sande
e al.
[159]
Ma ı
´nez-
Gonza
´lez
e al. [26]
F ieboes
e al.
[21]
Zhang
e al.
[160]
F ieboes
e al.
[161]
Jiao e al.
[24]
Basan a
e al.
[22]
Swanson
e al.
[23]
(2D) CA &
(1D) PDE
(2D)
CA
(2D)
CA
(2D)
CPM
(2D)
PDE
(2D)
HYBRID (2D) LGCA
(2D)
LGCA
(2D)
LGCA
(2D)
PDE
(2D) CA &
(1D) PDE
(1D)
PDE
(2D)
HYBRID (1D) PDE
(2D)
PDE
(3D)
ABM
(3D)
HYBRID
(2D)
STATISTICAL EGT (1D) PDE
main ocus o
ma hema ical
models
in asi e cell
mig a ion
333333
pheno ypic plas ici y 33 3 333 3 3 3
umou
mo phology
33 3 33 3
malignan
p og ession
333
main biological
assump ions
cell–cell in e ac ions 3333333 3 333333
cell–ECM
in e ac ions
333 33
hypoxia-induced
mig a ion
3333333
cell densi y-
dependen
in asi eness
3333 3
changes in
me abolism
33 3
clonal
he e ogenei y
3
angiogenesis 33 3 3
si . oyalsocie ypublishing.o g J. R. Soc. In e ace 14: 20170490
8
homo ypic and he e o ypic si ua ions by only in oducing
a ac i e con ac be ween mig a ing umou cells. Howe e ,
he expe imen s conside ed in [154,162] only in ol ed ela i ely
small sphe oids wi hou cen al hypoxia o nec osis. Thus, o
s udy mig a ion pa e s o glioma cells in la ge sphe oids,
Aube e al. [163] assumed a chemo epellen ac o p oduced
by cells submi ed o s ess ul condi ions in he hypoxic/nec o-
ic mic o egions. A good ag eemen be ween model simula ions
and expe imen s allows o conclude he exis ence o epellen
oxic cues ha would p omo e glioma cell de achmen and
mig a ion, al hough u he wo k is needed o iden i y and
cha ac e ize hese chemo epulsi e ac o s.
The ole o hypoxia in he egula ion o glioma cell–cell
adhesion and cell mig a ion was in es iga ed by Khain e al.
[155]. A 2D disc e e s ochas ic model was p oposed o desc ibe
in i o expe imen s o U87 glioma cell mig a ion (i) away
om umou sphe oids placed on a subs a e and (ii) in ypical
sc a ch wound-healing assays. The dis ance mig a ed (i.e. in a-
si e adius) by bo h no moxic and hypoxic glioma cells was
measu ed. In he sphe oid expe imen s, he o e all mig a ion
a e o umou cells unde ei he no moxic o hypoxic condi ions
was simila . Howe e , hypoxic glioma cells in he wound-heal-
ing assays mig a ed less han cells unde no moxic condi ions.
This model sugges s ha lack o oxygen no only supp esses
cell mo ili y, bu also subs an ially educes he s eng h o cell–
cell adhesion. Al hough oxygen de iciency esul ed in educed
cell mo ili y, he dec eased cell–cell adhesion allows hypoxic
cells o de ach om he umou mass, leading o enhanced
glioma in asion. These model p edic ions a e consis en wi h
expe imen al da a showing ha hypoxia induces down egula-
ion o E-cadhe in, a ansmemb ane p o ein ha posi i ely
egula es ex ension and s eng hening o adhesi e con ac s,
and p omo es glioma cell in asion.
To explo e he in luence o he ECM on glioma cell
mig a ion, Szabo
´e al. [156] conside ed no only cell–cell
adhesion bu also cell–ECM in e ac ions. Cell agg ega es
we e p epa ed om con luen cul u es o wo di e en glio-
blas oma cell lines (GBM1 and U87) placed wi hin a 3D
ECM o collagen I gel. The aim was o cha ac e ize he collec-
i e, la ge-scale in asion o glioma cells om umou
sphe oids in o he su ounding ECM. The in e play be ween
hap o axis, ma ix deg ada ion and ac i e cell mo emen was
in es iga ed by means o a 2D CPM. Simula ion esul s
sugges ha he complex in e play be ween space-con-
s ained ac i e cell mo ion, cell–ECM adhesion and
deg ada ion o he ECM de e mines he pa e ns o mig a ion
and inc eases pe sis ence du ing cell in asion. In pa icula ,
hap o axis and ECM deg ada ion we e obse ed o des abi-
lize mul icellula sp ou s as each cell ies o in ade he
su ounding ma ix. By con as , when bo h hap o axis and
pola ized mo ion a e p esen , e en a homogeneous glioma
cell popula ion may be o ganized in o mul icellula sp ou s
wi hin an inhomogeneous ECM en i onmen .
Kim e al. [157] p oposed a model ha akes in o accoun
cell–cell adhesion, hap o axis and chemo ac ic e ec s o a glu-
cose g adien on glioma cell mig a ion in i o.Model
simula ions e eal ha depending on he chemo ac ic and hap-
o ac ic sensi i i ies, and he s eng h o cell–cell adhesion,
di e en mig a ion pa e ns o glioma cells a ise: dispe sion,
b anching, island o ma ion and a mix u e o hese pa e ns.
In pa icula , his model ep oduced he pa e ns obse ed in
a ious in asion assays o in i o sphe oids gene a ed om
glioma U87 and mu an U87DEGFR cell lines. Mo eo e ,
changes o adhesion, hap o ac ic and chemo ac ic pa ame e s
esul in a g adual shi om b anching o dispe sion as expe -
imen ally obse ed. The main inding was ha he on o cell
mig a ion can be slowed down by bo h inc easing cell–cell
adhesion and blocking he ECM deg ada ion e ec s o MMPs,
a amily o enzymes ha a e capable o b eaking down all
kinds o p o eins, such as collagen, no mally ound in spaces
be ween issues (ECM p o eins).
In a ollow-up s udy, Kim [158] de eloped a hyb id mul i-
scale model in which glioma cell mig a ion and p oli e a ion
a e egula ed by in acellula mechanisms in esponse o glucose
a ailabili y and physical cons ain s in he mic oen i onmen .
In pa icula , a co e con ol sys em o a single mic oRNA
(miR-451) ha egula es AMPK ( he 50-adenosine monophos-
pha e ac i a ed p o ein kinase) signalling [45,164] linked o
ex acellula glucose was simula ed. Recen expe imen al e i-
dence sugges s ha , in a glucose- ich en i onmen , miR-451 is
up- egula ed by umou cells, leading o AMPK pa hway inhi-
bi ion and in u n cell p oli e a ion. Con e sely, sus ained
AMPK ac i a ion unde low glucose condi ions esul s in sup-
p ession o miR-451, which induces pheno ypic changes o
glioma cells om a p oli e a i e o a mig a o y pheno ype
[165]. Based on he assump ion ha glucose le els may induce
pheno ypic changes in glioma cells, luc ua ions o he glucose
concen a ion we e p edic ed o igge mig a ion–p oli e a ion
cycles, which in u n inc eased gliomacell in asion and esul ed
in as e umou g ow h.
5.2. Pheno ypic plas ici y
The abili y o glioma cells o swi ch hei pheno ype in
esponse o local cell densi y and changes in he mic oen i -
onmen allows adap a ion and is belie ed o ha e impo an
implica ions o glioma in asion. In pa icula , glioma cells
can change om a p oli e a i e o a mig a o y pheno ype
depending on mic oen i onmen al condi ions [43,44]. I is
hus c ucial o in es iga e he ac o s and condi ions ha
d i e he ansi ion om he p oli e a i e o he mo ile pheno-
ype. Se e al ma hema ical models ha e been in oduced o
analyse implica ions o his ‘Go-o -G ow’ dicho omy on
glioma in asion. Tek onidis e al. [25] p oposed a la ice-
LGCA model o explain he spa io- empo al e olu ion o
U87 umou sphe oids in i o epo ed in [166]. I u ns
ou ha he ‘Go-o -G ow’ mechanism combined wi h sel -
epulsion and a densi y-dependen pheno ypic swi ch is
equi ed o quan i a i ely ep oduce he expe imen al
obse a ions ( igu e 3).
(a) (b)
Figu e 2. In asi e cell mig a ion. F on in e ace o small (a) and high (b) e ec-
i e cell–cell adhesion alues. Shown a e he simula ions o a disc e e s ochas ic
la ice model; e e y black do ep esen s a cell, and e e y whi e do co esponds o
an emp y si e. The sys em size is 400 400 (in uni s o cell diame e ). Figu e
ep oduced wi h pe mission om [27].
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