Cell death and life in cancer: mathematical modeling of cell fate decisions

0.39 MB·English

by  Andrei Zinovyev

Cell death and life in cancer: mathematical
modeling of cell fate decisions
AndreiZinovyev,SimonFourquet,LaurentTournier,LaurenceCalzoneand
EmmanuelBarillot
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1 AbstractTumordevelopmentischaracterizedbyacompromisedbalancebetween

celllifeanddeathdecisionmechanisms,whicharetighlyregulatedinnormalcells.
]
N Understanding this process provides insights for developing new treatments for
M fighting with cancer. We present a study of a mathematical model describing cel-
lular choice between survival and two alternative cell death modalities: apoptosis
.
o andnecrosis.Themodelisimplementedindiscretemodelingformalismandallows
i topredictprobabilitiesofhavingaparticularcellularphenotypeinresponsetoen-
b
gagementof cell death receptors. Using an originalparameter sensitivity analysis
-
q developedfordiscrete dynamicsystems, we determinevariablesthat appearto be
[
criticalin thecellularfatedecisionanddiscusshowtheyareexploitedbyexisting

1 cancertherapies.
v
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1
0 AndreiZinovyev
3 U900INSERM/InstitutCurie/EcoledeMines,InstitutCurie,26rued’Ulm,Paris,France,75005
1 e-mail:[email protected]
:
v SimonFourquet
i U900INSERM/InstitutCurie/EcoledeMines,InstitutCurie,26rued’Ulm,Paris,France,75005
X
e-mail:[email protected]
r
a LaurentTournier
INRA, Unit MIG (Mathe´matiques, Informatique et Ge´nome), Domaine Vilvert, Jouy en Josas,
France,78350,e-mail:[email protected]
LaurenceCalzone
U900INSERM/InstitutCurie/EcoledeMines,InstitutCurie,26rued’Ulm,Paris,France,75005
e-mail:[email protected]
EmmanuelBarillot
U900INSERM/InstitutCurie/EcoledeMines,InstitutCurie,26rued’Ulm,Paris,France,75005
e-mail:[email protected]
1
2 AuthorsSuppressedDuetoExcessiveLength
1 Introduction
Evadingvariousprogrammedcelldeathmodalitiesisconsideredasoneofthemajor
hallmarksofcancercells[1].Abetterunderstandingofthepro-deathorprosurvival
rolesofthegenesassociatedwithvariouscancers,andtheirinteractionswithother
pathwayswouldsetagroundforre-establishingalostdeathphenotypeandidenti-
fyingpotentialdrugtargets.
Recentprogressinstudyingthemechanismsofcelllife/deathdecisionsrevealed
itsastoundingcomplexity.Amongmany,onecanmentionthreedifficultiesonthe
way to characterize, describe and create strict mathematical descriptions of these
mechanisms.
First,thesignalingnetworkallowingacelltoreacttoanexternalstress(suchas
damageofDNA,nutrientandoxygendeprivation,toxicenvironment)isassembled
from highly redundantpathways which are able to compensate each other in one
wayoranother.Forexample,thereexistatleastsevendistinctandparallelsurvival
pathways associated with action of AKT protein [2]. Disruption of one of these
pathwaysinapotentialcelldeath-inducingcancertherapycanbeinprinciplecom-
pensatedbytheothers.Thus,understandingandmodelingthesurvivalresponsein
itsfullcomplexityisadauntingtask.
Second, cellular death is an extremely complex phenotype that cannot merely
be described as a simple disaggregation of cellular components driven by purely
thermodynamicallaws. Several distinct modesof cell death were identified in the
lastdecade[3],suchasnecrosis,apoptosisandautophagy.Importantly,allthesecell
deathmodalitiesarecontrolledbycellularbiochemicalmechanisms,activatedinre-
sponsetodiversetypesofstress:roughlyspeaking,acellisusuallypre-programmed
to diein a certainmanner,sendingappropriatesignalstoits surroundingsso asto
limit tissue toxicity and allow recycling of its components. Necrosis is a type of
celldeathusuallyassociatedwithalackofimportantcellularresourcesuchasATP,
whichmakesfunctioningofmanybiochemicalpathwaysimpossible.Thisiswhyit
was long thoughtof as an uncontrolledand purely thermodynamics-drivendegra-
dationofcellularstructures.However,recentresearchshowedthatnecrosiscanbe
triggered by specific signals through the activation of tightly regulated pathways,
andcanevenproceedwithoutATPdepletion[3].By contrast,apoptosisasaform
ofcellularsuicidewas,fromtheverybeginning,described asamodeofcelldeath
requiringenergyfor the permeabilizationof mitochondrialmembranesand cleav-
age of intracellular structures. Autophagy remains a relatively poorly understood
cell death mechanism, which seems to serve both as a survival or a death modal-
ity.Uponcertainstressconditions,anduntilthisstressisrelieved,cellularcompo-
nentssuchasdamagedproteinsororganellesaredigestedandrecycledintoreusable
metabolites,andmetabolismisreorientedsoastosparevitalfunctions.Longlast-
ing,non-relievablestresswasdescribedastriggeringautophagiccelldeath,through
unaffordable cellular self-digestion. However, no experimental evidence ever un-
ambiguouslydemonstratedthatsuchcelldeathisdirectlyexecutedbyautophagyin
vivo,butinthespecialcaseoftheinvolutionofDrosophilamelanogastersalivary
glands[3].
Celldeathandlifeincancer:mathematicalmodelingofcellfatedecisions 3
The third difficulty can be attributed not directly to the complexity of the bio-
chemicalmechanismsbutrathertoourcapabilitiesofapprehendingthedesignprin-
ciples used by biological evolution. Inspired by engineeringpractices, we tend to
investigatecomplexsystemsbysplittingthemintorelativelyindependentmodules
andassociatingwell-characterizednon-overlappingfunctionstoeachmolecularde-
tail. Applyingsuch reductionistapproachesto biologycomes with a caveat. Most
cellular molecular machineries cannot be naturally dissected or associated with
well-definedfunctions,andsetsofoverlappingfunctionscanbedistributedamong
groupsofmolecularplayers.
Not having the ambition to deal with the whole complexity of cell fate deci-
sionsinvivo,wedecidedtoconcentrateonmodelingtheoutcomeofaclassicaland
ratherwell-definedexperimentofinducingcelldeath:addingtoacellculturespe-
cificligands(TumorNecrosisFactor,TNF,orothermembersofitsfamilysuchas
FASL).Theseso-calleddeathligandscanengagedeathreceptorsandtriggerapop-
tosisornecrosis,oractivatepro-survivalmechanisms[5].Thenetoutcomeofsuch
experimentsdependsonmanycircumstances:celltype,doseoftheligand,duration
of the treatment, specific mutations in cell genomes, etc. Moreover,it is believed
thattheoutcomecanhaveintrinsicstochasticnaturegovernedbycellulardecision
making mechanisms and intrinsic molecular noise [6]. Trying to characterize the
biochemicalresponseofacelltothisrelativelysimplekindofperturbationallows
tounderstandcertaincellfatedecisionmechanisms.
Inthispaper,webrieflydescribeandcarefullyanalyzeamathematicalmodelof
cellfatedecisionbetweensurvivalandtwoalternativemodesofcelldeath:apoptosis
andnecrosis.Themodelwascreatedandintroducedin[4].Hereproposetheprin-
ciplesforwiringandparametrizingabiologicaldiagramthatdescribesthiscellular
switch.Inadditionto[4],here,byapplyinganovelsensitivityanalysisspecifically
developedfor discrete modeling,we identify fragile sites of the cell fate decision
mechanism.Inconclusion,wecompareouranalysiswithourcurrentknowledgeof
cellulardecisionmakingfragilitiesutilizedbycancerandcancertherapies.
2 Mathematical model ofcell fatedecision
In [4] we summarizedthe currentknowledgeonthe interactionsbetweencellfate
decisionmechanismsinasimplisticwiringdiagram(seeFig.1)whereanoderep-
resentseithera protein(TNF, FADD, FASL,TNFR, CASP8, cFLIP,BCL2, BAX,
IKK,NFk B,CYT C,SMAC,XIAP,CASP3),astateofprotein(RIP1ub,RIP1K),a
smallmolecule(ROS,ATP),amolecularcomplex(Apoptosome,C2 TNF,DISC FAS),
agroupofmolecularentitiessharingthesamefunction(BAXcanthusrepresentei-
therofBAX andBAK,cIAP eithercIAP1orcIAP2,andBCL2 anyoftheBH1-4
BCL2familymembers,),amolecularprocess(Mitochondriapermeabilizationtran-
sition,MPT,Mitochondrialoutermembranepermeabilization,MOMP)orapheno-
type(Survival,Apoptosis,Non-apoptoticcelldeath,NonACD).Eachdirectedand
4 AuthorsSuppressedDuetoExcessiveLength
signededgerepresentsaninfluenceofonemolecularentityonanother,eitherposi-
tive(arrowededge)ornegative(headededge).
Thephenotypenodesonthediagramaresimpleinterpretationsofthefollowing
molecularconditions: 1) activated NFk B is read as survivalstate; 2) lack of ATP
is read as nonapoptotic cell death state; 3) activated CASP3 is read as apoptotic
celldeath.Absenceofanyofsuchconditionsisinterpretedasa”naive“cellstate,
correspondingtothefourthcellularphenotype.
Afterextensiveexaminationofthebiologicalliteratureweconvertedthediagram
into a logical mathematicalmodelof cell fate decisions triggeredby activation of
cell death receptors. The wiring diagram and the logical rules defining the model
areshownonFig.1.
Byapplyingatechniqueadaptedtodiscreteformalism[7],wereducedthismodel
toa11-dimensionalnetwork,thusenablingacompleteanalysisoftheasynchronous
dynamics(see[4]fordetails).Thisanalysisidentified27stablelogicalstatesandno
cyclicattractors.Moreover,itshowedthatthedistributionofthestablelogicalstates
inthediscrete22-dimensionalspaceofinternalmodelvariables(withoutconsider-
inginputandoutputvariables)formsfourcompactclusters,eachcorrespondingtoa
particularcellularphenotype.Threeoftheseclusterscanbeattributedtoaparticular
cellfate(survival,apoptosis,necrosis)whiletheforthrepresentsa“naive”survival
state,wherenodeathreceptorsareinduced.
3 Computing phenotype probabilities
Aswehavealreadymentioned,thecellularfatedecisionmachineryischaracterized
bystochasticresponse,i.e.givenastimuli,thecellcanreachseveralfinalstates,cor-
respondingtodifferentphenotypes,withdifferentprobabilities.Theroleofmathe-
maticalmodelinginthiscasecanbetopredicttheseprobabilitiesasabsolutevalues
thatcanbematchedtoanexperiment,oratleasttopredicttherelativechangesof
theprobabilitiesafterintroducingsomeperturbationsto thesystem.
Wehaveimplementedthisideaforthemathematicalmodelofcellfatedecisions
describedaboveinthefollowingmanner.
Inordertodescribeourresults,letusintroducethenotionofasynchronousstate
transition graph. On this graph, each node represents a state of the system which
in this case can be encoded by a n-dimensional vector of 0s and 1s (n being the
dimensionofthesystem).Adirectededgeexistsbetweentwostatesxandyifthere
existsanindexi∈{1,...,n}suchthaty = f(x)6=x andy =x for j6=i(here, f
i i i j j i
denotesthelogicalruleofvariablex,seeFig.1foracompletelistofthemodellogi-
i
calrules).Inprinciple,thestatetransitiongraphcouldbedefinedindependentlyand
withoutthebiologicaldiagram,however,thiswouldrequirea tremendousamount
ofempiricalknowledgeaboutthesetofallpermissibletransitionsbetweenthecell
stateswhichisnotavailable.Hence,thebiologicaldiagramwithassociatedlogical
rulesisusedasacompactrepresentationandatooltogeneratethestatetransition
graph.Detailedinstructionsonthisprocedurecanbefoundin[8,9].
Celldeathandlifeincancer:mathematicalmodelingofcellfatedecisions 5
TNF FASL
FADD
TNFR C2_TNF DISC_FAS
RIP1 CASP8
survival
necrosis
RIP1ub RIP1K cFLIP apoptosis
cIAP
IKK
BCL2 BAX
MPT MOMP
ROS
NFkB SMAC CYT_C
XIAP
Apoptosome
ATP CASP3
Survival NonACD Apoptosis
DISCTNF’=TNFRANDFADD TNF’=TNF
RIP1’=(TNFRORDISCFAS)AND(NOTCASP8) FADD’=FADD
CASP8’=(DISCTNFORDISCFASORCASP3)AND(NOTcFlip)FAS’=FAS
RIPub’=RIP1ANDcIAP TNFR’=TNF
cIAP’=(NFkBORcIAP)AND(NOTSMAC) RIP1K’=RIP1
BAX’=CASP8AND(NOTBCL2) cFlip’=NFkB
ROS’=(RIP1KORMPT)AND(NOTNFkB) IKK’=RIP1ub
MPT’=ROSAND(NOTBCL2) BCL2’=NFkB
MOMP’=BAXORMPT SMAC’=MOMP
NFkB’=IKKAND(NOTCASP3) CYTC’=MOMP
XIAP’=NFkBAND(NOTSMAC) DISCFAS’=FASANDFADD
Apoptosome’=CYTCANDATPAND(NOTXIAP) ATP’=NOTMPT
CASP3’=ApoptosomeAND(NOTXIAP)
Fig.1 Biologicaldiagramofmolecularinteractionsinvolvedincellfatedecisionsderivedfrom
thebiologicalliterature.Thediagramisroughlydividedbydashedlinesintothreemodulescor-
responding to three submechanisms of cell fate decisions. Notations: 1) Proteins: TNF, FADD,
FASL,TNFR,CASP8,cIAP,cFLIP,BCL2,BAX,IKK,NFk B,CYTC,SMAC,XIAP,CASP3;
2)Statesofproteins:RIP1ub(ubiquitinatedformofRIP1),RIP1K(kinasefunctionofRIP1);3)
Small molecules: ATP, ROS (Reactive oxygen species); 4) Molecular complexes: Apoptosome,
C2 TNF, DISC FAS; 5) Molecularprocesses: MPT (Mitochondria permeabilization transition),
MOMP (Mitochondrial outermembrane permeabilization); 6) Phenotypes: Survival, Apoptosis,
NonACD(Non-apoptoticcelldeath).Belowthetableoflogicalrulesdefiningthediscretemathe-
maticalmodelisprovided.
6 AuthorsSuppressedDuetoExcessiveLength
Thesetofallpossiblestatesprovidesadiscretephasespaceofthesystem.The
statetransitiongraphcontainsallpossiblewaysofthesystemsdynamics(trajecto-
ries).Inotherwords,itisthemultidimensionalepigeneticlandscapeofthecellfate
decisionsystem.Notethatthestatetransitiongraphisassumedtoberathersparse
compared to the fully connected graph where any two state transitions would be
possible.Hence,on thislandscape,onecan determinebifurcatingstates, pointsof
noreturn,etc.
Thestatetransitiongraphallowstoaddressthefollowingquestion:Startingfrom
adistinguishedstateofacell,whatistheprobabilitytoarrivetoeachofthestable
states? In biologicalterms: Which proportionsof a populationof resting cells ex-
posedtodeathligandwilleventuallydisplayeachofthedifferentphenotypes-cell
fate?
To answer the question, we converted the state transition graph into a Markov
processof randomwalk on a graph,followingthe methoddescribedin [9]. To do
that,weassociatedtoeachtransitionbetweentwostatesaprobability(calledtran-
sition probability). By applying classical algorithms to the transition probability
matrix(stronglyconnecteddecompositionandtopologicalsort),weobtainedanab-
sorbingdiscreteMarkovchain,andthenanalyzeditwithclassicaltechniques[10].
Oneofthecriticalpointsinsuchtypeofanalysisliesinthechoiceofthetransi-
tionprobabilities.Onceagain,definingtheseprobabilitiesdirectlyfromsomeem-
piricalobservationsisimpossibleatpresenttime.Hence,theseprobabilitiesshould
bederivedfromthelogicalmodelwiththeuseofsomeadditionalassumptions.
The simplest assumption is to consider all transitions firing from a given state
as equiprobable.Biologicalinterpretationof such an assumption is notsimple. In
a way, we consider a “generic” cell in which all possible system trajectories take
place with equalprobabilities(withoutdominance,i.e. any preferableroute). One
can arguethat in any particularconcrete cell, this would notbe true anymoreand
thatthegenericcellisnotrepresentativeofanythingrealobservedinanybiological
experiment.Havinginmindthisdifficulty,weavoiddirectinterpretationofabsolute
valuesofprobabilities,concentratingratheronrelativechangesoftheminresponse
tosomesystemmodificationssuchasremovinganodeorfixinganode’sactivity.It
happensthatsucha“generic”cellmodelisalreadycapableofreproducinganumber
ofknownexperimentalfacts.
When the state transition graphis parametrizedby transition probabilities, one
canusestandardtechniquestocomputetheprobabilityofhittingagivenstablestate,
consideringthatarandomwalkstartsfromagiveninitialstate.Thenthisprobabil-
ity is associated with a probability of observing a particular phenotype in given
experimentalconditions. For doing this, it is convenientto define a unique initial
state,whichwechoosetorepresentthe“physiologicalstate”,theonerepresenting
un-inducedcells growingin a plate. In the modelof Fig. 1 it is the state in which
allelementsareinactiveexceptATP,FADDandcIAP.Thisisastablestate,which
looses its stability when TNF variable is changed from 0 to 1 and the dynamical
systemstartstoevolveintime.
Usingthisapproach,weperformedaseriesofinsilicoexperimentsinwhichthe
probability of arriving to stable states was computed for the initial (”wild-type”)
Celldeathandlifeincancer:mathematicalmodelingofcellfatedecisions 7
model,orfora series of modified(“mutant”)model.Typicalmodelmodifications
consisted in fixing some nodes’ activities to 0 or to 1. For our cell fate decision
model,theresultsareprovidedinFig.2.In[4]thistablewassystematicallycom-
paredwiththeexperimentaldataofthecelldeathphenotypemodificationsobserved
invariousmutantexperimentalsystems,includingcellculturesandmice.Themodel
was able to qualitativelyrecapitulateall of themand to suggestsome new yetun-
explored experimentally mutant phenotypes. The most interesting in this setting
wouldbetoconsidersyntheticinteractionsbetweenindividualmutants,whensev-
eralnodesonthediagramareaffectedbyamutationsimultaneously.
wild−type antiox APAF deletion BAX deletion
S N S N N N
0 0
A A S S
BCL2 o.e. CASP8 deletion CASP8 active cFlip deletion
N N
S N
0 S
A A
cIAP deletion FADD deletion NFkB deletion NFkB o.e.
N
A N A N
S
A
S
RIP1 deletion XIAP deletion z−VAD−fmk RIP+1 zd−eVleAtDio−nfmk
S
N N
S
A A 0
Fig.2 Changesinthephenotypeprobabilitiesfromtherandomwalkonthestatetransitiongraph,
startingfromtheinitialphysiologicalstate.Various“mutant”modificationsofthedynamicalsys-
temaretestedhere.Here“A“denotesApoptosis,“N“denotesNecrosisand“S“denotesSurvival,
“0” denotes Naive state. “O.e.” stands for overexpression of a protein, “antiox” corresponds to
bluntingthecapacityofNFk Btoprevent ROSformation,“z-VAD fmk”simulatestheeffect of
caspaseinhibitorz-VAD-fmk.
4 Identification offragilepoints ofthe cellfate decision
machinery
Changingdistributionoftransitionprobabilitiesontheasynchronousstatetransition
graphcan drastically changethe probabilistic outcomeof a computationalexperi-
8 AuthorsSuppressedDuetoExcessiveLength
ment. At the same time, the probabilities for a random walk to convergeto some
attractor depend also on the structure of the state transition graph which is deter-
mined solely from the discrete model.In orderto understand what are the critical
determinants of a cellular choice, we applied a novel strategy of discrete model
analysisconsistinginparametrizingthestatetransition graphbychangingrelative
importance of certain variables. In a certain sense, this strategy corresponds to a
sensitivity analysis, commonly applied for continuous models based on ordinary
differentialequationsandchemicalkineticsapproach[11].
Firstofall,wepostulatethatour“reference”parametrizationcorrespondstothe
equalprobabilitiesofanypossibletransitionfromastate.Asmentionedearlier,this
corresponds to a “generic” cell model, where the relative speeds of all biochem-
ical processes are assumed equal. Mathematically, considering the dynamics as a
Markovprocess,alltransitionsfromagivenstate xtoanyofitsasynchronoussuc-
cessorareassignedequalprobabilities(ifxhasrsuccessors,theseprobabilitiesare
equalto1/r).Wewillmodifythisdefaultparametrizationbysystematicallychang-
ing relative speeds of certain elements. This will lead to some re-parametrization
of the state transition graph and consequent changes in the probabilities to reach
attractors.
Thekeyideaofpriorityclasses[12,13]consistsingroupingvariablesofadis-
cretemodelintoclassesaccordingtothespeedsoftheunderlyingprocessesgovern-
ingtheirturnoverrates.Forinstance,inthe caseofgeneticregulatorynetworks,a
naturalgroupingconsistsinputtingdenovoproteinsynthesis(transcription+trans-
lation) in a slow transitionclass in comparisonwith otherprocessessuch as post-
translationalproteinmodifications(phosphorylation,ubiquitination,...)orcomplex
formation.Followingthisidea,wecanregroupnodesintopriorityclassestowhich
somepriorityratios w areassigned.Said differently,eachvariable x is assigneda
i
priorityvaluew.Foragivennode,avaluew >1correspondstoahigherthande-
i i
faultpriority,and a value w <1 to a lowerthan defaultpriority.The ratio w can
i i
beinterpretedasaglobalturnoverrateofthecomponentrepresentedbythisnode:
thosethatareproduced(activated)anddegraded(deactivated)fastwillhavealarge
w.
i
Considerastatex,withrasynchronoussuccessors.Bydefinition,betweenxand
eachofitssuccessors,oneandonlyonevariablecanbeupdated.Letydenoteoneof
thesuccessorsofx,andibetheindexofthecorrespondingupdatedvariable.With
the uniformassumptiondescribed before,the probabilityof the transition (x→y)
isindependentofiandisequalto1/r.Withpriorityclasses,thisprobabilityisnow
weighted by w, making the transition more probableif component i belongsto a
i
“fast”class(w greaterthanone)andlessprobableifitbelongstoa“slow”class(w
i i
lessthanone).Obviously,forcomputingtheactualtransitionprobabilities p ,a
x→y
normalizationshouldbeappliedsothat:
(cid:229)
p =1.
x→y
ysucc.ofx
Celldeathandlifeincancer:mathematicalmodelingofcellfatedecisions 9
Once the new valuesof the transitionprobabilitieshave been computed,the same
treatmentsas before can be applied, leading to new valuesfor the probabilitiesto
reachthedifferentphenotypes,startingfromagiveninitialcondition.
Thisgeneralmethodmaybeappliedintwodifferentways.First,onemayuseit
tocomputemorerealisticprobabilities,thatcouldbecomparedtoactualexperimen-
talresults(theprobabilitytoreachanattractorbeingcomparedwiththeproportion
ofcellsexhibitingthecorrespondingphenotype).However,suchcalculationswould
needacompleteclassificationoftherelativespeedsofallbiochemicalmechanisms
involvedinthemodel.Giventhenumberandheterogeneityofthesemechanisms,it
isstilldifficulttoobtainsuchclassification.Instead,weusedthemethodasa sen-
sitivityanalysistool,inordertodetectwhichvariablesaremorecriticalthanothers
in the decision-makingprocess.Using the reducedmodelevokedearlier(see [4]),
weconsideredeachvariableindependently,andsuccessivelyboosteditorslowedit
downbysomemultiplicativefactor.Moreprecisely,todetectthesensitivityofthe
networkwithrespecttotheturnoverofvariablex,weperformedthecalculationsfor
i
differentvaluesofw,theotherweightsw beingkeptatone(thereferencevalue).
i j
By comparing the probabilities to reach the three phenotypes-survival, apoptosis
and necrosis- with those of the initial model, one can detect whetherthe system’s
response is sensitive ornotto the turnoverrate of variable x. We performedsuch
i
experimentsforthenineinnervariablesofthereducedmodel.Figure3presentsthe
resultsweobtained.

Fig. 3 . Testing the effect of varying node turnovers on the resulting phenotypic probabilities.
Theabscissonthegraphs showsthevalueof wpriorityvalue, where w=1corresponds tothe
probabilitiescomputedforthedefaultwild-typemodel(seeFig.2).Thecolorsarethoseadopted
in[4]:orangecorrespondstoapoptosis,purpletonecrosisandgreentosurvival.
The plots revealseveralinteresting properties.First, the most sensitive compo-
nents,whichcorrespondtothecurveswiththehighestamplitude,areRIP1,NFkB
10 AuthorsSuppressedDuetoExcessiveLength
andCASP8.Thisreinforcestheideathatthesethreecomponentsplayacrucialrole
in the decision process. This seems reasonable, especially for RIP1 and CASP8,
astheyoccupyanupstreampositionintheregulatorygraph. Interestingly,CASP3
turnoverdoes not seem to be so important,althoughCASP3 is a markerof apop-
tosis.ThisconfirmsthateventhoughCASP3isessentialfortheexistenceofapop-
tosisinthemodel(itsremovalcompletelysuppressapoptoticoutcome,seeFig.2),
its turnover rate does not appear to be important in the dynamics of the decision
process (once it goes from 0 to 1, most of the decision has already been made).
Remarkably,theturnoversofMOMPandMPT,bothcontributingtothepermeabi-
lizationofmitochondrialmembrane,havedifferenteffects:MOMPseemstoaffect
mainly the decision between survivaland necrosis, while MPT playsa role in the
switchbetweenapoptosisandnecrosis.
Thesensitivityanalysisthatispresentedhereisanextensionoftheresultspro-
posed in [4]. In contrastwith the all-or-noneperturbationsevokedin the previous
part(whereanodeisfixedto0or1),hereweconsiderfinerperturbationsbymod-
ifyingtheturnoverratesofthemodel’svariables.Anextstepwouldbetoconsider
the relative strengthsof the model’s interactions,instead of the model’svariables.
Suchanapproachiscurrentlyinvestigated.
5 Comparisonwiththe fragilitiesexploitedby cancer and its
treatment
Deregulationsofthesignallingpathwaysstudiedherecanleadtodrasticandserious
consequences.HanahanandWeinbergproposedthatescape of apoptosis,together
with other alterations of cellular physiology,represents a necessary event in can-
cer promotion and progression [1]. As a result, somatic mutations leading to im-
paired apoptosis are expected to be associated with cancer. In the cell fate model
presentedhere,mostnodescan beclassified as pro-apoptoticoranti-apoptoticac-
cording to the results of “mutant” model simulations, which are correlated with
experimental results found in the literature. Genes classified as pro-apoptotic in
ourmodelincludecaspases-8 and -3, APAF1 as partof the apoptosomecomplex,
cytochromec (Cyt c), BAX, and SMAC. Anti-apoptotic genes encompass BCL2,
cIAP1/2,XIAP,cFLIP,anddifferentgenesinvolvedintheNFkBpathway,includ-
ingNFKB1,RELA,IKBKGandIKBKB(notexplicitinthemodel).Geneticalter-
ations leadingto loss of activity of pro-apoptoticgenesor to increasedactivity of
anti-apoptoticgeneshavebeenassociatedwithvariouscancers.Thus,wecancross-
listthealterationsofthesegenesdeducedfromthemodelwithwhatisreportedin
theliteratureandverifytheirroleandimplicationsincancer.
Forinstance, concerningpro-apoptoticgenes, frameshift mutationsin the ORF
oftheBAXgenearereportedin>50%ofcolorectaltumoursofthemicro-satellite
mutatorphenotype[14].ExpressionofCASP8isreducedin≈24%oftumoursfrom
patientswithEwing’ssarcoma[15].Caspase-8wassuggestedinseveralstudiesto