Solutions to Exercises
x x
A First Course in Systems Biology
x x x x x
EBERHARD O. VOIT x x
(with the assistance of I-Chun Chou, Po-
x x x x x x
Wei Chen, Sepideh Dolatshahi, Yun Lee, Zhen Qi and W
x x x x x x x x x
eiwei Yin) x
Mostx exercisesx inx Ax Firstx Coursex inx Systemsx Biologyx arex structuredx tox bex open-
endedx andxstimulatexself-
motivatedxlearningxandxexploration.xAsxaxconsequence,xtheyxdoxnotxhavexuniquexsolutions.xSomexst
udentsxfindxthisxambiguityxuncomfortablexandxwouldxmuchxratherxbexassuredxthatxtherexisxonexcorre
ctxsolution.xHowever,xafterxaxwhile,xtheyxoftenxseexthatxopen-
endedxquestionsxarexmuchxcloserxtoxreality,xespeciallyxwithxregardxtoxcomplexxphenomenaxinxbiolog
y.xFurthermore,xstudentsxrecognizexthatxtheyxcanxstructurextheirxsolutions,xtoxsomexdegree,xaccordin
gxtoxtheirxownxpreference:xSomexstudentsxlikexconceptualxapproaches,xothersxlikexsimulations,xyetxot
hersxarexintriguedxbyxrigorousxproofs.xSomexenjoyxtryingxoutxmultiplexchangesxinxmodelxsettingsxan
dxstudyingxthexresponsesxofxaxsystem,xothersxwouldxmuchxratherxextractxthexessencexofxaxproblemxan
dxtryxtoxsolvexitxasxconciselyxasxpossible,xwhilexsomexpreferxtoxspendxtheirxtimexscreeningxthexliterat
urexforxexperts’xanswersxorxsolutionsxtoxsimilarxproblems.xManyxstudentsxhavexaskedxme:xhowxmany
xsimulationsxdoxIxhavextoxdo? xInitially,xtheyxsometimesxdoxnotxlikexmyxanswer:xBeforex youxexecutex
axsimulation,xmakexaxpredictionxofxwhatxyouxexpectxtoxhappen.xIfxyourxpredictionsxarexconsistentlyx
correct,xatxleastxqualitatively,xyouxmayxstop.xHowever,xifxyourxpredictionsxarexsometimesxcorrectxan
dxsometimesxfalse,xthenxtherexarexaspectsxofxthexsystemxthatxyouxdon’txreallyxunderstand.xYouxneedx
toxkeepxonxsimulating,xanalyzingxandxinterpreting.
Manyxexercisesxpermitxaxlotxofxlatitudexinxtermsxofxbreadthxandxdepth,xandxthexinstructorxmi
ghtx wantx tox specifyx thexexpectedx lengthx ofxax report,x levelx ofxdetailx ofx anx analysis,x andx possiblyxaxsp
ecificxfocus.xForxinstance,xifxstudentsxarexaskedxtoxexplorexdifferentxvisualizationsxofxproteinxstructu
resxinxthexProteinxDataxBankx(PDB),xonexcouldxaskxthemxtoxfocusxonxspecificxproteinsxthat,xforx som
ex reason,x arex ofx particularx interestx tox thex student,x classx orx thex program.x Somex exercisesxaskxforxre
portsxexcerptingxinformationxfromxthexliteraturexorxthexInternet.xThexanswersxproposedxherexusually
xdoxnotxofferxasxmuchxdetailxasxonexmightxexpectxfromxaxstudent,xbutxmerelyxpointxtoxrelevantxinfor
mationxandxhighlightximportantxtopics.xSimilarly,xthexexplorationxofxsoftwarexrequiresxhands-
onxworkingxwithxthexprogram,xandxthexsolutionsxjustxprovidexpointersxasxtoxwherexandxhowxtoxstart.x
Again,xitxmightxbexusefulxtoxconnectxthesexsoftwarexquestionsxwithxaxspecificxbiologicalxquestion.
Thextotalxnumberxofxexercisesxperxchapterxisxprobablyxtooxhighxforxaxtypicalxone-
semesterxclass,xbutxaffordsxthexinstructorxsomexflexibilityxinxchoosingxexercisesxthatxarexdeemedxmo
stxrelevantx forx thex typesx ofx studentsx takingx thex class,x theirx backgroundsx inx biology,x mathematics
,xandxcomputing,xandxthexdepartmentxorxprogramxinxwhichxthexcoursexisxtaught.xFinally,xthexlargexnu
mberxandxvarietyxofxexercises,xandxthexinbuiltxflexibilityxinxsolutionxstrategies,xsuggestxthatxsomexof
xthexproposedxsolutionsxcouldxprobablyxbeximproved.xIxwouldxbexveryxhappyxtoxreceivexbetterxsoluti
onsxandxpossiblyxincludexthemxinxfuturexversionsxofxthisxsolutionxmanual.
,Solutions to Exercises in Chapter 1
x x x x x x
1.1. Searchx thex Internet,x asx wellx asx differentx dictionaries,x forx definitionsx ofx ax “system.”x
Extractxcommonalitiesxamongxthesexdefinitionsxandxformulatexyourxownxdefinition.
Solution:
AxgoodxstartxisxanxInternetxsearchxwithx“definitionxofxsystem”xasxthexsearchxterm,xwhichxleadsxtoxaxlo
tx ofx hits.x Therex isx ax hugex literaturex aboutx systems,x andx philosophersx consideredx thex conceptxeve
nx beforex Aristotlex andx Plato.x Thex definitionsx ofx thex termx arex ofx coursex allx slightlyx different,xbutx
manyxofxthemxhavexsomexkeyxfeaturesxinxcommon.xAccordingxtoxthesexcommonalities:
• Axsystemxisxaxgroup,xassemblage,xorxorganizedxsetxofxseveralxorxmanyxparts,xelements,xobjects,xo
rxitems.
• Thexpartsxarexinterconnectedxorxinterrelated;xtheyxregularlyxinteract.
• Thex partsx andx theirx interconnectionsx createx ax unifiedx orx integratedx wholex thatx hasx definedxb
oundaries;xeverythingxoutsidexthexboundariesxisxconsideredxasxthexenvironment.
• Thexinterconnectionsxwithinxthexsystemxcreatexsomexfunctionality.
• Thex functionalityxisxcomplexx andx sometimesx emergent,x whichx meansx thatxitxcannotx bexidentifie
dxinxthexcomponentsxalone.
• Systemsxhavexstructurexandxbehavior.
• Manyxsystemsxhavexinternalxregulators.
• Openxsystemsx processxinputx and/orx generatex output;x closedx systemsx dox notx exchangexmassx orxe
nergyxwithxthexenvironment.
• Termsx sometimesx seenx asx synonymsx (atx leastx ofx somex systems)x arex network;x scheme;xcomplex
xofxmethods;xsetxofxrules.
• Thex wordx “system”x comesx fromx Greekx andx refersx tox ax compositionx orx combinedx set-
upx ofxseveralxparts.
1.2. SearchxthexInternetxforxdefinitionsxofx“systemsx biology.”xExtractx commonalitiesxamongxt
hesexdefinitionsxandxformulatexyourxownxdefinition.
Solution:
Thextermx“systemsxbiology”xisxroughlyxsynonymousxwithx“analysisxofxbiologicalxsystems.”xThus,xt
hexconceptxandxdefinitionxofx“systemsxbiology”xsharexmuchxwithxthexgenericxdefinitionsxofxsystemsx
inxExercisex1.1,xbutxspecificallyxappliedxtoxbiology.
Axgenuinexaspectxofxsystemsxbiologyxisxthatxitxisxoftenxcontrastedxtoxreductionism,xthatxis,xth
exphilosophy,xespeciallyxinxbiology,xofxtakingxthingsxfurtherxandxfurtherxapartxinxorderxtoxstudyxthexp
ropertiesxofxthexultimatexcomponents.xWhilexsystemsxbiologyxaimsxtoxreconstructxsystemsxfromxco
mponents,xthexdichotomyxbetweenxsystemsxbiologyxandxreductionismxshouldxnotxbexseenxasxaxcomp
etitionxofxwhatxisxrightxandxwhatxnot,xbecausexsystemsxbiologyxwouldxnotxbexablextoxfunctionxwitho
utxtargetedxreductionisticxresearch.xAtxthexsamextime,xonlyxknowingxthexcomponentsxisxinsufficientx
andxrequiresxaxcomplementaryxphasexofxreconstruction.
, Otherxgenuinexfeaturesxofxsystemxbiologyxincludexthexfactxthatxbiologicalx systemsxnaturally
xspanxmultiplexorganizational,xspatial,xandxtemporalxscales,xwhichxarextoxbexintegratedxinxcomprehe
nsivexsystemsxstudiesxtoxexplainxoverallxfunction.xAlso,xthexaspectxofxemergingxpropertiesxisxusuall
yxassociatedxwithxbiologicalxsystems.xFinally,xsystemsxbiologyxisxveryxinterestedxinxdynamics,xandx
somexdefinitionsxofxsystemsxbiologyxdeclarexitxasxthexapplicationxofxdynamicalxsystemsxtheoryxtoxbi
ologicalxphenomena.
Whilexsomexauthorsxdefinexsystemsxbiologyxasxanxextensionxofxmolecularxandx-
omicsxbiology,xonexshouldxkeepxinxmindxthatxphysiologyxandxecologyxhavexbeenxpracticingxsystems
xanalysisx inx biologyx forx ax longx time,x andx thatx fieldsx likex cyberneticsx andx biomathematicsx couldxa
lsoxbexseenxasxitsxprecursors.xUltimately,xasxthextextxexplains,xsystemsxbiologyxisxreallyxthexresultxofxt
hexconfluencexofxmanyxfields,xandxthisxfactxshouldxenterxitsxdefinition.
1.3. Listx10xsystemsxwithinxthexhumanxbody.
Solution:
Obviousxexamplesxinclude:
• thexnervousxsystem;
• thexgastrointestinalxsystem;
• thexcardiovascularxsystem.
However,xthexhumanxbodyxisxfullxofxuncountedx“smaller”xorxlessxprominentxsystems,xsuchxas:
• thexsystemxwithxwhichxthexeyexrespondsxtoxlight;
• thexsystemxinxwhichxneurotransmittersxarexpassedxthroughxdifferentxbrainxsections;
• thexuptakexsystemxwithxwhichxcellsxincorporatexmaterialsxorxsignals;
• axlargexnumberxofxspecificxmetabolicxpathwayxsystems;
• thexsystemxofxthexribosomexthatxtranslatesxmRNAxintoxproteins;
• thexmanyxgenexregulatoryxsystemsxthatxrespondxtoxspecificxsituationsxorxdemands;
• thexinformationxsystemxwithinxthexgeneticxcode.
1.4. Exactlyxwhatxfeaturesx makex thex systemx inx Figurex 1.10x sox muchx morex complicatedx thanxt
hexsystemxinxFigurex1.8?
Solution:
ThexmainxreasonxthatxthexsystemxinxFigurex1.8xisxsoxmuchxeasierxtoxunderstandxthanxthexsystemxinxFi
gurex1.10xisxitsxlinearxstructure.xOurxintuitionxisxcorrectxwhenxwexsayxthatxanxincreasexinxExwillxhaste
nxthexconversionxofxXxintoxYxandxthexproductionxofxZ.xWexcannotxsayxbyxhowxmuch,xbutxwexcanxima
ginexsomextypexofxmonotonicxresponse,xbecausextherexarexnoxcounteractingxorxcompetingxprocesses
.xByxcontrast,xFigurex1.10xcontainsxaxlogicalxfeedbackxloopxthroughxwhichxchangesxinxZxfeedxbackxo
nxearlierxevents,xwhichxthemselvesxdrivexthexdynamicsxofxZ.xNow,xtherexarexcompetingxprocesses,xn
amelyxthexproductionxofxZx(tendingxtoxincreasexZ)xandxitsxultimatelyxinhibitoryxeffectxonxthisxproduc
tionx(tendingxtoxdiminishxZ).xThesexprocessesxarexnotxblackxorxwhite,xonxorxoff,xbutxdependx onx num
ericalx featuresx thatx wex cannotx reallyx processx wellx inx ourx minds,x especiallyx ifx we
, arexinterestedxinxquantitativexstatements.xIndeed,xwexhavexseenxthatxdrasticallyxdifferentxresponsesxo
fxthexsamexsystemxarexpossiblex(seexFigurex1.11),xifxthexparameterxsettingsxarexslightlyxaltered.xInxpar
ticular,xitxisximpossiblextoxintuitxthexthresholdxwherexonexbehaviorxswitchesxintoxaxdifferentxbehavio
r.xMathematicsxandxcomputerxsimulationsxoftenxcharacterizexsuchxsituationsxratherxeasily.
1.5. ImaginexthatxFigurex1.10xrepresentsxaxsystemxthatxhasxbecomexfaultyxowingxtoxdisease.xD
escribexthexconsequencesxofxitsxcomplexityxforxanyxmedicalxtreatmentxstrategy.
Solution:
Evenxifxwexknowxthexstructurexofxthexsystem,xrepairxmechanismsxarexnotxeasyxtoxinstall.xForxinstanc
e,ximaginexthatxonexofxthexprocessesxrepresentedxbyxaxgreenxarrowxisxdisrupted.xBecausexofxthisxdisr
uption,xthexsystemxisxnoxlongerxregulatedxandxdoesxnotxadapt,xforxinstance,xtoxanxincreasedxorxdecrea
sedxinput.xThus,xaxmedicalxtreatmentxofxthexdisruptedxsystemxwouldxhavextoxmimicxthisxcontrol.xAsx
axspecificxexample,xsupposexthexmodelxisxaxveryxmuchxsimplifiedxsystemxregulatingxbloodxsugar.xIfx
wexhadxaxconstantxsugarxinputxatxjustxthexrightxconcentration,xthexdisruptedxsystemxwouldxfunctionx
well.xHowever,xifxthexinputxisxincreased,xmorexZxisxproduced,xandxthexdisruptedxsystemxcannotxdoxa
nythingxaboutxit.xMedically,xwexwouldxthusxhavextoxrespondxtoxeveryxspecificxinputxwithxaxcorrespo
ndingxreduction,xforxinstance,xinxE.xAsxdiabeticsxknow,xtheyxhavextoxtakexinsulinxnotxcontinuouslyxb
utxatxspecificxtimes,xinxconnectionsxwithxmeals,xand,xideally,xinxjustxthexrightxamounts,xtherebyxmim
ickingxthexnaturalxcontrolxsystem.
Inxmanyxcases,xthexstructurexofxaxdiseasedxsystemxisxnotxevenxknown,xandxtreatmentxofxaxdisr
uptedxsystemxbecomesxaxhit-or-
missxstrategy.xIfxaxfeedbackxsystemxactsxveryxslowly,xwexmightxbexablextoxrespondxappropriately,xbut
xifxitxactsxfast,xitsxcontrolxbecomesxproblematic.
1.6. InxFigurex1.2,xarextherexcontrolxpathsxalongxwhichxABAxeitherxactivatesxorxinhibitsxclosu
rexofxstomata?xIfxso,xlistxatxleastxonexpathxeach.xIfxbothxpathsxexistxinxparallel,xdiscussxwhatxyo
uxexpectxthexeffectxofxanxincreasexinxABAxtoxbexonxstomataxclosure.
Solution:
TherexarexindeedxpositivexandxnegativexpathwaysxconnectingxABAxtoxthexclosurexsystem.xForxinsta
nce,xthexpathwayxthroughxRAC1x(centerxofxthexgraph)xandxActinxincludesxtwoxnegativexeffects,xwhi
chxmakexthexentirexpathwayxpositive:xIfxonlyxthisxpathwayxwerexthere,xthenxmorexABAxwouldxleadxt
oxmorexclosure.xByxcontrast,xthexpathwayxthroughxpHcx(centerxtowardxthexright)xandxKAPx(rightxabo
vexclosure)xcontainsxonlyxonexnegativexsignal.xThus,xifxthisxpathwayxwerexthexonlyxonexpresent,xthenx
morexABAxwouldxleadxtoxlessxclosure.
Thexsituationxthatxthexsystemxcontainsxthesextwoxcounteractingxpathways,xalongxwithxthexnu
merousxotherxsignals,xmakesxintuitivexpredictionsxentirelyxunreliable.xForxinstance,xsupposexonlyx t
hex twox pathwaysx mentionedx abovex werex present.x Withoutx morex information,x wex don’txknowx
whichxofxthextwoxhasxaxstrongerxeffect.xAlso,xwexdon’txknowxwhetherxthextwoxpathwaysxactxwithxthe
xsamexspeed.xItxcouldxwell xbexthatxthexfasterxpathwayxinitiallyx“wins,”xbutxthatxthexslowerxpathwayxh
asxaxstrongerxeffectxandxovercomesxthexfasterxpathwayxafterxsomextime,x therebyxcreatingxaxtemporar
yxresponse.xWhenxallxpathwaysxshownxarexactive,xwexhavexnoxchancexofxmakingxquantitativelyxcorr
ectxpredictionsxwithoutxaxdetailedxcomputationalxmodel.
x x
A First Course in Systems Biology
x x x x x
EBERHARD O. VOIT x x
(with the assistance of I-Chun Chou, Po-
x x x x x x
Wei Chen, Sepideh Dolatshahi, Yun Lee, Zhen Qi and W
x x x x x x x x x
eiwei Yin) x
Mostx exercisesx inx Ax Firstx Coursex inx Systemsx Biologyx arex structuredx tox bex open-
endedx andxstimulatexself-
motivatedxlearningxandxexploration.xAsxaxconsequence,xtheyxdoxnotxhavexuniquexsolutions.xSomexst
udentsxfindxthisxambiguityxuncomfortablexandxwouldxmuchxratherxbexassuredxthatxtherexisxonexcorre
ctxsolution.xHowever,xafterxaxwhile,xtheyxoftenxseexthatxopen-
endedxquestionsxarexmuchxcloserxtoxreality,xespeciallyxwithxregardxtoxcomplexxphenomenaxinxbiolog
y.xFurthermore,xstudentsxrecognizexthatxtheyxcanxstructurextheirxsolutions,xtoxsomexdegree,xaccordin
gxtoxtheirxownxpreference:xSomexstudentsxlikexconceptualxapproaches,xothersxlikexsimulations,xyetxot
hersxarexintriguedxbyxrigorousxproofs.xSomexenjoyxtryingxoutxmultiplexchangesxinxmodelxsettingsxan
dxstudyingxthexresponsesxofxaxsystem,xothersxwouldxmuchxratherxextractxthexessencexofxaxproblemxan
dxtryxtoxsolvexitxasxconciselyxasxpossible,xwhilexsomexpreferxtoxspendxtheirxtimexscreeningxthexliterat
urexforxexperts’xanswersxorxsolutionsxtoxsimilarxproblems.xManyxstudentsxhavexaskedxme:xhowxmany
xsimulationsxdoxIxhavextoxdo? xInitially,xtheyxsometimesxdoxnotxlikexmyxanswer:xBeforex youxexecutex
axsimulation,xmakexaxpredictionxofxwhatxyouxexpectxtoxhappen.xIfxyourxpredictionsxarexconsistentlyx
correct,xatxleastxqualitatively,xyouxmayxstop.xHowever,xifxyourxpredictionsxarexsometimesxcorrectxan
dxsometimesxfalse,xthenxtherexarexaspectsxofxthexsystemxthatxyouxdon’txreallyxunderstand.xYouxneedx
toxkeepxonxsimulating,xanalyzingxandxinterpreting.
Manyxexercisesxpermitxaxlotxofxlatitudexinxtermsxofxbreadthxandxdepth,xandxthexinstructorxmi
ghtx wantx tox specifyx thexexpectedx lengthx ofxax report,x levelx ofxdetailx ofx anx analysis,x andx possiblyxaxsp
ecificxfocus.xForxinstance,xifxstudentsxarexaskedxtoxexplorexdifferentxvisualizationsxofxproteinxstructu
resxinxthexProteinxDataxBankx(PDB),xonexcouldxaskxthemxtoxfocusxonxspecificxproteinsxthat,xforx som
ex reason,x arex ofx particularx interestx tox thex student,x classx orx thex program.x Somex exercisesxaskxforxre
portsxexcerptingxinformationxfromxthexliteraturexorxthexInternet.xThexanswersxproposedxherexusually
xdoxnotxofferxasxmuchxdetailxasxonexmightxexpectxfromxaxstudent,xbutxmerelyxpointxtoxrelevantxinfor
mationxandxhighlightximportantxtopics.xSimilarly,xthexexplorationxofxsoftwarexrequiresxhands-
onxworkingxwithxthexprogram,xandxthexsolutionsxjustxprovidexpointersxasxtoxwherexandxhowxtoxstart.x
Again,xitxmightxbexusefulxtoxconnectxthesexsoftwarexquestionsxwithxaxspecificxbiologicalxquestion.
Thextotalxnumberxofxexercisesxperxchapterxisxprobablyxtooxhighxforxaxtypicalxone-
semesterxclass,xbutxaffordsxthexinstructorxsomexflexibilityxinxchoosingxexercisesxthatxarexdeemedxmo
stxrelevantx forx thex typesx ofx studentsx takingx thex class,x theirx backgroundsx inx biology,x mathematics
,xandxcomputing,xandxthexdepartmentxorxprogramxinxwhichxthexcoursexisxtaught.xFinally,xthexlargexnu
mberxandxvarietyxofxexercises,xandxthexinbuiltxflexibilityxinxsolutionxstrategies,xsuggestxthatxsomexof
xthexproposedxsolutionsxcouldxprobablyxbeximproved.xIxwouldxbexveryxhappyxtoxreceivexbetterxsoluti
onsxandxpossiblyxincludexthemxinxfuturexversionsxofxthisxsolutionxmanual.
,Solutions to Exercises in Chapter 1
x x x x x x
1.1. Searchx thex Internet,x asx wellx asx differentx dictionaries,x forx definitionsx ofx ax “system.”x
Extractxcommonalitiesxamongxthesexdefinitionsxandxformulatexyourxownxdefinition.
Solution:
AxgoodxstartxisxanxInternetxsearchxwithx“definitionxofxsystem”xasxthexsearchxterm,xwhichxleadsxtoxaxlo
tx ofx hits.x Therex isx ax hugex literaturex aboutx systems,x andx philosophersx consideredx thex conceptxeve
nx beforex Aristotlex andx Plato.x Thex definitionsx ofx thex termx arex ofx coursex allx slightlyx different,xbutx
manyxofxthemxhavexsomexkeyxfeaturesxinxcommon.xAccordingxtoxthesexcommonalities:
• Axsystemxisxaxgroup,xassemblage,xorxorganizedxsetxofxseveralxorxmanyxparts,xelements,xobjects,xo
rxitems.
• Thexpartsxarexinterconnectedxorxinterrelated;xtheyxregularlyxinteract.
• Thex partsx andx theirx interconnectionsx createx ax unifiedx orx integratedx wholex thatx hasx definedxb
oundaries;xeverythingxoutsidexthexboundariesxisxconsideredxasxthexenvironment.
• Thexinterconnectionsxwithinxthexsystemxcreatexsomexfunctionality.
• Thex functionalityxisxcomplexx andx sometimesx emergent,x whichx meansx thatxitxcannotx bexidentifie
dxinxthexcomponentsxalone.
• Systemsxhavexstructurexandxbehavior.
• Manyxsystemsxhavexinternalxregulators.
• Openxsystemsx processxinputx and/orx generatex output;x closedx systemsx dox notx exchangexmassx orxe
nergyxwithxthexenvironment.
• Termsx sometimesx seenx asx synonymsx (atx leastx ofx somex systems)x arex network;x scheme;xcomplex
xofxmethods;xsetxofxrules.
• Thex wordx “system”x comesx fromx Greekx andx refersx tox ax compositionx orx combinedx set-
upx ofxseveralxparts.
1.2. SearchxthexInternetxforxdefinitionsxofx“systemsx biology.”xExtractx commonalitiesxamongxt
hesexdefinitionsxandxformulatexyourxownxdefinition.
Solution:
Thextermx“systemsxbiology”xisxroughlyxsynonymousxwithx“analysisxofxbiologicalxsystems.”xThus,xt
hexconceptxandxdefinitionxofx“systemsxbiology”xsharexmuchxwithxthexgenericxdefinitionsxofxsystemsx
inxExercisex1.1,xbutxspecificallyxappliedxtoxbiology.
Axgenuinexaspectxofxsystemsxbiologyxisxthatxitxisxoftenxcontrastedxtoxreductionism,xthatxis,xth
exphilosophy,xespeciallyxinxbiology,xofxtakingxthingsxfurtherxandxfurtherxapartxinxorderxtoxstudyxthexp
ropertiesxofxthexultimatexcomponents.xWhilexsystemsxbiologyxaimsxtoxreconstructxsystemsxfromxco
mponents,xthexdichotomyxbetweenxsystemsxbiologyxandxreductionismxshouldxnotxbexseenxasxaxcomp
etitionxofxwhatxisxrightxandxwhatxnot,xbecausexsystemsxbiologyxwouldxnotxbexablextoxfunctionxwitho
utxtargetedxreductionisticxresearch.xAtxthexsamextime,xonlyxknowingxthexcomponentsxisxinsufficientx
andxrequiresxaxcomplementaryxphasexofxreconstruction.
, Otherxgenuinexfeaturesxofxsystemxbiologyxincludexthexfactxthatxbiologicalx systemsxnaturally
xspanxmultiplexorganizational,xspatial,xandxtemporalxscales,xwhichxarextoxbexintegratedxinxcomprehe
nsivexsystemsxstudiesxtoxexplainxoverallxfunction.xAlso,xthexaspectxofxemergingxpropertiesxisxusuall
yxassociatedxwithxbiologicalxsystems.xFinally,xsystemsxbiologyxisxveryxinterestedxinxdynamics,xandx
somexdefinitionsxofxsystemsxbiologyxdeclarexitxasxthexapplicationxofxdynamicalxsystemsxtheoryxtoxbi
ologicalxphenomena.
Whilexsomexauthorsxdefinexsystemsxbiologyxasxanxextensionxofxmolecularxandx-
omicsxbiology,xonexshouldxkeepxinxmindxthatxphysiologyxandxecologyxhavexbeenxpracticingxsystems
xanalysisx inx biologyx forx ax longx time,x andx thatx fieldsx likex cyberneticsx andx biomathematicsx couldxa
lsoxbexseenxasxitsxprecursors.xUltimately,xasxthextextxexplains,xsystemsxbiologyxisxreallyxthexresultxofxt
hexconfluencexofxmanyxfields,xandxthisxfactxshouldxenterxitsxdefinition.
1.3. Listx10xsystemsxwithinxthexhumanxbody.
Solution:
Obviousxexamplesxinclude:
• thexnervousxsystem;
• thexgastrointestinalxsystem;
• thexcardiovascularxsystem.
However,xthexhumanxbodyxisxfullxofxuncountedx“smaller”xorxlessxprominentxsystems,xsuchxas:
• thexsystemxwithxwhichxthexeyexrespondsxtoxlight;
• thexsystemxinxwhichxneurotransmittersxarexpassedxthroughxdifferentxbrainxsections;
• thexuptakexsystemxwithxwhichxcellsxincorporatexmaterialsxorxsignals;
• axlargexnumberxofxspecificxmetabolicxpathwayxsystems;
• thexsystemxofxthexribosomexthatxtranslatesxmRNAxintoxproteins;
• thexmanyxgenexregulatoryxsystemsxthatxrespondxtoxspecificxsituationsxorxdemands;
• thexinformationxsystemxwithinxthexgeneticxcode.
1.4. Exactlyxwhatxfeaturesx makex thex systemx inx Figurex 1.10x sox muchx morex complicatedx thanxt
hexsystemxinxFigurex1.8?
Solution:
ThexmainxreasonxthatxthexsystemxinxFigurex1.8xisxsoxmuchxeasierxtoxunderstandxthanxthexsystemxinxFi
gurex1.10xisxitsxlinearxstructure.xOurxintuitionxisxcorrectxwhenxwexsayxthatxanxincreasexinxExwillxhaste
nxthexconversionxofxXxintoxYxandxthexproductionxofxZ.xWexcannotxsayxbyxhowxmuch,xbutxwexcanxima
ginexsomextypexofxmonotonicxresponse,xbecausextherexarexnoxcounteractingxorxcompetingxprocesses
.xByxcontrast,xFigurex1.10xcontainsxaxlogicalxfeedbackxloopxthroughxwhichxchangesxinxZxfeedxbackxo
nxearlierxevents,xwhichxthemselvesxdrivexthexdynamicsxofxZ.xNow,xtherexarexcompetingxprocesses,xn
amelyxthexproductionxofxZx(tendingxtoxincreasexZ)xandxitsxultimatelyxinhibitoryxeffectxonxthisxproduc
tionx(tendingxtoxdiminishxZ).xThesexprocessesxarexnotxblackxorxwhite,xonxorxoff,xbutxdependx onx num
ericalx featuresx thatx wex cannotx reallyx processx wellx inx ourx minds,x especiallyx ifx we
, arexinterestedxinxquantitativexstatements.xIndeed,xwexhavexseenxthatxdrasticallyxdifferentxresponsesxo
fxthexsamexsystemxarexpossiblex(seexFigurex1.11),xifxthexparameterxsettingsxarexslightlyxaltered.xInxpar
ticular,xitxisximpossiblextoxintuitxthexthresholdxwherexonexbehaviorxswitchesxintoxaxdifferentxbehavio
r.xMathematicsxandxcomputerxsimulationsxoftenxcharacterizexsuchxsituationsxratherxeasily.
1.5. ImaginexthatxFigurex1.10xrepresentsxaxsystemxthatxhasxbecomexfaultyxowingxtoxdisease.xD
escribexthexconsequencesxofxitsxcomplexityxforxanyxmedicalxtreatmentxstrategy.
Solution:
Evenxifxwexknowxthexstructurexofxthexsystem,xrepairxmechanismsxarexnotxeasyxtoxinstall.xForxinstanc
e,ximaginexthatxonexofxthexprocessesxrepresentedxbyxaxgreenxarrowxisxdisrupted.xBecausexofxthisxdisr
uption,xthexsystemxisxnoxlongerxregulatedxandxdoesxnotxadapt,xforxinstance,xtoxanxincreasedxorxdecrea
sedxinput.xThus,xaxmedicalxtreatmentxofxthexdisruptedxsystemxwouldxhavextoxmimicxthisxcontrol.xAsx
axspecificxexample,xsupposexthexmodelxisxaxveryxmuchxsimplifiedxsystemxregulatingxbloodxsugar.xIfx
wexhadxaxconstantxsugarxinputxatxjustxthexrightxconcentration,xthexdisruptedxsystemxwouldxfunctionx
well.xHowever,xifxthexinputxisxincreased,xmorexZxisxproduced,xandxthexdisruptedxsystemxcannotxdoxa
nythingxaboutxit.xMedically,xwexwouldxthusxhavextoxrespondxtoxeveryxspecificxinputxwithxaxcorrespo
ndingxreduction,xforxinstance,xinxE.xAsxdiabeticsxknow,xtheyxhavextoxtakexinsulinxnotxcontinuouslyxb
utxatxspecificxtimes,xinxconnectionsxwithxmeals,xand,xideally,xinxjustxthexrightxamounts,xtherebyxmim
ickingxthexnaturalxcontrolxsystem.
Inxmanyxcases,xthexstructurexofxaxdiseasedxsystemxisxnotxevenxknown,xandxtreatmentxofxaxdisr
uptedxsystemxbecomesxaxhit-or-
missxstrategy.xIfxaxfeedbackxsystemxactsxveryxslowly,xwexmightxbexablextoxrespondxappropriately,xbut
xifxitxactsxfast,xitsxcontrolxbecomesxproblematic.
1.6. InxFigurex1.2,xarextherexcontrolxpathsxalongxwhichxABAxeitherxactivatesxorxinhibitsxclosu
rexofxstomata?xIfxso,xlistxatxleastxonexpathxeach.xIfxbothxpathsxexistxinxparallel,xdiscussxwhatxyo
uxexpectxthexeffectxofxanxincreasexinxABAxtoxbexonxstomataxclosure.
Solution:
TherexarexindeedxpositivexandxnegativexpathwaysxconnectingxABAxtoxthexclosurexsystem.xForxinsta
nce,xthexpathwayxthroughxRAC1x(centerxofxthexgraph)xandxActinxincludesxtwoxnegativexeffects,xwhi
chxmakexthexentirexpathwayxpositive:xIfxonlyxthisxpathwayxwerexthere,xthenxmorexABAxwouldxleadxt
oxmorexclosure.xByxcontrast,xthexpathwayxthroughxpHcx(centerxtowardxthexright)xandxKAPx(rightxabo
vexclosure)xcontainsxonlyxonexnegativexsignal.xThus,xifxthisxpathwayxwerexthexonlyxonexpresent,xthenx
morexABAxwouldxleadxtoxlessxclosure.
Thexsituationxthatxthexsystemxcontainsxthesextwoxcounteractingxpathways,xalongxwithxthexnu
merousxotherxsignals,xmakesxintuitivexpredictionsxentirelyxunreliable.xForxinstance,xsupposexonlyx t
hex twox pathwaysx mentionedx abovex werex present.x Withoutx morex information,x wex don’txknowx
whichxofxthextwoxhasxaxstrongerxeffect.xAlso,xwexdon’txknowxwhetherxthextwoxpathwaysxactxwithxthe
xsamexspeed.xItxcouldxwell xbexthatxthexfasterxpathwayxinitiallyx“wins,”xbutxthatxthexslowerxpathwayxh
asxaxstrongerxeffectxandxovercomesxthexfasterxpathwayxafterxsomextime,x therebyxcreatingxaxtemporar
yxresponse.xWhenxallxpathwaysxshownxarexactive,xwexhavexnoxchancexofxmakingxquantitativelyxcorr
ectxpredictionsxwithoutxaxdetailedxcomputationalxmodel.
