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8/3/2019 Erwin Schroedinger, Francis Crick and epigenetic stability
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ErwinSchroedinger,FrancisCrickandepigeneticstability
VasilyV.Ogryzko
UniversitéParis-Sud11
CNRS,InteractionsmoléculairesetcancerUMR8126
InstitutdeCancérologieGustave-Roussy
Villejuif,France
Emailaddress:[email protected]
8/3/2019 Erwin Schroedinger, Francis Crick and epigenetic stability
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Abstract
Schroedinger'sbook'WhatisLife?'iswidelycreditedforhavingplayedacrucialroleindevelopmentof
molecular and cellular biology. My essay revisits the issues raised by this book from the modern
perspective of epigenetics and systems biology. I contrast two classes of potential mechanisms of
epigeneticstability:‘epigenetictemplating’and‘systemsbiology’approaches,andconsiderthemfrom
thepointofviewexpressedbySchroedinger.Ialsodiscusshowquantumentanglement,anonclassical
featureofquantummechanics,canhelptoaddressthe‘problemofsmallnumbers’thatledSchroedinger
topromotetheideaofamolecularcode-scriptforexplainingthestabilityofbiologicalorder.
Reviewers
ThisarticlewasreviewedbyEugeneKoonin,VlatkoVedral(nominatedbySergeiMaslov)andEricKarsenti(nominatedbyArcadyMushegian).Forthefullreviews,pleasegototheReviewers'
Commentssection.
‘Molecularbiologyhasbeensuccessfullargelybecauseithasconcentratedonthetypeofproblem[…]thatcanbeattackedbyisolatinga
ll f bi l i l ’
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the role of DNA sequence as the dominant contributor to the persistence of biological order, the
emergingviewoffersaricherspectrumofadditionalfactorsthatcontributetobiologicalorganizationin
amannersomewhatindependentfromDNA.Alargesubsetofthesefactors,summedupunderthename
ofepigeneticinformation,isresponsibleforthemaintenanceofdifferentiatedcelltypesindevelopment,
playsanimportantroleincancerandhasbeenmakingheadlineslatelyastheculpritresponsibleforthe
setbacks in reproductivecloning. Could the insights ofSchroedinger's little book into thephysics of
biologicalorderbeusefulinsortingoutthenatureandpotentialmechanismsofprocessing,storageand
transmissionofepigeneticinformation?
ForSchroedinger,themostobviousmanifestationofbiologicalstabilitywasheredity,hencehisinterest
in thephysicsof inheritance.Likewise, currentepigeneticstudiesalso emphasizeheritableaspectsof
epigeneticphenomena.Thisfocus,however,unnecessarilylimitsthescopeofepigenetics.Terminally
differentiatedcellslivefordecades,maintainingtheirdistinctphenotypictraitsinspiteofenvironmental
stresses,thermalnoiseandDNAdamage/repair.Thesecellsdonotproliferate,thustheterm‘heritable’
does not apply to their traits. The term ‘epigenetic stability’ refers to a broader phenomenon that
encompassesmaintenanceofphenotypictraitsinbothnonreplicatingandreplicatingcellsindependent
f DNA I thi I t t t l f t ti l h i f i ti t bilit
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interactions and post-translational modifications) and might propagate independently from theDNA
sequence.
Moreover,itwasCrickwho,laterinhiscareer,becamepreoccupiedwiththemolecularmechanismsof
the essentially ‘epigenetic’ phenomenon of neurobiological memory. Crick did not believe that the
strengthofanindividualsynapse,oftenlocatedfarfromthenucleus,couldbeencodedinanucleicacid,
andinsteadfavoredaproteinmodificationastheeffector.Buthowthencanthesynapticstrength(the
elementalbasisofmemory)persistfordecades,inspiteofthemolecularturnoverthattendstoerase,ina
matterofdaysorweeks,themolecularrecordsstoredinproteinstructures?
Crickpostulatedthati)thestrengthofasynapseisdeterminedbyphosphorylationofaproteinmolecule,
ii)thisproteincanformdimers(oroligomers)andiii)thekinaseresponsibleforthemodificationwill
onlymodifymonomer inadimer that alreadyhastheothermonomer phosphorylated.Thismodelofkinaseaction(inspiredby thesemi-conservativemechanismfor themaintenancemethylationofDNA
[2])wouldallow thecell to restore theoverallphosphorylatedstate of thedimer/oligomerwhenever
molecular turnover replaceseithermonomer byanewone.The result isanextended half-life ofthe
structure,i.e.,memory,as‘themoleculesinthesynapse[…]canbereplacedwithnewmaterial,oneat
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onmacromolecularcomplexesalreadycontainingthesamemark(Fig.1).
Therecentproposalofasemi-conservativemechanismofnucleosomeduplication[9]mightmeanthat
epigenetic templating alsoworks for chromatinmarks of a different kind, e.g., varianthistones. All
variantsofhistoneH3formsocalledhomotypicnucleosomes,havingbothH3moleculesofthesame
type in the histone octamer.However, newH3histones are deposited onDNA only in the form of
H3/H4dimers[9];thusthedepositionmachinerymustmatchthetypesofnewandoldH3histonesifit
istokeepthenucleosomehomotypic.Suchamechanismcouldcontributetoanunderstandingofthe
role of CenpA, the centromere-specific version of histone H3, in the epigenetic maintenance of
centromerestructureindependentofDNAsequence[10].
Intriguingly,thedesignofsomeproteinkinasesissuggestiveofepigenetictemplatingalsooperatingin
the cytoplasm. Tyrosine kinases often containSH2domains,which recognize phosphotyrosine [11],
whereas some serine/threonine kinases contain FHA domains that recognize
phosphoserine/phosphothreonine[12].Thesestructuralfeaturesareusuallyunderstoodin termsofthe
signaling cascade paradigm, with a phosphoprotein A modulating a protein kinase targeting a
d t t i B H if f th ki t t f di ( li ) th
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enforce epigenetic templating, as considered in [8]. Future studies should reveal towhat extent this
model,promisingtocomplementtheCentralDogmaofmolecularbiology,couldexplainthestabilityof
epigeneticphenomena.
‘Systemsbiology’approachestoepigeneticstabilityandtheproblemoffluctuations
ThatFrancisCrick,thefatherofCentralDogma,entertainedideasextendingbeyonditsboundaries, is
notsurprisingandservestoillustratethatthebetteryouknowaconcept,themoreyouseeitslimitations.
Yet,althoughatoddswiththegenocentricviewoflife,theepigenetictemplatingidearemainstruetothe
general spirit of molecular biology, which, following Schroedinger, looks for the keys to life in
molecular structure. The model shares with the Watson-Crick mechanism of DNA replication one
essential feature incommon- thelocalized ‘bit bybit’ characterof informationstorage and transfer.
Informationis stored inaparticularmacromolecularstate (e.g., proteinmodification) andits transfer
reliesoninter-molecularcontactsandphysicallinkagebetweendifferent(modification-depositionand
modification-recognition) activities. Clearly, such a model has the advantage of being testable by
traditionalbiochemicalexperimentsincell-freesystems.However,isittheonlygameintown?
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‘systemsbiology’approachestoepigeneticstability?Theharshreality testfacing themisthe intrinsic
noisiness of the intracellular dynamics due to the small numbers of participating molecules. The
fluctuations in thenumbers ofmolecules of transcriptional regulators renderquestionable therole of
genenetworkdynamicsinstabilityofgeneexpressionpatterns[16,17](althoughthestochasticnatureof
geneticcircuitsislikelyinvolvedinmaking choicesbetweenthesepatternsduringdifferentiation).The
‘smallnumbers curse’1 loomsequallywhen theconcepts fromnon-equilibriumstatistical physicsand
classical chemical kinetics, whichwork reasonablywell on amacroscopic scale, are applied to the
organizationofsuchnano-objectsasbacterialcellsoreukaryoticcells’compartments,havingonlyafew
copiesofmanyvitalmolecularcomponents[18].
Exacerbating the ‘small numbers’ problem are two factors: the great variety of different molecular
speciespresentineventhesimplestlivingcellandtheneedtotakeintoaccountthelocalcontextofeach
molecule.Bothleadtoaverylargenumberofvariablesnecessarytodescribethestateofacell.Tosee
howtheproblemsoffluctuationsandhighdimensionalityofintracellulardynamicscombine,consider
thefollowingtoyexample.Asingle E.colicellcontains2000moleculesofRNA-polymeraseenzyme
[19].Asameasureofthestabilityofaparticularvariabler ,letustakethecostofitsmaintenance( Mr ),
i d d t b di i t d i d t k th l f i t bl f th
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insteadofasingleone)becomesproportionalto Nrinsteadof√ Nr(sinceifthenumberoflabels i=N ,
theΣ√ Nr i=Nr dueto√1=1).
If molecular biology tellsusanything, it is that themorewe learn of the intricacies of intracellular
regulation,themorefunctionaldifferencesbetweendifferentmoleculesofthesamespecieswefind,due
totheirmanymodificationsandtheirplacementinparticularintracellularcontexts.If,inthespiritofthe
‘omics’ approach, we consider all this information to be essential for the complete description of
intracellular dynamics, the number of variables will expand dramatically, together with the cost of
keepingfluctuationsundercontrol.Thisreflectsthefactthatincreasingtheresolutioninourdescription
ofthecellstateisthereverseof‘coarsegraining’,aprocedureusedinstatisticalmechanicstotransit
from a detailed ‘microscopic’ description of a physical system to its description in terms of
‘macroscopic’ degrees of freedom by averaging out all nonessential variables. Thus, the more
informationaboutthecellweconsiderasessential,thelesswecanrelyonthelawoflargenumbersto
accountforthestabilityofintracellulardynamics.
CouldthelessonsofSchroedinger’sbookhelptogetusoutoftrouble?Infact,theverysame‘small
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contributetothe‘systemsbiology’approachestoepigeneticstability,similarlyhelpingthemtodealwith
the‘smallnumbersproblem’?
Schroedingerandquantumentanglement
At first glance, appealing to quantum mechanics to solve the fluctuation problem only seems to
complicatethesituation. Inquantum theory,the dimensionalityof acomposite systemdoesnotgrow
linearlywiththenumberofitsparts(asitdoesintheclassicalcase),butexponentially[21].Thus,asthe
numberof variablesused todescribeintracellulardynamicsmultiplies,the Mr neededtokeepallthe
fluctuationsundercontrolhastogrowexponentially.Wouldnot,then,appealingtoquantummechanical
principlesinexplainingintracellulardynamicsamounttoshootingourselvesinthefoot?Woulditbe
wiser of us to restrict the biological applications of quantum theory to the time-honed studies of
molecular structure and intermolecularinteractions only?This does notseem tobe thebest strategy.
Quantum theory is a general theory of the stability of matter, indispensable for understanding the
behaviorofobjectsbothsmallandlarge.Beingaparticularcaseofcondensedmatterphysics,itisvery
unlikelythatthephysicsoflifecanbeproperlyunderstoodwithoutquantumtheory.Asweperfectour
t h l t th hi h t l ti th d i ti f i t ll l d i t ti f fi t (i
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materialsystems[27,28].Myexpectationisthatthephysicaldescriptionofintracellularprocessesfrom
firstprincipleswillrequiretakingentanglementintoaccount.Thesystemsbiologyapproachesbasedon
approximations that get ridofentanglement at theoutsetwillhave seriousdifficulties explaining the
stabilityofintracellulardynamics.
Howmayentanglementsubstitute‘largenumbers’instabilizingbiologicalorder?Similartothecoarse
graining procedure, it can reduce the number of degrees of freedom that have tobeprotected from
fluctuations,butinamoresubtlewaythanbysimpleaveraging.Considerthesimplestexampleofan
entangledsystem–socalledBellpairofelementaryparticles[26]:
Ψ⟩ = (↑⟩1↓⟩2 + ↓⟩1↑⟩2)/√2, (1)
wherethearrowsdesignatethespinorientationofparticles1and2,
andcompareitwithanon-entangledpair(productstate):
Ψ⟩ = →⟩1→⟩2=((↑⟩1+ ↓⟩1)/√2)((↑⟩2+ ↓⟩2)/√2) =
= (↑⟩1↓⟩2+ ↑⟩1↑⟩2 + ↓⟩1↑⟩2 + ↓⟩1↓⟩2)/2 (2)
Whereas, in the ‘spin up’/’spin down’ representation, all combinations of the states of the two
particles areallowedfor theproductstate(2),in the caseof theBellpair(1)onlytwoare.It is
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concomitant growth in the cost of maintenance4. These arguments suggest that the proper
descriptionofthecell’sfunctioningwillrequiretakingsomeofthisentanglementintoaccount,in
ordertokeeptheexpectedtotalcostofmaintenanceundercontrol.Theresultantacknowledgment
ofcorrelations betweenmolecularevents inside thecell can help tounderstand howintracellular
dynamics remains robust in spite of the fluctuations in the numbers of its many participating
components.
Findingsupport for theproposed role of entanglementmeetswithboth experimental and theoretical
challenges.First,wewillneedtolearnhowtodetectcorrelationsinthefluctuationsofmanyobservable
characteristicsoflivingcells,andtobeabletodoitona singlecelllevel.Thistaskisstilldifficultwith
currenttechnologyandwillrequirethemarriageof‘nano-’and‘-omic’approaches,stillintheirinfancy.
Second,entanglementiscommonlyperceivedtobeveryfragileandtobequicklydestroyedduetothe
interaction of the physical system with its environment. This phenomenon, called environmentally
induceddecoherence(EID),hashindered theotherwiseremarkabledevelopmentofprotocolsthatuse
entanglement for more efficient computation and secure cryptography [24]. There are grounds for
optimism,however.Theperceivedfragilityof anyentanglementisamisconceptionresultingfromthe
k h ll i t lli ti l l f t l d t t f th f t
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‘decoherence free subspaces’ are related to the concept of ‘preferred states’ proposed to explain
transition from the quantumworld to the classical [36]. In this approach, EID does not destroy all
entangled states - some are stabilized via a process called environmentally-induced superselection.
Accordingly, theentangled states inbiologicalsystems couldbeprotected fromEIDexactlybecause
theyarethe‘preferredstates’ survivinginteractionwiththeenvironment.Theimplicationsofthisidea
could be interesting for both information technology and the understanding of life. It suggests a
perspectiveontheadaptationoflifetoitsenvironmentthatdiffersfromthecanonicalDarwinianviewin
thatadaptationvia‘survivalofthefittest’canhappenonthelevelofanindividualobject,i.e.,doesnot
involvereplication[22,23].Ontheotherhand,itindicatesanewpotentialsourceofentangledstates
preparedforusbybiologicalevolution,whichcouldbeusedinquantuminformationprotocols.
Tosummarize,entanglementcanprovidebiologywithaconceptualingredientthathadbeenmissing
fromthemolecularexplanationsoflifedominatingthefieldforthelast50years.Aphilosophercould
seeinitthephysicalcounterpartofanolddictum–‘thewholeismorethanasumofitsparts’,reflecting
theaspectoflifethatcannotbereducedtomolecularstructureandinteractions.Amoderninformation
theoristwouldseeentanglementasanindependentresourceforinformationprocessingin livingcells,
dditi l t th l l ‘ t d b lt ’ h i (i l di i ti t l ti ) hi h ld
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shedmorelightontheimportanceofepigenetictemplatingbyagenome-widecomputationalanalysisof
proteindomainarchitectures.
Thesecondfacetofepigeneticstabilitydiscussedhereiscompletelydifferentincharacteranddecidedlynon-orthodox.Inessence,Ogryzkoproposesthatthe“smallnumberscurse”,whichisatthe
centerofSchroedinger’treatise,i.e.,thewayacellcopeswithdisruptiveeffectsofmolecular
fluctuations,couldinvolvequantumentanglement,thefamednon-localaspectofquantumphysics.The
fluctuationsproblemisrealandtroubling,andtheproposedsolutionseemstobeingeniousand,potentially,powerful(caveatemptor:myownunderstandingofentanglementisatthelevelofNews&
Viewsarticles).Theideaofstabilizationofparticularentangledstatesviaenvironmentallyinduced
superselectionisparticularlyattractive.Inprinciple,thiscouldbe“it”,theHolyGrailofBiological
Physics,anon-trivial(notlimitedtopropertiesofmolecules)roleofquantumeffectsinbiologicalsystems.Ofcourse,itmustbeclearlyrealizedthattheproposaloutlinedinthispaperisnotatheoryand
notevenafull-fledgedhypothesis:itis“just”anideabut,Ithink,onethatbiologistscannotaffordto
dismiss.
Thehistoricalcontextofthepaper,withallthemultifacetedramificationsofCrick’sandSchroedinger’s
classics,mightnotbeexactlyessentialforthepresentationsofOgryzko’sideas,butthissurelymakes
forenticingreading.TheonlyaspectofthepaperthatIdonotlikeistheuseofthe“systemsbiology”
jargoninthesecondpart.Itrequiresthinkingbuttheresurelymustbeabetterwaytodescribetheeffectsoffluctuationsoncellfunctioning.
Author'sresponse–IthankDr.Kooninforhiscomments.Iappreciatetheideaofusinggenome-wide
computationalanalysisofproteindomainstotestthecontributionoftemplatingmechanismsto
epigeneticstability;somethingdefinitelycouldbedonewiththis.
I l th t th id b t th t ti l l f t l t i i th ‘ ll b ’
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toharnessitforthepurposesofquantuminformationprocessing,butagain,itcouldbedoneonlywith
thehelpofbiologists.
EricKarsenti,CellBiologyandBiophysicsunit,EMBLHeidelberg,Heidelberg,Germany.
Idon'tfindanythingdramaticallywronginwhatOgryzkowritesaboutbiology,andIthinkthat
theideaisveryinteresting.Istillthinkthatineukaryoticcells,statisticalmechanicsandreactiondiffusionmechanismsarethemostrelevantscaletoanalyzetheself-organizationofhighlydynamic
steadystateofrelativelylargestructureslikethespindle,organellesandoverallcellorganization.
However,itisquitepossiblethatcoherencederivedfromentanglementisalsoatworkunderneaththe
averagingoflargenumbersofmolecules.Obviously,somekindofexperimentalapproacheswouldbewelcometoaddressthisquestionofentanglementatthecelllevel.
Author'sresponse–IthankDr.Karsentiforhiscommentsandagreethatexperimenterswillhavethe
lastwordinthismatter.
Endnotes1.AcaseinpointisthecalculationofthenumberoffreeprotonsinasinglecellofE.coli[38].Giventhe
intracellularpH7.5andcellvolumeπ /6x10-15liters,thereare,ontheaverage,only10protonsincell[39].
2.Aresource,whichhelpstoovercomelimitationsonwhatcanbeachievedbythesocalledLOCC(Local
OperationsandClassicalCommunications)classofprocessesinquantuminformationtheory[26].
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References
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Figurelegends
Figure1.Generalschemeofepigenetictemplating.
Thismechanism impliestwoessential features: a.Physical linkagebetween theenzymatic activitydepositingaparticular
epigeneticmark(covalentmodification,alternativehistone,etc.)andtherecognitionmoduleforthismark;b.Formationof
dimers(oroligomers)bythetargetofenzymaticactivity(protein,nucleicacid,etc.).Shownarethreescenarios:I–presence
ofthemarkononemonomerwilldirectitsdepositiononthesecondmonomerviarecruitmentofthedepositingactivity(can
alsoinvolveallostericeffectsofR-modulebindingonD-moduleactivity),II–unmarkeddimerwillnotrecruitmodifier,III–
ifbothmonomersaremarked,theywillnotbeaffected.R–recognitionmodule,D–depositionmodule,T–target.
Figure2.Quantumentanglement.
2.A.Oneexampleofsystemsetuptoobservequantumentanglement
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Figure 2