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On the principles of multicellular organism development
David Frigola,* José M. Sancho, Marta Ibañes
Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, Catalonia. Universitat de Barcelona Institute of Complex Systems (UBICS),Barcelona, Catalonia
Summary. Non-equilibriumphysicshastraditionallydealtmostlywithinanimatematter.Yet,inthelastdecadestherehasbeenincreasinginterestinunderstandinglivingsystemsfromthisperspective.Oneexampleisusingtheframeworkandtoolsofnon-equilibriumstatisticalmechanicsandnonlinearphysicstostudyhowlivingorganismscomposedofmanydifferentiatedcellsdevelopfromasingleinitialcell.Thedynamicprocessofmulticellularorganismdevelopmentisoutofequilibrium,inthat it consumes and dissipates energy. It also involves the formation of manyprecise and complex structures. Hereinwe review some of the paradigms beingused that focus on how these multicellular structures initially emerge at themolecularlevel.[Contrib Sci11(2):215-223(2015)]
*Correspondence: DavidFrigolaDepartament de Física de la Matèria CondensadaUniversitat de BarcelonaMartíiFranqués108028Barcelona,Catalonia
E-mail:frigola@ecm.ub.edu
A historical overview
Anexampleof thebeautyandcomplexityofNature is thedevelopmentofmulticellularorganisms.Animalsandplantsdevelopfromasinglecell,whichthroughdivisiongivesrisetoall thecellsoftheorganism.Duringdevelopment,thesecells become distinct in an organized and precise mannerto robustly form complex structures such as organs. Howdoes this occur?What are the principles behind it?Manyphysicistsarenowengagedininvestigationsofmulticellular
organismdevelopment,withtheaimofunderstandinghowitproceedsandfindingitsfundamentalprinciples.Resolvingthese questions is expected to help shed light on moreapplied challenges ranging frombiomedical issues, suchasembryonicmalformationsandcancer,toagriculturalissues,suchastheoptimizationofcropgrowth.However,thequestforunderlyingprinciplesisstillinitsownearlydevelopmentalstage,andanimmenseuniverseofknowledgeliesahead.Inthefollowing,weconsidersomeoftheideasandinsightsthatappearedearlyonandthathaveinfluencedcurrentresearch.
O P E N A A C C E S S
BIOPHYSICS Institut d’Estudis Catalans, Barcelona, Catalonia
www.cat-science.cat
CONTRIBUTIONS to SCIENCE 11:215-223 (2015) ISSN (print): 1575-6343 e-ISSN: 2013-410X
Keywords: development·morphogen·attractor·non-equilibrium·differentiation·self-organization·lateralinhibition·multistepsignaling·ultrasensitiveresponse·bistability·fluctuation
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Over 70 years ago, Conrad H. Waddington used themetaphorthatduringdevelopmentcellsrolldownthroughvalleysthatbifurcate[25],havingtochoosewhattobecomeateachbifurcation.Thismetaphorforcelldifferentiationisnowcommonlyused,withafreeenergylandscapeofwhichWaddington’svalleysaretheminima.
Alan Turing, very well known for his contributions tocomputerscience,proposed,inaseminalworkpublishedin1952,thatpatternsarisingduringdevelopmentmightbethenaturaloutputofchemicalreactionsbetweenmoleculesthatdiffusewithdifferentdiffusioncoefficientsacrossspace[23].That chemical systems can form spatiotemporal patterns,inwhich the concentrations ofmolecules are organized inspaceandtime,wasprovenlaterinwell-controlledchemicaland physical assays. However, these were not linked tomulticellular organism development, but instead droveintense research in the field of nonlinear dynamics. Therelevanceof thismechanism, knownas Turing’s instability,in the contextof development is nowappreciatedbut stilldebated[15,18,19].
In1970,theNobelLaureateFrancisCrickproposedthatthe diffusion of molecules could create gradients acrossdevelopingtissues[4].ThesegradientscouldconveytothecellsthepositionalinformationthatLewisWolperthadalreadyproposed [26], guiding them in their furtherdevelopment.This is the morphogen gradient paradigm, which hasdominatedresearchonpatterningindevelopmentalbiology.Thefindingthatnumerousmoleculesformgradientsduringdevelopmentandthatthegradientsthemselvesarerelevantfor the development of different tissues has led to manyothercomplexquestions:Howdoesthegradientform?Howis it sensed?Andwhat informationfromthegradientdoesthecelluse?
StuartKauffmannshowedthattheinteractionsbetweengenesstronglyrestrictthepossiblecelltypes[14].Inthiscase,celltypesareunderstoodastheattractorsofthedynamicsofgeneticinteractions.Atpresent,decipheringthelargegeneregulatory and signaling networks and their dynamics in adevelopingcellisanintensefieldofresearch.
These conceptual frameworks, i.e., bifurcations toproduce changes of cell types, self-organization out ofequilibriumandcelltypesasattractors,weremathematicallyformulatedanddeveloped.However, inthelastdecadesofthe20th century, theuseofmathematical formulations tounderstand development became unpopular because theyfailedatdescribingandpredictingpatterns.The resultwasa split between developmental biologists and physicists/mathematicians[16].Morerecently,however,knowledgeof
whichbiologicalmoleculesparticipate indevelopment, theability tomanipulate them, and their spatial and temporalresolution, have increased dramatically. At the same time,important progress has been made in non-equilibriumstatisticalmechanics,dissipativesystems,complexsystems,nonlinear dynamics, and networks, accompanied by anextraordinary increase incomputationalpower.Asaresult,interdisciplinary research involving both physicists andbiologistshasbecomemorecommonandtheadvantagestothisapproacharenowacknowledged[20].Thus,weareinanexceptionalpositiontoembracethechallengetounderstanddevelopmentandtheprinciplesbehindit.
Patterning the embryo
Acrucialstepinunderstandinghowmulticellularorganismsdevelop is to unravel how cells become distinct in acoordinated and organized manner. In the language ofdevelopmentalbiology,thiscanberephrasedashowacellattainsaspecificfateintowhichitultimatelydifferentiates.Twomainmechanismshavebeenproposedforcoordinatedcell differentiation in tissues. One mechanism is throughpositional information, proposed by Lewis Wolpert asmentionedabove [26]: the fateofacell isa readoutof itsspatiallocalizationfromareferencesystem(Fig.1A).Cellsreadtheinformationofwheretheyarelocatedanddifferentiateaccordingly. Gradients ofmolecules, previously referred toasmorphogens(weretainthistermhereforconvenience),havebeenproposed toconfer suchpositional information.Theoriginofthereferencesystemisthesourcewherethemorphogenisproduced.Theamountorconcentrationofthemorphogendecaysasthedistancefromthesourceincreasesandtherebyconveyspositionalinformationtothecell.Thisinformation can be conferred to cells through moleculesthatbecomeactivatedatdistinctthresholdsofmorphogenconcentrations (Fig. 1A). There are multiple proteins thathavebeenshowntobedistributedalonggradientsindifferentdeveloping embryos and that seem to convey positionalinformation. Specifically, if the gradient is altered, the fateof the cells changes accordingly (Fig. 1B). This is the case,for instance, for theproteinBicoid,whichformsagradientalong the anterior-posterior axis of the embryoduring theveryearlystagesofinsectdevelopment,includingthatofthefruitflyDrosophila [10].TheregionwhereBicoid isathighconcentrationbecomestheheadofthefly.
The other proposed mechanism is that cells becomedistinct only because of coupling. This is an example of
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self-organization in which a structure or order emergesspontaneously because of the interactions betweenelements. Coupled dynamics enable the emergence ofrobust proportions and periodic distributions of cell types.In contrast with the positional information mechanism,couplingdoesnotdriveaspecificcelltypeinagivenspatialposition.Inadevelopingorganismthisself-organizationcanhappen indifferentways. Thefirstone corresponds to thedynamicsAlanTuringstudied[23].Whenchemicalsinitiallydistributedhomogeneouslythroughoutagivenspacereactanddiffuse,theyformheterogeneousdistributions.Becausethereactantsdiffusewithdifferentdiffusioncoefficients,tinysmall random fluctuations in the reactant concentrationsbecome amplified, such that the homogeneous statebecomes destabilized. This happens for a wide range ofdiffusioncoefficientsandreactionkinetics. It isanexampleofanon-equilibriumpatternformationprocess,inwhichthe
balancebetweenantagonisticprocesses,suchasdrivinganddissipation, results in the formation of non-homogeneousstructures [5]. Thus, for instance, periodic stationarydistributions of the molecules can emerge. Cells produceproteins,whichreactanddiffuseintheextracellularspace.Accordingly,whenaperiodicpatternofproteindistributionsemergesfromthesedynamics,somecellsendupproducingor sensing large amounts of proteinswhile others do not.Therefore, cells become distinct (Fig. 1C,D). A change inthe spatial interactions, as in the diffusion coefficient,results in relevant changes of themolecular pattern beingformed.Accordingly,thepattern, ifperiodicandstationary,canchangeitsperiodicity(Fig.1D).Empiricalevidencethatsuch amechanism candrive the formationof thedigits invertebrateshasrecentlybeenprovided[21].Thedigitsformfromaninitialrathertwo-dimensionalroundpalette.Inthispaletteastripe-likepatternemergesthatdividesitintotwo
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Fig. 1. Patternformationmechanismsthatrelyondiffusionalonganextracellularmedium. (A–B)Morphogen gradient mechanism.Theleftmost,greencellgeneratesamoleculethatactsasamorphogen.Themoleculediffusestotherightandgeneratesagradient,asshowninthecurveabovethecells.Theamountofmorphogensensedbyeachcellconveyspositionalinformationtoit.Therearetwothresholds,oneatconcentration1andanotheratconcentration10,andcellsdifferentiatedependingonwhethertheconcentrationisaboveorbelowthesethresholds.InAthereisextensivediffusion,asindicatedbythelargercurvyarrow.InB,thereislessdiffusion,alteringthegradientandthepositionofcelltypesaccordingly.(C–D)Turing pattern mechanism.Twoormorechemicalsthatdiffuseandreactareneededtoestablishapattern.InCthepatternforcertainvaluesoftheparametersisshown.InD,whendiffusionismodifiedsoisthepatternandthecorrespondingcellfates.(Notethattheterm“morphogen”isnolongerusedwiththemechanismshowninCandD.WeusethetermherebecauseitwasintroducedbyTuringpreciselyinthiscontext).
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intercalating regions: interdigitalanddigital regions. In thisspecific case the reaction-diffusion mechanism does notact in isolationbut it iscoupledtoapositional informationmechanism.
Another way that could drive the differentiation ofcells in a self-organized manner but does not require thetransportofamoleculeisthroughdirectcell-to-cellcontact.Inthiscase,cellsinteractthroughmoleculespresentonthecellmembrane that, uponbinding, send signals to the cellnucleus.Anexampleofthisislateralinhibitionwithfeedback[3].Inthiscase,thesignalacellreceivesarisesfromproteinligands in adjacent cells and it decreases the amount ofligand inthecell.Thus,acell thathasmore ligandthan itsneighboring cells, even if the difference is very small, willreducetheiramountofligandand,atthesametime,increaseitsownligandproductionbypreventinginhibitionbythoseneighbors. Ultimately, the cell with an initially very smallexcessofligandwillendupwitharelativelylargeamountofthat ligand,while ligand inneighboringcellswillbealmostcompletelyeliminated.Thistypeofinteractionunderliesthespecificationofneurons,forinstance.
In the 1970s,Meinhardt andGierer proposed a theoryfor biological pattern formation based on two elements:(1) self-activation and (2) long-range inhibition [9]. Turing-like reaction-diffusion dynamics and lateral inhibition withfeedback can both be understood in terms of these twoelements.Moreover, self-activationevidences a key aspectin thedynamicsofcoupledelementsthatdrivepatterning:nonlinearities.Alltheseself-organizinginteractingdynamicsdrive the emergence of robust proportions and periodicdistributions of cell types. In this mechanism based oncoupling, thecell typesarise inacoordinatedmannerbut,unlikeinthepositionalinformationmechanism,itdoesnotenabletherobustspecificationofacelltypeinagivenspatialposition.Nevertheless,ifspatialasymmetriccuesareaddedto interactingdynamics, then spatial precision can arise aswell.
It isworthnotingthathowthepatternwillbemodifiedwhen the elements driving it are altered can be predictedby constructing mathematical and computational modelsofthedynamics.Theresultingpredictionscanthenbeusedto test whether assumptions regarding the mechanism ofpatterning are correct, by comparing the predicted resultswith the empirically derived data. This task is nowadayscommonroutinelydonebutithasnotalwaysbeensoeasilypossible.Nowwecanproposewhichspecificmoleculesareactingand,inseveralcases,wecanexperimentallyseehowtheirdistributionchangesovertimeandspacewithdetailed
resolution.Manipulationsof the interactionsand reactionsandhowthemoleculardistributionchangesaccordinglycannowbedoneandtheresultsmeasured.
The mechanisms described herein assume that, intermsof their patterning, cells canbedescribedbyonly afew relevantmolecules. The role of cell dynamics and theparticularmechanicalforcesthatareactivearenottakenintoaccount. This simplification is valid in some circumstances,especially when the dynamics that control the molecularconcentrationsaremuchfasterthanthoseofthecell.Manyefforts arebeingdoneon the role ofmechanical forces inshaping developingmulticellular organisms, which are notreviewedherein.A challenge that remains is todeterminehowmechanical forcesand thedynamicsof themolecularcomponents that direct cell signaling or impinge on generegulationarecoupledtoeachother.
Nonlinear responses
We have discussed how molecular gradients can conferpositionalinformation,inwhicheachcelltypeisdictatedbyathreshold,cell-type-dependent,morphogenconcentration.In Fig. 1A, cell type “blue” is induced above amorphogenconcentration of 10 (arbitrary units), whereas cell type“white” is inducedaboveamorphogenconcentrationof1.Yet, isthistypeofthresholdresponsepossibleinbiologicalsystems? It is, thanks to ultrasensitivity. As opposed to agradual or linear response, in which the relative changesin input (signal) and output (response) are equal, anultrasensitiveresponseisthatinwhichasmallrelativechangeinthesignalgeneratesaverylarge(relative)response.Sincea cellular response usually saturates (i.e., when the inputsignalislargeenough,theresponsenolongerchanges),anultrasensitiveresponseincellscantranslatetoathresholdor“all-or-nothing”response(Fig.2A).
Buthowisthisultrasensitivityachievedbycells?Avarietyofmechanismshavebeenelucidatedthroughmathematicsandthenexperimentallydemonstrated[27].Afewofthemaresummarized inFig.2andreviewed in[27].“Zero-orderultrasensitivity” was the first of these mechanisms to beproposed, in 1981 [11]. In this mechanism, an enzymecovalently modifies a protein (covalent modification is acommon regulatory mechanism in which a molecule suchasaphosphateormethylgroupisboundtoaproteinbyanenzyme), and an opposing enzyme restores the protein toits unmodified state. When both enzymes are working atsaturation,asmallchangeintheamountofoneofthemcan
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produce a large change in the proportion of themodifiedand unmodified proteins, thus enabling an ultrasensitiveresponse(Fig.2B).
Another,verycommonmechanismismultistepsignaling,inwhichanelementrepresentingthesignal,orproportionalto the signal intensity, acts on twoormore elements thatindependently affect the strength of the response. Anexample is a signal that acts on twodifferent steps of themodificationofaproteinthatwillultimatelyturn it into itsactive form. The multiplied effect elicits an ultrasensitivebehavior.Mathematically,therepeatedeffectofthesignalisrepresentedasmultiplicativetermsthatcanraiseituptothepowerofthenumberofpointsatwhichthesignalaffectsthesystemindependently(Fig.2D).
Director indirect self-activation,alsoknownaspositivefeedback,candriveultrasensitiveresponsesaswell.Positivefeedback occurs, for instance, when a protein binds to itsown DNA promoter to boost its own transcription (auto-activation),orwhenaprotein inhibitstheproductionof itsinhibitor(mutualinhibition)(Fig.2F).
Bistability
Apositivefeedbackloopcanalsoenablebistability,i.e.,twodifferent responses to thesame input (mathematically, theequationthatrepresentsthesystemhastwostablesolutionsinstead of one). In other words, genetically identical cellsexposed to the same environmental conditions can be intwo different states and hence become two distinct celltypes. An example of bistability in development occurs inthe vulval development of the hermaphroditic nematodewormCaenorhabditis elegans[10,12].Beforethisegg-layingorganisformed,twoadjacentcells,whichcanbelabeled1and2,forinstance,becomedistinctfromeachotherbasedon their position in the embryo. One becomes an anchorcell(AC)andtheotheraventraluterine(VU)cell.Eachcellhasa50%probabilityofbecominganAC.Hence,underthesameconditions twostatescanarise,with50%probabilityeach: (AC,VU) or (VU,AC), in which the first term withinthe parentheses denotes the type acquired by cell 1, andthesecondtermreferstocell2. Inthiscase,thebistabilityof these two states arises through a positive feedbackthat involves the above-described lateral inhibition withfeedback. Nonlinearities are essential for this bistability.Figure 3 provides an example of this case and shows howa mathematical model of the interactions can help us tounderstandandvisualizethisprocess.
Fluctuations
Aswehaveseen,cellshavemechanismstoprocesssignalscomingfromneighboringcellsandfromtheirsurroundingsthatcanyieldpreciseresults.However,thesesignalscannot
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Fig. 2. Mechanisms that generate ultrasensitivity. (A) A signal-responsefunctionshowingultrasensitivityandanall-or-nothingresponse,asshownin panels B, D, E, F. (B) Zero-order ultrasensitivity. As explained in thetext,thepurpleenzyme,correspondingtosignalS,enhancesthecovalentmodificationoftheredprotein,whiletheyellowenzymemediates itsde-modification.ThemodifiedproteinamountcorrespondstotheresponseR.(C)Molecular titration. FreemoleculeA (corresponding toor activatingaresponseR)canbesequesteredbyB,whichispresentinverylargeamounts.MoleculeAexhibitsanultrasensitiveresponsetochangesinitsproduction.TherearefreeAmoleculesonlywhentheirproductionlevelsurpassesthesequesteringeffect.Atthisthreshold,theamountofAsuddenlyincreases.This behavior is not like that shown in A, because its response does notsaturate.(D)Multistep signaling.ThesignalS,orsomeelementproportionalto it, aids in twodifferent stepsof themodificationofaprotein thatwillultimatelyassumeitsactiveform,whichthenenactsresponseR.Itseffectismultipliedandcanelicitanultrasensitiveresponse.(E)Cooperative binding. A receptor, in green, has several binding sites for the same ligand, theamountofwhichcorrespondstosignalstrengthS.Iffulloccupancyofthereceptor’sbindingsitesisneededtoelicitaresponseR,orifeachoccupiedsiteincreasesthechancethatanewligandwillbind(thickerarrowsindicatelargeramountsofboundligand),ultrasensitivityarises.(F)Positive feedback loop. A signal S (here a blue enzyme) activates a protein (in red). ThisactiveproteinelicitsresponseR,butitcanalsobindtoDNAandenhancetheproductionof itsownunmodified form.This increases theamountofsubstrateuponwhichthesignalcanact,multiplying itseffectandmakingtheresponseultrasensitive.Thesemechansimsarereviewedin[27].
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be sensed with perfect precision due to the physical lawsthatgovernmoleculardynamics[2].Thesesignals,andtheproteins that process them, consist of discrete moleculesthat jiggle around, embedded in the thermal bath of thecytoplasm. This aqueous medium is crowded with manymovingmolecules suchasproteins. Somemoleculesmovestochastically without a preferred direction, because ofthermalforcescomingfromcollisionswithwatermolecules.Others,suchasmolecularmotors,movedirectionallyusingelectrochemical forces. Several of these electrochemicalreactions have associated energies (such as the energyrequiredforsomereactionstostart,ortheenergyrequiredtobreakspecificchemicalbonds)comparabletothethermalenergy of the medium. Therefore the stochastic “jiggling”ofmoleculescanspontaneouslyactivatereactionsorbreakchemicalbonds.
These fluctuations also affect the production anddegradationofdifferentproteinsinthecell,whichstochas-tically vary in time. This could not be directly observeduntil the very recent advances in the spatial and temporalresolution of fluorescence microscopy techniques. Beforethat (but also only recently), temporal fluctuations in the
amountofspecificmoleculescouldonlybeinferredfromtheheterogeneous amounts found among genetically identicalcellsinthesameenvironment.Eventhoughfluctuationsareacommonobjectofstudyinnon-equilibriumandstatisticalphysics,ourdirectknowledgeofthemotionandfluctuationsofparticlesembeddedinthecrowdedmediumofacellisstillincipient. Yet,with theadventofnanotechnologiesweareenteringanewerainwhichitwillbepossibletocharacterizethemotionsofandfluctuationsincellularcomponents.
Fluctuations and cell decisions
Because fluctuations are ubiquitous in the cell, they mustsomehow be relevant to an understanding of all cellularprocesses,includingthoseinthepreviouslymentionedexamplesof morphogen diffusion, cellular sensing of thesemolecules,andtherelatedsignalingprocesses.Theexquisiteprecisionandregularityofdevelopmentalprocesses indicates thatcells cancopewiththisvariability,orperhapsevenprofitfromit.
One obvious way of avoiding the effect of fluctuationsis by producing large amounts of molecules to minimize
Fig. 3. Bistability.(A)Lateralinhibitionwithfeedback.Theligandincell1inhibitstheligandinneighboringcell2andviceversa,establishingpositivefeedback.Inhibitionisrepresentedbythebluntarrows.Thereisa50%probabilityforthe(AC,VU)outcomeand50%forthe(VU,CA)outcome,determinedbywhichcellachievesahighorlowamountofligand.(B)Theequationthatgovernsthetemporalevolutionofaligandincell i (1or2). /idl dt isthetimederivativeofconcentration
il andrepresentsitschangesovertime.Theproductionterm ( )jg l decreasesnonlinearlywhen jl (theligandintheothercell)increases.(C)Phasediagramofthistwo-cellsystem.Eachpointcorrespondstoauniquepairof
1 2l l− values.Theevolutionofeitheroneisfullydeterminedandshownbythebluearrowsofthevectorfield.Theredandbluedashedlinesarecallednullclinesandcorrespondtothepointsatwhichthetimederivative,i.e.,therateofchange,fortheligandatoneofthecells(blueforcell1andredfor2)iszero.Atthepointswherethenullclinescrossbothderivativeshavethevaluesofzero,sothesystem,ifunperturbed,willnotmoveawayfromthem.Becauseofthenonlinearityofthenullclines,therearethreeofthesepoints;iftheywerenotnonlinear,therewouldonlybeonesuchpoint.Ofthese,theblackpointsarestablestates:whenthesystemisatoneofthem,itwillreturntoitafterasmallperturbation(thisstateisthereforealsocalledanattractor).Indeed,alltrajectoriesstartinginthepurplehalfoftheportrait(calledthebasinofattraction)willevolvetowardsthe(AC,VU)stablestateatthebottomleft(onesuchtrajectoryisshowninblack).Similarly,thegreenareaisthebasinofattractionforthe(VU,AC)stablestate.Theorangepointrepresentsastatewithintermediatevaluesofligandforbothcells,asshowningray,thatisnotstable.Asmallperturbationfromthisstatecanleadthesystemawayfromitandtooneofthestablesolutions.ThescenarioinBwasobtainedfromsimulationsperformedbyJuanCamiloLuna-Escalante,Dept.ofCondensedMatterPhysics,UniversityofBarcelona).Thedataareusedwithpermission.
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their effects. This is not always worthwhile, or possible.For instance,when a cell receives a fluctuating signal thatit cannot control, how can it cope with the fluctuations?Onewaytobufferfluctuationsistorespondtotheamountof signaling molecules received only during an interval oftime [2]. This corresponds to an integration over time ofthenumberofmolecules, the resultofwhich ismuch lessvariable than the number ofmolecules at any given time.Therefore, the input towhich the cell responds is not thehighlyfluctuatingnumberofmoleculesbutthemuchmoreconstanttotalnumberofmoleculesreceivedperunittime.Thistimeintegrationisperformed,forinstance,bybacteriato sense the level of nutrients in their environment [2]. Italsoisthemechanismproposedfordevelopingembryos,inthe cellular response tomorphogen gradients [6]. In casesin which cells respond too rapidly compared to the timeinterval thatwouldbe required for integration tofilteroutfluctuations, the additional interactions of neighboring
cellsmayreinforcethecorrectcelldecisionandincreaseitsrobustness[13].
There are several examples of biological systems thatprofitfromfluctuations[7].Mostofthemareinunicellularrather than multicellular developing organisms, but theirexistence can suggest that fluctuations may also be usedduring development. For instance, fluctuations enablewide-ranging heterogeneity between genetically identicalcells in the same environment. This heterogeneity can bebeneficial when the environment changes rapidly and thecellular response is heterogeneous. If this heterogeneouspopulationofcellscomprisesdifferentcelltypesthatresponddifferently,thenwhentheenvironmentchangessomeofthecelltypesmaydiewhileotherswillprevail.Becauseofthisheterogeneous response toenvironmental change, thecellpopulationpersists,providingabenefit.Thisisknownasbet-hedging(thecolonyofcellshedgesitsbetsinsteadofputting“all of its eggs in one basket”) and has been described in
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Fig. 4.Stochasticswitching.(A)Amodelofabistablesystem.Theblackcontinuouslineistheenergylandscapeofthesystem;thebottomsofthetwowellsarethestablestates.Thebluecirclerepresentsthesystematoneofthesestates,andthebluearrowsthefluctuations,whichcandrivethesystemtohigherenergies.Ifthefluctuationsarelargeenough,ortheenergybarrier ( )U∆ lowenough,thesystemcanjumptotheleftmostwellandswitchstates.(B)Timeevolutionoftheamountsofaproteinforasinglecellintwodifferentcases.Therearetwoclearlydefinedstates,ahighconcentrationstateat270proteincopiesandalowconcentrationstateat50copies.Thecellsswitchfromonestatetotheother.Notethatthetransitionsareveryfastandthatthesystemspendsmostofitstimearoundoneofthetwostablestates.(C)Evolutionovertimeoftheconcentrationsofaproteinofinterestinacellculture,asshowninahistogram.Whenasubpopulationinoneofthestatesfromanoriginallybistablepopulationisseparatedandlefttoevolveovertime,stochasticswitchingallowstherecoveryofthetwostates.Thecellsinapopulationareshownontheright.Notehowonecellmayswitchstatesmorethanonetime.PanelsB and Caresimulationsofamutualinhibitionsystem,simulatedthroughtheGillespiealgorithm,whichallowsexactsimulationsbasedonthetheoreticaldescriptionofdiscretestochasticsystemsintheformofmasterequations.
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differenttypesofbacteria[24].Fluctuations inthenumberof molecules can drive large heterogeneities among cellsin differentways. One is through positive feedback,whichcandrive themolecule tobepresentateitherhighor lowconcentrations. These two concentration states can beunderstood,atleastconceptually,asfreeenergyminimaandareseparatedbyanenergybarrier[1].Dissipationdrivesthemolecularconcentrationtoreachoneofthesetwostatesandremainthereforeverafter.Whichconcentrationisachieveddependsontheinitialstate;thatis,onwhichconcentrationwaspresentinitially.Thisscenariochangeswhenwetakeintoaccountthattherearefluctuations.Theyprovidetheenergyrequired to surpass the energy barrier that separates thestates,allowingaswitchfromalowtoahighconcentrationorviceversa(Fig.4).
An example of heterogeneous cell populations comesfromexperimentsusingmouseembryonicstemcells (ESC),which in culture express pluripotency factor NANOG in ahighly stochastic manner [8]. NANOG allows ESCs to self-renew and to maintain their pluripotency. When NANOGlevels of individual ESCs in a culture are measured, thedistributionofvaluesisverybroad.Ifcellswith,forinstance,low NANOG expression are selected, separated from theothers,andallowedtodivideovertime,measurementsshowthat the very broad distribution of NANOG concentrationsis eventually recovered.Hence, somecells, despite initiallybeing in the lowNANOG concentration state, have clearlyswitched and now express very high concentrations ofNANOG. Whether this stochastic switching correspondsto bistable or other type of dynamics is a current topic ofresearch.
A role of fluctuations in multicellular development hasbeenproposedforcellsthatneedtoestablishapatternthatisnot spatiallyorderedbut, instead,onlyneeds topreservecertainproportionsofdifferenttypesofcells,randomlyspacedaroundthetissue.Astochasticdecisionmechanismhasbeenproposedforprocessessuchasthedifferentiationofdifferentphotoreceptorsintheretinaofhumansandflies,orofolfactorycells in themouse [17].Mice have 1000 olfactory proteins,with only one expressed in any given cell to avoid sensoryconfusion. Hence, initially equivalent cells become distinct,reachingoneof1000differentstates.Thishasbeenproposedtobeaccomplishedbytheactivationofoneolfactoryproteintypestochasticallyandsubsequentinhibitionofalltheotherremainingtypesofolfactoryproteins.Inaddition,fluctuationsofmolecularcomponentscanbeexpectedtotriggerpatternsarising from interacting self-organizing dynamics such asreaction-diffusionandlateralinhibition.
Ourknowledgeontheeffectandroleoffluctuations indevelopmentalprocesses is still limited.However, researchin physics over the last few decades has evidenced thatnonlinear systems can take advantage of fluctuations[22]. Thus, it is to be expected that developingorganisms,whichexhibithighlynonlineardynamicsandaresubjecttofluctuations,profitfromthemaswell.Theconceptsandtoolstostudythistopichavealreadybeendevelopedbyphysicistsandbiologists,andtheresultsshouldsoonbeavailable.
Conclusions
The development of multicellular organisms is subject tothe physical laws that governNature. It is indeed becausecellsliveoutofequilibriumthattheyareabletocreatethemyriadofrichandcomplexstructuresthatformmulticellularorganisms. Insights have been gained into some of themolecular gene regulatory and signalingmechanisms usedbycellsinthespatiallyandtemporallycoordinatedprocessesthat allow them to become distinct in an organized andreproducible manner. These processes require nonlinearresponsesanddynamics.Previously,developmentwasmostlyunderstood as a succession of stationary states andmanyaspectswere described through averages overmany cells.However,we nowhave strong evidence that developmentis a highly dynamicprocess and that cellular dynamics arestrongly stochastic. Althoughmany technical limitations toadvancing our knowledge remain, new data are expectedthatwill reveal the highly complex and dynamic nature ofdevelopingorganisms.Asphysicists,weexpect tocontinuetoworktogetherwithbiologiststodefinetheprinciplesthatgovernmulticellularorganismdevelopment.
Competing interests. None declared
Acknowledgements. The authors acknowledge financial support byproject FIS2012-37655-C02-02 by the Spanish Ministry de Economy andCompetitivenessand2014SGR878fromtheGeneralitatdeCatalunya.
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About the image on the first page of this article. ThisphotographwasmadebyProf.DouglasZook(BostonUniversity)forhisbookEarth Gazes Back [www.douglaszookphotography.com].Seethearticle“Reflections:Theenduringsymbiosisbetweenartandscience,”byD.Zook,onpages249-251ofthis issue [http://revistes.iec.cat/index.php/CtS/article/view/142178/141126].This thematic issueon “Non-equilibriumphysics” canbeunloaded inISSUUformatandtheindividualarticlescanbefoundintheInstituteforCatalanStudiesjournals’repository[www.cat-science.cat;http://revistes.iec.cat/contributions].
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