Mechanisms of developmental robustness

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Mechanisms*of*developmental*robustness" " Vitaly"V."Gursky1,*,"Svetlana"Yu."Surkova2,"Maria"G."Samsonova2" " 1" Theoretical"Department,"Ioffe"PhysicalBTechnical"Institute"of"the"Russian"Academy"of"Sciences," St."Petersburg,"194021"Russia," 2" Department"of"Computational"Biology,"Center"for"Advanced"Studies,"St."Petersburg"State" Polytechnic"University,"St."Petersburg,"195259"Russia" " *" Corresponding"author:"[email protected]" " Abstract" " We"present"a"review"of"noise"buffering"mechanisms"responsible"for"developmental"robustness." We"focus"on"functions"of"chaperone"Hsp90,"miRNA,"and"crossBregulation"of"gap"genes"in" Drosophila."The"noise"buffering"mechanisms"associated"with"these"functions"represent"specific" examples"of"the"developmental"canalization,"reducing"the"phenotypical"variability"in"presence" of"either"genetic"or"environmental"perturbations."We"demonstrate"that"robustness"often" appears"as"a"function"of"a"network"of"interacting"elements"and"that"the"system"level"approach" is"needed"to"understand"the"mechanisms"of"noise"filtering." " Keywords:"systems"biology;"development;"robustness;"canalization;"Hsp90;"miRNA;"gap"genes" " Introduction" " Biological"organisms"exhibit"robustness"in"the"face"of"environmental"perturbations"and" potential"lesions"such"as"mutations."Throughout"evolution,"there"has"been"a"constant"selection" for"inherited"mechanisms"that"are"able"to"keep"a"trait"constant"and"reproduce"stereotyped" phenotypic"outcomes."Genetic"buffering"is"a"term"coined"to"describe"these"mechanisms."In"the" literature"robustness"and"canalization"are"effectively"used"as"synonyms"of"genetic"buffering," however"evolutionary"nomenclature"distinguishes"these"terms"and"understands"under" canalization"genetic"buffering"that"has"evolved"under"natural"selection"in"order"to"stabilize"the" phenotype"and"decreases"its"variability."Canalization"allows"the"accumulation"of"‘cryptic"genetic" variation’"caused"by"mutations"that"do"not"affect"the"phenotype."Canalized"traits"are" phenotypically"expressed"only"in"particular"environments"or"genetic"backgrounds"and"become" available"for"natural"selection,"a"mechanism"that"can"lead"to"the"assimilation"of"novel"traits." The"idea"of"canalization"is"first"introduced"in"the"1940s,"by"the"developmental"biologist" and"geneticist"C.H."Waddington."He"noted"that"as"opposed"to"mutants,"wild"type"organisms"are" able"to"suppress"phenotypic"variation"caused"by"genetic"and"environmental"changes."In"order" to"explain"this"fact"C.H."Waddington"hypothesized"that"in"organism"under"natural"selection"the" developmental"processes"are"canalized:"since"cells"make"discrete"fate"decisions"there"must"only" be"a"finite"number"of"distinct"developmental"trajectories"possible"and"each"such"trajectory,"

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called"a"chreod,"must"be"stable"against"small"perturbations"(Waddington"1962;"Waddington" 1940;"Waddington"1957)." A"metaphorical"representation"of"canalization,"the"C.H."Waddington"epigenetic" landscape,"represents"a"developing"system"as"a"mountainous"landscape"down"which"a"ball"rolls." The"ball"represents"a"cell"and"the"selection"of"developmental"pathway"happens"at"each"valley" branchpoint"by"the"action"of"embryonic"inducing"factors"or"genes."Each"landscape"valley" corresponds"to"а"collection"of"similar"developmental"trajectories."If"to"give"the"ball"a"little"push" towards"the"hill"slope,"it"will"return"to"the"same"valley"as"before,"but"will"end"up"in"another" point"than"before"the"push."This"analogy"allows"us"to"understand"what"canalization"means:"up" to"a"certain"threshold,"any"genetic"variation"or"environmental"noise"will"be"‘buffered’"and"not" affect"development,"but"above"this"threshold,"the"cell"would"flip"over"into"another" developmental"pathway."Contrary"to"homeostasis,"which"denotes"the"stability"of"the" developmental"system"state,"Waddington"coined"homeoresis"as"a"term"to"describe"the" robustness"of"developmental"pathways*(Waddington"1957)."" Canalization"is"thought"to"be"mediated"by"the"buffering"activity"of"specific"genes;" however,"with"the"one"notable"exception"of"hsp90,"there"have"been"no"facts"successfully" explaining"the"molecular"mechanisms"of"canalization"as"a"result"of"one"gene"action."On"the" contrary,"new"data"point"that"canalization"emerges"at"the"level"of"gene"regulatory"networks" (Wagner"1996;"Bergman"and"Siegal"2003;"Siegal"and"Bergman"2002)."For"example,"a"biological" system"can"be"robust"if"the"underlying"genetic"network"has"redundant"interactions"–"where"one" interaction"can"compensate"for"the"loss"of"another"–"and/or"if"the"system"has"distributed" robustness"–"when"mutations"in"one"pathway"can"be"compensated"by"other"processes"in"the" system"(Wagner"2005)."It"is"evident"that"if"robustness"is"indeed"an"emergent"property"of"a" genetic"network,"we"would"expect"it"to"break"down"in"mutants"affecting"factors"other"than" Hsp90."Each"mutation"in"a"system—and"in"particular"those"affecting"regulatory"factors—can" potentially"reduce"redundancy"and"distributed"robustness,"and"render"the"system"more" vulnerable"to"further"perturbations."Indeed,"Levy"and"Siegal"(2008)"identified"over"300"mutants" in"yeast,"which"exhibit"reduced"robustness"to"environmental"fluctuations,"and"Bergman"and" Siegal"(2003)"observed"widespread"loss"of"canalization"when"they"simulated"large"numbers"of" single"(oneBstep)"mutants"of"evolved"robust"gene"regulatory"networks."" Thus,"the"mechanism"of"canalization"and"biological"robustness"remains"controversial." However,"this"problem"is"at"the"heart"of"biology"research"over"the"past"decade,"and"the"number" of"publications"on"this"topic"is"growing"rapidly."Here,"we"summarize"the"current"state"of" knowledge"about"several"genetic"buffering"mechanisms.* * Mechanisms*underlying*canalization*by*molecular*chaperone*Hsp90" " An"important"implication"of"the"canalization"concept"is"that"the"buffering"mechanism"could"be" genetically"controlled."Studies"on"Hsp90,"a"molecular"chaperone"involved"in"several"cellular" processes"and"development"pathways,"indicate"that"it"is"a"possible"molecular"mechanism"for" canalization"and"genetic"assimilation." Hsp90"is"unusual"among"chaperones"due"to"the"diverse"but"selective"nature"of"its" substrates,"most"of"which"are"key"regulators"of"growth"and"development."Hsp90"itself"is"one"of"

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the"most"abundant"cytosolic"proteins"in"eukaryotes,"even"in"the"absence"of"stress."In"all"tested" eukaryotes,"it"is"essential"for"viability"and"further"induced"during"stressful"conditions"(Buchner" 1999;"Picard"2002;"Young"et"al."2001)."Recent"studies"revealed"an"unexpected"consequence"of" the"Hsp90’s"central"role"regulating"growth"and"development." When"Hsp90’s"function"was"impaired,"different"developmental"pathways"became" sensitive"to"the"effects"of"cryptic"genetic"variation."In"the"fly"Drosophila*melanogaster" (Rutherford"and"Lindquist"1998)"and"the"plant"Arabidopsis*thaliana"(Queitch"et"al."2002),"an" extraordinary"variety"of"phenotypes"were"observed"when"Hsp90"function"was"impaired"by" pharmacological"inhibition"or"genetic"manipulation,"or"its"capacity"was"taxed"by"moderate" environmental"stress"(Sangster"et"al."2004)."Different"individuals"had"different"defects," collectively"affecting"virtually"every"visible"structure."Many"manipulations"could"produce" pleiotropic"phenotypes"in"different"genetic"backgrounds,"but"the"number"and"variety"of" phenotypes"revealed"was"remarkable."Most"importantly,"the"particular"phenotype"depends"on" the"individual’s"genetic"background"in"both"Arabidopsis*and"Drosophila"(Rutherford"and" Lindquist"1998;"Queitch"et"al."2002)."Surprisingly,"the"Hsp90Bdependent"traits"quickly"became" independent"of"Hsp90"deficiency,"could"be"inherited"in"later"generations"and"could"be"subject" to"natural"selection."This"finding"was"fundamental"to"the"possible"evolutionary"consequences"of" the"Hsp90"buffering"(Rutherford"and"Lindquist"1998).""" In"Drosophila,"Hsp90"is"encoded"by"the"Hsp83"gene,"which"has"both"maternal"and" zygotic"expression."The"maternal"Hsp83"RNA"is"uniformly"distributed"and"present"at"high"level" until"cleavage"cycle"6,"forms"the"gradient"decreasing"towards"the"anterior"at"cleavage"cycle"7" and"is"only"detected"in"the"pole"cells"by"the"syncytial"blastoderm"stage."At"the"blastoderm" stage,"the"zygotic"transcription"of"this"gene"is"restricted"to"the"anterior"third"of"the"embryo"and" is"regulated"by"Bcd"(Ding"et"al."1993)."" In"vertebrates,"Hsp90"is"also"able"to"buffer"hidden"genetic"variation."Zebrafish"studies" imply"that"mild"perturbation"of"Hsp90"function"at"critical"developmental"stages"may"underpin" the"variable"penetrance"and"expressivity"of"many"developmental"anomalies"(Yeyati"et"al."2007)." Sollars"et"al."expanded"the"scope"of"Hsp90"buffering"to"epigenetically"determined"traits." It"was"shown"that"the"reduced"activity"of"Hsp90"induces"a"heritably"altered"chromatin"state," thus"suggesting"an"‘epigenetic"canalization"model’"(Sollars"et"al."2003)."Later"study"proved"that" a"chromatin"regulatory"network"interacts"with"chaperone"Hsp90"(Gilbert"et"al."2007)." Thus,"Hsp90"acts"as"a"buffer"or"capacitor"of"genetic"variation,"which"accumulates"under" normal"circumstances"with"little"phenotypic"consequence"and"is"revealed"in"times"of"stress."This" evolutionarily"conserved"buffering"mechanism"provides"the"genetic"material"for"natural" selection." Above"studies"suggest"that"the"chaperoneBmediated"storage"and"release"of"genetic" variation"is"rooted"in"proteinBfolding"phenomenon,"which"crucially"affects"the"trajectory"from" genotype"to"phenotype"(Sangster"et"al."2004)."However,"recent"discoveries"proposed"an" additional,"perhaps"alternative,"explanation"for"a"concrete"mechanism"underlying"canalization." It"was"shown"that"in"Drosophila"functional"alterations"of"Hsp90"affect"the"PiwiBinteracting"RNA" silencing"mechanism"leading"to"transposon"activation"and"the"induction"of"morphological" mutants"(Specchia"et"al."2010)."Piwi"are"RNABbinding"proteins"that"are"produced"in"the"germ"

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cells,"use"piRNAs"to"silence"transposons"and"other"parasitic"DNAs"(Lin"2007)"and"are"implicated" in"epigenetic"regulation"(Yin"and"Lin"2007)."" Further"study"validated"the"existence"of"a"piRNABpathway–dependent"mechanism"for" preventing"phenotypic"variation"(Gangaraju"et"al."2011)."A"protein"complex"composed"of" Hsp90,"Piwi"and"Hop,"the"Hsp70/Hsp90"organizing"protein"homolog,"was"isolated."It"was"shown" that"in"Drosophila"Hsp90"and"Hop"regulate"the"piRNA"pathway"through"Piwi."Hence,"postB translational"regulation"of"Piwi"by"Hsp90"and"Hop"may"allow"Piwi"to"both"suppress"the" generation"of"new"genotypes"and"epigenetically"silence"the"expression"of"existing"genetic" variants."This"study"also"showed"that"Piwi"acts"at"two"distinct"phases"of"fly"development"in" mediating"phenotypic"capacitance."First,"maternal"Piwi"plays"a"direct"role"in"canalization"and/or" suppresses"transposonBinduced"mutagenesis"during"embryogenesis."This"allows"the"inheritance" of"correct"epigenetic"and"genetic"codes"from"parental"cells"to"daughter"cells,"thereby"ensuring" the"robustness"of"the"developmental"programs."Afterwards,"zygotic"Piwi"is"required"for" maintaining"the"inherited"developmental"programs"during"subsequent"stages"of"development" (Gangaraju"et"al."2011).* * Noise*buffering*by*miRNA:*the*role*of*feedBforward*loops* * One"of"the"regulatory"mechanisms"of"gene"expression"extensively"studied"in"the"last"years" involves"microRNA"(miRNA)"(Bushati"and"Cohen"2007;"Bartel"2009)."These"are"small"regulatory" molecules"which"bind"a"recognition"sequence"of"the"target"proteinBcoding"mRNAs"and"preclude" them"from"translation."Attached"to"mRNA"molecules,"miRNAs"can"make"them"either"unable"for" translation"or"destabilize"them,"thus"decreasing"the"translation"rate"or"increasing"the" degradation"rate,"respectively"(ValenciaBSanchez"et"al."2006)."miRNAs"therefore"provide"a" means"for"gene"repression"at"the"postBtranscriptional"level." " Mutants"for"miRNABcoding"genes"mostly"show"no"essential"phenotypic"defects"in" normal"conditions,"but"do"so"under"stress."In"addition"to"various"case"studies"of"the"miRNA" function"in"eukaryotes,"these"results"led"to"a"hypothesis"that"miRNAs"participate"in"robustness" mechanisms"and,"in"particular,"provide"the"genetic"basis"for"canalization"of"developmental" trajectories"(Hornstein"and"Shomron"2006;"Herranz"and"Cohen"2010)."miRNAs"help"to"buffer" the"genetic"noise"in"the"regulatory"systems"and"reduce"the"phenotypic"variability." It"is"realized"now"that"this"function"of"miRNA"can"be"explained"only"via"understanding"its" role"in"the"regulatory"network"comprising"miRNA"interacting"with"transcription"factors"(TFs)." These"two"types"of"the"gene"expression"regulators"exhibit"a"strong"tendency"to"regulate"each" other"and"coBregulate"other"genes"(Yu"et"al."2008;"Martinez"and"Walhout"2009)."Conserved" miRNABbinding"sequences"were"predicted"in"more"than"oneBthird"of"all"genes"(Hornstein"and" Shomron"2006)."miRNA"binding"sites"in"3’BUTR"regions"of"genes"encoding"TFs"are" overrepresented"comparing"to"other"proteinBcoding"genes,"and,"vice"versa,"miRNABcoding" genes"have"more"TF"binding"sites"in"their"promoters"than"do"proteinBcoding"genes"(Yu"et"al." 2008)." The"miRNA"function"can"be"dissected"from"the"integrated"miRNABTF"regulatory"network" by"analyzing"the"network"motifs,"which"are"the"interaction"patterns"occurring"in"the"network" more"often"than"expected"from"a"random"graph"having"same"connectivity"properties"(Milo"et"

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al."2002;"Alon"2007)."The"miRNA"mediated"feedBforward"loops"(FFLs)"present"one"of"the" significantly"overrepresented"motifs"comprising"the"coordinated"action"of"TF"and"miRNA"(Fig."1)" (Shalgi"et"al."2007;"Tsang"et"al."2007;"Re"et"al."2009)."The"upstream"TF"regulates"the"target"gene" in"a"FFL"along"two"parallel"pathways,"directly"and"by"interacting"with"miRNA,"which"represses" the"target"gene."A"pathway"has"a"sign,"defined"as"positive"if"the"number"of"negative"interactions" in"the"pathway"is"either"even"or"zero,"and"negative"otherwise."Positive"pathways"provide"the" net"positive"regulation"of"the"target"gene"by"the"upstream"regulator,"no"matter"how"many" intermediate"interactions"it"includes,"and"negative"pathways"lead"to"the"negative"regulation."A" FFL"is"called"coherent"if"the"signs"of"its"parallel"pathways"are"the"same,"i.e."if"the"upstream" regulator"performs"the"same"net"result"along"the"two"pathways,"and"incoherent"otherwise." Both"coherent"and"incoherent"miRNABmediated"FFLs"are"capable"to"dampen"molecular" fluctuations"in"the"network."For"the"coherent"FFLs"(Fig."1A),"the"noise"buffering"mechanism"is" based"on"the"fact"that"the"dynamics"of"the"target"gene"expression"in"these"FFLs"has"a"delayed" response"to"activation"or"deactivation"of"the"upstream"TF."The"delay"guarantees"that"shortB lived"pulses"(fluctuations)"in"the"TF"level"are"filtered,"so"that"the"target"gene"will"switch"to"a" new"state"only"in"response"to"sustained"expression"of"the"TF"(Alon"2007;"Mangan"and"Alon" 2003)." The"logic"of"the"delay"can"easily"be"explained"for"the"coherent"FFL"with"both"pathways" negative"as"an"example"(Fig."1B)."The"upstream"TF"inhibits"the"target"expression"via"two" channels,"directly"and"by"activating"miRNA"as"the"additional"repressor."The"presence"of"this" additional"repressor"guarantees"that"a"shortBlived"decrease"in"the"upstream"TF"level"will"not" stop"repression"on"the"target."However,"if"the"decrease"is"sustained,"e.g."serving"as"a"new" developmental"cue,"the"activation"of"the"miRNA"gene"will"eventually"be"shut"down,"thus"closing" both"repression"channels"and"allowing"the"target"to"switch"to"the"on"state."This"noise"buffering" mechanism"is"utilized"by"miR47"mediated"coherent"FFL"in"Drosophila"photoreceptor" differentiation"(Fig."1C)"(Li"et"al."2009;"Herranz"and"Cohen"2010)."The"expression"of"Yan,"a" transcription"factor"essential"for"the"process,"is"buffered"in"this"FFL"against"fluctuations"in"the" upstream"TF"PntBP1." The"parallel"pathways"in"miRNABmediated"incoherent"FFLs"have"different"signs,"so"that" the"upstream"TF"activates"the"target"along"one"branch"and"represses"via"miRNA"along"the"other" (Fig."1D)."The"activation"of"the"upstream"TF"in"this"case"leads"to"a"pulseBlike"dynamics"of"the" target"followed"by"a"lower"level"steady"state"as"compared"with"the"simple"activation"case"(Alon" 2007)."Therefore,"one"of"the"functions"of"miRNA"in"the"incoherent"FFL"is"to"fineBtune"the"target" steady"state."For"example,"it"was"shown"that"miR48"provides"exactly"this"function"in"regulation" of"the"atrophin*gene"in"Drosophila,"keeping"the"atrophin*level"in"the"correct"range"(Karres"et"al." 2007)." In"order"to"clarify"the"noise"buffering"function"of"miRNABmediated"incoherent"FFLs,"the" authors"of"Osella"et"al."2011"investigated"a"stochastic"model"of"the"target"gene"expression"in" this"FFL"and"compared"results"to"similar"models"of"the"simple"activation"pathway"(no"miRNA" branch)"and"the"open"circuit"(independent"upstream"activators"of"the"target"gene"and"miRNA" instead"of"one"common"upstream"activator)."They"calculated"how"the"gene"expression"noise" appearing"due"to"stochastic"nature"of"transcription,"translation,"and"degradation"steps"of"the" process"propagates"to"the"target"gene."The"results"revealed"that"the"target"gene"expression"

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noise"in"the"FFL"is"much"lower"than"in"the"cases"of"the"simple"regulation"and"open"circuit"(Fig." 1E)."Thus,"the"introduction"of"the"miRNA"reduces"the"relative"fluctuations"in"the"circuit."The" origin"of"this"noise"buffering"effect"is"in"the"fact"that,"in"response"to"the"upstream"TF" fluctuations,"the"target"mRNA"and"miRNA"concentrations"tend"to"vary"coherently"in"the"FFL," since"they"both"experience"activation"from"the"TF."As"a"consequence,"miRNAs"can"tune"the" target"protein"production"against"TF"fluctuations." As"an"example"of"miRNABmediated"incoherent"FFLs,"Fig."1F"shows"an"miR47Bmediated" circuit"participating"in"Drosophila"sense"organ"specification"(Li"et"al."2009;"Herranz"and"Cohen" 2010)."The"TF"Atonal"activates"expression"of"both"the"proneural"gene"E(spl)"and"miR47,"and"the" latter"translationally"inhibits"the"same"gene."The"dynamics"of"E(spl)"expression"has"a"form"of"a" pulse"followed"by"a"lower"level"of"steadyBstate"expression."The"noise"buffering"function"of"this" motif"is"particularly"important"as"the"pulseBlike"E(spl)*expression"serves"as"a"trigger"for"other" regulatory"events." Both"coherent"and"incoherent"miRNABmediated"FFLs"are"common"motives"in"many" regulatory"networks,"which"function"at"different"stages"of"development"and"organism" functioning"(Hornstein"and"Shomron"2006)."When"a"miRNA"participates"in"a"coherent"FFL,"it" exhibits"an"expression"pattern"mutually"exclusive"with"the"pattern"for"its"target,"with"high" miRNA"levels"coexistent"with"low"target"expression"levels"or"vice"versa."Noise"reduction"with" the"help"of"the"incoherent"FFL"is"associated"with"coexpression"of"the"miRNA"and"its"target."One" of"the"miRNAs"showing"both"types"of"the"expression"pattern"is"miR4iab4445p"(iab4),"a"HoxB cluster"related"miRNA"mediating"expression"of"the"homeobox"transcription"factor"Ubx"in"the" developing"Drosophila*melanogaster"embryo"(Ronshaugen"et"al."2005,"Hornstein"and"Shomron" 2006)."During"the"preBgastrulation"period,"the"expression"domain"of"iab4"is"adjacent"to"the" stripe"of"Ubx"expression."After"gastrulation,"a"new"domain"appears"in"which"iab4"and"Ubx"are" coexpressed."These"different"types"of"expression"patterns"can"be"explained"by"different"FFLs" comprising"iab4." " Noise*buffering*as*an*emergent*property*of*networks:*Variance*reduction*by*crossBregulation* of*gap*genes*in*Drosophila*" " The"above"examples"show"that"the"noiseBreduction"mechanism"associated"with"miRNA"action" essentially"can"be"elucidated"by"analyzing"functions"of"corresponding"FFLs."As"FFLs"present" rather"simple"motifs,"their"functions"can"be"understood"intuitively."The"noise"reduction" mechanism"can"also"exist"as"a"function"of"more"complex"(highly"wired)"networks,"although"it" may"be"less"intuitive"due"to"the"network"complexity."A"relevant"example"of"this"case"is"the" Drosophila"gap"gene"network"(Jaeger"2011)." " The"gap"genes"form"a"subclass"of"the"zygotic"segmentation"genes"expressed"in"the"form" of"partially"overlapping"spatial"patterns"(domains)"along"the"anteriorBposterior"axis"of"the" embryo"(Fig."2B)."These"expression"patterns"determine"a"segment"prepattern"during"the"early" stages"of"the"Drosophila"embryo"(Akam"1987)."The"quantitative"data"shows"a"significant" variation"in"the"segmentation"gene"expression"patterns"in"individual"embryos"at"the"early" developmental"stages,"which"significantly"decreases"by"the"onset"of"gastrulation"(Surkova"et"al." 2008)."As"the"positions"of"the"segmentation"gene"expression"patterns"provide"information"for"

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placement"of"future"body"segments,"the"positional"variation"of"these"patterns"is"of"special" importance."The"product"of"the"maternal"bcd"gene"in"the"embryo"was"shown"to"be"a" morphogen,"providing"an"initial"cue"for"positioning"of"the"gap"gene"patterns."However,"the" positional"error"in"the"gap"gene"patterns"is"lower"than"that"in"the"Bcd"one."This"manifests"a" filtration"effect"(canalization)"which"consists"in"reduction"of"the"Bcd"variability"at"the"level"of" zygotic"genes"(Houchmandzadeh"et"al."2002;"Gregor"et"al."2007;"Hardway"et"al."2008;"He"et"al." 2008)."This"effect"was"originally"formulated"and"usually"discussed"for"the"case"of"the"gap"gene" hb"response"to"the"noisy"signal"from"the"morphogen"Bcd"(Fig."2A,D)."However,"similar"filtration" was"demonstrated"for"other"gap"genes"both"experimentally"(Surkova"et"al."2008)"and"in"a" mathematical"model"(Manu"et"al."2009a)." " There"are"different"estimates"for"the"magnitude"of"the"filtration"effect"in"the"literature," arising"from"different"measurements"of"the"Bcd"and"Hb"positional"variations"(the"case"of"the" FlyEx"data"is"shown"in"Fig."2A,D;"Manu"et"al."2009a)."The"largest"ratio"of"these"variations"was" suggested"in"ref."Houchmandzadeh"et"al."2002,"but"it"was"shown"later"that"a"significant"part"of" the"variance"should"be"explained"by"a"specific"normalization"method"used"by"the"authors" (Gregor"et"al."2007)."Comparing"BcdBGFP"data"from"live"embryos"and"Hb"data"from"fixed" immunostained"embryos"and"applying"a"multiBstep"procedure"to"estimate"measurement"noise" in"the"embryo"images,"Gregor"et"al."obtained"approximately"the"same"positional"variation"for" Bcd"and"Hb"(Gregor"et"al."2007)."The"authors"thus"stated"the"absence"of"the"filtration"effect," favoring"the"precisionist"view"against"the"noisyBinputBrobustBoutput"hypothesis"in"the"problem" of"transmission"of"the"positional"information"from"Bcd"to"the"level"of"the"zygotic"genes." However,"it"follows"from"later"study"of"this"group"that"the"live"imaged"BcdBGFP"data"gives" incorrect"estimates"for"the"true"Bcd"nuclear"concentration"because"of"delayed"GFP"maturation" (Little"et"al."2011),"and"this"fact"questions"the"strong"conclusions"of"ref."Gregor"et"al."2007." Other"studies"reported"that"the"Bcd"gradient"is"precise"but"still"has"positional"errors"that"are" greater"than"Hb"boundary"variations"(He"et"al."2008)."Our"personal"understanding"is"that"the" filtration"effect"exists,"but"has"a"smaller"magnitude"than"originally"proposed"in"ref." Houchmandzadeh"et"al."2002." " Recent"findings"show"that"the"filtration"of"the"Bcd"variability"in"the"gap"gene"system" results"from"crossBregulation"of"gap"genes"in"the"network"(Manu"et"al."2009a)."It"follows"from" the"fact"that"the"mathematical"model"predicts,"for"example,"for"hb"expression"the"positional" variance"almost"equal"to"that"of"Bcd"when"regulatory"effects"on"the"hb"gene"by"other"gap"genes" are"excluded."The"experimental"results"strongly"support"the"model"and"rule"out"a"picture"in" which"Bcd"provides"the"sole"input"to"hb."Namely,"in"Kr;kni"double"mutants"the"standard" deviation"of"the"location"of"the"anterior"hb"border"doubles"and"that"of"the"posterior"border"of" the"anterior"gt*domain"increases"significantly"(Manu"et"al."2009a)."The"gap"gene"network" topology"assessed"by"modeling"exhibits"three"features:"activation"from"maternal"factors"(Bcd" and"Cad),"selfBactivation,"and"mutual"repression"(Fig."2C)"(Jaeger"et"al."2004;"Manu"et"al." 2009a)."The"analysis"of"regulatory"interactions"in"the"model"showed"that"each"gap"gene" expression"domain"forms"under"the"influence"of"selfBactivation,"an"additional"activator"(Bcd"or" Cad),"and"two"repressors"among"the"other"gap"genes."For"example,"the"posterior"border"of"the" anterior"hb"domain"is"mostly"under"control"of"selfBactivation,"Bcd"as"an"activator,"and"gap" proteins"Kr"and"Kni"as"repressors"(Jaeger"2011)."The"positions"of"gap"domains"are"a"result"of"the"

7" "

balance"between"regulatory"inputs"from"activators"and"repressors."Simulation"of"the"Bcd" variability"in"the"model"revealed"that"the"activating"and"repressing"inputs"correlate"with"each" other"at"gap"domain"positions."The"hb"border"has"variable"position"in"the"model"solutions" corresponding"to"various"spatial"profiles"of"the"Bcd"concentration"given"as"an"external"input"in" the"model"equations."More"posterior"positions"of"this"border"exhibit"higher"levels"of"hb" activation,"but"this"activation"is"compensated"by"higher"repression"levels"(Fig."2E)."Therefore," crossBrepression"of"gap"genes"provides"a"mechanism"effectively"filtering"the"noise"in"the" morphogen"and"leading"to"a"more"stable"arrangement"of"gap"domain"borders."This"mechanism" also"explains"robustness"of"gap"domains"to"variation"of"the"embryo"size"(Manu"et"al."2009a;" Vakulenko"et"al."2009)." " The"regulatory"interactions"in"the"model"cause"the"state"of"the"system"to"approach"a" stable"steady"state,"also"called"an"attractor."The"observed"noise"buffering"mechanism"can"be" explained"in"terms"of"attractors"and"geometry"of"their"attraction"basins"in"the"phase"space"of" the"dynamical"system."High"variance"of"gap"gene"patterns"at"early"developmental"stages"is" dynamically"reduced"during"the"preBgastrulation"period"by"action"of"attractors"(Manu"et"al." 2009b)."The"expression"patterns"from"the"early"embryos"can"be"interpreted"as"the"initial" conditions"in"the"dynamical"system,"giving"rise"to"the"gap"gene"expression"trajectories" converging"to"same"steady"states"by"later"stages."For"most"gap"genes,"their"expression"domain" borders"in"the"model"solution"appear"because"the"solution"switches"from"one"attractor"to" another"in"a"neighborhood"of"the"border"position."For"example,"the"hb"border"forms"as"a"switch" from"an"attractor"with"the"Hb"component"at"ON"state"to"an"attractor"with"the"HbBOFF"state." Calculating"the"boundary"between"attraction"basins"for"these"two"attractors"as"a"function"of" spatial"position,"one"can"find"that,"as"the"Bcd"profile"is"varied,"the"hb"border"position"correlates" with"the"intersection"point"between"this"boundary"and"the"initial"Hb"concentration"profile" (Gursky"et"al."2011)."As"a"consequence,"the"range"of"hb"positional"variation"is"determined"by" the"corresponding"range"for"the"intersection"points"(Fig."2F)."The"latter"essentially"depends"on"a" geometrical"configuration"in"which"the"initial"Hb"profile"and"the"basin"boundaries"relate"to"each" other:"the"range"is"minimal"when"the"Hb"profile"and"the"boundaries"have"opposite"dependence" on"the"spatial"variable"(decreasing"Hb"profile"against"increasing"boundary,"or"vice"versa),"and" tend"to"increase"otherwise"(Fig."2G,H)."Therefore,"the"noise"buffering"mechanism"in"the"gap" circuit"can"be"related"to"the"purely"geometrical"properties"of"the"phase"space"objects." The"idea"that"the"robustness"of"biological"systems"emerges"as"a"result"of"gene" interactions"is"also"supported"by"data"obtained"in"Lott"et"al"(2007)."These"authors"investigated" whether"the"establishment"of"segmental"boundaries,"measured"by"the"expression"of"the"gap" genes"giant"and"Kruppel"and"the"pairBrule"gene"even4skipped,"is"buffered"developmentally" against"genetic"variability"for"egg"(embryo)"length"both"within"and"between"species."Two"wildB derived"strains"of"D.*melanogaster"were"identified,"whose"eggs"differ"by"25%"in"length"when" reared"under"identical"conditions."These"two"lines,"a"D.*melanogaster"laboratory"stock"(w1118)," and"offspring"from"crosses"between"the"lines"all"exhibit"precise"scaling"in"the"placement"of"gap" and"pairBrule"gene"expression"along"the"anterior–posterior"axis"in"relation"to"embryo"length."" The"absolute"stripe"positioning"and"egg"size"are"maternally"inherited"phenotypes,"and"it"was" shown"by"authors"that"the"buffering"of"the"segmentation"phenotype"with"respect"to"embryo" length"is"a"polygenetic"trait"which"also"maternally"inherited."These"results"indicate"that"the"

8" "

robustness"of"pattern"formation"in"relation"to"the"embryo"length"variation"is"under"control"of" genetic"network"composed"of"maternally"derived"determinants."" " " Hidden*mechanisms:*Dynamical*role*of*cell*divisions" " As"the"state"of"a"multicellular"system"is"dictated"by"the"state"of"each"cell,"the"full"state"space"for" such"system"may"have"extremely"great"dimensions."Development"of"the"system"can"be" represented"as"a"trajectory"inside"this"space"going"from"an"initial"to"a"final"state"(attractor)." When"the"total"number"of"attractors"is"large,"the"correct"choice"of"an"appropriate"one"becomes" an"important"issue."Attractors"can"be"numerous,"for"example,"when"the"coupling"between"cells" (cellBtoBcell"communication"via"signaling"or"molecular"transport)"is"weak:"the"attractor"of"the" full"system"in"this"case"is"most"probably"a"combination"of"single"cell"attractors,"providing" combinatorial"complexity"in"the"total"number"of"attractors"in"the"full"system."Many"possible" attractors"in"a"system"can"theoretically"be"related"to"the"property"of"evolvability."To"ensure" robust"development,"however,"mechanisms"should"exist"constraining"this"evolvability"and" helping"the"system"to"reliably"choose"a"proper"attractor"among"many"possible."Cell"divisions" may"provide"one"of"such"mechanisms"(Gursky"et"al."2006)." The"segmentation"network"in"Drosophila"provides"an"example"of"genes"whose" expression"lasts"through"several"nuclear"divisions"at"the"blastoderm"stage"of"development"(at" this"stage"the"Drosophila"embryo"is"a"syncytium,"and"nuclei"are"not"separated"by"cell" membranes)."The"state"variables"for"this"process"are"protein"concentrations"for"each"gap"gene" in"each"nucleus."The"dynamical"equations"for"such"gene"circuits"have"the"form"of"hybrid" systems"with"the"state"space"of"variable"dimension,"as"each"daughter"nucleus"appearing"after" division"adds"new"state"variables"to"the"system."The"complexity"of"the"final"phase"space"allows" the"model"to"have"many"stable"steady"states,"which"can"be"identified"as"the"potential"final" expression"patterns."However,"because"the"system"starts"in"a"space"of"smaller"dimension,"only" a"limited"number"of"these"steady"states"are"actually"accessible"to"the"system,"regardless"of"the" initial"state."Therefore,"presence"of"cell"divisions"as"a"background"for"gene"expression"helps"to" get"a"compromise"between"evolvability,"associated"with"the"richness"of"potential"attracting" states"at"later"cleavage"cycles,"and"robustness,"arisen"from"the"constraining"of"gene"expression" dynamics"to"a"limited"number"of"these"attracting"states"when"the"dynamics"starts"at"earlier" cleavage"cycles." This"dynamical"role"of"cell"divisions"is"illustrated"in"Fig."2I."The"expression"patterns"in"the" model"system"of"two"genes"are"stabilized"on"four"cells"and"have"form"of"one"of"twelve" attracting"states"shown"as"stars"in"the"figure."If"the"system"arrives"to"these"four"cells"by"cell" division,"selection"of"some"attractors"as"reachable"for"dynamics"takes"place"ruling"out"the" others."The"more"acts"of"division"happen,"the"less"number"of"attractors"are"reachable"for" dynamics"and,"hence,"less"variable"the"expression"patterns"can"be." " Two"factors"can"be"mentioned"underlying"the"mechanism"of"selection."First,"some" basins"of"attraction"are"inaccessible"due"to"symmetry"of"nuclear"divisions:"the"protein" concentrations"captured"by"two"daughter"nuclei"are"approximately"the"same,"or"follow"the" nuclear"pattern"for"the"protein"formed"in"the"embryo"right"before"the"cleavage."In"the"case"of"

9" "

the"Drosophila"early"development,"the"former"approximation"should"be"valid"at"later"cleavage" cycles,"when"dividing"nuclei"stay"close"enough"to"each"other,"and"the"latter"one"should"be"true" for"earlier"cleavage"cycles."In"both"cases,"the"protein"concentrations"in"daughter"nuclei"are"not" fully"stochastic,"and"this"fact"rules"out"many"states"of"the"system"right"after"the"cleavage"and" excludes"attractors"that"the"dynamics"from"these"states"leads"to"(Gursky"et"al."2006)."Second," the"dynamics"at"early"times"arranges"the"solution"trajectories"in"narrow"domains"in"the"phase" space"of"smaller"dimension,"such"that"the"attracting"sets"of"some"steady"states"are"not" captured"by"these"domains"when"the"system"proceeds"into"the"phase"space"of"higher" dimension"(Gursky"et"al."2006)."This"reduction"of"the"number"of"available"attractors"is"not" determined"by"a"certain"implementation"of"the"model"and"will"take"place"in"any"biological" system"exhibiting"pattern"formation"during"cell"division." " Conclusions" " We"presented"a"brief"overview"of"recent"experimental"and"theoretical"results"showing"how" noise"buffering"happens"in"development."This"review"is"far"from"being"complete,"as"we" concentrated"only"on"main"issues,"which"currently"are"under"extensive"discussion"and"on"our" own"input"in"this"field."" The"mechanisms"described"in"the"paper"can"be"related"to"the"developmental" canalization,"taking"into"account"various"interpretations"of"this"term"(Hornstein"and"Shomron" 2006)."The"Hsp90"and"miRNA"functions"provide"the"noise"buffering"mechanisms"under"classical" definition"of"canalization."They"form"the"genetic"mechanism"underlying"the"robustness"of" developmental"pathways."Hsp90’s"function"leads"to"accumulation"of"genetic"variations,"which" do"not"affect"the"phenotype"until"normal"conditions"change"to"stress."Similarly,"the"miRNA" action"is"essential"for"robust"functioning"of"various"cell"processes"and"manifests"itself"only"in" presence"of"stress"conditions."" In"contrast,"the"noise"filtration"by"crossBregulation"of"gap"genes"is"an"integral"property"of" the"gene"network"that"is"also"required"for"correct"formation"of"the"segmental"prepattern." However,"the"corresponding"mechanism"of"robustness"finely"fits"in"canalization"framework"via" the"general"analogy"with"the"Waddington’s"epigenetic"landscape."We"also"can"suggest"that"the" objects"for"natural"selection"in"this"case"would"be"the"regulatory"regions"of"gap"genes"that" concurrently"evolved"to"provide"for"strength"of"interaction"with"corresponding"transcription" factors"favoring"robust"pattering." Finally,"the"hypothetical"mechanism"associated"with"the"dynamical"role"of"cell"divisions" in"a"developing"system"can"be"linked"to"the"control"of"the"total"number"of"chreods"possible"for" this"system,"with"genes"controlling"the"mitosis"schedule"being"the"target"for"natural"selection" shaping"this"mechanism." The"above"examples"demonstrate"that"robustness"often"appears"as"a"function"of"a" network"of"interacting"elements"and"that"the"system"level"approach"is"needed"to"understand" the"mechanisms"of"noise"filtering."With"the"help"of"modeling,"one"can"sometimes"clarify"various" aspects"of"the"noise"buffering"mechanisms"in"terms"of"objects"in"the"phase"space"of"the"model." Such"a"multiBscale"view"on"the"problem"is"promising"for"understanding"fundamental"rules" governing"robust"development."

10" "

" Acknowledgments" The"study"was"supported"by"RFBR"grants"10B01B00627a,"11B01B00573a,"and"11B04B01162a"and" the"State"contract"N"14.740.11.0166"from"the"Russian"Ministry"of"Education"and"Science." " References" Akam"M"(1987)"The"molecular"basis"for"metameric"pattern"in"the"Drosophila"embryo." Development"101:"1B22." Alon"U"(2007)"Network"motifs:"Theory"and"experimental"approaches."Nat"Rev"Genet"8:" 450B461." Bartel"DP"(2009)"MicroRNAs:"Target"recognition"and"regulatory"functions."Cell"136:"215B 233." Bergman"A,"Siegal"ML"(2003)"Evolutionary"capacitance"as"a"general"feature"of"complex" gene"networks."Nature"424:"549B552." Buchner"J"(1999)"Hsp90"&"Co."—"a"holding"for"folding."Trends"BiochemSci"24:"136B141." Bushati"N,"Cohen"SM"(2007)"MicroRNA"functions."Annu"Rev"Cell"Dev"Biol"23:"175B205." Ding"D,"Parkhurst"SM,"Halsell"SR,"Lipshitz"HD"(1993)"Dynamic"hsp83"rna"localization" during"drosophila"oogenesis"and"embryogenesis."Mol."Cell"Biol."13(6):"3773B3781." Gangaraju"VK,"Yin"H,"Weiner"MM,"Wang"J,"Huang"XA,"Lin"H"(2011)"Drosophila"Piwi" functions"in"Hsp90Bmediated"suppression"of"phenotypic"variation."Nat"genet"43(2):"153B158." Gibert"GBM,"Peronnet"F,"Schlotterer"C"(2007)"Phenotypic"plasticity"in"Drosophila* pigmentation"caused"by"temperature"sensitivity"of"a"chromatin"regulator"network."PLoS" Genetics"3"(2):"e30." Gregor"T,"Tank"DW,"Wieschaus"EF,"Bialek"W"(2007)"Probing"the"limits"to"positional" information."Cell"130:"153B164." Gursky"VV,"Kozlov"KN,"Samsonov"AM,"Reinitz"J"(2006)"Cell"divisions"as"a"mechanism"for" selection"in"stable"steady"states"of"multiBstationary"gene"circuits."Physica"D"218:"70B76." Gursky"VV,"Panok"L,"Myasnikova"EM,"Manu,"Samsonova"MG,"Reinitz"J,"Samsonov"AM" (2011)"Mechanisms"of"gap"gene"expression"canalization"in"the"Drosophila"blastoderm."BMC" Systems"Biology"5:118." Hardway"H,"Mukhopadhyay"B,"Burke"T,"Hitchman"TJ,"Forman"R"(2008)"Modeling"the" precision"and"robustness"of"hunchback"border"during"Drosophila"embryonic"development."J." Theor."Biol."254:"390B399." He"F,"Wen"Y,"Deng"J,"Lin"X,"Lu"LJ,"Jiao"R,"Ma"J"(2008)"Probing"intrinsic"properties"of"a" robust"morphogen"gradient"in"Drosophila."Dev."Cell"15:"558B567." Herranz"H,"Cohen"SM"(2010)"MicroRNAs"and"gene"regulatory"networks:"managing"the" impact"of"noise"in"biological"systems."Genes"Dev."24:"1339B1344." Hornstein"E,"Shomron"N"(2006)"Canalization"of"development"by"microRNAs."Nat"Genet" 38:"S20BS2410.1038/ng1803." Houchmandzadeh"B,"Wieschaus"E,"Leibler"S"(2002)"Establishment"of"developmental" precision"and"proportions"in"the"early"Drosophila"embryo."Nature"415:"798B780." Jaeger"J"(2011)"The"gap"gene"network."Cell."Mol."Life"Sci."68:"243B274."

11" "

Jaeger"J,"Surkova"S,"Blagov"M,"Janssens"H,Kosman"D,"Kozlov"KN,"Manu,"Myasnikova"E," VanarioBAlonso"CE,"Samsonova"M,"Sharp"DH,"Reinitz"J"(2004)"Dynamic"control"of"positional" information"in"the"early"Drosophila"embryo."Nature"430:"368B371." Karres"JS,"Hilgers"V,"Carrera"I,"Treisman"J,"Cohen"SM"(2007)"The"conserved"microRNA" mirB8"tunes"atrophin"levels"to"prevent"neurodegeneration"in"Drosophila."Cell"131:"136B145." Levy"SF,"Siegal"ML"(2008)"Network"hubs"buffer"environmental"variation"in" Saccharomyces"cerevisiae."PLoS"Biol."6(11):"e264." Li"X,"Cassidy"JJ,"Reinke"CA,"Fischboeck"S,"Carthew"RW"(2009)"A"microRNA"imparts" robustness"against"environmental"fluctuation"during"development."Cell"137:"273B282." Lin"H"(2007)"piRNAs"in"the"germ"line."Science"316:"397." Little"SC,"Tkacik"G,"Kneeland"TB,"Wieschaus"EF,"Gregor"T"(2011)"The"formation"of"the" Bicoid"morphogen"gradient"requires"protein"movement"from"anteriorly"localized"mRNA."PLoS" Biol"9(3):"e1000596." Lott"SE,"Kreitman"M,"Palsson"A,"Alekseeva"E,"Ludwig"MZ"(2007)"Canalization"of" segmentation"and"its"evolution"in"Drosophila."PNAS"104:"10926B10931." Mangan"S,"Alon"U"(2003)"Structure"and"function"of"the"feedBforward"loop"network" motif."Proc."Natl"Acad."Sci."USA"100:"11980B11985." Manu,"Surkova"S,"Spirov"AV,"Gursky"VV,"Janssens"H,"Kim"AR,"Radulescu"O,"VanarioB Alonso"CE,"Sharp"DH,"Samsonova"M,"Reinitz"J"(2009a)"Canalization"of"gene"expression"in"the" Drosophila"blastoderm"by"gap"gene"cross"regulation."PLoS"Biol."7(3):"e1000049." Manu,"Surkova"S,"Spirov"AV,"Gursky"VV,"Janssens"H,"Kim"AR,"Radulescu"O,"VanarioB Alonso"CE,"Sharp"DH,"Samsonova"M,"Reinitz"J"(2009b)"Canalization"of"gene"expression"and" domain"shifts"in"the"Drosophila"blastoderm"by"dynamical"attractors."PLoS"Comp."Biol."5(3):" e1000303." Martinez"NJ,"Walhout"AJM"(2009)"The"interplay"between"transcription"factors"and" microRNAs"in"genomeBscale"regulatory"networks."Bio"Essays"31:"435B445." Milo"R,"ShenBOrr"S,"Itzkovitz"S,"Kashtan"N,"Chklovskii"D,"et"al."(2002)"Network"motifs:" simple"building"blocks"of"complex"networks."Science"303:"1538B1542." Osella"M,"Bosia"C,"Cora"D,"Caselle"M"(2011)"The"role"of"incoherent"microRNABmediated" feedforward"loops"in"noise"buffering."PLoS"Comput"Biol"7(3):"e1001101." Picard"D"(2002)"HeatBshock"protein"90,"a"chaperone"for"folding"andregulation."Cell"Mol" Life"Sci"59:"1640B1648." Pisarev"A,"Poustelnikova"E,"Samsonova"M,"Reinitz"J"(2009)"FlyEx,"the"quantitative"atlas" on"segmentation"gene"expression"at"cellular"resolution."Nucleic"Acids"Res."37:"D560BD566." Queitsch"C,"Sangster"TA,"Lindquist"S"(2002)"Hsp90"as"a"capacitor"of"phenotypic"variation." Nature"417:"618B624." Re"A,"Cora"D,"Taverna"D,"Caselle"M"(2009)"GenomeBwide"survey"of"microRNAB transcription"factor"feedBforward"regulatory"circuits"in"human."Mol" BioSyst"5:"854B867." Ronshaugen"M,"Biemar"F,"Piel"J,"Levine"M,"Lai"EC"(2005)"The"Drosophila*microRNA"iabB4" causes"a"dominant"homeotic"transformation"of"halteres"to"wings."Genes"Dev."19:"2947B2952." " Rutherford"SL,"Lindquist"S"(1998)"Hsp90"as"a"capacitor"for"morphological"evolution." Nature"396:"336B342."

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" Sangster"TA,"Lindquist"S,"Queitsch"C"(2004)"Under"cover:"causes,"effects"and"implications" of"Hsp90Bmediated"genetic"capacitance."BioEssays"26:"348B362." Shalgi"R,"Lieber"D,"Oren"M,"Pilpel"Y"(2007)"Global"and"local"architecture"of"the" mammalian"microRNABtranscription"factor"regulatory"network."PLoS"Comput"Biol"3(7):"e131." Siegal"ML,"Bergman"A"(2002)"Waddindton's"canalization"revisited:"Developmental" stability"and"evolution."Proc."Nat."Acad."Sci."USA"99(16):"10528B10532." Sollars"V,"Lu"X,"Xiao"L,"Wang"X,"Garfinkel"MD,"Ruden"DM"(2003)"Evidence"for"an" epigenetic"mechanism"by"which"Hsp90"acts"as"a"capacitor"for"morphological"evolution."Nat" Genet"33:"70B74." Specchia"V,"Piacentini"L,"Tritto"P,"Fanti"L,"D’Alessandro"R,"Palumbo"G,"Pimpinelli"S," Bozzetti"MP"(2010)"Hsp90"prevents"phenotypic"variation"by"suppressing"the"mutagenic"activity" of"transposons."Nature"463:"662B666." Surkova"S,"Kosman"D,"Kozlov"K,"Manu,"Myasnikova"E,"Samsonova"AA,"Spirov"A,"VanarioB Alonso"CE,"Samsonova"M,"Reinitz"J"(2008)"Characterization"of"the"Drosophila"segment" determination"morphome."Dev."Biol."313:"844B862." Tsang"J,"Zhu"J,"van"Oudenaarden"A"(2007)"MicroRNABmediated"feedback"and" feedforward"loops"are"recurrent"network"motifs"in"mammals."Mol"Cell"26:"753B767." Vakulenko"S,"Manu,"Reinitz"J,"Radulescu"O"(2009)"Size"regulation"in"the"segmentation"of" Drosophila:"Interacting"interfaces"between"localized"domains"of"gene"expression"ensure"robust" spatial"patterning."Phys."Rev."Lett."103:"168102." ValenciaBSanchez"MA,"Liu"J,"Hannon"GJ,"Parker"R"(2006)"Control"of"translation"and"mRNA" degradation"by"miRNAs"and"siRNAs."Genes"Dev"20:"515B524." Waddington"CH"(1940)"Organisers"and"Genes."Cambridge"University"Press."Cambridge," UK."" Waddington"CH"(1957)"The"Strategy"of"Genes."George"Allen"&"Unwin."London,"UK." Waddington"CH"(1962)"New"Patterns"in"Genetics"and"Development."Columbia"University" Press."New"York,"USA." Wagner"A"(1996)"Does"evolution"plasticity"evolve?"Evolution"50:"1008B1023." Wagner"A"(2005)"Robustness"and"evolvability"in"living"systems."Princeton"Studies"in" Complexity."Princeton"University"Press,"Princeton,"NJ." Yeyati"PL,"Bancewicz"RM,"Maule"J,"Heyningen"V"(2007)"Hsp90"selectively"modulates" phenotype"in"vertebrate"development."PLoS"Genetics"3"(3):"e43." Yin"H,"Lin"H"(2007)"An"epigenetic"activation"role"of"Piwi"and"a"PiwiBassociated"piRNA"in" Drosophila*melanogaster."Nature"450:"304B308." Young"JC,"Moarefi"I,"Hartl"FU"(2001)"Hsp90:"a"specialized"but"essential"proteinBfolding" tool."J"Cell"Biol"154:"267B273." Yu"X,"Lin"J,"Zack"DJ,"Mendell"JT,"Qian"J"(2008)"Analysis"of"regulatory"network"topology" reveals"functionally"distinct"classes"of"microRNAs."Nucleic"Acids"Research"36:"6494B6503." " Figures* * Figure*1."MiRNABmediated"feedBforward"loops,"their"functions,"and"examples"in"the"Drosophila" development."(A):"A"coherent"FFL"with"the"upstream"TF"repressing"the"target"directly"and"via"

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activating"miRNA."(B):"The"shortBlived"fluctuations"from"the"upstream"TF"steady"state"level"lead" to"immediate"response"of"miRNA,"but"not"the"target."When"the"TF"is"off"for"a"longer"time,"the" miRNA"level"decreases"enough"to"cross"the"activation"threshold"for"the"target"and"expression"of" the"latter"starts."This"results"in"the"response"delay"(the"time"between"t1"and"t2)"for"the"target." (C):"miR47"mediated"coherent"FFL"involved"in"the"specification"of"photoreceptor"cells"in"the" Drosophila"eye."(D):"An"incoherent"FFL"with"the"upstream"TF"activating"the"target"directly"and" repressing"it"indirectly"via"activating"miRNA."(E):"Under"noisy"input"from"the"upstream"TF,"a" stochastic"model"for"the"circuit"from"(D)"predicts"the"protein"number"distribution"for"the"target" around"the"steady"state"having"shifted"mean"and"smaller"variance"as"compared"to"the"simple" TFBtarget"regulation"(without"the"miRNA"branch)"(the"figure"is"an"art"reproduction"of"Figure"3C" from"Osella"et"al."2011)."This"is"a"reflection"of"two"functions"of"the"incoherent"FFL:"fineBtuning" of"the"target"steady"state"and"noise"buffering."(F):"miR47"mediated"incoherent"FFL"involved"in" Drosophila"sense"organ"specification." " Figure*2."Noise"filtering"mechanisms"deciphered"from"the"analysis"of"the"gap"gene"network." (A,D):"Bcd"morphogen"variation"is"filtrated"at"the"level"of"the"gap"gene"hb."Bcd"concentration" profiles"from"80"embryos"are"shown"in"(A)"as"the"functions"of"position"at"the"ABP"axis"of"the" embryo"at"late"cleavage"cycle"14A,"and"(D)"shows"the"same"for"the"Hb"protein."The"black" horizontal"lines"and"the"gray"background"in"the"panels"indicate"the"spatial"variance"for"the"two" proteins"at"the"spatial"position"marked"by"the"vertical"dashed"line."(B):"The"averaged"expression" patterns"for"six"gap"genes"formed"by"the"onset"of"gastrulation."The"data"presented"in"(A,B,D)"is" from"FlyEx"database"(Pisarev"et"al."2009)."(C):"The"topology"of"the"gap"gene"network"as" predicted"by"modeling"in"Manu"et"al."2009a."bcd"and"cad"are"maternally"expressed"genes"taken" into"account"in"the"model"as"external"factors."The"solid"lines"represent"more"strong"interactions" as"compared"to"interactions"marked"by"the"dashed"line."(E):"Illustration"of"the"balance"between" activation"and"repression"in"the"formation"of"the"posterior"border"of"the"anterior"hb"domain" (the"border"shown"in"the"gray"region"in"(D))."The"red"bars"show"the"averaged"activation"level"by" Bcd"for"the"borders"formed"in"corresponding"spatial"positions,"and"the"blue"ones"represent"the" repression"level"from"Kr"and"Kni"at"the"same"positions"(see"details"in"Manu"et"al."2009a)."(F):"hb" variance"expressed"at"the"level"of"attraction"basin"boundaries"in"the"model"of"gap"gene" expression."The"red"curves"show"the"boundaries"separating"the"attraction"basins"for"two" attractors"responsible"for"the"hb"border"formation,"for"variable"Bcd"profiles"in"the"model."These" attractors"have"the"Hb"component"in"either"ON"or"OFF"state."The"positions"of"intersection" points"between"these"boundaries"and"the"initial"Hb"profile"(black)"encode"the"hb"border" positions"in"the"solution."The"gray"background"shows"the"positional"range"of"the"intersection" points,"while"the"green"interval"covers"the"range"of"the"border"positions"in"the"solution"(see" details"in"Gursky"et"al."2011)."(G,H):"Illustration"of"how"geometrical"properties"of"the"attraction" basin"boundaries"control"the"hb*positional"variance."The"red"lines"represent"the"boundaries" from"(F)"for"different"Bcd"profiles,"and"the"black"line"v"shows"the"initial"Hb"profile"from"(F)." Despite"the"same"variance"ΔC"for"the"boundaries"in"the"two"panels,"their"distinct"dispositions" with"respect"to"the"Hb"initial"profile"provide"essentially"different"magnitudes"Δx"for"variation"of" the"intersection"points."(I):"Illustration"of"the"dynamical"role"of"cell"divisions."A"simple"model" was"considered"in"Gursky"et"al."2006"for"a"twoBgene"network"expressing"in"dividing"cells"(brown"

14" "

circles),"with"both"network"topology"and"the"division"schedule"borrowed"from"the"gap"gene" system"in"the"early"Drosophila"embryos."The"system"in"four"cells"has"twelve"possible"attractors" (stars),"but"only"four"of"them"are"available"for"the"dynamics"initially"starting"from"two"cells"(one" division,"left"column)"and"only"two"if"the"system"starts"from"one"cell"(two"divisions,"right" column),"whatever"initial"conditions"the"system"takes"(allowed"and"forbidden"attractors"are" shown"as"green"and"red"stars,"respectively).""

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A: Coherent

B: Function TF miRNA Target

Concentrations

TF

miRNA

D: Incoherent

Target

Probability

miRNA

Time

t2

E: Function

TF

Pnt-P1

miR-7

t1

Target

C: Example

FFL TF-Target

Yan

F: Example Ato

miR-7

Protein Number

E(spl)

60

150

40

50

D

Protein Conc.

200

150 100 50 0 40 50 60 70 80 90 A-P Position, %EL G v C

40 50 60 70 80 90 A-P Position, %EL E

46 47 48 49 A-P Position, %EL

kni

Kr

gt

x

x

A-P Position

C

tll bcd cad

80 F 60 40 20 0

I

H v C1 C2

C1 C2

0

Hb concentration

40 50 60 70 80 90 A-P Position, %EL

250

Hb concentration

hb

100

20 0

200 B

Kr/Kni rep. Bcd act.

Protein Conc.

A

cad bcd tll

C

Hb Kr Gt Kni Tll

39

43 47 51 55 A-P Position, %EL

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