では始めましょう。おはようございます。お楽しみください。今まで私はこの一般的な美術研究所のスタンドポイントを紹介しました。そして私はこのような製品の製品を同じ製品の製品に時計の製品に関して本物製品を一般的な製品につなげて2の製品についてこちらの製品がこれはクラスティスティー新しい製品で改めて共同製品についてそのようなバスネスやホメオスタシスその最後に今、エヴォルションについて話しますエヴォルションは実際にビアオジカルシステムはとても違うタイムスケールのフェロメナーです最初のリスポンスはインプルが出てきますそして、ヌテリアンスや他のコンポーネントのアイテムを再び、オリジナルステイトのステイトを保持することができますホメオスタシスを保持することができますそして、エヴォルションのステイトを変更することができますそして、タイムを持ち込む時にセラメモリを話します最後に、最後の日に、このプロセスのレクションがどこかに関してエヴォルションについて話しますそして、このエヴォルションについて話します実際に、もう少し前に2012年12月2009年メモリアルの日にダーウィンが生まれましたそして、ダーウィンとアブラハム・リンカンが同じ日に生まれました同じ日、同じ年に生まれましたこのエヴォルションはかなりサンデモリーを選んでいますサバイドで guitar supportedダイナメコリテロkell sms使用して、ダブラハム・リンカンの方を使用することができますそれが面白いと言うと、ダウン・リンカのような意図があるかもしれませんが、インターネクショリーはとても似ています。そのため、彼らはそのような意図があるかもしれません。それに対して、スレイヴやスレイヴ・リンカのような意図があるかもしれません。それに対して、人の良さを持ち、彼らはそのような意図を似ているかもしれません。その瞬間、まだ不足しているかもしれません。でも、そのように、彼らは同じように似ているかもしれません。それに対して、このような意図があるかもしれません。基本的には、エボネクション、またはジーンのようなものがあります。ジーンとか、またはジーンのようなものという承知のようなものです。そして、彼らは次のエボネクションを切断することに捉えています。しかし、エボネクションがないかもしれません。如果良いジーン、患者のジーン、良いジーンを使用すると、それは非常に便利ですが、でも実際に、この真実のバロジェクトのシステムでGINがフェノタイプを作ることができますつまり、ディベロクメントやセルダーダイナミックを作ることができますこのフェノタイプは、このようなプロテインのアバンダンスやプロテインのコンセンツレーションなどまたは、アバンダンスを作ることができますまたは、エイトなどなどなどなのかこのようなプロパティを作ることができますそして、このように良いフィッネスや悪いフィッネスはこのようなフィッネスを作ることができますそして、このようなフィッネスはサバイバブリータやオフスプリングを作ることができますそして、このように次のエイトなどのフィッネスを作ることができます良いフェノタイプや悪いフェノタイプでも、ここにフェノタイプは実際に、フェノタイプは not directly transferred only transferred is the genotypethat's a structure状態で、general structure in the evolutionこのようにまずは、最初はジーンとフェノタイプを使うと、フィットネスのセレクションはPのファンクションですしかしフェノタイプはジーンとファンクションのセレクションを使うと、その場合は、ジーンとフェノタイプのセレクションを使うと、このフェノタイプは1つ1の簡単なマッピングを使うと、フェノタイプのファンクションやフェノタイプのフィットネスを使うと、このセレクションのセレクションがファンクションを使うと、フェノタイプのフィットネスを使うと、アンクションのセレクションやフェノタイプを使うと、フェノタイプを使うと、とても簡単に言うことは人間の人間的なものですもちろんどのように人間の影響についてどのような人間の影響についてそれを話す必要がありますかまたその場合このオフスプリングのプロダクションは父と母とその場合このプロダクションについて人間の影響についてどのようなミューテーショナルな影響についてこのディステルビューションについてもちろん少し変わった場合その場合人間の影響についてこのようなフォッカープランクのイクレーションについてこのようなこのようなでもたくさん私たちはこのマッピングを考えたらこのマッピングをどうするかこのマッピングは彼らの影響について実際去年私は同じグミのバクテリアを持っているプロダクションは同じそのように彼らはディステルビューションについて私はこのディステルビューションについてそれが普通に小さくない大きなディステルビューションについてこのディステルビューションも少し少し同じグミのフェノタイプも同じグミのバクテリアのも少し小さくないバクテリアのも少し大きくないそれがその影響このエボルシナリーのプロダクションについてこれがこれが少し小さくないフェノタイプも同じグミのバクテリアのも少し同じグミのバクテリアのも少し同じグミのバクテリアのも少し同じグミのバクテリアのフェノタイプも同じグミのバクテリアのも少し同じグミのバクテリアのも少し同じグミのバクテリアのも少しも少しとても少ししかし、このような量のバリアンは、GENであると、GENバクテリアのディスティスビューションを使うことができます。そして、このディスティスビューションを使うことができます。このディスティスビューションは、エボリューションに関しての影響を受けます。その理由は、ここの問題です。とても、この自然に関して、アディスティスビューションに関して、アディスティスビューションに関して、アディスティスビューションに関して、私は本当に言えませんが 私たちは生物のインプレッションを持っていますキャッツはとても楽しみです私たちはこのキャッツの生物の歴史を見るために キャッツはとても早くなっています私たちは生物のインプレッションを持っています私は not sure this is just scientifically supported and there maybe some other reasonsbut maybe, or some living fossils, some strange fish in this there,彼らは同じ形に伸びて、長い歴史があるかもしれませんしかし、インセクトの種類が少し早く増えますこの動物の変化の速度や、または、生徒の性能の影響については、自分自身ではありませんが、このフェノタイプの重要性は、この動物の速度のフェノタイプの変化については、この動物の変化については、このマッピングの時点の可能性は、このマッピングの変化を小さくすると、フェノタイプの速度の変化については、これが1つの問題です。私は、フェノタイプの記憶については、この動物の変化については、そう、それは不可言。だけど、この理由はバクティリアルなのです。はい、はい。この理由は不可言と言います。真の真の真では不可言です。しかし、少しのディスカッションがあるかもしれません。遺体的なメモリーがあるかもしれません。そして、次のオフスプレイに関することができます。実際に、ユイチ's ワカモトの話をしています。これが、バクテリアの販売があるかもしれません。次のオフスプレイに関することはないかもしれません。また、次のオフスプレイに関することはないかもしれません。そのため、エピジネティックメモリーではありません。バクテリアのようなものが存在するかもしれませんユニセルのオーガニズムのようなものです基本的にはセルが存在すると2つの分離ができます大きな量のプロテインがあったら次のスプリングも大きいかもしれませんこのスプリングも大きいかもしれません次のスプリングも大きいかもしれませんしかしこのプロテインのようなものです2つの分離ができます1つの分離ができますこの分離ができますこの分離ができます1つの分離ができますもし2つの分離ができますこの分離ができますこの分離ができますこの分離ができます次のスプリングも大きいかもしれません2つの分離ができます次のスプリングも大きいかもしれません次のスプリングも大きいかもしれませんそのようにこの分離ができます今から去年の分離に関する人はそのような問題で100年代以上で残っているかもでも、この記憶の場合は10年代以上で残っているかも100年代以上で残っているかもでも、1,000年代以上で残っているかもそうこの変化のような変化は同じチーンでは同じように同じようにしかし、実際に少しの勉強に同じチーンではでもこのようなエピジネティック記憶についてついて同じチーンでは同じDNAでは同じA, G, C, C同じシークエンスシークエンス同じシークエンスでもしかし、エピジネティック記憶についてモリキュウについてそしてフォースフォリレーションやメカニズムヒストンモリキュウについてもしこのチーンをもっと簡単に使っているかもそうしかし長い1年間でもこのチーンは変わりませんシークエンスは変わりませんこの記憶は短いDNA記憶ではそれがこのチーンではとても普通に人々はこのとても変わりませんでもこの変わりはとてもとてもとてもとてもとてもとてもとてもこの記憶を総織にバ进化するこの変わりも體 get現わまりそう変わる2カ礡変わるまた使う前にこのデヴルションの 競争となっています今の場所は 今の場所にあるとこのような 非ジェネティックな気持ちがマイクライアの 技術や技術の 設定が必要だとこのような 性能の種類この非ジェネティックな気持ちの 例えその時には誰が知り合っているのか、何かが知っているか、何かが知らないか、フェイマスバイオルジストラムアルクを話したメモリーの改善をどうなったのか、前代のシーンです。そのシーンはラムアルクです。マルクの意味は、例えば、高い練習をしている場合、オフスプリングは、強い脚のような技術をすることができます。オフスプリングは、強い脚のような技術をすることができます。そのような技術をすることができます。オフスプリングは、1つの創造を使う場合、この脚を使う場合、脚を使う場合、脚を使う場合、脚を使う場合、次の創造を使う場合、脚を使う場合、その中に called Ramalkism。その必要があるis good to study,if you study now, maybe your son or daughter will know initially from differential equation or something that would be better.それはラマルキズムの意図ですとりあえずこのテノメナーにはラマルキズムがあるかもしれませんがとりあえずそれについては不明的なサポートがありませんしかしこの体験を考えているかもしれませんこの体験はメカニズムがあるかもしれませんでも実際にこの体験はユニセラの体験ですでもユニセラの体験はラマルキズムがあるかもしれませんなぜ私たちは強い肌肉を持っているかもしれませんそれはこの体験ですこの体験はこの体験の中でユニセラの体験を説明していますこの体験はユニセラの体験ですユニセラの体験です体験が増えてそしてこの体験はユニセラの体験を徠っていますユニセラの体験ですユニセラの体験とユニセラの体験ですそしてユニセラの体験整体の体験ですユニセラの体験を当たりましたこの体験は肌肌の体験の体験を重ねます肌を重ねました肌や肩やこのようなものをとっても素直なものですしかしこのものが変化されているそしてこのものが変化されていませんさらに私が効果的な効果を作っているだからそうするとオーガニスムを避けるためにラマルキズムを避けるためにこのようなものがラマルキズムを避けるためにラマルキズムを避けるためにラマルキズムは良くないかもしれませんそれはこの常にダウニアメカジスムが良いかもしれませんだからそれを自分で考えますしかしラマルキズムの中一つのアサンプションは一つのアサンプションは良いかもしれませんそのようなフェノタイプは次の世代の良いかもしれません例えば肌を増やすために次の世代の良いかもしれませんでも次の世代の良いかもしれませんこのような形状も変化されているかもしれませんまたは強い肌がまたはスマートブレインを持っているかもしれませんそれが変化されているかもしれませんこのようなラマルキズムはとても良いかもしれませんそのようにラマルキズムはこのような新たな次世代の良いかもしれませんまたはそれを改めてこのような環境についてラマルキズミの理由は少しずつ覚えているかもしれませんしかしこれがスペキュレーションのようなものですこれが一部の話題ですそして私はこの本来の質問に戻りたいと思いますこの質問のようなマッピングはこのようなものですフラクチュレーションのようなものですフラクチュレーションのようなものですそしてこの…OK今後に戻りたいかもしれませんOKそれについてお話ししましょうGeneはこのストラクチュレーションのようなものですしかしフェノタイプはそれについてお伺いしますGeneはこのシステムのパラメータを確認できることはできるかもしれませんフェノタイプはそれについてお伺いしますパラメータセットのようなものですそしてダイナミックセットを使うことですダイナミックセットはそれについてお伺いしますそれだけである化学のリアクションモデルもそれについてお伺いしますそれがむしろダイナミックセットのようなものですこのフェノタイプをプロデューしています基本的にここにGDynamicsのパラメータがありますフェノタイプXVariableDetermined by thisこれは just a kind of fixed dynamical systemthen there is no fluctuationbut herewe havenoise hereand sometimesthis is broadly distributedsomehow or times this is sharply distributedit depends on this parameter alsoso that's the basic question hereso this is a kind of theoretical or speculative backgroundand I discuss about some kind of experimentand so this isnow 20 years agoand actually my friendIto and Yomothey are working on some experimentsand that is put bacteriato put some kind of fluorescent proteinor increase the fluorescent proteinso in this experimentso this is a celland thisfrom this geneso there is this geneyou have some kind ofG to produce fluorescent proteinand accordinglyif this isso fluorescent protein isso produces high fluorescentthen this cell is veryso highly fluorescentso you can measureokay this is a very fluorescent onemaybe some other casesso what they want to dois that by mutating genesto get a kind of high fluorescent genesso that is what they are doingthat genetic changeand accordingly in this dynamicsso proteins are produced and thereso some are highly fluorescentsome are less fluorescentand they choose a highly fluorescent oneand only by thatso this is a kind of standardkind of selectionartificial evolution procedureto get a better function proteinor something like thatget a better function bacteriaor something like thatand many kind ofapplied evolution biologistsare working on thatto get some kind of good proteinor good cellsso they are basicallyin that directionso actuallywhen they measure the fluorescentso average fluorescent over cellsso average fluorescenceaverage over cellsso initially this leveland they what they didwas that okaythey put some kind of mutationof mutationand actually in this experimentto enhance the speed of evolutionthey artificially add more mutation hereso usually mutation rate is smallbut they add more genetic changeand then they get a differentso some mutants have avery low fluorescent oneso maybethen they can find a better onein the next generation hereand they repeat the processand then from this generation firstand then make some kind of thingand okay this is betterso this generation tooand then okay maybe nextsomething like thatso what they findokay they are happyto having a better fluorescent celland thenso I discussed thateven for the same gene bacteriathe fluorescent phenotypeso phenotype is distributedso they can measure the fluorescenceeven for the same gene bacteria hereactually actual distributionis something like thatso they measure fluorescenceand the measurement is easyso as I said that this kind offlow cytometer or cell solderthis and they put this laserand okay we can then get this distributionand so for the same gene bacteriaso they can produce many manysame gene bacteria clonesso easily so thousand cells or moreso from that they get this distributionand then againso we have this better onefor the first generationthey get for this onethey get this distributionsomething like thatand for this onemaybe they get some distributionand this is the overall resultthe 0th generation first second celland this is log fluorescenceso again we use logbecause basically the distributionis log normalso roughly speaking maybenot completely Gaussianbut roughly speakinglog it's close to Gaussian distributionand so first, second, thirdso this increase 0, 1, 2, 3, 4, 5this is due to genetic changebut the distribution hereis just this maybe stochastic processstochastic dynamic process in this cellso fluctuation existbut you can seethe evolution speed per generationin this log phenotypeso phenotypic evolution speedper generation it somehow decreasesand also this variance also decreasesso somehow this varianceand evolution speedlooks like correlatedso they actually plotted this varianceand so what they plot is thathow much it increases delta xper generationand how much this variance deltaso this is just for the same gene bacteria distributionand so they plot thisper each generationand I mentioned thatthe fluctuation decreasesand evolution speed decreasesand what they plot isdelta x per mutation rateper mutation ratebut actually this is not so important hereso I just skip the detailsso delta xand delta x squarevarianceand so initially this is largeand thenso the evolution step gets smallerand the variance gets smallerso that meansso some kind of naturethis red oneOK forget about this black onethis is a kind of different storyso basically this oneand this oneand this oneand this oneand this oneso looks like thisand thisare somehow correlatedbut this is a biology experimentso maybe the result may not be so goodso now we do the simulationOK again we use this kind ofkind of modelmaybe you are familiar with thisand so this kind ofneutrant is coming inand this reaction process is going onand cell growsand then in this casehow this cellthis protopathy of celldepend on the network structureand previously we justchooserandom networkbut for instancemaybe OKin this simple toy modelmaybe this corresponds to some kind offlorescent oneso we choose some kind ofspecific xspecific so this networkmaybe x20is some kind of a proteinthat we try to increaseso what wechoose is thatthe concentration of x20for instanceand thenso with this mutationin this toy cell modelwhat we didis that change this reactionnetwork a little bitso maybeOK remove thisand add this other pathso just changingthis reaction patha little bitso maybe if you changeonly one path per generationso this is a kind ofmutation rateand then we do this modeland slightly differentdifferent cellswith the different genesand OKin somecells with thisthis is largebut for some other cell typethis is much smallerthen we select thisso that'smaybe similar to experimentin thisbut of course this is simpleyes toy modelbut you may feel thatsomehow this simpleso toy model works rather wellso we can use this modelfor evolutionOKand thenwe check thisOK with this processsomaybe if you succeededin this toymaybe you can thenevolve this cellto have this kind of thingand thenso againthen so for instancethis is thatagain maybeprecisely speakingthis Xis kind oflog Xso for example X20and sothen what we plotis that delta Xversus varianceand actually theseresult with a differentresultation ratemeans the ratio of this path changeandso for each casestarting from this initial oneand select the good onenext generation this oneso similar to thisand we have this behaviorOK so we can see thatOK OKthis is the other sidesomehow I don't know whyand this evolution speedOKsojust a questionso is thismore or less thisfisher theoremI talk about the differencefrom fisher theoremOKand also this idea thatyou are getting closerto a maximum and then the distributionthe more you get closerto the maximum the moreso fluctuationgetting closer maybeit's sharperactually the differenceso I will talk aboutthe difference between fisher's theoremactually this isrelated but differentOK thanksjust please waitmaybe 10 minutesor somethingOK soanyway we havethis kind ofproportionalityand when I sawOKactuallywhen I sawthis experimentI firstremembered, recalledthe fluctuationresponse relationshipand you might have heardfor the firstlectures by Holheand sowhat thisso fluctuationresponse saysthatresponse ratioso they put some kind of external forceapply for examplevoltage and thenresponse is the electric currentsohow much thisresponsepower force so that is the response ratioand butthis X variablefor example electric currentor some otherproperty in physicsso this shows fluctuationdue to perennial motionor so this Einstein theoremand thisis proportionalso that'skind of fluctuationresponse relationshipso maybeimportant thing is thatOKflactuationwhen they measureflactuationis that they are not applying without forceand thenresponseunder some external forcethis is proportionalso that isan interesting important pointof this Einstein's perennial motion theoryso it'smicroscopically they are fluctuatingwithout applying any external forceand thenmacroscopically they apply forceand they changestructure maybe a little bitsimilar becauseso when they measurethis variancethere is nogenetic changeand no selectionat this momentactually this is the differencefromthe Einstein theoremso this isso no genetic changesobut this iskind ofevolutionaryresponse by putting mutationand selectionfor this you put some genetic changeand selectionso if you considerthis kind of evolutionary processbecause in this casex or increase the fluorescenceso this isexternally we try toincrease this by putting some mutationand selection pressureso that is kind ofthis is not the physics forcebut a kind ofgeneralized forcehereso here is some kind ofgeneralized forcebut this is just fluctuationwithout any applying mutationor any selectionso in thatthat structure is quite similarso withoutforce fluctuationand response with forceis proportionalso okaymaybe this is a kind ofEinstein's fluctuationresponse relationship that I thoughtand actuallythis waswhen I was doingthis is just a kind ofcentury memory ofEinstein's Brownian motion theorythat is 90 or 5soand but of coursethisfor thisyou need to assume that kind ofthe system is nearthermal equilibriumand then around thisthermal equilibrium there is fluctuationand put some kind of small forcethis kind of state innearly equilibriumso that's the structure of fluctuationresponse theoremby Einstein and Kuboand otherssothis is of coursenotthermal equilibriumbut still we can assumethat this is a kind of stabledistribution statethen probablywe can have something similarsoand actuallyby some approximationso I'm not sayingthis is a derivationwe can show thathow this changesso if you changegeneticbutthisbasically you changexsoa is parameterand this is parameterand I say thatthis isdetermined by genesoif you change parameterthen how itsx increasesor decreasesand this isok proportionaltoyesso this relation isgenerate throughwhenever the distributionof x is likeexponential familyand a is the conjugate parameteryeahso actuallymaybe kind of derivationis thatassuming that this is roughly Gaussian distributionand thenmaybe if you changeso initially this distributionat a initial aand then putsome kind of external forceand then maybethis distribution changesandthen maybein a linear regimeso you justdo not need to discussthis higher order term in delta aor higher order termof delta xmaybe for the linear regimeyou can put this kind of thingand thentake kind of linearlinearization so everybodyeverything is linearizedactually this is linearizedand so you canfrom this equationthis is just a square termand we can get this kind of relationshipso this is justassuming thiskind of Gaussian type distributionand linear regimeso we can derive thatbut of course this is not a derivationin general but assumingthat Gaussian distributionand linear regimethenmaybe you can understandwhy I used log xbecauseby usinglog concentrationx becomesGaussian distributionoriginal concentration distributionvariable xthis is far from gaussian distributionbut by taking logthis becomes large xand this large xso log normal distributionso accordingly this isclose to gaussianso that's why I used this gaussiandistribution and alsoexperimentalist to uselog fluorescencefor this and then thisfits rather wellso that's gaussianlinear regimewe are not so surethis isso when we have somethinginitially physicists assumelet's linearize everythingor something like thatso that's the standpoint herethis relation is not only truefor gaussian distributionwhich is an exponential familyso the only thingis that a should bethe conjugate parameter toxmaybe this could be extendedto that highmaybe exponential familyyou can probablyerive thatso assumptionof gaussian maybemaybe too strongmaybeit's always truefor infinitesimal deltayeah infinitesimalbut if infinitesimal range is much smallerand gaussian maybeyeah sufficientlyokno more questionsI have a question because looking at the modelI think I realized I didn't understand the experimentso in the experimentwhat you do is that you have like thisbacterial population they growthen you select the5%in the rightmost tailand then you let them grow againand then you selectyeah actually whatin this experimentso in the initial experimentso they have maybedifferent later experimentbut in this initial versionof thiswhat they didis thatok they havesome bacteriaso with the geneand you put some kind of mutation artificiallyand so some genemutation some other genemutation andthey make colonyand they make this colonythisandso colony is that cellso sampleso you have many cellsand so you can measureaverageaverage fluorescence sothis is average fluorescence largeand this isaverage fluorescence is lowerof course each cellshows some kind of variancebut on the averagethis is larger and this is lowerso theychoose this gene celland then do the next generationso it's some kind ofvery artificialso they put externally mutationand make a kind ofaverage fluorescence andthey select those cellsthose mutantswith a higher fluorescence largebut then the varianceyou see in fluorescence is the combinationof the phenotypic varianceand the genotypic variancevariability that you haveok so in this caseand when they measure thisvariancethen again they chooseok this celland make some kind of clonesand clonesso they may be overmany cellsand maybe within justso 100 generationsthe mutations are notso important so they basicallyhave the same gene cellsand then plot this distributionso basically the varianceis the variance conditionto having a genotypegiven genotypeoksois it alrightnowso alreadymate asks aboutthe fissure theoremand okso nowthere is a famousfissure theoremas Mateo mentionedand that also says thatsoevolution speedrelationship between evolution speedand variancebut in this caseso varianceis notdue to the noisevariance due to the genetic variationso basicallyso if yousome kind of population of a differentgeneso you have apopulation of different genesso this one and this oneand you have a populationof a different gene bacteriasometimes yougo for this gene parameterbut anyway thisand so you have some kind of distributionfor differentand thenthis guyshowsaverage phenotypehereso this is average phenotypeforthis geneand for thisthis may have thisand for thisso if you have a distribution of genesthen accordinglyso without considering anynoise or stochastic processso just considering the averagedue to thisso you have a distributionof this phenotypeand this variancethis varianceby genethis isproportional to evolution speedthat issomehowkind of very importanttheoreminpopulation geneticsand that is calledtheoremthat is also saidthe fundamentalokaythis is Fischer's theoremand that is also calledfundamental theory ofnatural selectionso fundamental theoremso this should bemost important inpopulation geneticsactually Fischer is avery important personhe is the father ofcurrent statisticsso most statistics studiesso come from this Fischer'sideaandbut when Ihe has a book ofexplaining this fundamental theorembut there is no equation at allhe explains only in wordswhere is the theorembut anywaythis is themental theoremokayso you can seesomedifference between thisokayI discussed the same genebacteriabut due to noisethere is a variationbut Fischer's theorem saysdue to a different genetic changethis isso there is a barrierso and that iswhat they call vgso todistinguish vgand what we discussedhere maybeI'm not surethis is a good termbut vip isisogenicgenic phenotypicvarianceor you can saythis is a kind ofsometimesbiologists useasymmetryasymmetric fluctuationthere are many namesfor thatv due to noiseso v instead I usefor this maybe v noiseor sometimes they use fluctuating asymmetrythey usethis termso basicallybut maybe here I usethis isogenicso phenotypic varianceso we havetwo resultsthe famousfischer's theorem saysboth arephenotypichow phenotype changesphenotypic evolution speedis proportional tovgso this is famous fischerandbut this is proportional to vb byby noiseso what we found thisso that means this and this should be proportionalsomehowso that'sthat's a kind ofquestion herebut before maybemaybe weI slightly mentioned about this fischer's theoremfischer's theoremit seems to be a little bit naturalbecause in this casethis is a genetic changeso this can be transferredto the next offspringso for exampleif you try toselectsome kind of a highervalue of this xthen maybe if you choosethis guy for the next generationthen that meansif this distribution islargersmallerthis is largeryou can start from this sidefor the next generationbecause this is soinheritedand if this is smallermaybe you can have only thisso in that senseso kind of stepgenerationthis is largerand this is smallerbecause in some sensefischer's theorem isquite naturalmaybe that's the reason whyhe did not use any equationand justdiscussing words in his bookso that's fischer's theoremand actuallywe canI'm not sure this isthis derivation isstandard or notbut considerokay gand okay this gthis is goodthis value is goodthenthe growth rate of fitness gand then the distribution of pat one generationand then the average gis thatmaybe thisthis is the average of thisand the next generationis thatadapted according to this kindof fitness or growth rateso this is proportionaland then youneed to normalize thisso this totaland normalize thisand so that means we have thisso this is the distributionfor the next generationand so that meansif you try tocompute howit increases per generationthengn plus oneis thatmultiply gand average thisso this isthe nextso thisgn plusoneno the average is thatjust you needthis is gn plus oneso that meansyou can buythisso applying thisyou get thisfor gn plus oneand minus gnand thenyou can get thisthis is justminus gngpnand this comesg squarepngyou can check thisand thenso that means thisso it's proportionalto the variance of thisdelta g squareso this varianceis proportional to evolution speedso in that senseo official theorem is naturalsoso in contrastour discoveryis not sook if I usekind ofso fluctuation response relationshipto extend this fluctuation responserelationshipmaybe this is ok but we are notso surebiologicallybut anywayso these two observations meanthese two observations meanthat somehowthese two variancesbecause this is bothproportionalto phenotypic evolution speedpic evolution speedso first we check thisif this is really true inthe simulationactually experimentallythere are some recentyeah supports butit's sometimesit's not so easy to do thisall of theseso actually so this is the result from thiskind ofthis cell modelso againI'm using this cell modeloftenso againso VIPand VG so initiallyboth are largeand through the course of evolutionboth decreaseso that looks fineand actuallyhere these different colorcorresponds to a differentmutation ratemutation rate is thathow many mutationyou put into theto produce the next generationso if you increasemore then basicallythis increasesbecause you have moremutation then this distributionincreasesbut each VIPitself does not necessarilyincreasethat means if you increasethe mutation rate basicallythis goes upthis goes upand but for given mutation rateok both decreasein proportion to thisso that's the observation hereand then okif you want to have a higherevolution speedmaybe basicallyincreasing mutation ratebecause you can havemore and more mutantand then this speed increasessoactually each colorful celldid this simulationincreasing mutation ratemutation rateand somehow therethe evolution no longer worksno longer worksmeans thatif you havedistribution of thisand actually this distributionforlow mutation rateis something like thatand if you increase the mutation rateok thisand if you increase furtherthen okthen if you increasemuch largerthen the peak structuredisappearedso basicallygoes like thisand like thisand at some stagetotallyalmost flat distributionso thenthere is no way to produceselection procedurebecause if you haveokincreased at this rangeso maybeyou can select this partoksodue to Fischer's theorem it increasesbut at some stagethe distributiontotally becomes flatso thenbasically the assumption of gaussiantype distribution all thesetotally collapseand such thing occurswhen you increase some kind ofmute so mutation ratethisand at somemute criticalthis distribution becomes flatsorry I have a questionon the previous plotthe one on vip versus vgyesso in that case vip is stillthe average condition on the genomeor it's the average of the phenotypealso including the variation of the genomevip is alwayswithoutthat exchangeso for example in this caseso I choose this onesome kind of noiseand thenso take byputting noiseand so same genesame gene means in this simulationsame reaction networkand then maybe thisx value is fluctuatingbut then I do not understandif I increase the mutation ratewhat I'm doing is basically just increasethe distribution of the genotypesbut then I shouldthat the varianceof the phenotypes vipshould be more or less constantyeah more or less constantyeah sobut thensoI do this kindof selection procedureand thenso after thisselection procedure network structure changesand then the variancecan changeso basicallyhereso through thissowhat you said this is truefor this and comparisonthis and this and thisso then vip is identicalbut vg changesbut along thisdirectionso the network structure changesso thisevolutionary processthe network structure changesthenthe dynamics changesso basicallyeven for the same genethe same noise level externallyso consider some dynamicprocess of thissome kind of afunction of axplus some noisenoiseand thenso this depends on thisthis ratiodepends on the network structureso somesome dynamics is more stableand sometimes dynamics are less stableand thenso basicallyaccording to the changevip changesit's clear to everybodysorry the dynamics you aresimulating on the network is that oneso you have a sort of externalthis network structure changes sobut what I mean is the dynamics of expressionis the one where you inputan external noiseor it's like just driven by internalstochasticitybasically by internal stochasticitybut then if it is driven by internalstochasticitysuppose that I have just one single proteinright?suppose that I have just one singleprotein and it's just internalnoiseif I increase the level of expressionwhat I expect is that the coefficientof variation of this expression decreasesbecause it's proportional tothe sand elevationis proportional to the square root of theso if I have one proteinis expressed stochasticallyjust by increasing the average level of expressionI expect a decrease of the coefficientof variationbut actually this is a kind of complexdynamics hereand then so according to thatso if this isI do due to noise it may begoing up thenwith this other dynamicsinfluencing with othersso as long as this is a attractorof this stateand then maybeif you part of this it comes backand how fast it comes backdepending on the structureand if it's a very stableit's coming backto here very fastso in that case of this fluctuationsmallbut if this structure offeedback or to stabilizeis not so largethen you have this kind of distributionand this structure changesdepending on the dynamics hereor network hereso in some sensethe decrease of Vso thisdecrease of VIPhere in thiscaseis due tothis decrease is due tokind ofif this is more stablethis decreasesso robustnessincreasesand thisdepend on kind of structureof the networkif this is increased maybesome others due tonegative feedback decreasesand through the evolutionthis process occursis it clearsorry I don't understandif I understand correctlybut like the experiment isyou have the toy modelof the sale andfor each generationyou modify the reaction networka bit and thenVG is measuredas the variance oflike thevariance in the networkin each generationok soif you put some kind ofokhere sothis network you haveandto make this evolutionwe need mutationand mutation meansdifferent one this oneso you haveby increasingthe mutationkind ofdifferentnetworkso and ifmute is largermutation is largeryou have moremuch more so distributedso ifthis mutation is lowmaybe you have a distributiononly the network isjust one path is changedand if you increasemutation rateyou have a distributionof these three pathsand for eachof mutantswe computethis averageaverage Xaverage meansthat averageovernoiseso this is justdue tomutation outchangeso the calculation is a little bitcomplicated becauseif you justmeasure this kind of makingsome mutants and justdistribute and thenaverage over all thesemutantsthen thatincludes bothby noisevariance by noise and by mutationbecause if youhave twoso for instanceyou have twinsand then maybe genes are samebutthenthis phenotype is due to noiseit's different so that is VIPbut if youyou and methen bothgenetic changebut also noise changethrough the course of developmentexistsso usually if one justcompare all the people herethe variance overall the people herethat includes bothVIP and VGso to compute thatwe need to separatelytake the same geneorganismso that is clonesso it's difficult todo that in human butinbacteria and thenyou can make this and then VIPbut for VGwe need to befurther carefullywe need to clearly definebecauseif we just compare thistotal different organismwith the different genesso they usuallyinclude bothby genetic changeand bynoiseso in this simulationwe do choosewe choose this kind ofgiven mutantand then we computeaverageso for given mutantwe considerthis kind of distributionfor given mutantand then you computeexaverage of this mutantand then for thisother mutantyou have this Xand for other mutant Xand thendistributionof X barand from thatyou compute varianceso it's a little bitcomplicated procedureto calculateso very naively thinkingso if bothprocesses are independentif you just naivelycompute this variance of the people heremaybe that isincludes VIPplus VGbut if this is a kind ofassuming that this is some otherindependent or somethingthen if that is the caseit's just VIP plus VGokayso the question is whyand Iit is some kind ofvery trickyassumptionor somethingpreviouslyI talked about this kind ofso in the case offirst fluctuation responsephenotypeand genotypeand this is parameterfor given parameterwe consider the distribution of Xso then through thethe course of evolutionboth changes X and Aso then we canconsider akind of distributionin thisPXAspaceand thenat some pointdistributedand thenthrough the course of Aso this distribution changesthenjust considertwo variabledistribution hereand assuming thatthis keepssingle peak structureso it's kind ofstable evolutionary processso thissingle peak structure is always preservedthrough this courseand thenif you have this distributionfrom this distributionone can considerthese two variancesVIP and VGand thenagainwe assume thatXand Awithin this two variable distributionso bothA shows some kind ofGaussian mutationchanges some kind of Gaussian distribution over Aand then X changesdue to noiseso assumingthis kind ofokaythis is kind ofdistribution due to noisedue to noiseX is distributed by Gaussianand due to mutationthis is alsoand there is some kind of couplingmaybe okayagain we assumethe linear regimeand this kind of thingand thenfrom thisso this is just rewriting thissquare formwe can get this kind of structureand alpha is that kindof variance due to noiseso that is basically VIPand thisis the variance due tomutation, mu is the mutationso from thiswe can get thisthis is justrewriting thisnot nothing, this is justsquareand thenif this should be stableso that meansthis should be negativeso that meansmu should beless than this valueso previouslyin this experimentso Chikara Fulsarfound thatat some mutation ratethissingle-picked structure collapsesand at this mutation rate0.05collapsesso single-picked structuredisappearsthen that meansat thisup to this valueso this is finesingle-picked structurebut beyond this mutation rateso thisbecomespositive and thenthis destabilizesso we can expectthis and from thatso we can considerbasicallyVIP is this alpha becausefor this same geneso mutation is identicalbutvarianceand VGif VG isjustthis kind of mumultiplied Csomething is simplebut we can considerVG just usingthis distribution carefullyandmaybe you can check thisthis is just Gaussiandistribution so Gaussiancalculation so we canget thisthat meansthissothis is just a simpleGaussian typecalculation soif you aredoing some kind of statistical physicsmaybe you can easily derive thisand thenthat meansthis according to thisokay wederive thisso if the mutation rate is smallthat meansassuming this issmall thenVGand alphaso basicallyin this calculationof this Gaussian type calculationVGis alphaVIPandmule over mu maxmule is the mutation rateand mu max is this kind ofthe point that stability is lostand if mu is smallas long as mu isnot so largethen basicallyyou havethis kind ofthat is so this is VIPso you haveso we getthis kind ofrelationship between this and thisandthis proportion coefficient is thisso okaythis is some kind ofkind ofto so gaussianthis peak this distributionofPXAandkind ofstabilitysingle peak structurethenwe get thisso in that sensesomehow we canapproximately derive this proportionalityassuming this kind ofstabilitybut that's okayif this is really good or notso that's another questionso okayso I'll go to themyeahso any questionsno questionsokaythanks againsee you at 11yeahit's that kind of