今日のキーフィギュアです。OK。だから、たぶん、このキーフィギュアを見てみてください。たぶん、このキーフィギュアを見てみてください。このキーフィギュアを見てみてください。OK。昨日、昨日、このエボリューション、アリーフラプチュエーション、エボリューションの効果がに関しては、このプラクチュエーションでエボリューションの速度を提供します。フェノタイプの速度を提供します。フィッシャーでは、このキーフィギュアを見てみてください。そして、あとはこのキーフィギュアを見てみてください。そして、このフェノタイプとジェノタイプを使うことができますこの XA スペースのスターブルを使うことができますそしてこのような関係をつなげることができますこのシミュレーションを使うことができますこのリアクションネットワークモデルとジンオレギュレーションネットワークモデルを使うことができますこのシスモデルとも似ているかもしれないフィジックスターブルとも似ているような似ているようですこのシミュレーションが幾分に見えますシミュレーションは幾分に見えますもっと多くのディメンションを持つことができますそれとも少しディグリスの自由化についてこの1日の質問に返すことができますたくさんのコンポーネットを持つことができますこのX1はたくさんのコンポーネットを持つことができますX3とX4のコンセンテレーションを持つことができますこのコンポーネットのコンセンテレーションはとても高いディメンションですこのフェノタイプスペースはとても高いディメンションですこのフェノタイプスペースは100,000のディメンションなどのディメンションなどを持つことができますしかし、この点は少しマクロスコピックなどのディメンションです少しディメンションなどのディメンションですマクロスコピックのようなものですそのため、この高いディメンションのためにこのディメンションのためにような高いディメンションなどのディメンションなどのディメンションですそれが、この点のコンセンテレーションですこれについては、この初日のコンセンテレーションでこの初日についてもたくさんのコンポーネットが非常に大きくなっているのですがしかし、研究値については少し簡単な値段があるかもしれませんそして、その後、残りの質問がありますまず、このような関係についてお伺いしますそして、このような関係についてお伺いすることができます同じようなストレスについて、力を変えますもし、小さな変化があるかもしれませんそれから、全てをリニューアライトすることができますそして、このようなレニアの関係についてお伺いすることができますこのような関係についてお伺いしますその時、そのような関係についてお伺いしますこのようなレニアの関係についてお伺いすることができます常に、小さな変化があるかもしれませんしかし、小さな変化があるかもしれませんそれから、このような問題ですそして、このような問題についてお伺いすることはこのような問題で、同じようなストレスについてお伺いすることができますそして、少しも力を変えますそして全部をリニュアしていくときにこの変化があるために大きな空間に変化するために1つの一つの場合はそれらの一つの場合はこの一つの場合はこの一つの場合に変化するためにその場合はOKまず1つの問題はリニュアリゼーションが2度で変化するために2つの問題はとにかくとても大きなストレスをとにかくまたこの高さの空間に変化するためにアシウムを考えたことがかなり難しいでもこのようなイベントが大きなベースで改善し1つのポイントは2つのメッセージアレンのコンセンテレーションもう1つのオーミックスメフォルムを聞いたと思います今、このメッセージアレンのコンセンテレーションが変わります1つのポイントは1つのメッセージアレンのコンセンテレーション4000円のポイントは4000円のポイントですしかし、ほとんど非常に値段が高いときに、このポイントは2つのメッセージアレンのコンセンテレーションその問題は何ですか?ここにあるデータがありますこれはフランスクリプトームのメッセージアレンのコンセンテレーションこれはプロテオンのメッセージアレンのコンセンテレーションこのプロテインのコンセンテレーションは多くのプロテインの種類ですここにあるデータがありますここで様々なコンセンテレーションを冷やすことができましたそして、このプロテインはそれを再生する理由はありませんこのプロテインはこのプロテインとなり、このプロテインのカードにあまり性格が増えるのです過去のテーマについては、グロスレイクの改善について説明しました。そのため、この問題は良いのです。ここで残りの問題は、この問題は良いのです。そのため、このテーマについては、私は just assumed that ok is just steady growth state and linearization.but of course bacteria is not just a steady growth system.it's a result of evolution over many many years.so maybe this is a result of evolved systemand in this discussion yesterday,so maybe in the study of evolutionhow robustness of this kind of good fitter stateis important, this robustness is important.so then the question is thatok maybe this is a result of evolved system.I mean when you say it's achieved in an evolved systemyou mean that the linearity is adaptive itselfbecause like in general I mean it's true that isyes so maybe a linear region is expandedbut the point is that it is expandedbecause it provides a fitness advantageor it's a constraintit may be a, we do not put anythingso maybe this will be aprobably a result of some robustness of this fitter stateso even if you make some perturbationso but of coursewe do not know what wasecolyte before evolutionbecause we know ecolyte only after evolution we haveso then so experimentallythis question is difficult to answerso again we use thisthe same model of thisyou are already familiar with this modeland okthis is maybe some already did a tutorialand succeeded in getting deep flowfor instance then yeahwe are not sure but anyway we use thisand thenso and we assume that this kind of transporterso this is a nutrient transportis not just diffusionit's catalyzed by some componentthen so as we discussedmaybe four days ago or somethingso in some regionsso this shows this deep flow power lawrank abundance power lawand also so in this regionso some kind of adaptation to this stateis possibleso that's a general propertyeven for just randomly chosen networkthen maybestill if you change the networkmaybe this cellcan grow much fasterso what we didis that okevolve the system againso I mentioned about this evolutiona little bittwo days agoanyway what we didis that we have this celland there is environmentand this is maybe nutrientconcentration in this simple systemand for this simulationwe assume that there is ten nutrientsten nutrientsten different nutrient speciesso we have X1, X2, X10these are nutrient chemicaland then we apply some external conditionso in this external conditionnutrient concentration is basically justsome value hereand evolve this systemwith this environmentand what we are trying to dois that after evolution of this systemwe put some stressso this is what we did in this experimentso this experimentwe put some stressso stress in this simple modelmaybe change this concentrationso stress mayfor example this may 0,0,0and this is much largere12 or something like thatso we put some stressso that is basicallyso the stress we apply lateris that ok we havethis is originaland thenso this is stressand so this givesstress directione so if e1 directione2 direction or something like thatso this is stressthis vector is a stress typethis stress or this stressand lambda is theso stress strengthso this is somewhat similar to the experimentso this is a simple modelbut maybe with this simple modelmaybe what we can do is something like thatok so firstso before putting this stresswe can evolve this systemand thenso in this evolution againwe change a little bit the networkby mutation and select a higher growth cellso that's the evolution methodso thenso initially the growth rate is hereand then per generationthis growth rate increasesso the strategy hereis that okcompare thisand this celland can we havesome kind of what this deep linearityso large linearity regimeand across a different type of stresseswe have such kind of proportionalityif this statebut not this stateso that's what we are trying to doand actually sook so maybemaybe I can showok from thisand so firstfor changing lambdathe linear regimeand how this linear regimeincreasesis that okso ok maybemaybe I can come to thisand so in that previous discussionthis if you have this kind ofand then so this slopeis proportional to delta mu growth rate changeand so here we plotthe slope and slope maybe sometimes badbut we just compute the slopeand slope versus this relationshipand this isthe initial red one is the initial oneso it's just scatteredbut green one is after evolutionand so this isand even if you increaseok increase the stressso this lambdawhen you increase the lambdaok maybeif lambda is very smallrandom net caseso initial case can show this slopeand this relationship is finethis is because even for therandom netstill we can use steady growth conditionand in this model steady growthand the first theory says that just steady growthand then in that caseso for the same type of stressand this stress is smallthis initial theoryjust steady growth can workso that is herebut if you increasethis environmental stressthen as we expectedthis is scattered much much largerso it does not work so wellfor the random net initial networkbut after the evolutionthis green pointthis seems to be workmaybe after evolutionlinear regime is expandedso maybe thisfirst question is clearedand the second question is thatok this is athe next question is about the different directionso the previous one is that given thisand just changesso this is something likeso given stressso the same directionand same stress directionwe have seenso what we have observed is that somehow this linear regime increasedin thisand then the next questionis that different type of stressso we have different vector hereso it may go to a different directionthen the result may be changedso acrossdifferent directionswe made this kind ofchange so this is one exampleso this is one vectorof thisand another vector hereso that is one vector hereand another vector hereand again we plotall delta xiso this is logarithmic changeas we discussedand thenok thisinitial network result is something likethis blue onenothing peculiarjust scattered aroundand thenafter evolution maybethis is 10 generation maybe there is some structureand after 150 generationsso all points showed this behaviorso this isso what we have observedin the experimentso after evolutionwe can get thisand so we this is just two examplesof different stressesbut we canhave many many different types of stressesand actually we did many different type of stressesand then this kind ofcorrelation coefficientand for this evolved networkit's very close to oneand but for random network it's justso average 0and very broadly distributedand this kind of correlation coefficientso initially almost 0and then after evolutionit's approaches to ok 1 or 0.9so that's whatso we obtained what we haveok expectedok one interesting point hereis that ok weput evolution occursunder this stressat this environmentthis is not expectedthrough the course of evolutionso we always put this environmentfixed environmentbut these are different environmental directionsand but somehow across thesethe result here somehowknows thatso the question is whyok this isso we have good resultand thenstill we do not know whyand okso in this modelas we explainedthis is okvery high dimensionalsimulation we usedthousand componentsthousand componentsand asso you know in this kind of tutorialthis is a model of stochasticso this is very noisyit's just randomly chosen reactionmovicals and react so it's a stochastic modelso this is very high dimensionso basically the final statefinal steady state showsthis direction of changeok x1,x2,x3xthousandso this is very very high dimensionso then it's hard to seewe cannot see thousand dimensional spaceso oftenthe statistical methodis that they useprinciple component analysisor some other moreadvanced one but basically the idea is thatthis principle component analysis is thatthis is thousand dimensionmaybe if some directionvariance is dominantwe choose this the firstpc1 componentand then ok if thisthe points are scattered like thisthen maybe this is pc1and then maybe next towe choose the most variable directionplease give the first principle componentaxisand thenthe next variable direction is pc2so that's kind ofmaybe you might have usedsome data analysis but that'sa kind of standard techniqueso what we did hereis that ok originally this isthousand dimensionaland we may put many manydifferent environmental conditionand then the state of delta xso this x changes according tothe environmental stressesand then okinstead of plotting this originalthousand dimensional spacepc2 or pc1or pc3 or something like thatand so forto see well we useonly up to pc3 hereso basically this is just a transformationof axis so we are not doing something specialand then okwe compare thischange of state against environmentalstressingand compare this resultafter evolution and before evolutionbefore evolution is basically just random networkand then so as you cansee herein thisrandom network caseso basically it's togetherthere is no special one axisso all axis are almost similarand so it's just points are scatteredbasically in thisthousanddimensional space so that'smaybe if it's random we might expect thatand then after evolutionas you can seethe points are soand basically in this caseso roughly one dimensional manifoldmaybe the second manifoldtwo dimensional direction there are somea little bit so basicallythis one dimension classmaybe a little bit sothis structure emerges after evolutionand that is probablyrelated to this kind of globalrelationship we have seenok maybeso then ok maybeI should say that okthis is the resultacrossdifferent environmental conditionand maybethis is interesting aftermaybe later is that ok this is the resultacrossdifferent environmental conditionbut we can do this kind ofplot by fixingthe environment butputting some kind of genetic change mutationso changing the network structureso for example in this original stategiven for environment conditionand now fixing the environmentand putting mutationand then we can get something similarand interesting this is alsoconstrained into a one dimensional manifoldor low dimensional manifold and alsoit's same manifoldconstrained sothis is so ok this is due toenvironmental change and this is due tomutation and actuallywe also put some noise to this systemfurther noiseactually this model is already stochastic soit's sufficiently noisybut still we put more noise in this simulationthen it's alsoconstrained in thisso basicallyin this case of this backgroundthis grey one is this due to environmentand this red one is due to mutationand this is backgroundis due to environment and this red oneis due to noiseit seems that we have different answersfor these two different kinds of noisecan we say that the componentsare already going to be oh if we haveenvironmental variation the changes alwayswill appear in these components more likewe choose some fittedso networkso this network is given first and thenput environmental conditionstress and that follows thisand then we choose this and fix the environmentand put some mutationso and of course if youchoose a totally different network afterrevolution maybe this structure maybea little bit different but it's againone dimensional manifold and this so thisstructure is samepca in order to reduce the dimensionso how do you make sure of the consistency of your result thenthis contribution of thispc1pc2 you meanI'm asking how do you make sure of the consistency of your resultbecause since you are using pca there will be a causeso how do you make sure that result will be consistentok what do you mean it's okin this result so even if Itake more samples basically the results are sameand alsoactually this shows thatcontribution of thispca1 is quite highand pca2 is small and in this case maybe 70%so that means it's mostlyconstraint into one dimensional manifoldis it cleanand the three components are consistentthe direction of the three components are consistentalong the different trialsyou didconsistent with the waterlike if you try and run again the system starting from differentinitial condition or something the first three components remainsay the samefor this evolved networkthis is always this kind of behavior hereand if you choose so if you evolve again this systemand then we may have a different networkafter evolution even though the fitness is highand in this case so maybe the point is differentwe may have slightly differentspaceand in that casemaybe it may go to a different direction but againthis is one-dimensionallyconstraintso probably this is importantto understand thislinear relationship because this may suggestokay even though this is very high-dimensionalbasically we can understand this change in one-dimensionso if it's one-dimension that by this one-dimensionso every other components change are derivedaccordingly so then probably we can expectthis global relationship and that I'll come back laterbut before going to thatokay why this kind of structure appearsafter evolution and sowe do not have a complete theory to derive this structurebut we can havesome kind of argument hereso after evolution in this environment we have a kind of good stateprobably good state is not so commonso you need to producesomehow difficult to produce thisand then the model is stochasticso actually through this kind of dynamical processthere are many ways to perturb this statethere are many many possible perturbations due to this kind of stochasticitybut if it goes there it's not so goodso good state is not so commonso once you have a very fit state then it decreasesif you go out so that meansthere should be strong globalattraction from all other pointsso in the phenotype high-dimensional spacethis state and there isso strong attraction so in dynamical systemsglobal attraction here thenbut if this is attracted to any attraction stronglythen it's very difficult to change this statebut this state is obtainedafter evolution and also maybe it's still evolvingso along this directionevolution so how evolution progressedand maybe next how it goeslater along that directionthis state should be changeableif this is very very much strongly attractiveso that is good for robustnessbut if totally robust to any directionthen probably the system cannot evolveso this system has evolved and maybe will evolveso maybe along this evolutiondirection this can be changeableand that is also calledplasticity andplasticity robustnessbut you need to plastic along the direction ofin evolutionadaptationadaptation alsoso if youconsider this kind of environmental stressadapt to thatadaptationadaptationadaptationadaptationadaptationadaptation雲にcan I ask the questionsdoes this mean that if you look at the eigenvalue spectrum of the networkthe one with this single adaptationdirection corresponding to the most positive eigenvalue and all other eigenvalues are negativenot positivebut still basicallyif you have this if it's positiveif it's unstable it can easily without anything it can go outso here it means it's easy to changebut if you fix the networkand if you fix the environment it always stays herebut if you slightly part up the networkjust put the environmental stressin this direction it can be changedthis means that all other eigenvalues more or less stay negativeonly one which is the change over timeone single eigenvalue change over timeso he's asking about this kind of stability of this stateand so we have this kind ofsystems here and then thisstate here so the stability of thisstate is so okay discussed firstwe get so we get fixed point herein this some given environmental conditionso that is here and then the stabilityof this is discussed sookay and then this eigenvalueof this jacqueline matrixgives how it's attracted or notand if the fixed point is stable the eigenvalue of thislamdai so eigenvaluethen all of these eigenvalues should beless than 0 so this is stabilitythis strong attraction means thatnot only this is negative but it'smagnitude absolute magnitudethis is large along this directionbut here there is one directionthat is lambda1 is close to 0it's negative but close to 0that means lambda1 is self fluctuatingso that sometimes it can become positiveit's not fluctuatingfor thisto discuss this we do notconsider scarcity we just usual dynamical systemsjust yeah and thenwe compute this and then along thisokay this is yeah and as long as this is stablethis is still negativeif this is close to 0 and then you have somechangeability as you said and you update the network structureokay maybe if you change the network maybesome of them becomes unstablesomehow maybe even if you change the network structuremaybe this structurejust to clarify my questionI want to think about lambda abasing some random processthis only single lambda1 I don't say about other lambdaall other lambda I agree they are negative but this single lambda1can be modeled as some stochastic processesaccording to some Langevin equation for instanceand that one describing the process of updating the network structurewhenever the network structure updateit puts some perturbation in that lambda1and that lambda1 is negative but close to 0due to fluctuation sometimes it can cross the 0 axisand then you move away from this global attractionand it's changing by Langevin equation or somethingmaybe what you said could occurbut in this evolutionary process as long as we select a fitted onethis lambda remains negativebut then everything just global attraction is no way to escapeno no but thisthis is close to 0 so you can change a little bit herebut the networks of course to change thisyou need to add some kind of mutationso that means maybe this state will changeand then yeahof course then there could be some fatal networkthat lambda1 becomes positivebut that ishardly to occur or some kind of this is constrained to this evolution for the stabilityalso you are not evolving this j you are evolving the networkso it depends on the dynamics what i mean there might be that the dynamics is such that there is no networkthat makes the system unstablethey find some kind of path around thisalways it's stablejust random process of lambdabut that's an interesting pointactually so herein this figure so this is what we did laterand in this case so instead of stochastic modelso we compute this kind of dynamical systemsand then so obtain this lambda iand then yeahwhat we plot here is that instead of lambda iso we plot the inverse of this lambda iso that means if it's close it's very largeso then you can see one exponentone eigenvalue is very close to 0so inverse of this is quite largeso here we have actually in this case we have just 100 dimensionso just 100 exponent eigenvaluesand so one is here then second one is maybe a little bitso maybe that suggests this is also a little bit largerand but others are almostyeah much much larger so it'syeah 5 timesback again about lambdaso we said lambda one is going to be negativeso if it's negative we will be in the steady stepso if you are in this I mean a group by one stepa steady step so what can make then the change of lambda onebecause you said that line is going to changeso in this case this is evolutionary processthis network and this network is differentso you change a little bit networkand then this changes this dynamicsand then accordingly this eigenvalue also changesso that's the plot hereyeah is it okayI don't ask the questionbut I don'twe are seeing that the direction is robustand the attractormaybe this state should be attracted toyeah many from many directionsfor given network and for given conditionbut if you change the network there is a plasticityokay yeahonetwork or environmental condition thisso if you put some other yeahso if you put some kind of environmentso maybe you put some additional termthen it may change so that is adaptationand if it's evolving networkboth in the same directiongiven by this yeahim value directionlove the one is it okayyes so how much are the eigenvectorslocalized on particular componentsactually in this case it's not necessarilyconcentrated on one component or a few componentsyeah rather extendedand then okay so here for instancewe check this kind ofprincipal component direction and versus this eigenvector of this first mode and thenokay that is almost okay this isthis is 1.0 so this red one is thatokay so basicallyyou haveso what we have seen is here thislamdai and so one is very closeto zero and maybe so something like thatso lamdai and so the first eigenvalueis very close to zero this is zero andother than much and then you canconsider this kind ofso this is eigenvector corresponding to thethis lambda one and so this v1direction is probably this directionof this pc1 mode so that everything changesand so and actuallythis v1 and that so thisdue to environmental change or due tokind of a mutationand or due to noise this agreesthis direction and this is thisyeah in a product of this directionand v1 mode direction and after evolutionokay this is 1.0 and it approaches to 1.0so basically this direction and thisdirection is alignedokay so this is the structure andprobably the intuitive explanation for thisis thatmaybe this attractbut many perturbation it's attracted to thisglobaly but there it leavessome kind of yeah direction that can bemore changeable through the evolutionso and that is this okay this argument stillmaybe kind of yeahand waving argument and also we cannotprove this direction is just one dimensionokay maybe evolution through this two dimensionaldirection that we cannot denythat it's not the case so but stillprobably it's still low dimensional yeahso maybe Imade this comment other time and we discussed it butmemories so this looks like similarto the case where you have aconserved quantity like say for exampleif you take a physical system with say interaction between particlesthen the state of relative positions are fixedbut then you have a center of mass that movesexactly and this isalso in financial market you have the sametype of idea that you have one saymarket mode which isand so the ideathere is essentially a conserved quantity or there is a transformationlike say for example if youtranslate all the particles then essentially the state does not changecan one interpret this as ifyou have a similarsay invariance in this system you multiplyevery I don't knowevery excise by the same quantitythat's a difficult question yes and nospecial model in this category action network sodue to this growth rate every component is diluted so growth rate is aspecial variable and by that every others are constrainedand so this growth rate plays the roleof this direction in this modelbut actually we didactually so this Takuya Sato did some simulationusing gene regulation network and in that case there is nodilution effect by growthand still in some fitness condition we can seesomething similar and in that casewe are not so sure if such kind of globalvariable that constrains everythingif this or not that's we are not so sureyeah okay so basicallyassuming this structure and thenmaybe from that it's not so difficult toderive this original relationship andactually I'm not going into details this so thispreviously so in the first day we discussed this kind ofstate growth condition but instead ofdiscussing this kind of in this case againthis jacobi matrix and this kind of thing butif only one eigenvalue is special and others are much more negativeso you can just choose thisdirection or otherwisein another way it's if you have something differentdirection but everything changes project itto this direction so instead of takingthis all eigenvalues from herethis there is a some special direction andthen everything is okaysorry in this slide I use instead of one okay andanyway special direction 0 1and then every change is basicallygoverned by this okayI use v okay v0so everything is projected to this directionv0 and so lambda 0 soso instead of computing all theseyeah jacobi matrixjacobi matrix is everything is just change occurs along thisdirection so every change in delta x1 delta x2 delta x3can be projected to this eigenvalue eigenvector direction because yeah this is mostly changeableand this is a little small then sothen with some kind of yeah calculationokay finally we get this kind of delta xacross a different environmental condition it's proportional to thisit's just a kind of linear algebra typecalculation so I do not go into detailsbut it's natural this is just one dimension and thisglobal proportionality also says thateverything is proportional along one directionso that is yeah we canlike this so probably this kindof structure isthe essence of this dimensional reduction andthis kind of behavior we observed in the first day and that was mysterybut and if this direction is very largeso if this is close to 0 then we can extendextend this direction only by this modeso then it's just linearyeah it's just one eigenvalue and one eigenvector and then along thatso then this global linearityor deep linearity we callmaybe a result of this so maybe it's a kind ofimportant point is that it's robust to many direction butx is somewhat plastic changeableagainst some other only one or few directionsso this structure is importantso now we finallysolve the mystery of the first day I hopebut of course it's okay we did thissome kind of theoretical argument and plus some simulationsyou see sure about this experimentthen there's another yeahinteresting point here so this directionand in the simulation alsothis occurs against evolution, mutationand also againstadaptation, adaptation is environmental changeso the change by genetic mutationand the change by environmental changeadaptation is somehow very much correlatedand this isyou may find similarity of thisrelationship between vg and vipwe discussed yesterday so in that casethis is not environmental change this is noiseand this is a mutationbut here somehowenvironmental change and thisis correlated this suggestsso we can thenso previously we have seen thatsome environmental changeis given byacross many manydirection so this is given by justso that yeah so from this structurewe can derive but we have seenso this is the result for different type of environmentand this environment so we get thisbut this result says thatadaptation versus evolutionso that means instead of using thismaybe you can some kind of genetic changegenetic change if I use eso I use g in genetic changeso this suggests thatgenetic change and thensome environmental changeso instead of plotting previously we plottedso delta xe versus delta xe primebut instead we can plot delta xe versus delta xe and acrossmany different componentsthen we can have some kind of proportionalityand this is given by this loopso now we can check thisand this actuallyokay then we can so derive this kind of relationshipand then okaythis is an experiment by Chikara Furusawaand so he will talk abouthe will talk tomorrowhe has much more advanced much morelater experiments this is a kind of very oldyeah almost 10 years ago so he has developedinteresting experiments so tomorrow he shows much more advanced resultsbut this is his kind of old resultand what in his experiment he didthis is E. coli bacteriaand then he put some kind of stress conditionstress condition is that okayactually ethanolbacteria likesalcohol but anywaythey do not like and the growth rate increasesso original value actually original growth rate is somewhere hereand then by putting ethanolso this growth rate increasesso this is some kind of result by kind of environmental stressactually this is rather largebut they put thisand then he didculture this bacteria under this ethanol conditionlong tire and over over generationthen by mutation this growth rate is recoveredgrowth rate initially here and by thisand then after some generationsit recovers slowly recoverso g1 g2 some genetic changeoption they are genetic and maybe epigenetic changeso that's yeahso more difficult part but anyway this argument is thatokay we can use this genetic or epigenetic changein the same wayso anyway some kind of genetic or epigeneticso change occurs hereand then so this is recoveredso we can check delta mu gso for example delta mu gin this conditionand thenwe can compute delta mu hereso this is this here from this we can compute thisand then again we use transcriptome analysisso that gives this kind ofthousand or few thousand dimensional delta xwe get thatand then againwe plot in the same way as thisdelta x bydelta x by genetic changeand delta x by eso if this kind of argument completely variesthis change across different messenger RNAconcentrate constraint along this one dimensional lineand this slope is given by thisand this is measured by thisso that's a theoretical argumentand so the experimental result is herefor instance they use some kind of positionthousand generations or no nothousand time so that may besomething more than a few hundred generations afterand each point is a different messenger RNAokay you may think okayit's not so clearthere are more scattered pointsso most points are along this lineand there are some a little scatteredso we can see rather well this kind of correlation resultand then we can compute this slopefrom this dataand then we can compute this and thisactually they measure this growth rate changehere they measure that directlyand then checkif this slope agrees with this or notand that's the result hereso now each point is not a messenger RNAeach point is that this slope versusthisdelta mu at given generationso for instance herehere here hereand we plot here okay maybe this is afterten generation after twenty generation thirty generations or something like thatso theory says thatthis is equal so there is no fittingsomething so it's justthis should be diagonal this and this should beokay looks fineyeah so this is a rather complicatedbacterial evolution experimentso this agreement is yeah i think it's quiteyeah surprising or goodand another pointthat i said is a kind of the shattery principleis that okay in thisevolution initially we put some stresshere and then it goes down and thisevolution occurs to decrease thisdecrease of growth so the growth rate should increaseto recover the original level so that meansthis is always less than one because this islarge change and this is recovered sothis is somehow yeah recover then sofor instance here actually around hereit's maybe fifty percent large recovered so that iszero point five here sothis so that means thisslope change this slope slope alsoshould be less than one so that meansokayinitially no maybevery little genetic change then this is almost sameso in that case so initiallythis is almost slope one around hereand then as evolution is going onmaybe this maybe here okay later thisis and maybe perfectlyrecovered maybe it comes back here sothat means genetic changeso this so delta x by genetic changeis somehow try tocompensate the delta x induced byenvironmental change and hereit's always this stress exists soit's a system could be different because there is somekind of stress but the system tries tosomehow cancel out to the directionto cancel out the induced change by stressso this occurs by genetic changethe mutation so inthe first day I talked aboutsome kind of possible similarity orpossibility to have some kind of thermodynamicstype theory for biological systemsand so yesterday we discussed thispollutionary fluctuation response relationship that is somehowkind of maybeextension of fluctuation response relationship in thermodynamics to biological evolutionand this is maybeI'm not sure how many know theprinciple but that is a very important principlein thermodynamics when you put thisthermodynamic system to a different conditionthen internal statecancel out the induced change generally occursso for instance if you put thissome kind of chemical reaction system into a high temperaturethen the reaction ratetoI'm not sure so reduce the heatreduce the temperature occursthe direction so maybe absorbing some heator some this direction occursso that's generally so kind of propertyover thermodynamic system and that's a resultthat stability over the thermodynamic equilibrium stateand ok this may be alsosimilar to that this kind of initial biologicalsystem is somewhat stable so thatit's very difficult but it's reached some kind of stable statethen by genetic changethey try to come back to this original levelyeah so it's notbecause after all life is chemical reactionso if you take a batch of many chemical reactionwhat they should tell you about oneshould be also consequence for a huge number of chemical reactionsyeah but this is a hugehuge number of chemical reactionsbut in usual thermodynamics it's a huge number of moleculesyeah so that point is different and also maybethis is not a equilibrium systembut of course it's stable systemprobably important thing is thatok that isactually this is alsowe discussed with yuichi wakamotowe talked some time ago so if you put some kind ofexternal changethere are some kind of homeostasis and the system tries tocome back to this original state to keep thisas much as possible to the direction and of coursewithout so maybe that is slightly possiblewithout genetic change so by adaptationand then furthermore with this genetic changethey try to come back to this kind of homeostatic stateso this is homeostatic quoteso most genes try to come backand interesting point is that here through the coursealways environmental stress existso the system here from the original and here is differentso large ethanol condition so stillgenetic change tries to somehowbuffers the external induced changeso that's maybe reasonable if thisbiological system is robustbut this is kind of interesting result herecan I ask another questionin your opinion our relation with if you want the other courseso the protein allocation models etc. becauseif you think about protein allocation models they say thatthe expression of different genesdepends on the specific sector but it's always linear with the growth rateI think it's somehowthis is kind of maybe general formand so maybeamong this kind of relationshipmaybe in this other in that caseribosomal RNA ribosome is quite important so it's kind ofautocatallic process and so it's autocatallic processplus others and then maybe this is somewhat specialand we can discuss using this kind of special thingbut maybe we don't see that it's moregenerally expressed inand thenso I discussed this kind of principal component analysischange so actually he didthis kind of principal component analysisor through the course of evolutionso this is not due to the adaptation so we put thisinitially we discussed and then through this courseof adaptation so how it changesso maybe this is a little bit strong discussion of thisso this is PC1, PC2 or PC3and then so this delta X space is project to thisand then original statehere and thenevolution occurs herelike this so that's thisand hereactually here they repeated6th experiment andthey each casemutation occurs in a different positionso evolutionary in genetic sense it's not completely sameit's different but phenotypicallythey basically follow the same curveso it's a kind of very strong statementso genetically maybe change can occurin a different way if we repeat the same evolution experimentbecause maybe genetic mutation can occur in a different positionso it can not be completely samebut still phenotypicallythey are almost sameactually there is one so up to somewhere but there is one changeactually in this case so it's more gene duplicationthe number of gene changes through this evolutionso that's a very strong change so maybe this is a little bit exceptional onebut as long as the gene number is sameand then some mutation occursthen it follows the same curveso sometimes okaythe evolution again we can have the same thing or notthere is often discussionso many people discussif this replaying the type of evolutionthe same evolution occurs or notand in this simulationso phenotypic path occursso phenotypic evolution occursbut genetically differentso that's a very interesting pointand this is a little bit strong result of this originalthis low dimensional constraintbut through the course of evolutionmaybe it's similarprevious discussion after evolution we considered thisbut here we put this here and then along thisbut actually this is also a result ofevolvable systemthis is also a result of evolved bacteriaunder different environmental conditionand this is so in this ethanol conditionyou have evolved bacteria under ethanol conditionhere evolved bacteriaunder original usual conditionso maybe here it's also constraintand here it's also constraint so maybesomething like thatso that's this experimentsince we have this experiment maybeyou will show this very beautiful experiment of this systemtomorrowand then of course we also checkedthis simulationafter experiments maybe simulationnot so remarkableso we have thise0e0e0of this nutrient concentrationand make a totally differente1e2e10 vectorsand then so at this stageso after evolved this systemthat's similar to thisand then again the growth rate decreasesso this is the growth rate of this evolved bacteriaso over generation under this conditionit's evolved so the growth rate increasesand then we put a different conditionand then the growth rate decreaseskind of evolution mutation plus selection process againand then it's increasedand then again we can check the same thing hereso that's completely the same thing hereso could you say some words aboutwhich type of experiment you mentionedmassive sequencing of messenger RNAsin this measurementdeltax is measured by transcriptionso all messenger RNAthat's basically in this kind of plotof this deltax we usually extractall the RNA from the transcriptfrom the cell from the...and then you massively sequenceall the messenger RNAsand you identify the sequencebasically so how this concentration of messenger RNAchanged from the original state and this changebasically in this case messenger RNA has a bacteriaso it's something like 4000and how long is the messenger RNA typicallyhow long are the RNAs that you sequencethis length of RNAbut this transcript analysisbasically so distinguish all different messenger RNAand so since this equal I havesomething 4000 genes so basically 4000 messenger RNAbasically they can measure each differentmessenger RNA concentrationof course if it's very tinyso maybe we don't have4000point maybe 3000pointsand maybeprotein analysis is more proteome analysismaybe more reliableor maybe has a betterdataand that's actuallyin this delta xiand delta xj and only this resultis kind of due to the proteinmany different protein concentration but that is more difficult to experimentand we usually use messenger RNAthe point is that most are two types of RNAscoding RNAs and these are the messenger RNAsand noncoding RNAs which are a lot of thembasically transcriptso it's transcribed from genes so basically coding RNAscoding RNAsit corresponds to each proteinmaybe protein data is moreclear proportionality thancompared similar I'm not suremaybe protein case is a little bit better I don't knowbut the theory itself is thatjust any component Xor messenger RNAok so okwe are talking about the result of the simulationand actually the simulation says again this delta xso after generation so what we did is the same thingand we put delta x changeand again so after some generation delta xe versus delta xg and delta xeversus delta xg 50 so 50 generationsand so the slope starts to decreaseand this slope agrees with this growth rate changeso ok simulation is also consistentyeah and alsothe result of here actuallyafter taking this evolution okthen they followthe same curve so in this simulationso actually subtle did repeat this kind ofso many so starting from this same network and bychanging the network by mutation so eachcase has a different network of mutatedbut if you use non-evolved genejust random gene then this does not happenso this just diversifiesso maybe everything is consistentwith simulation and experimentand some theoretical argumentokokwe cannot finish thisok maybe it's already 10.30so I talk a little bit about this relationshipthis and VGVIP relationshipso I will talk tomorrowand actually there are two more picturesso I'm not sureyeah one morebut I prepared two moreand the slides are uploaded two more slides are uploadedbut probably I cannot discuss the last oneonly the next onethat good suggestionbut maybe they will not allow methey are so willing to learnokok just a reminder that the next classso there are other questionsthat important questionsok so if there are no questions just a reminder that after the breakwe will reconvene in the labat 11